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diff --git a/.gitattributes b/.gitattributes new file mode 100644 index 0000000..6833f05 --- /dev/null +++ b/.gitattributes @@ -0,0 +1,3 @@ +* text=auto +*.txt text +*.md text diff --git a/12648-0.txt b/12648-0.txt new file mode 100644 index 0000000..c8ff5a0 --- /dev/null +++ b/12648-0.txt @@ -0,0 +1,2490 @@ +*** START OF THE PROJECT GUTENBERG EBOOK 12648 *** + +THE BEAUTIFUL NECESSITY + +Seven Essays on Theosophy and Architecture + +by CLAUDE BRAGDON, F.A.I.A. + +MCMXXII + + + + + + + + "Let us build altars to the Beautiful Necessity" + --EMERSON + + + +By the Same Author: + Episodes From An Unwritten History + The Golden Person In The Heart + Architecture And Democracy + A Primer Of Higher Space + Four Dimensional Vistas + Projective Ornament + Oracle + + + + +CONTENTS + + I THE ART OF ARCHITECTURE + + II UNITY AND POLARITY + + III CHANGELESS CHANGE + + IV THE BODILY TEMPLE + + V LATENT GEOMETRY + + VI THE ARITHMETIC OF BEAUTY + + VII FROZEN MUSIC + + CONCLUSION + + + + +PREFACE TO THE SECOND EDITION + + +_The Beautiful Necessity_ was first published in 1910. Save for a slim +volume of privately printed verse it was my first book. I worked hard +on it. Fifteen years elapsed between its beginning and completion; +it was twice published serially--written, rewritten and +tre-written--before it reached its ultimate incarnation in book form. + +Confronted now with the opportunity to revise the text again, I find +myself in the position of a surgeon who feels that the operation he +is called upon to perform may perhaps harm more than it can help. +Prudence therefore prevails over my passion for dissection: warned by +eminent examples, I fear that any injection of my more mature and less +cocksure consciousness into this book might impair its unity--that I +"never could recapture the first fine careless rapture." + +The text stands therefore as originally published save for a few +verbal changes, and whatever reservations I have about it shall +be stated in this preface. These are not many nor important: _The +Beautiful Necessity_ contains nothing that I need repudiate or care to +contradict. + +Its thesis, briefly stated, is that art in all its manifestations is +an expression of the cosmic life, and that its symbols constitute a +language by means of which this life is published and represented. Art +is at all times subject to the _Beautiful Necessity_ of proclaiming +the _world order_. + +In attempting to develop this thesis it was not necessary (nor as +I now think, desirable) to link it up in so definite a manner with +theosophy. The individual consciousness is colored by the particular +medium through which it receives truth, and for me that medium was +theosophy. Though the book might gain a more unprejudiced hearing, +and from a larger audience, by the removal of the theosophic +"color-screen," it shall remain, for its removal now might seem to +imply a loss of faith in the fundamental tenets of theosophy, and such +an implication would not be true. + +The ideas in regard to time and space are those commonly current +in the world until the advent of the Theory of Relativity. To a +generation brought up on Einstein and Ouspensky they are bound to +appear "lower dimensional." Merely to state this fact is to deal +with it to the extent it needs to be dealt with. The integrity of my +argument is not impaired by these new views. + +The one important influence that has operated to modify my opinions +concerning the mathematical basis of the arts of space has been the +discoveries of Mr. Jay Hambidge with regard to the practice of the +Greeks in these matters, as exemplified in their temples and their +ceramics, and named by him _Dynamic Symmetry_. + +In tracing everything back to the logarithmic spiral (which embodies +the principle of extreme and mean ratios) I consider that Mr. Hambidge +has made one of those generalizations which reorganizes the old +knowledge and organizes the new. It would be only natural if in his +immersion in his idea he overworks it, but Mr. Hambidge is a man of +such intellectual integrity and thoroughness of method that he may be +trusted not to warp the facts to fit his theories. The truth of the +matter is that the entire field of research into the mathematics of +Beauty is of such richness that wherever a man plants his metaphysical +spade he is sure to come upon "pay dirt." _The_ _Beautiful Necessity_ +represents the result of my own prospecting; _Dynamic Symmetry_ +represents the result of his. If at any point our findings appear to +conflict, it is less likely that one or the other of us is mistaken +than that each is right from his own point of view. Be that as it may, +I should be the last man in the world to differ from Mr. Hambidge, +for if he convicted me of every conceivable error his work would still +remain the greatest justification and confirmation of my fundamental +contention--that art is an expression of the _world order_ and +is therefore orderly, organic; subject to mathematical law, and +susceptible of mathematical analysis. + +CLAUDE BRAGDON + +Rochester, N.Y. + +April, 1922 + + + + +I + +THE ART OF ARCHITECTURE + + +One of the advantages of a thorough assimilation of what may be called +the theosophic idea is that it can be applied with advantage to every +department of knowledge and of human activity: like the key to a +cryptogram it renders clear and simple that which before seemed +intricate and obscure. Let us apply this key to the subject of art, +and to the art of architecture in particular, and see if by so +doing we may not learn more of art than we knew before, and more of +theosophy too. + +The theosophic idea is that everything is an expression of the +Self--or whatever other name one may choose to give to that immanent +unknown reality which forever hides behind all phenomenal life--but +because, immersed as we are in materiality, our chief avenue of +knowledge is sense perception, a more exact expression of the +theosophic idea would be: Everything is the expression of the Self +in terms of sense. Art, accordingly, is the expression of the Self in +terms of sense. Now though the Self is _one_, sense is not one, but +manifold: and therefore there are _arts_, each addressed to some +particular faculty or group of faculties, and each expressing some +particular quality or group of qualities of the Self. The white light +of Truth is thus broken up into a rainbow-tinted spectrum of Beauty, +in which the various arts are colors, each distinct, yet merging one +into another--poetry into music; painting into decoration; decoration +becoming sculpture; sculpture--architecture, and so on. + +In such a spectrum of the arts each one occupies a definite place, and +all together form a series of which music and architecture are the two +extremes. That such is their relative position may be demonstrated in +various ways. The theosophic explanation involving the familiar idea +of the "pairs of opposites" would be something as follows. According +to the Hindu-Aryan theory, Brahma, that the world might be born, fell +asunder into man and wife--became in other words _name and form_[A] +The two universal aspects of name and form are what philosophers call +the two "modes of consciousness," one of time, and the other of space. +These are the two gates through which ideas enter phenomenal life; the +two boxes, as it were, that contain all the toys with which we play. +Everything, were we only keen enough to perceive it, bears the mark of +one or the other of them, and may be classified accordingly. In such a +classification music is seen to be allied to time, and architecture to +space, because music is successive in its mode of manifestation, and +in time alone everything would occur successively, one thing following +another; while architecture, on the other hand, impresses itself upon +the beholder all at once, and in space alone all things would exist +simultaneously. Music, which is in time alone, without any relation to +space; and architecture, which is in space alone, without any relation +to time, are thus seen to stand at opposite ends of the art spectrum, +and to be, in a sense, the only "pure" arts, because in all the others +the elements of both time and space enter in varying proportion, +either actually or by implication. Poetry and the drama are allied to +music inasmuch as the ideas and images of which they are made up are +presented successively, yet these images are for the most part +forms of space. Sculpture on the other hand is clearly allied to +architecture, and so to space, but the element of _action_, suspended +though it be, affiliates it with the opposite or time pole. Painting +occupies a middle position, since in it space instead of being +actual has become ideal--three dimensions being expressed through +the mediumship of two--and time enters into it more largely than into +sculpture by reason of the greater ease with which complicated action +can be indicated: a picture being nearly always time arrested in +midcourse as it were--a moment transfixed. + +In order to form a just conception of the relation between music and +architecture it is necessary that the two should be conceived of not +as standing at opposite ends of a series represented by a straight +line, but rather in juxtaposition, as in the ancient Egyptian symbol +of a serpent holding its tail in its mouth, the head in this case +corresponding to music, and the tail to architecture; in other words, +though in one sense they are the most-widely separated of the arts, in +another they are the most closely related. + +Music being purely in time and architecture being purely in space, +each is, in a manner and to a degree not possible with any of +the other arts, convertible into the other, by reason of the +correspondence subsisting between intervals of time and intervals of +space. A perception of this may have inspired the famous saying +that architecture is _frozen music_, a poetical statement of a +philosophical truth, since that which in music is expressed by means +of harmonious intervals of time and pitch, successively, after the +manner of time, may be translated into corresponding intervals of +architectural void and solid, height and width. + +In another sense music and architecture are allied. They alone of +all the arts are purely creative, since in them is presented, not +a likeness of some known idea, but _a thing-in-itself_ brought to +a distinct and complete expression of its nature. Neither a musical +composition nor a work of architecture depends for its effectiveness +upon resemblances to natural sounds in the one case, or to natural +forms in the other. Of none of the other arts is this to such a degree +true: they are not so much creative as re-creative, for in them all +the artist takes his subject ready made from nature and presents it +anew according to the dictates of his genius. + +The characteristic differences between music and architecture are the +same as those which subsist between time and space. Now time and space +are such abstract ideas that they can be dealt with best through +their corresponding correlatives in the natural world, for it is a +fundamental theosophic tenet that nature everywhere abounds in such +correspondences; that nature, in its myriad forms, is indeed the +concrete presentment of abstract unities. The energy which everywhere +animates form is a type of time within space; the mind working in +and through the body is another expression of the same thing. +Correspondingly, music is dynamic, subjective, mental, of one +dimension; while architecture is static, objective, physical, of three +dimensions; sustaining the same relation to music and the other +arts as does the human body to the various organs which compose, and +consciousnesses which animate it (it being the reservatory of these +organs and the vehicle of these consciousnesses); and a work of +architecture in like manner may and sometimes does include all of the +other arts within itself. Sculpture accentuates and enriches, painting +adorns, works of literature are stored within it, poetry and the drama +awake its echoes, while music thrills to its uttermost recesses, like +the very spirit of life tingling through the body's fibres. + +Such being the relation between them, the difference in the nature of +the ideas bodied forth in music and in architecture becomes apparent. +Music is interior, abstract, subjective, speaking directly to the soul +in a simple and universal language whose meaning is made personal and +particular in the breast of each listener: "Music alone of all the +arts," says Balzac, "has power to make us live within ourselves." +A work of architecture is the exact opposite of this: existing +principally and primarily for the uses of the body, it is like the +body a concrete organism, attaining to esthetic expression only in +the reconciliation and fulfilment of many conflicting practical +requirements. Music is pure beauty, the voice of the unfettered +and perpetually vanishing soul of things; architecture is that soul +imprisoned in a form, become subject to the law of causality, beaten +upon by the elements, at war with gravity, the slave of man. One is +the Ariel of the arts; the other, Caliban. + +Coming now to the consideration of architecture in its historical +rather than its philosophical aspect, it will be shown how certain +theosophical concepts are applicable here. Of these none is more +familiar and none more fundamental than the idea of reincarnation. By +reincarnation more than mere physical re-birth is meant, for physical +re-birth is but a single manifestation of that universal law of +alternation of state, of animation of vehicles, and progression +through related planes, in accordance with which all things move, +and as it were make music--each cycle complete, yet part of a larger +cycle, the incarnate monad passing through correlated changes, +carrying along and bringing into manifestation in each successive arc +of the spiral the experience accumulated in all preceding states, +and at the same time unfolding that power of the Self peculiar to the +plane in which it is momentarily manifesting. + +This law finds exemplification in the history of architecture in the +orderly flow of the building impulse from one nation and one country +to a different nation and a different country: its new vehicle of +manifestation; also in the continuity and increasing complexity of +the development of that impulse in manifestation; each "incarnation" +summarizing all those which have gone before, and adding some new +factor peculiar to itself alone; each being a growth, a life, with +periods corresponding to childhood, youth, maturity and decadence; +each also typifying in its entirety some single one of these +life-periods, and revealing some special aspect or power of the Self. + +For the sake of clearness and brevity the consideration of only one +of several architectural evolutions will be attempted: that which, +arising in the north of Africa, spread to southern Europe, thence to +the northwest of Europe and to England--the architecture, in short, of +the so-called civilized world. + +This architecture, anterior to the Christian era, may be broadly +divided into three great periods, during which it was successively +practiced by three peoples: the Egyptians, the Greeks and the Romans. +Then intervened the Dark Ages, and a new art arose, the Gothic, which +was a flowering out in stone of the spirit of Christianity. This was +in turn succeeded by the Renaissance, the impulse of which remains +to-day unexhausted. In each of these architectures the peculiar genius +of a people and of a period attained to a beautiful, complete and +coherent utterance, and notwithstanding the considerable intervals +of time which sometimes separated them they succeeded one another +logically and inevitably, and each was related to the one which +preceded and which followed it in a particular and intimate manner. + +The power and wisdom of ancient Egypt was vested in its priesthood, +which was composed of individuals exceptionally qualified by birth +and training for their high office, tried by the severest ordeals +and bound by the most solemn oaths. The priests were honored and +privileged above all other men, and spent their lives dwelling +apart from the multitude in vast and magnificent temples, dedicating +themselves to the study and practice of religion, philosophy, science +and art--subjects then intimately related, not widely separated as +they are now. These men were the architects of ancient Egypt: theirs +the minds which directed the hands that built those time-defying +monuments. + +The rites that the priests practiced centered about what are known +as the Lesser and the Greater Mysteries. These consisted of +representations by means of symbol and allegory, under conditions +and amid surroundings the most awe-inspiring, of those great truths +concerning man's nature, origin and destiny of which the priests--in +reality a brotherhood of initiates and their pupils--were the +custodians. These ceremonies were made the occasion for the initiation +of neophytes into the order, and the advancement of the already +initiated into its successive degrees. For the practice of such rites, +and others designed to impress not the elect but the multitude, the +great temples of Egypt were constructed. Everything about them was +calculated to induce a deep seriousness of mind, and to inspire +feelings of awe, dread and even terror, so as to test the candidate's +fortitude of soul to the utmost. + +The avenue of approach to an Egyptian temple was flanked on both +sides, sometimes for a mile or more, with great stone sphinxes--that +emblem of man's dual nature, the god emerging from the beast. The +entrance was through a single high doorway between two towering +pylons, presenting a vast surface sculptured and painted over with +many strange and enigmatic figures, and flanked by aspiring obelisks +and seated colossi with faces austere and calm. The large court thus +entered was surrounded by high walls and colonnades, but was open +to the sky. Opposite the first doorway was another, admitting to a +somewhat smaller enclosure, a forest of enormous carved and painted +columns supporting a roof through the apertures of which sunshine +gleamed or dim light filtered down. Beyond this in turn were other +courts and apartments culminating in some inmost sacred sanctuary. + +Not alone in their temples, but in their tombs and pyramids and +all the sculptured monuments of the Egyptians, there is the same +insistence upon the sublimity, mystery and awefulness of life, +which they seem to have felt so profoundly. But more than this, the +conscious thought of the masters who conceived them, the buildings of +Egypt give utterance also to the toil and suffering of the thousands +of slaves and captives which hewed the stones out of the heart of the +rock, dragged them long distances and placed them one upon another, so +that these buildings oppress while they inspire, for there is in them +no freedom, no spontaneity, no individuality, but everywhere the felt +presence of an iron conventionality, of a stern immutable law. + +In Egyptian architecture is symbolized the condition of the human soul +awakened from its long sleep in nature, and become conscious at once +of its divine source and of the leaden burden of its fleshy envelope. +Egypt is humanity new-born, bound still with an umbilical cord to +nature, and strong not so much with its own strength as with the +strength of its mother. This idea is aptly symbolized in those +gigantic colossi flanking the entrance to some rock-cut temple, which +though entire are yet part of the living cliff out of which they were +fashioned. + +In the architecture of Greece the note of dread and mystery yields to +one of pure joyousness and freedom. The terrors of childhood have been +outgrown, and man revels in the indulgence of his unjaded appetites +and in the exercise of his awakened reasoning faculties. In Greek art +is preserved that evanescent beauty of youth which, coming but once +and continuing but for a short interval in every human life, is yet +that for which all antecedent states seem a preparation, and of +which all subsequent ones are in some sort an effect. Greece typifies +adolescence, the love age, and so throughout the centuries humanity +has turned to the contemplation of her, just as a man all his life +long secretly cherishes the memory of his first love. + +An impassioned sense of beauty and an enlightened reason characterize +the productions of Greek architecture during its best period. The +perfection then attained was possible only in a nation whereof the +citizens were themselves critics and amateurs of art, one wherein +the artist was honored and his work appreciated in all its beauty +and subtlety. The Greek architect was less bound by tradition and +precedent than was the Egyptian, and he worked unhampered by any +restrictions save such as, like the laws of harmony in music, helped +rather than hindered his genius to express itself--restrictions +founded on sound reason, the value of which had been proved by +experience. + +The Doric order was employed for all large temples, since it possessed +in fullest measure the qualities of simplicity and dignity, the +attributes appropriate to greatness. Quite properly also its formulas +were more fixed than those of any other style. The Ionic order, +the feminine of which the Doric may be considered the corresponding +masculine, was employed for smaller temples; like a woman it was more +supple and adaptable than the Doric, its proportions were more slender +and graceful, its lines more flowing, and its ornament more delicate +and profuse. A freer and more elaborate style than either of these, +infinitely various, seeming to obey no law save that of beauty, was +used sometimes for small monuments and temples, such as the Tower of +the Winds, and the monument of Lysicrates at Athens. + +[Illustration 1] + +Because the Greek architect was at liberty to improve upon the work of +his predecessors if he could, no temple was just like any other, +and they form an ascending scale of excellence, culminating in the +Acropolis group. Every detail was considered not only with relation +to its position and function, but in regard to its intrinsic beauty as +well, so that the merest fragment, detached from the building of which +it formed a part, is found worthy of being treasured in our museums +for its own sake. + +Just as every detail of a Greek temple was adjusted to its position +and expressed its office, so the building itself was made to fit +its site and to show forth its purpose, forming with the surrounding +buildings a unit of a larger whole. The Athenian Acropolis is an +illustration of this: it is an irregular fortified hill, bearing +diverse monuments in various styles, at unequal levels and at +different angles with one another, yet the whole arrangement seems as +organic and inevitable as the disposition of the features of a face. +The Acropolis is an example of the ideal architectural republic +wherein each individual contributes to the welfare of all, and at the +same time enjoys the utmost personal liberty (Illustration 1). + +Very different is the spirit bodied forth in the architecture of +Imperial Rome. The iron hand of its sovereignty encased within the +silken glove of its luxury finds its prototype in buildings which were +stupendous crude brute masses of brick and concrete, hidden within a +covering of rich marbles and mosaics, wrought in beautiful but often +meaningless forms by clever degenerate Greeks. The genius of Rome +finds its most characteristic expression, not in temples to the high +gods, but rather in those vast and complicated structures--basilicas, +amphitheatres, baths--built for the amusement and purely temporal +needs of the people. + +If Egypt typifies the childhood of the race and Greece its beautiful +youth, Republican Rome represents its strong manhood--a soldier filled +with the lust of war and the love of glory--and Imperial Rome its +degeneracy: that soldier become conqueror, decked out in plundered +finery and sunk in sensuality, tolerant of all who minister to his +pleasures but terrible to all who interfere with them. + +The fall of Rome marked the end of the ancient Pagan world. Above +its ruin Christian civilization in the course of time arose. Gothic +architecture is an expression of the Christian spirit; in it is +manifest the reaction from licentiousness to asceticism. Man's +spiritual nature, awakening in a body worn and weakened by +debaucheries, longs ardently and tries vainly to escape. Of some such +mood a Gothic cathedral is the expression: its vaulting, marvelously +supported upon slender shafts by reason of a nicely adjusted +equilibrium of forces; its restless, upward-reaching pinnacles and +spires; its ornament, intricate and enigmatic--all these suggest the +over-strained organism of an ascetic; while its vast shadowy interior +lit by marvelously traceried and jeweled windows, which hold the eyes +in a hypnotic thrall, is like his soul: filled with world sadness, +dead to the bright brief joys of sense, seeing only heavenly visions, +knowing none but mystic raptures. + +Thus it is that the history of architecture illustrates and enforces +the theosophical teaching that everything of man's creating is made in +his own image. Architecture mirrors the life of the individual and of +the race, which is the life of the individual written large in time +and space. The terrors of childhood; the keen interests and appetites +of youth; the strong stern joy of conflict which comes with manhood; +the lust, the greed, the cruelty of a materialized old age--all these +serve but as a preparation for the life of the spirit, in which the +man becomes again as a little child, going over the whole round, but +on a higher arc of the spiral. + +The final, or fourth state being only in some sort a repetition of +the first, it would be reasonable to look for a certain correspondence +between Egyptian and Gothic architecture, and such a correspondence +there is, though it is more easily divined than demonstrated. In +both there is the same deeply religious spirit; both convey, in some +obscure yet potent manner, a sense of the soul being near the surface +of life. There is the same love of mystery and of symbolism; and in +both may be observed the tendency to create strange composite figures +to typify transcendental ideas, the sphinx seeming a blood-brother to +the gargoyle. The conditions under which each architecture flourished +were not dissimilar, for each was formulated and controlled by small +well-organized bodies of sincerely religious and highly enlightened +men--the priesthood in the one case, the masonic guilds in the +other--working together toward the consummation of great undertakings +amid a populace for the most part oblivious of the profound and subtle +meanings of which their work was full. In MediƦval Europe, as in +ancient Egypt, fragments of the Ancient Wisdom--transmitted in the +symbols and secrets of the cathedral builders--determined much of +Gothic architecture. + +The architecture of the Renaissance period, which succeeded the +Gothic, corresponds again, in the spirit which animates it, to Greek +architecture, which succeeded the Egyptian, for the Renaissance as +the name implies was nothing other than an attempt to revive Classical +antiquity. Scholars writing in what they conceived to be a Classical +style, sculptors modeling Pagan deities, and architects building +according to their understanding of Vitruvian methods succeeded +in producing works like, yet different from the originals they +followed--different because, animated by a spirit unknown to the +ancients, they embodied a new ideal. + +In all the productions of the early Renaissance, "that first +transcendent springtide of the modern world," there is the evanescent +grace and beauty of youth which was seen to have pervaded Greek art, +but it is a grace and beauty of a different sort. The Greek artist +sought to attain to a certain abstract perfection of type; to build +a temple which should combine all the excellencies of every similar +temple, to carve a figure, impersonal in the highest sense, which +should embody every beauty. The artist of the Renaissance on the other +hand delighted not so much in the type as in the variation from it. +Preoccupied with the unique mystery of the individual soul--a sense of +which was Christianity's gift to Christendom--he endeavored to portray +that wherein a particular person is unique and singular. Acutely +conscious also of his own individuality, instead of effacing it he +made his work the vehicle and expression of that individuality. The +history of Renaissance architecture, as Symonds has pointed out, +is the history of a few eminent individuals, each one moulding and +modifying the style in a manner peculiar to himself alone. In the +hands of Brunelleschi it was stern and powerful; Bramante made +it chaste, elegant and graceful; Palladio made it formal, cold, +symmetrical; while with Sansovino and Sammichele it became sumptuous +and bombastic. + +As the Renaissance ripened to decay its architecture assumed more and +more the characteristics which distinguished that of Rome during the +decadence. In both there is the same lack of simplicity and sincerity, +the same profusion of debased and meaningless ornament, and there is +an increasing disposition to conceal and falsify the construction by +surface decoration. + +The final part of this second or modern architectural cycle lies still +in the future. It is not unreasonable to believe that the movement +toward mysticism, of which modern theosophy is a phase and the +spiritualization of science an episode, will flower out into an +architecture which will be in some sort a reincarnation of and a +return to the Gothic spirit, employing new materials, new methods, +and developing new forms to show forth the spirit of the modern world, +without violating ancient verities. + +In studying these crucial periods in the history of European +architecture it is possible to trace a gradual growth or unfolding +as of a plant. It is a fact fairly well established that the Greeks +derived their architecture and ornament from Egypt; the Romans in +turn borrowed from the Greeks; while a Gothic cathedral is a lineal +descendant from a Roman basilica. + +[Illustration 2] + +[Illustration 3] + +The Egyptians in their constructions did little more than to place +enormous stones on end, and pile one huge block upon another. They +used many columns placed close together: the spaces which they spanned +were inconsiderable. The upright or supporting member may be said to +have been in Egyptian architecture the predominant one. A vertical +line therefore may be taken as the simplest and most abstract symbol +of Egyptian architecture (Illustration 2). It remained for the Greeks +fully to develop the lintel. In their architecture the vertical +member, or column, existed solely for the sake of the horizontal +member, or lintel; it rarely stood alone as in the case of an Egyptian +obelisk. The columns of the Greek temples were reduced to those +proportions most consistent with strength and beauty, and the +intercolumnations were relatively greater than in Egyptian examples. +It may truly be said that Greek architecture exhibits the perfect +equality and equipoise of vertical and horizontal elements and these +only, no other factor entering in. Its graphic symbol would therefore +be composed of a vertical and a horizontal line (Illustration 3). The +Romans, while retaining the column and lintel of the Greeks, deprived +them of their structural significance and subordinated them to the +semicircular arch and the semi-cylindrical and hemispherical vault, +the truly characteristic and determining forms of Roman architecture. +Our symbol grows therefore by the addition of the arc of a circle +(Illustration 4). In Gothic architecture column, lintel, arch and +vault are all retained in changed form, but that which more than +anything else differentiates Gothic architecture from any style which +preceded it is the introduction of the principle of an equilibrium of +forces, of a state of balance rather than a state of rest, arrived at +by the opposition of one thrust with another contrary to it. This fact +can be indicated graphically by two opposing inclined lines, and +these united to the preceding symbol yield an accurate abstract of the +elements of Gothic architecture (Illustration 5). + +[Illustration 4] + +[Illustration 5] + +All this is but an unusual application of a familiar theosophic +teaching, namely, that it is the method of nature on every plane and +in every department not to omit anything that has gone before, but to +store it up and carry it along and bring it into manifestation later. +Nature everywhere proceeds like the jingle of _The House that Jack +Built_: she repeats each time all she has learned, and adds another +line for subsequent repetition. + +[Footnote A: The quaint Oriental imagery here employed should not +blind the reader to the precise scientific accuracy of the idea of +which this imagery is the vehicle. Schopenhauer says: "Polarity, or +the sundering of a force into two quantitively different and opposed +activities striving after re-union,... is a fundamental type of almost +all the phenomena of nature, from the magnet and the crystal to man +himself."] + + + + +II + +UNITY AND POLARITY + + +Theosophy, both as a philosophy, or system of thought, which discovers +correlations between things apparently unrelated, and as a life, +or system of training whereby it is possible to gain the power to +perceive and use these correlations for worthy ends, is of great value +to the creative artist, whose success depends on the extent to which +he works organically, conforming to the cosmic pattern, proceeding +rationally and rhythmically to some predetermined end. It is of value +no less to the layman, the critic, the art amateur--to anyone in +fact who would come to an accurate and intimate understanding and +appreciation of every variety of esthetic endeavor. For the benefit of +such I shall try to trace some of those correlations which theosophy +affirms, and indicate their bearing upon art, and upon the art of +architecture in particular. + +One of the things which theosophy teaches is that those transcendent +glimpses of a divine order and harmony throughout the universe +vouchsafed the poet and the mystic in their moments of vision are not +the paradoxes--the paronomasia as it were--of an intoxicated state of +consciousness, but glimpses of reality. We are all of us participators +in a world of concrete music, geometry and number--a world of +sounds, odors, forms, motions, colors, so mathematically related and +coordinated that our pigmy bodies, equally with the farthest star, +vibrate to the music of the spheres. There is a _Beautiful Necessity_ +which rules the world, which is a law of nature and equally a law of +art, for art is idealized creation: nature carried to a higher power +by reason of its passage through a human consciousness. Thought and +emotion tend to crystallize into forms of beauty as inevitably as does +the frost on a window pane. Art therefore in one of its aspects is the +weaving of a pattern, the communication of an order and a method to +the material or medium employed. Although no masterpiece was ever +created by the conscious following to set rules, for the true artist +works unconsciously, instinctively, as the bird sings or as the bee +builds its honey-cell, yet an analysis of any masterpiece reveals the +fact that its author (like the bird and the bee) has "followed the +rules without knowing them." + +Helmholtz says, "No doubt is now entertained that beauty is subject +to laws and rules dependent on the nature of human intelligence. The +difficulty consists in the fact that these laws and rules, on whose +fulfilment beauty depends, are not consciously present in the mind of +the artist who creates the work, or of the observer who contemplates +it." Nevertheless they are discoverable, and can be formulated, +after a fashion. We have only to read aright the lessons everywhere +portrayed in the vast picture-books of nature and of art. + +The first truth therein published is the law of _Unity_--oneness; for +there is one Self, one Life, which, myriad in manifestation, is yet +in essence ever _one_. Atom and universe, man and the world--each is +a unit, an organic and coherent whole. The application of this law to +art is so obvious as to be almost unnecessary of elucidation, for to +say that a work of art must possess unity, must seem to proceed from a +single impulse and be the embodiment of one dominant idea, is to state +a truism. In a work of architecture the coƶrdination of its various +parts with one another is almost the measure of its success. We +remember any masterpiece--the cathedral of Paris no less than the +pyramids of Egypt--by the singleness of its appeal; complex it may be, +but it is a coordinated complexity; variety it may possess, but it is +a variety in an all-embracing unity. + +The second law, not contradicting but supplementing the first is the +law of _Polarity_, i.e., duality. All things have sex, are either +masculine or feminine. This too is the reflection on a lower plane +of one of those transcendental truths taught by the Ancient Wisdom, +namely that the Logos, in his voluntarily circumscribing his infinite +life in order that he may manifest, encloses himself within his +limiting veil, _maya_, and that his life appears as spirit (male), and +his _maya_ as matter (female), the two being never disjoined during +manifestation. The two terms of this polarity are endlessly repeated +throughout nature: in sun and moon, day and night, fire and water, man +and woman--and so on. A close inter-relation is always seen to subsist +between corresponding members of such pairs of opposites: sun, day, +fire, man express and embody the primal and active aspect of the +manifesting deity; moon, night, water, woman, its secondary and +passive aspect. Moreover, each implies or brings to mind the others +of its class: man, like the sun, is lord of day; he is like fire, a +devastating force; woman is subject to the lunar rhythm; like water, +she is soft, sinuous, fecund. + +The part which this polarity plays in the arts is important, and the +constant and characteristic distinction between the two terms is a +thing far beyond mere contrast. + +In music they are the major and minor modes: the typical, or +representative chords of the dominant seventh, and of the tonic (the +two chords into which Schopenhauer says all music can be resolved): a +partial dissonance, and a consonance: a chord of suspense, and a chord +of satisfaction. In speech the two are vowel, and consonant sounds: +the type of the first being _a_, a sound of suspense, made with the +mouth open; and of the second _m_, a sound of satisfaction, made by +closing the mouth; their combination forms the sacred syllable Om +(_Aum_). In painting they are warm colors, and cold: the pole of +the first being in red, the color of fire, which excites; and of the +second in blue, the color of water, which calms; in the Arts of design +they are lines straight (like fire), and flowing (like water); masses +light (like the day), and dark (like night). In architecture they are +the column, or vertical member, which resists the force of gravity; +and the lintel, or horizontal member, which succumbs to it; they are +vertical lines, which are aspiring, effortful; and horizontal lines, +which are restful to the eye and mind. + +It is desirable to have an instant and keen realization of this sex +quality, and to make this easier some sort of classification and +analysis must be attempted. Those things which are allied to and +partake of the nature of _time_ are masculine, and those which are +allied to and partake of the nature of _space_ are feminine: as +motion, and matter; mind, and body; etc. The English words "masculine" +and "feminine" are too intimately associated with the idea of physical +sex properly to designate the terms of this polarity. In Japanese +philosophy and art (derived from the Chinese) the two are called _In_ +and _Yo_ (In, feminine; Yo, masculine); and these little words, being +free from the limitations of their English correlatives, will be found +convenient, Yo to designate that which is simple, direct, primary, +active, positive; and In, that which is complex, indirect, derivative, +passive, negative. Things hard, straight, fixed, vertical, are Yo; +things soft, curved, horizontal, fluctuating, are In--and so on. + +[Illustration 6: WILD CHERRY; MAPLE LEAF] + +[Illustration 7: CALLAS IN YO] + +In passing it may be said that the superiority of the line, mass, and +color composition of Japanese prints and kakemonos to that exhibited +in the vastly more pretentious easel pictures of modern Occidental +artists--a superiority now generally acknowledged by connoisseurs--is +largely due to the conscious following, on the part of the Japanese, +of this principle of sex-complementaries. + +Nowhere are In and Yo more simply and adequately imaged than in the +vegetable kingdom. The trunk of a tree is Yo, its foliage, In; and +in each stem and leaf the two are repeated. A calla, consisting of +a single straight and rigid spadix embraced by a soft and tenderly +curved spathe, affords an almost perfect expression of the +characteristic differences between Yo and In and their reciprocal +relation to each other. The two are not often combined in such +simplicity and perfection in a single form. The straight, vertical +reeds which so often grow in still, shallow water, find their +complement in the curved lily-pads which lie horizontally on its +surface. Trees such as pine and hemlock, which are excurrent--those in +which the branches start successively (i.e., after the manner of time) +from a straight and vertical central stem--are Yo; trees such as +the elm and willow, which are deliquescent--those in which the trunk +dissolves as it were simultaneously (after the manner of space) into +its branches--are In. All tree forms lie in or between these two +extremes, and leaves are susceptible of a similar classification. It +will be seen to be a classification according to time and space, +for the characteristic of time is _succession_, and of space, +_simultaneousness_: the first is expressed symbolically by elements +arranged with relation to axial lines; the second, by elements +arranged with relation to focal points (Illustrations 6,7). + +The student should train himself to recognize In and Yo in all +their Protean presentments throughout nature--in the cloud upon the +mountain, the wave against the cliff, in the tracery of trees against +the sky--that he may the more readily recognize them in his chosen +art, whatever that art may be. If it happens to be painting, he will +endeavor to discern this law of duality in the composition of every +masterpiece, recognizing an instinctive obedience to it in that +favorite device of the great Renaissance masters of making an +architectural setting for their groups of figures, and he will +delight to trace the law in all its ramifications of contrast between +complementaries in line, color, and mass (Illustration 8). + +[Illustration 8: THE LAW OF POLARITY CLEOPATRA MELTING THE PEARL. BY +TIEPOLO] + +With reference to architecture, it is true, generally speaking, +that architectural forms have been developed through necessity, the +function seeking and finding its appropriate form. For example, the +buttress of a Gothic cathedral was developed by the necessity of +resisting the thrust of the interior vaulting without encroaching upon +the nave; the main lines of a buttress conform to the direction of the +thrust, and the pinnacle with which it terminates is a logical shape +for the masonry necessary to hold the top in position (Illustration +9). Research along these lines is interesting and fruitful of result, +but there remains a certain number of architectural forms whose origin +cannot be explained in any such manner. The secret of their undying +charm lies in the fact that in them In and Yo stand symbolized and +contrasted. They no longer obey a law of utility, but an abstract +law of beauty, for in becoming sexually expressive as it were, the +construction itself is sometimes weakened or falsified. The familiar +classic console or modillion is an example: although in general +contour it is well adapted to its function as a supporting bracket, +embedded in, and projecting from a wall, yet the scroll-like ornament +with which its sides are embellished gives it the appearance of +not entering the wall at all, but of being stuck against it in some +miraculous manner. This defect in functional expressiveness is +more than compensated for by the perfection with which feminine +and masculine characteristics are expressed and contrasted in the +exquisite double spiral, opposed to the straight lines of the moulding +which it subtends (Illustration 10). Again, by fluting the shaft of a +column its area of cross-section is diminished but the appearance of +strength is enhanced because its masculine character--as a supporting +member resisting the force of gravity--is emphasized. + +[Illustration 9: CROSS SECTION OF BUTTRESS.] + +The importance of the so-called "orders" lies in the fact that they +are architecture epitomized as it were. A building consists of a wall +upholding a roof: support and weight. The type of the first is the +column, which may be conceived of as a condensed section of wall; and +of the second, the lintel, which may be conceived of as a condensed +section of roof. The column, being vertical, is Yo; the lintel, being +horizontal, is In. To mark an entablature with horizontal lines in the +form of mouldings, and the columns with vertical lines in the form +of flutes, as is done in all the "classic orders," is a gain +in functional and sex expressiveness, and consequently in art +(Illustration 11). + +[Illustration 10: CORINTHIAN MODILLION; CLASSIC CONSOLE; IONIC CAP] + +The column is again divided into the shaft, which is Yo; and the +capital, which is In. The capital is itself twofold, consisting of a +curved member and an angular member. These two appear in their utmost +simplicity in the _echinus_ (In) and the _abacus_ (Yo) of a +Greek Doric cap. The former was adorned with painted leaf forms, +characteristically feminine, and the latter with the angular fret +and meander (Illustration 12). The Ionic capital, belonging to a more +feminine style, exhibits the abacus subordinated to that beautiful +cushion-shaped member with its two spirally marked volutes. This, +though a less rational and expressive form for its particular office +than is the echinus of the Doric cap, is a far more perfect symbol of +the feminine element in nature. There is an essential identity between +the Ionic cap and the classic console before referred to--although +superficially the two do not resemble each other--for a straight line +and a double spiral are elements common to both (Illustration 10). +The Corinthian capital consists of an ordered mass of delicately +sculptured leaf and scroll forms sustaining an abacus which though +relatively masculine is yet more curved and feminine than that of any +other style. In the caulicole of a Corinthian cap In and Yo are again +contrasted. In the unique and exquisite capital from the Tower of the +Winds at Athens, the two are well suggested in the simple, erect, and +pointed leaf forms of the upper part, contrasted with the complex, +deliquescent, rounded ones from which they spring. The essential +identity of principle subsisting between this cap and the Renaissance +baluster by San Gallo is easily seen (Illustration 13). + +[Illustration 11] + +[Illustration 12] + +This law of sex-expressiveness is of such universality that it can +be made the basis of an analysis of the architectural ornament of any +style or period. It is more than mere opposition and contrast. The egg +and tongue motif, which has persisted throughout so many centuries and +survived so many styles, exhibits an alternation of forms resembling +phallic emblems. Yo and In are well suggested in the channeled +triglyphs and the sculptured metopes of a Doric frieze, in the +straight and vertical mullions and the flowing tracery of Gothic +windows, in the banded torus, the bead and reel, and other familiar +ornamented mouldings (Illustrations 14, 15, 16). + +There are indications that at some time during the development +of Gothic architecture in France, this sex-distinction became a +recognized principle, moulding and modifying the design of a cathedral +in much the same way that sex modifies bodily structure. The masonic +guilds of the Middle Ages were custodians of the esoteric--which is +the theosophic--side of the Christian faith, and every student of +esotericism knows how fundamental and how far-reaching is this idea of +sex. + +[Illustration 13: CAPITAL FROM THE TOWER OF THE WINDS, ATHENS; +CORINTHIAN CAP FROM HADRIAN BUILDINGS, ATHENS; ROSETTE FROM TEMPLE OF +MARS, ROME; CAULICULUS OF CORINTHIAN CAP; BULUSTER BY SAN GALLO] + +[Illustration 14: EGG AND TONGUE; BEAD AND REEL; BANDED TORUS] + +The entire cathedral symbolized the crucified body of Christ; its two +towers, man and woman--that Adam and that Eve for whose redemption +according to current teaching Christ suffered and was crucified. The +north or right-hand tower ("the man's side") was called the sacred +male pillar, Jachin; and the south, or left-hand tower ("the woman's +side"), the sacred female pillar, Boaz, from the two columns flanking +the gate to Solomon's Temple--itself an allegory to the bodily temple. +In only a few of the French cathedrals is this distinction clearly +and consistently maintained, and of these Tours forms perhaps the most +remarkable example, for in its flamboyant faƧade, over and above the +difference in actual breadth and apparent sturdiness of the two towers +(the south being the more slender and delicate), there is a clearly +marked distinction in the character of the ornamentation, that of the +north tower being more salient, angular, radial--more masculine in +point of fact (Illustration 17). In Notre Dame, the cathedral of +Paris, as in the cathedral of Tours, the north tower is perceptibly +broader than the south. The only other important difference appears to +be in the angular label-mould above the north entrance: whatever may +have been its original function or significance, it serves to define +the tower sexually, so to speak, as effectively as does the beard on +a man's face. In Amiens the north tower is taller than the south, and +more massive in its upper stages. The only traceable indication of +sex in the ornamentation occurs in the spandrels at the sides of the +entrance arches: those of the north tower containing single circles, +and those of the south tower containing two in one. This difference, +small as it may seem, is significant, for in Europe during the Middle +Ages, just as anciently in Egypt and again in Greece--in fact wherever +and whenever the Secret Doctrine was known--sex was attributed to +numbers, odd numbers being conceived of as masculine, and even, as +feminine. Two, the first feminine number, thus became a symbol of +femininity, accepted as such so universally at the time the cathedrals +were built, that two strokes of a bell announced the death of a woman, +three, the death of a man. + +[Illustration 15: FRIEZE OF THE FARNESE PALACE; ROMAN CONSOLE. VATICAN +MUSEUM; FRIEZE IN THE EMPIRE STYLE BY PERCIER AND FONTAINE. +FRIEZE FROM THE TEMPLE OF VESTA AT TIVOLI. (ROMAN); ROMAN DORIC +FRIEZE--VIGNOLE] + +[Illustration 16] + +[Illustration 17] + +The vital, organic quality so conspicuous in the best Gothic +architecture has been attributed to the fact that necessity determined +its characteristic forms. Professor Goodyear has demonstrated that +it may be due also in part to certain subtle vertical leans and +horizontal bends; and to nicely calculated variations from strict +uniformity, which find their analogue in nature, where structure is +seldom rigidly geometrical. The author hazards the theory that still +another reason why a Gothic cathedral seems so living a thing is +because it abounds in contrasts between what, for lack of more +descriptive adjectives, he is forced to call masculine and feminine +forms. + +[Illustration 18] + +[Illustration 19] + +Ruskin says, in _Stones of Venice_, "All good Gothic is nothing more +than the development, in various ways, and on every conceivable scale, +of the group formed by the pointed arch for the bearing line below, +and the gable for the protecting line above, and from the huge, gray, +shaly slope of the cathedral roof, with its elastic pointed vaults +beneath, to the crown-like points that enrich the smallest niche of +its doorway, one law and one expression will be found in all. The +modes of support and of decoration are infinitely various, but the +real character of the building, in all good Gothic, depends on the +single lines of the gable over the pointed arch endlessly rearranged +and repeated." These two, an angular and a curved form, like the +everywhere recurring column and lintel of classic architecture, +are but presentments of Yo and In (Illustration 18). Every Gothic +traceried window, with straight and vertical mullions in the +rectangle, losing themselves in the intricate foliations of the arch, +celebrates the marriage of this ever diverse pair. The circle and the +triangle are the In and Yo of Gothic tracery, its Eve and Adam, as +it were, for from their union springs that progeny of trefoil, +quatrefoil, cinquefoil, of shapes flowing like water, and shapes +darting like flame, which makes such visible music to the entranced +ear. + +[Illustration 20: SAN GIMIGNANO S. JACOPO.] + +By seeking to discover In and Yo in their myriad manifestations, by +learning to discriminate between them, and by attempting to express +their characteristic qualities in new forms of beauty--from +the disposition of a faƧade to the shaping of a moulding--the +architectural designer will charge his work with that esoteric +significance, that excess of beauty, by which architecture rises +to the dignity of a "fine" art (Illustrations 19, 20). In so doing, +however, he should never forget, and the layman also should ever +remember, that the supreme architectural excellence is fitness, +appropriateness, the perfect adaptation of means to ends, and the +adequate expression of both means and ends. These two aims, the one +abstract and universal, the other concrete and individual, can always +be combined, just as in every human countenance are combined a type, +which is universal, and a character, which is individual. + + + + +III + +CHANGELESS CHANGE + +TRINITY, CONSONANCE, DIVERSITY IN MONOTONY, BALANCE, RHYTHMIC CHANGE, +RADIATION + + +The preceding essay was devoted for the most part to that "inevitable +duality" which finds concrete expression in countless pairs of +opposites, such as day and night, fire and water, man and woman; +in the art of music by two chords, one of suspense and the other of +fulfilment; in speech by vowel and consonant sounds, epitomized in _a_ +and in _m_; in painting by warm colors and cold, epitomized in red +and blue; in architecture by the vertical column and the horizontal +lintel, by void and solid--and so on. + + +TRINITY + +This concept should now be modified by another, namely, that in every +duality a third is latent; that two implies three, for each sex so +to speak is in process of becoming the other, and this alternation +engenders and is accomplished by means of a third term or neuter, +which is like neither of the original two but partakes of the nature +of them both, just as a child may resemble both its parents. Twilight +comes between day and night; earth is the child of fire and water; +in music, besides the chord of longing and striving, and the chord of +rest and satisfaction (the dominant seventh and the tonic), there is +a third or resolving chord in which the two are reconciled. In the +sacred syllable Om (_Aum_), which epitomizes all speech, the _u_ sound +effects a transition between the _a_ sound and the _m_; among the +so-called primary colors yellow comes between red and blue; and in +architecture the arch, which is both weight and support, which is +neither vertical nor horizontal, may be considered the neuter of the +group of which the column and the lintel are respectively masculine +and feminine. "These are the three," says Mr. Louis Sullivan, "the +only three letters from which has been expanded the architectural art, +as a great and superb language wherewith man has expressed, through +the generations, the changing drift of his thoughts." + +[Illustration 21: THE LAW OF TRINITY. A ROMAN IONIC ARCADE, BY +VIGNOLE.--THE COLUMN, THE ENTABLATURE, AND THE ARCH CORRESPOND TO LINES +VERTICAL, HORIZONTAL AND CURVED.] + +It would be supererogatory to dwell at any length on this "trinity +of manifestation" as the concrete expression of that unmanifest and +mystical trinity, that _three-in-one_ which under various names occurs +in every world-religion, where, defying definition, it was wont +to find expression symbolically in some combination of vertical, +horizontal and curved lines. The anstated cross of the Egyptians +is such a symbol, the Buddhist wheel, and the fylfot or swastika +inscribed within a circle, also those numerous Christian symbols +combining the circle and the cross. Such ideographs have spelled +profound meaning to the thinkers of past ages. We of to-day are not +given to discovering anything wonderful in three strokes of a pen, +but every artist in the weaving of his pattern must needs employ these +mystic symbols in one form or another, and if he employs them with +a full sense of their hidden meaning his work will be apt to gain +in originality and beauty--for originality is a new and personal +perception of beauty, and beauty is the name we give to truth we +cannot understand. + +In architecture, this trinity of vertical, horizontal and curved +lines finds admirable illustration in the application of columns and +entablature to an arch and impost construction, so common in Roman and +Renaissance work. This is a redundancy, and finds no justification in +reason, because the weight is sustained by the arch, and the "order" +is an appendage merely; yet the combination, illogical as it is, +satisfies the sense of beauty because the arch effects a transition +between the columns and the entablature, and completes the trinity +of vertical, horizontal and curved lines (Illustration 21). In the +entrances to many of the Gothic cathedrals and churches the same +elements are better because more logically disposed. Here the +horizontal lintel and its vertical supports are not decorative merely, +but really perform their proper functions, while the arch, too, has +a raison d'ĆŖtre in that it serves to relieve the lintel of the +superincumbent weight of masonry. The same arrangement sometimes +occurs in classic architecture also, as when an opening spanned by a +single arch is subdivided by means of an order (Illustration 22). + +Three is pre-eminently the number of architecture, because it is the +number of space, which for us is three-dimensional, and of all the +arts architecture is most concerned with the expression of spatial +relations. The division of a composition into three related parts is +so universal that it would seem to be the result of an instinctive +action of the human mind. The twin pylons of an Egyptian temple with +its entrance between, for a third division, has its correspondence in +the two towers of a Gothic cathedral and the intervening screen +wall of the nave. In the palaces of the Renaissance a threefold +division--vertically by means of quoins or pilasters, and horizontally +by means of cornices or string courses--was common, as was also the +division into a principal and two subordinate masses (Illustration +23). + +[Illustration 22: THE LAW OF TRINITY. THE TRINITY OF HORIZONTAL VERTICAL +AND CURVED LINES.] + +The architectural "orders" are divided threefold into pedestal or +stylobate, column and entablature; and each of these is again divided +threefold: the first into plinth, die and cornice; the second into +base, shaft and capital; the third into architrave, frieze and +cornice. In many cases these again lend themselves to a threefold +subdivision. A more detailed analysis of the capitals already shown to +be twofold reveals a third member: in the Greek Doric this consists +of the annulets immediately below the abacus; in the other orders, the +necking which divides the shaft from the cap. + + +CONSONANCE + +"As is the small, so is the great" is a perpetually recurring phrase +in the literature of theosophy, and naturally so, for it is a succinct +statement of a fundamental and far-reaching truth. The scientist +recognizes it now and then and here and there, but the occultist +trusts it always and utterly. To him the microcosm and the macrocosm +are one and the same in essence, and the forth-going impulse +which calls a universe into being and the indrawing impulse which +extinguishes it again, each lasting millions of years, are echoed and +repeated in the inflow and outflow of the breath through the nostrils, +in nutrition and excretion, in daily activity and nightly rest, in +that longer day which we name a lifetime, and that longer rest in +_Devachan_--and so on until time itself is transcended. + +[Illustration 23] + +In the same way, in nature, a thing is echoed and repeated throughout +its parts. Each leaf on a tree is itself a tree in miniature, each +blossom a modified leaf; every vertebrate animal is a complicated +system of spines; the ripple is the wave of a larger wave, and that +larger wave is a part of the ebbing and flowing tide. In music this +law is illustrated in the return of the tonic to itself in the octave, +and its partial return in the dominant; also in a more extended sense +in the repetition of a major theme in the minor, or in the treble and +again in the bass, with modifications perhaps of time and key. In +the art of painting the law is exemplified in the repetition with +variation of certain colors and combinations of lines in different +parts of the same picture, so disposed as to lead the eye to some +focal point. Every painter knows that any important color in his +picture must be echoed, as it were, in different places, for harmony +of the whole. + +[Illustration 24] + +In the drama the repetition of a speech or of an entire scene, but +under circumstances which give it a different meaning, is often most +effective, as when Gratiano, in the trial scene of _The Merchant +of Venice_ taunts Shylock with his own words, "A Daniel come to +judgment!" or, as when in one of the later scenes of _As You Like It_ +an earlier scene is repeated, but with Rosalind speaking in her proper +person and no longer as the boy Ganymede. + +These recurrences, these inner consonances, these repetitions with +variations are common in architecture also. The channeled triglyphs of +a Greek Doric frieze echo the fluted columns below (Illustration 24). +The balustrade which crowns a colonnade is a repetition, in some sort, +of the colonnade itself. The modillions of a Corinthian cornice are +but elaborated and embellished dentils. Each pinnacle of a Gothic +cathedral is a little tower with its spire. As Ruskin has pointed out, +the great vault of the cathedral nave, together with the pointed roof +above it, is repeated in the entrance arch with its gable, and the +same two elements appear in every statue-enshrining niche of the +doorway. In classic architecture, as has been shown, instead of the +arch and gable, the column and entablature everywhere recur under +different forms. The minor domes which flank the great dome of the +cathedral of Florence enhance and reinforce the latter, and prepare +the eye for a climax which would otherwise be too abrupt. The central +pavilion of the ChĆ¢teau Maintenon, with its two turrets, echoes the +entire faƧade with its two towers. Like the overture to an opera, it +introduces themes which find a more extended development elsewhere +(Illustration 26). + +[Illustration 25] + +[Illustration 26] + +[Illustration 27] + +This law of Consonance is operative in architecture more obscurely +in the form of recurring numerical ratios, identical geometrical +determining figures, parallel diagonals and the like, which will be +discussed in a subsequent essay. It has also to do with style and +scale, the adherence to substantially one method of construction and +manner of ornament, just as in music the key, or chosen series of +notes, may not be departed from except through proper modulations, or +in a specific manner. + +Thus it is seen that in a work of art, as in a piece of tapestry, +the same thread runs through the web, but goes to make up different +figures. The idea is deeply theosophic: one life, many manifestations; +hence, inevitably, echoes, resemblances--_Consonance_. + + +DIVERSITY IN MONOTONY + +Another principle of natural beauty, closely allied to the foregoing, +its complement as it were, is that of _Diversity in Monotony_--not +identity, but difference. It shows itself for the most part as a +perceptible and piquant variation between individual units belonging +to the same class, type, or species. + +No two trees put forth their branches in just the same manner, and no +two leaves from the same tree exactly correspond; no two persons +look alike, though they have similiar members and features; even the +markings on the skin of the thumb are different in every human hand. +Browning says, + + "As like as a hand to another hand! + Whoever said that foolish thing, + Could not have studied to understand--" + +Now every principle of natural beauty is but the presentment of some +occult law, some theosophical truth; and this law of Diversity in +Monotony is the presentment of the truth that identity does not +exclude difference. The law is binding, yet the will is free: all men +are brothers united by the ties of brotherhood, yet each is unique, a +free agent, and never so free as when most bound by the Good Law. This +truth nature beautifully proclaims, and art also. In architecture it +is admirably exemplified in the metopes of the Parthenon frieze: seen +at a distance these must have presented a scarcely distinguishable +texture of sunlit marble and cool shadow, yet in reality each is +a separate work of art. So with the capitals of the columns of the +wonderful sea-arcade of the Venetian Ducal palace: alike in general +contour they differ widely in detail, and unfold a Bible story. +In Gothic cathedrals, in Romanesque monastery cloisters, a teeming +variety of invention is hidden beneath apparent uniformity. The +gargoyles of Notre Dame make similiar silhouettes against the sky, +but seen near at hand what a menagerie of monsters! The same spirit of +controlled individuality, of liberty subservient to the law of all, is +exemplified in the bases of the columns of the temple of Apollo near +Miletus--each one a separate masterpiece of various ornamentation +adorning an established architectural form (Illustration 28). + +[Illustration 28] + +[Illustration 29] + +The builders of the early Italian churches, instinctively obeying this +law of Diversity in Monotony, varied the size of the arches in the +same arcade (Illustration 29), and that this was an effect of art and +not of accident or carelessness Ruskin long ago discovered, and the +Brooklyn Institute surveys have amply confirmed his view. Although +by these means the builders of that day produced effects of deceptive +perspective, of subtle concord and contrast, their sheer hatred of +monotony and meaningless repetition may have led them to diversify +their arcades in the manner described, for a rigidly equal and regular +division lacks interest and vitality. + + +BALANCE + +If one were to establish an axial plane vertically through the center +of a tree, in most cases it would be found that the masses of foliage, +however irregularly shaped on either side of such an axis, just about +balanced each other. Similarly, in all our bodily movements, for every +change of equilibrium there occurs an opposition and adjustment of +members of such a nature that an axial plane through the center of +gravity would divide the body into two substantially equal masses, +as in the case of the tree. This physical plane law of Balance +shows itself for the most part on the human plane as the law of +Compensation, whereby, to the vision of the occultist, all accounts +are "squared," so to speak. It is in effect the law of Justice, aptly +symbolized by the scales. + +The law of Balance finds abundant illustration in art: in music by +the opposition, the answering, of one phrase by another of the same +elements and the same length, but involving a different sequence of +intervals; in painting by the disposition of masses in such a way that +they about equalize one another, so that there is no sense of "strain" +in the composition. + +In architecture the common and obvious recognition of the law of +Balance is in the symmetrical disposition of the elements, whether of +plan or of elevation, on either side of axial lines. A far more subtle +and vital illustration of the law occurs when the opposed elements do +not exactly match, but differ from each other, as in the case of the +two towers of Amiens, for example. This sort of balance may be said to +be characteristic of Gothic, as symmetry is characteristic of Classic, +architecture. + + +RHYTHMIC CHANGE + +There is in nature a universal tendency toward refinement and +compactness of form in space, or contrariwise, toward increment +and diffusion; and this manifests itself in time as acceleration or +retardation. It is governed, in either case, by an exact mathematical +law, like the law of falling bodies. It shows itself in the widening +circles which appear when one drops a stone into still water, in the +convolutions of shells, in the branching of trees and the veining +of leaves; the diminution in the size of the pipes of an organ +illustrates it, and the spacing of the frets of a guitar. More and +more science is coming to recognize, what theosophy affirms, that the +spiral vortex, which so beautifully illustrates this law, both in its +time and its space aspects is the universal archetype, the pattern of +all that is, has been, or will be, since it is the form assumed by the +ultimate physical atom, and the ultimate physical atom is the physical +cosmos in miniature. + +This Rhythmic Diminution is everywhere: it is in the eye itself, for +any series of mathematically equal units, such for example as the +columns and intercolumnations of a colonnade, become when seen +in perspective rhythmically unequal, diminishing according to the +universal law. The entasis of a Classic column is determined by this +law, the spirals of the Ionic volute, the annulets of the Parthenon +cap, obey it (Illustration 30). + +In recognition of the same principle of Rhythmic Diminution a building +is often made to grow, or appear to grow lighter, more intricate, +finer, from the ground upward, an end attained by various devices, +one of the most common being the employment of the more attenuated +and highly ornamented orders above the simpler and sturdier, as in the +Roman Colosseum, or in the Palazzo Uguccioni, in Florence--to mention +only two examples out of a great number. In the Riccardi Palace +an effect of increasing refinement is obtained by diminishing the +boldness of the rustication of the ashlar in successive stories; in +the Farnese, by the gradual reduction of the size of the angle quoins +(Illustration 30). In an Egyptian pylon it is achieved most simply by +battering the wall; in a Gothic cathedral most elaborately by a +kind of segregation, or breaking up, analogous to that which a tree +undergoes--the strong, relatively unbroken base corresponding to +the trunk, the diminishing buttresses to the tapering limbs, and +the multitude of delicate pinnacles and crockets, to the outermost +branches and twigs, seen against the sky. + + +RADIATION + +The final principle of natural beauty to which the author would call +attention is the law of _Radiation_, which is in a manner a return +to the first, the law of _Unity_. The various parts of any organism +radiate from, or otherwise refer back to common centers, or foci, +and these to centers of their own. The law is represented in its +simplicity in the star-fish, in its complexity in the body of man; a +tree springs from a seed, the solar system centers in the sun. + +The idea here expressed by the term "radiation" is a familiar one +to all students of theosophy. The Logos radiates his life and light +throughout his universe, bringing into activity a host of entities +which become themselves radial centers; these generate still others, +and so on endlessly. This principle, like every other, patiently +publishes itself to us, unheeding, everywhere in nature, and in +all great art as well; it is a law of optics, for example, that all +straight lines having a common direction if sufficiently prolonged +appear to meet in a point, i.e., radiate from it (Illustration 31). +Leonardo da Vinci employed this principle of perspective in his Last +Supper to draw the spectator's eye to the picture's central figure, +the point of sight toward which the lines of the walls and ceiling +converge centering in the head of Christ. Puvis de Chavannes, in his +Boston Library decoration, leads the eye by a system of triangulation +to the small figure of the Genius of Enlightenment above the central +door (Illustration 32); and Ruskin, in his _Elements of Drawing_, has +shown how artfully Turner arranged some of his compositions to attract +attention to a focal point. + +This law of Radiation enters largely into architecture. The Colosseum, +based upon the ellipse, a figure generated from two points or foci, +and the Pantheon, based upon the circle, a figure generated from a +central point, are familiar examples. The distinctive characteristic +of Gothic construction, the concentration or focalization of the +weight of the vaults and arches at certain points, is another +illustration of the same principle applied to architecture, +beautifully exemplified in the semicircular apse of a cathedral, where +the lines of the plan converge to a common center, and the ribs of the +vaulting meet upon the capitals of the piers and columns, seeming +to radiate thence to still other centers in the loftier vaults which +finally meet in a center common to all. + +[Illustration 30] + +[Illustration 31] + +[Illustration 32] + +The tracery of the great roses, high up in the faƧades of the +cathedrals of Paris and of Amiens, illustrate Radiation, in the one +case masculine: straight, angular, direct; in the feminine: curved, +flowing, sinuous. The same _Beautiful Necessity_ determined the +characteristics of much of the ornament of widely separated styles +and periods: the Egyptian lotus, the Greek honeysuckle, the Roman +acanthus, Gothic leaf work--to snatch at random four blossoms from +the sheaf of time. The radial principle still inherent in the debased +ornament of the late Renaissance gives that ornament a unity, a +coherence, and a kind of beauty all its own (Illustration 35). + +[Illustration 33] + +[Illustration 34] + +Such are a few of the more obvious laws of natural beauty and their +application to the art of architecture. The list is by no means +exhausted, but it is not the multiplicity and diversity of these laws +which is important to keep in mind, so much as their relatedness and +coƶrdination, for they are but different aspects of the One Law, that +whereby the Logos manifests in time and space. A brief recapitulation +will serve to make this correlation plain, and at the same time fix +what has been written more firmly in the reader's mind. + +[Illustration 35] + +[Illustration 36] + +First comes the law of _Unity_; then, since every unit is in its +essence twofold, there is the law of _Polarity_; but this duality is +not static but dynamic, the two parts acting and reacting upon one +another to produce a third--hence the law of _Trinity_. Given this +third term, and the innumerable combinations made possible by +its relations to and reactions upon the original pair, the law +of _Multiplicity in Unity_ naturally follows, as does the law +of _Consonance_, or repetition, since the primal process of +differentiation tends to repeat itself, and the original combinations +to reappear--but to reappear in changed form, hence the law of +_Diversity in Monotony_. The law of _Balance_ is seen to be but a +modification of the law of Polarity, and since all things are waxing +and waning, there is the law whereby they wax and wane, that of +_Rhythmic Change_. _Radiation_ rediscovers and reaffirms, even in the +utmost complexity, that essential and fundamental unity from which +complexity was wrought. + +Everything, beautiful or ugly, obeys and illustrates one or another of +these laws, so universal are they, so inseparably attendant upon every +kind of manifestation in time and space. It is the number of them +which finds illustration within small compass, and the aptness and +completeness of such illustration, which makes for beauty, because +beauty is the fine flower of a sort of sublime ingenuity. A work of +art is nothing if not _artful_: like an acrostic, the more different +ways it can be read--up, down, across, from right to left and from +left to right--the better it is, other things being equal. This +statement, of course, may be construed in such a way as to appear +absurd; what is meant is simply that the more a work of art is +freighted and fraught with meaning beyond meaning, the more secure its +immortality, the more powerful its appeal. For enjoyment, it is not +necessary that all these meanings should be fathomed, it is only +necessary that they should be felt. + +Consider for a moment the manner in which Leonardo da Vinci's Last +Supper, an acknowledged masterpiece, conforms to everyone of the laws +of beauty enumerated above (Illustration 32). It illustrates the law +of Unity in that it movingly portrays a single significant episode in +the life of Christ. The eye is led to dwell upon the central personage +of this drama by many artful expedients: the visible part of the +figure of Christ conforms to the lines of an equilateral triangle +placed exactly in the center of the picture; the figure is separated +by a considerable space from the groups of the disciples on either +hand, and stands relieved against the largest parallelogram of light, +and the vanishing point of the perspective is in the head of Christ, +at the apex, therefore, of the triangle. The law of Polarity finds +fulfilment in the complex and flowing lines of the draped figures +contrasted with the simple parallelogram of the cloth-covered table, +and the severe architecture of the room. The law of Trinity is +exemplified in the three windows, and in the subdivision of the twelve +figures of the disciples into four groups of three figures each. The +law of Consonance appears in the repetition of the horizontal lines +of the table in the ceiling above; and in the central triangle before +referred to, continued and echoed, as it were, in the triangular +supports of the table visible underneath the cloth. The law of +Diversity in Monotony is illustrated in the varying disposition of the +heads of the figures in the four groups of three; the law of Balance +in the essential symmetry of the entire composition; the law of +Rhythmic Change in the diminishing of the wall and ceiling spaces; and +the law of Radiation in the convergence of all the perspective lines +to a single significant point. + +To illustrate further the universality of these laws, consider now +their application to a single work of architecture: the Taj Mahal, one +of the most beautiful buildings of the world (Illustration 36). It is +a unit, but twofold, for it consists of a curved part and an angular +part, roughly figured as an inverted cup upon a cube; each of these +(seen in parallel perspective, at the end of the principal vista) is +threefold, for there are two sides and a central parallelogram, and +two lesser domes flank the great dome. The composition is rich in +consonances, for the side arches echo the central one, the subordinate +domes the great dome, and the lanterns of the outstanding minarets +repeat the principal motif. Diversity in Monotony appears abundantly +in the ornament, which is intricate and infinitely various; the law of +Balance is everywhere operative in the symmetry of the entire design. +Rhythmic Change appears in the tapering of the minarets, the outlines +of the domes and their mass relations to one another; and finally, +the whole effect is of radiation from a central point, of elements +disposed on radial lines. + +It would be fatuous to contend that the prime object of a work of +architecture is to obey and illustrate these laws. The prime object of +a work of architecture is to fulfill certain definite conditions in a +practical, economical, and admirable way, and in fulfilling to express +as far as possible these conditions, making the form express the +function. The architect who is also an artist however will do this +and something beyond: working for the most part unconsciously, +harmoniously, joyously, his building will obey and illustrate natural +laws--these laws of beauty--and to the extent it does so it will be a +work of art; for art is the method of nature carried into those higher +regions of thought and feeling which man alone inhabits: regions which +it is one of the purposes of theosophy to explore. + + + + +IV + +THE BODILY TEMPLE + + +Carlyle says: "There is but one temple in the world, and that is the +body of man." If the body is, as he declares, a temple, it is not less +true that a temple or any work of architectural art is a larger body +which man has created for his uses, just as the individual self is +housed within its stronghold of flesh and bones. Architectural beauty +like human beauty depends upon the proper subordination of parts +to the whole, the harmonious interrelation between these parts, the +expressiveness of each of its function or functions, and when these +are many and diverse, their reconcilement one with another. This being +so, a study of the human figure with a view to analyzing the sources +of its beauty cannot fail to be profitable. Pursued intelligently, +such a study will stimulate the mind to a perception of those simple +yet subtle laws according to which nature everywhere works, and +it will educate the eye in the finest known school of proportion, +training it to distinguish minute differences, in the same way that +the hearing of good music cultivates the ear. + +Those principles of natural beauty which formed the subject of the +two preceding essays are all exemplified in the ideally perfect human +figure. Though essentially a unit, there is a well marked division +into right and left--"Hands to hands, and feet to feet, in one body +grooms and brides." There are two arms, two legs, two ears, two eyes, +and two lids to each eye; the nose has two nostrils, the mouth has +two lips. Moreover, the terms of such pairs are masculine and feminine +with respect to each other, one being active and the other passive. +Owing to the great size and one-sided position of the liver, the right +half of the body is heavier than the left; the right arm is usually +longer and more muscular than the left; the right eye is slightly +higher than its fellow. In speaking and eating the lower jaw and under +lip are active and mobile with relation to the upper; in winking it is +the upper eyelid which is the more active. That "inevitable duality" +which is exhibited in the form of the body characterizes its motions +also. In the act of walking for example, a forward movement is +attained by means of a forward and a backward movement of the thighs +on the axis of the hips; this leg movement becomes twofold again below +the knee, and the feet move up and down independently on the axis of +the ankle. A similar progression is followed in raising the arm and +hand: motion is communicated first to the larger parts, through them +to the smaller and thence to the extremities, becoming more rapid and +complex as it progresses, so that all free and natural movements of +the limbs describe invisible lines of beauty in the air. Coexistent +with this pervasive duality there is a threefold division of the +figure into trunk, head and limbs: a superior trinity of head and +arms, and an inferior trinity of trunk and legs. The limbs are divided +threefold into upper-arm, forearm and hand; thigh, leg and foot. The +hand flowers out into fingers and the foot into toes, each with a +threefold articulation; and in this way is effected that transition +from unity to multiplicity, from simplicity to complexity, which +appears to be so universal throughout nature, and of which a tree is +the perfect symbol. + +[Illustration 37: THE LAW OF RHYTHMIC DIMINUTION ILLUSTRATED IN THE +TAPERING BODY, LIMBS, FINGERS & TOES.] + +[Illustration 38] + +[Illustration 39] + +The body is rich in veiled repetitions, echoes, _consonances_. The +head and arms are in a sense a refinement upon the trunk and legs, +there being a clearly traceable correspondence between their various +parts. The hand is the body in little--_"Your soft hand is a woman of +itself"_--the palm, the trunk; the four fingers, the four limbs; and +the thumb, the head;-each finger is a little arm, each finger tip a +little palm. The lips are the lids of the mouth, the lids are the +lips of the eyes--and so on. The law of _Rhythmic Diminution_ is +illustrated in the tapering of the entire body and of the limbs, in +the graduated sizes and lengths of the palm and the toes, and in +the successively decreasing length of the palm and the joints of the +fingers, so that in closing the hand the fingers describe natural +spirals (Illustrations 37, 38). Finally, the limbs radiate as it were +from the trunk, the fingers from a point in the wrist, the toes from +a point in the ankle. The ribs radiate from the spinal column like the +veins of a leaf from its midrib (Illustration 39). + +[Illustration 40] + +The relation of these laws of beauty to the art of architecture has +been shown already. They are reiterated here only to show that man is +indeed the microcosm--a little world fashioned from the same elements +and in accordance with the same _Beautiful Necessity_ as is the +greater world in which he dwells. When he builds a house or temple he +builds it not literally in his own image, but according to the laws of +his own being, and there are correspondences not altogether fanciful +between the animate body of flesh and the inanimate body of stone. Do +we not all of us, consciously or unconsciously, recognize the fact +of character and physiognomy in buildings? Are they not, to our +imagination, masculine or feminine, winning or forbidding--_human_, +in point of fact--to a greater degree than anything else of man's +creating? They are this certainly to a true lover and student of +architecture. Seen from a distance the great French cathedrals appear +like crouching monsters, half beast, half human: the two towers stand +like a man and a woman, mysterious and gigantic, looking out over city +and plain. The campaniles of Italy rise above the churches and houses +like the sentinels of a sleeping camp--nor is their strangely human +aspect wholly imaginary: these giants of mountain and campagna have +eyes and brazen tongues; rising four square, story above story, with +a belfry or lookout, like a head, atop, their likeness to a man is not +infrequently enhanced by a certain identity of proportion--of ratio, +that is, of height to width: Giotto's beautiful tower is an example. +The caryatid is a supporting member in the form of a woman; in the +Ionic column we discern her stiffened, like Lot's wife, into a pillar, +with nothing to show her feminine but the spirals of her beautiful +hair. The columns which uphold the pediment of the Parthenon are +unmistakably masculine: the ratio of their breadth to their height is +the ratio of the breadth to the height of a man (Illustration 40). + +[Illustration 41: THE BODY THE ARCHETYPE OF SACRED EDIFICES.] + +[Illustration 42: THE VESICA PISCIS AND THE PLAN OF CHARTRES.] + +At certain periods of the world's history, periods of mystical +enlightenment, men have been wont to use the human figure, the soul's +temple, as a sort of archetype for sacred edifices (Illustration 41). +The colossi, with calm inscrutable faces, which flank the entrance to +Egyptian temples; the great bronze Buddha of Japan, with its dreaming +eyes; the little known colossal figures of India and China--all these +belong scarcely less to the domain of architecture than of sculpture. +The relation above referred to however is a matter more subtle and +occult than mere obvious imitation on a large scale, being based upon +some correspondence of parts, or similarity of proportions, or both. +The correspondence between the innermost sanctuary or shrine of a +temple and the heart of a man, and between the gates of that temple +and the organs of sense is sufficiently obvious, and a relation once +established, the idea is susceptible of almost infinite development. +That the ancients proportioned their temples from the human figure +is no new idea, nor is it at all surprising. The sculpture of the +Egyptians and the Greeks reveals the fact that they studied the body +abstractly, in its exterior presentment. It is clear that the rules +of its proportions must have been established for sculpture, and it is +not unreasonable to suppose that they became canonical in architecture +also. Vitruvius and Alberti both lay stress on the fact that all +sacred buildings should be founded on the proportions of the human +body. + +[Illustration 43: A GOTHIC CATHEDRAL THE SYMBOL OF THE BODY OF JESUS +CHRIST] + +[Illustration 44: THE SYMBOLISM OF A GOTHIC CATHEDRAL FROM THE +ROSICRUCIANS: HARGRAVE JENNINGS] + +In France, during the Middle Ages, a Gothic cathedral became, at the +hands of the secret masonic guilds, a glorified symbol of the body +of Christ. To practical-minded students of architectural history, +familiar with the slow and halting evolution of a Gothic cathedral +from a Roman basilica, such an idea may seem to be only the +maunderings of a mystical imagination, a theory evolved from the inner +consciousness, entitled to no more consideration than the familiar +fallacy that vaulted nave of a Gothic church was an attempt to imitate +the green aisles of a forest. It should be remembered however that the +habit of the thought of that time was mystical, as that of our own age +is utilitarian and scientific; and the chosen language of mysticism is +always an elaborate and involved symbolism. What could be more natural +than that a building devoted to the worship of a crucified Savior +should be made a symbol, not of the cross only, but of the body +crucified? + +[Illustration 45: THE GEOMETRICAL BASIS OF THE HUMAN FIGURE] + +[Illustration 46] + +The _vesica piscis_ (a figure formed by the developing arcs of two +equilateral triangles having a common side) which in so many cases +seems to have determined the main proportion of a cathedral plan--the +interior length and width across the transepts--appears as an aureole +around the figure of Christ in early representations, a fact which +certainly points to a relation between the two (Illustrations 42, +43). A curious little book, _The Rosicrucians_, by Hargrave Jennings, +contains an interesting diagram which well illustrates this conception +of the symbolism of a cathedral. A copy of it is here given. The apse +is seen to correspond to the head of Christ, the north transept to his +right hand, the south transept to the left hand, the nave to the body, +and the north and south towers to the right and left feet respectively +(Illustration 44). + +[Illustration 47] + +The cathedral builders excelled all others in the artfulness with +which they established and maintained a relation between their +architecture and the stature of a man. This is perhaps one reason why +the French and English cathedrals, even those of moderate dimensions +are more truly impressive than even the largest of the great +Renaissance structures, such as St. Peter's in Rome. A gigantic order +furnishes no true measure for the eye: its vastness is revealed +only by the accident of some human presence which forms a basis +of comparison. That architecture is not necessarily the most +awe-inspiring which gives the impression of having been built by +giants for the abode of pigmies; like the other arts, architecture is +highest when it is most human. The mediƦval builders, true to this +dictum, employed stones of a size proportionate to the strength of +a man working without unusual mechanical aids; the great piers and +columns, built up of many such stones, were commonly subdivided +into clusters, and the circumference of each shaft of such a cluster +approximated the girth of a man; by this device the moulding of the +base and the foliation of the caps were easily kept in scale. Wherever +a balustrade occurred it was proportioned not with relation to the +height of the wall or the column below, as in classic architecture, +but with relation to a man's stature. + +[Illustration 48: FIGURE DIVIDED ACCORDING TO THE EGYPTIAN CANON] + +It may be stated as a general rule that every work of architecture, +of whatever style, should have somewhere about it something fixed and +enduring to relate it to the human figure, if it be only a flight of +steps in which each one is the measure of a stride. In the Farnese, +the Riccardi, the Strozzi, and many another Italian palace, the stone +seat about the base gives scale to the building because the beholder +knows instinctively that the height of such a seat must have some +relation to the length of a man's leg. In the Pitti palace the +balustrade which crowns each story answers a similar purpose: it +stands in no intimate relation to the gigantic arches below, but is +of a height convenient for lounging elbows. The door to Giotto's +campanile reveals the true size of the tower as nothing else could, +because it is so evidently related to the human figure and not to the +great windows higher up in the shaft. + +[Illustration 49: THE MEDIĆVAL METHOD OF DRAWING THE FIGURE] + +The geometrical plane figures which play the most important part in +architectural proportion are the square, the circle and the triangle; +and the human figure is intimately related to these elementary forms. +If a man stand with heels together, and arms outstretched horizontally +in opposite directions, he will be inscribed, as it were, within a +square; and his arms will mark, with fair accuracy, the base of an +inverted equilateral triangle, the apex of which will touch the ground +at his feet. If the arms be extended upward at an angle, and the +legs correspondingly separated, the extremities will touch +the circumferences of a circle having its center in the navel +(Illustrations 45, 46). + +[Illustration 50] + +The figure has been variously analyzed with a view to establishing +numerical ratios between its parts (Illustrations 47, 48, 49). Some +of these are so simple and easily remembered that they have obtained +a certain popular currency; such as that the length of the hand equals +the length of the face; that the span of the horizontally extended +arms equals the height; and the well known rule that twice around +the wrist is once around the neck, and twice around the neck is once +around the waist. The Roman architect Vitruvius, writing in the age of +Augustus CƦsar, formulated the important proportions of the statues +of classical antiquity, and except that he makes the head smaller than +the normal (as it should be in heroic statuary), the ratios which +he gives are those to which the ideally perfect male figure should +conform. Among the ancients the foot was probably the standard of all +large measurements, being a more determinate length than that of the +head or face, and the height was six lengths of the foot. If the head +be taken as a unit, the ratio becomes 1:8, and if the face--1:10. + +Doctor Rimmer, in his _Art Anatomy_, divides the figure into four +parts, three of which are equal, and correspond to the lengths of +the leg, the thigh and the trunk; while the fourth part, which is +two-thirds of one of these thirds, extends from the sternum to the +crown of the head. One excellence of such a division aside from its +simplicity, consists in the fact that it may be applied to the face as +well. The lowest of the three major divisions extends from the tip of +the chin to the base of the nose, the next coincides with the height +of the nose (its top being level with the eyebrows), and the last with +the height of the forehead, while the remaining two-thirds of one of +these thirds represents the horizontal projection from the beginning +of the hair on the forehead to the crown of the head. The middle of +the three larger divisions locates the ears, which are the same height +as the nose (Illustrations 45, 47). + +Such analyses of the figure, however conducted, reveals an +all-pervasive harmony of parts, between which definite numerical +relations are traceable, and an apprehension of these should assist +the architectural designer to arrive at beauty of proportion by +methods of his own, not perhaps in the shape of rigid formulƦ, but +present in the consciousness as a restraining influence, acting and +reacting upon the mind with a conscious intention toward rhythm and +harmony. By means of such exercises, he will approach nearer to an +understanding of that great mystery, the beauty and significance of +numbers, of which mystery music, architecture, and the human figure +are equally presentments--considered, that is, from the standpoint of +the occultist. + + + + +V + +LATENT GEOMETRY + + +[Illustration 51: THE HEXAGRAM AND EQUILATERAL TRIANGLE IN NATURE] + +It is a well known fact that in the microscopically minute of nature, +units everywhere tend to arrange themselves with relation to certain +simple geometrical solids, among which are the tetrahedron, the cube, +and the sphere. This process gives rise to harmony, which may be +defined as the relation between parts and unity, the simplicity latent +in the infinitely complex, the potential complexity of that which is +simple. Proceeding to things visible and tangible, this indwelling +harmony, rhythm, proportion, which has its basis in geometry and +number, is seen to exist in crystals, flower forms, leaf groups, and +the like, where it is obvious; and in the more highly organized world +of the animal kingdom also; though here the geometry is latent rather +than patent, eluding though not quite defying analysis, and thus +augmenting beauty, which like a woman is alluring in proportion as she +eludes (Illustrations 51, 52, 53). + +[Illustration 52: PROPORTIONS OF THE HORSE] + +[Illustration 53] + +By the true artist, in the crystal mirror of whose mind the universal +harmony is focused and reflected, this secret of the cause and source +of rhythm--that it dwells in a correlation of parts based on an +ultimate simplicity--is instinctively apprehended. A knowledge of it +formed part of the equipment of the painters who made glorious the +golden noon of pictorial art in Italy during the Renaissance. The +problem which preoccupied them was, as Symonds says of Leonardo, +"to submit the freest play of form to simple figures of geometry in +grouping." Alberti held that the painter should above all things have +mastered geometry, and it is known that the study of perspective and +kindred subjects was widespread and popular. + +[Illustration 54] + +The first painter who deliberately rather than instinctively based +his compositions on geometrical principles seems to have been Fra +Bartolommeo, in his Last Judgment, in the church of St. Maria Nuova, +in Florence. Symonds says of this picture, "Simple figures--the +pyramid and triangle, upright, inverted, and interwoven like the +rhymes of a sonnet--form the basis of the composition. This system was +adhered to by the Fratre in all his subsequent works" (Illustration +54). Raphael, with that power of assimilation which distinguishes +him among men of genius, learned from Fra Bartolommeo this method +of disposing figures and combining them in masses with almost +mathematical precision. It would have been indeed surprising if +Leonardo da Vinci, in whom the artist and the man of science were +so wonderfully united, had not been greatly preoccupied with the +mathematics of the art of painting. His Madonna of the Rocks, and +Virgin on the Lap of Saint Anne, in the Louvre, exhibit the very +perfection of pyramidal composition. It is however in his masterpiece, +The Last Supper, that he combines geometrical symmetry and precision +with perfect naturalness and freedom in the grouping of individually +interesting and dramatic figures. Michael Angelo, Andrea del Sarto, +and the great Venetians, in whose work the art of painting may be said +to have culminated, recognized and obeyed those mathematical laws of +composition known to their immediate predecessors, and the decadence +of the art in the ensuing period may be traced not alone to the false +sentiment and affectation of the times, but also in the abandonment by +the artists of those obscurely geometrical arrangements and groupings +which in the works of the greatest masters so satisfy the eye and +haunt the memory of the beholder (Illustrations 55, 56). + +[Illustration 55: THE EMPLOYMENT OF THE EQUILATERAL TRIANGLE IN +RENAISSANCE PAINTING] + +[Illustration 56: GEOMETRICAL BASIS OF THE SISTINE CEILING PAINTINGS] + +[Illustration 57: ASSYRIAN; GREEK] + +[Illustration 58: THE GEOMETRICAL BASIS OF THE PLAN IN ARCHITECTURAL +DESIGN] + +[Illustration 59] + +Sculpture, even more than painting, is based on geometry. The colossi +of Egypt, the bas-reliefs of Assyria, the figured pediments and +metopes of the temples of Greece, the carved tombs of Revenna, +the Della Robbia lunettes, the sculptured tympani of Gothic church +portals, all alike lend themselves in greater or less degree to a +geometrical synopsis (Illustration 57). Whenever sculpture suffered +divorce from architecture the geometrical element became less +prominent, doubtless because of all the arts architecture is the most +clearly and closely related to geometry. Indeed, it may be said that +architecture is geometry made visible, in the same sense that music +is number made audible. A building is an aggregation of the commonest +geometrical forms: parallelograms, prisms, pyramids and cones--the +cylinder appearing in the column, and the hemisphere in the dome. +The plans likewise of the world's famous buildings reduced to their +simplest expression are discovered to resolve themselves into a few +simple geometrical figures. (Illustration 58). This is the "bed rock" +of all excellent design. + +[Illustration 60: EGYPTIAN; GREEK; ROMAN; MEDIĆVAL] + +[Illustration 61: JEFFERSON'S PEN SKETCH FOR THE ROTUNDA OF THE +UNIVERSITY OF VIRGINIA] + +[Illustration 62: APPLICATION OF THE EQUILATERAL TRIANGLE TO THE +ERECHTHEUM AT ATHENS] + +[Illustration 63] + +[Illustration 64: THE EQUILATERAL TRIANGLE IN ROMAN ARCHITECTURE] + +But architecture is geometrical in another and a higher sense than +this. Emerson says: "The pleasure a palace or a temple gives the eye +is that an order and a method has been communicated to stones, so that +they speak and geometrize, become tender or sublime with expression." +All truly great and beautiful works of architecture from the Egyptian +pyramids to the cathedrals of Ile-de-France--are harmoniously +proportioned, their principal and subsidiary masses being related, +sometimes obviously, more often obscurely, to certain symmetrical +figures of geometry, which though invisible to the sight and not +consciously present in the mind of the beholder, yet perform the +important function of coƶrdinating the entire fabric into one easily +remembered whole. Upon some such principle is surely founded what +Symonds calls "that severe and lofty art of composition which seeks +the highest beauty of design in architectural harmony supreme, above +the melodies of gracefulness of detail." + +[Illustration 65: THE EQUILATERAL TRIANGLE IN ITALIAN ARCHITECTURE] + +[Illustration 66: THE HEXAGRAM IN GOTHIC ARCHITECTURE] + +There is abundant evidence in support of the theory that the +builders of antiquity, the masonic guilds of the Middle Ages, and +the architects of the Italian Renaissance, knew and followed certain +rules, but though this theory be denied or even disproved--if after +all these men obtained their results unconsciously--their creations +so lend themselves to a geometrical analysis that the claim for the +existence of certain canons of proportion, based on geometry, remains +unimpeached. + +[Illustration 67] + +[Illustration 68] + +The plane figures principally employed in determining architectural +proportion are the circle, the equilateral triangle, and the +square--which also yields the right angled isosceles triangle. It +will be noted that these are the two dimensional correlatives of the +sphere, the tetrahedron and the cube, mentioned as being among the +determining forms in molecular structure. The question naturally +arises, why the circle, the equilateral triangle and the square? +Because, aside from the fact that they are of all plane figures the +most elementary, they are intimately related to the body of man, as +has been shown (Illustration 45), and the body of man is as it were +the architectural archetype. But this simply removes the inquiry to +a different field, it is not an answer. Why is the body of man so +constructed and related? This leads us, as does every question, to +the threshold of a mystery upon which theosophy alone is able to throw +light. Any extended elucidation would be out of place here: it is +sufficient to remind the reader that the circle is the symbol of the +universe; the equilateral triangle, of the higher trinity (_atma, +buddhi, manas_); and the square, of the lower quaternary of man's +sevenfold nature. + +[Illustration 69] + +[Illustration 70] + +The square is principally used in preliminary plotting: it is the +determining figure in many of the palaces of the Italian Renaissance; +the Arc de Triomphe, in Paris is a modern example of its use +(Illustrations 59, 60). The circle is often employed in conjunction +with the square and the triangle. In Thomas Jefferson's Rotunda for +the University of Virginia, a single great circle was the determining +figure, as his original pen sketch of the building shows (Illustration +61). Some of the best Roman triumphal arches submit themselves to a +circular synopsis, and a system of double intersecting circles has +been applied, with interesting results, to faƧades as widely different +as those of the Parthenon and the Farnese Palace in Rome, though +it would be fatuous to claim that these figures determined the +proportions of the faƧades. + +By far the most important figure in architectural proportion, +considered from the standpoint of geometry, is the equilateral +triangle. It would seem that the eye has an especial fondness for +this figure, just as the ear has for certain related sounds. Indeed it +might not be too fanciful to assert that the common chord of any key +(the tonic with its third and fifth) is the musical equivalent of +the equilateral triangle. It is scarcely necessary to dwell upon +the properties and unique perfection of this figure. Of all regular +polygons it is the simplest: its three equal sides subtend equal +angles, each of 60 degrees; it trisects the circumference of a circle; +it is the graphic symbol of the number three, and hence of every +threefold thing; doubled, its generating arcs form the _vesica +piscis_, of so frequent occurrence in early Christian art; two +symmetrically intersecting equilateral triangles yield the figure +known as "Solomon's Seal," or the "Shield of David," to which mystic +properties have always been ascribed. + +It may be stated as a general rule that whenever three important +points in any architectural composition coincide (approximately or +exactly) with the three extremities of an equilateral triangle, it +makes for beauty of proportion. An ancient and notable example occurs +in the pyramids of Egypt, the sides of which, in their original +condition, are believed to have been equilateral triangles. It is a +demonstrable fact that certain geometrical intersections yield the +important proportions of Greek architecture. The perfect little +Erechtheum would seem to have been proportioned by means of the +equilateral triangle and the angle of 60 degrees, both in general and +in detail (Illustration 62). The same angle, erected from the central +axis of a column at the point where it intersects the architrave, +determines both the projection of the cornice and the height of +the architrave in many of the finest Greek and Roman temples +(Illustrations 67-70). The equilateral triangle used in conjunction +with the circle and the square was employed by the Romans in +determining the proportions of triumphal arches, basilicas and +baths. That the same figure was a factor in the designing of Gothic +cathedrals is sufficiently indicated in the accompanying facsimile +reproductions of an illustration from the Como Vitruvius, published in +Milan in 1521, which shows a vertical section of the Milan cathedral +and the system of equilateral triangles which determined its various +parts (Illustration 71). The _vesica piscis_ was often used to +establish the two main internal dimensions of the cathedral plan: the +greatest diameter of the figure corresponding with the width across +the transepts, the upper apex marking the limit of the apse, and the +lower, the termination of the nave. Such a proportion is seen to be +both subtle and simple, and possesses the advantage of being easily +laid out. The architects of the Italian Renaissance doubtless +inherited certain of the Roman canons of architectural proportion, +for they seem very generally to have recognized them as an essential +principle of design. + +[Illustration 71] + +Nevertheless, when all is said, it is easy to exaggerate the +importance of this matter of geometrical proportion. The designer +who seeks the ultimate secret of architectural harmony in mathematics +rather than in the trained eye, is following the wrong road to +success. A happy inspiration is worth all the formulƦ in the world--if +it be really happy, the artist will probably find that he has +"followed the rules without knowing them." Even while formulating +concepts of art, the author must reiterate Schopenhauer's dictum +that the _concept_ is unfruitful in art. The mathematical analysis +of spatial beauty is an interesting study, and a useful one to the +artist; but it can never take the place of the creative faculty, it +can only supplement, restrain, direct it. The study of proportion is +to the architect what the study of harmony is to a musician--it helps +his genius adequately to express itself. + + + + +VI + +THE ARITHMETIC OF BEAUTY + + +Although architecture is based primarily upon geometry, it is possible +to express all spatial relations numerically: for arithmetic, not +geometry, is the universal science of quantity. The relation of masses +one to another--of voids to solids, and of heights and lengths to +widths--forms ratios; and when such ratios are simple and harmonious, +architecture may be said, in Walter Pater's famous phrase, to +"aspire towards the condition of music." The trained eye, and not an +arithmetical formula, determines what is, and what is not, beautiful +proportion. Nevertheless the fact that the eye instinctively rejects +certain proportions as unpleasing, and accepts others as satisfactory, +is an indication of the existence of laws of space, based upon number, +not unlike those which govern musical harmony. The secret of the deep +reasonableness of such selection by the senses lies hidden in the very +nature of number itself, for number is the invisible thread on which +the worlds are strung--the universe abstractly symbolized. + +Number is the within of all things--the "first form of Brahman." It +is the measure of time and space; it lurks in the heart-beat and is +blazoned upon the starred canopy of night. Substance, in a state of +vibration, in other words conditioned by number, ceaselessly undergoes +the myriad transmutations which produce phenomenal life. Elements +separate and combine chemically according to numerical ratios: +"Moon, plant, gas, crystal, are concrete geometry and number." By +the Pythagoreans and by the ancient Egyptians sex was attributed to +numbers, odd numbers being conceived of as masculine or generating, +and even numbers as feminine or parturitive, on account of their +infinite divisibility. Harmonious combinations were those +involving the marriage of a masculine and a feminine--an odd and an +even--number. + +[Illustration 72: A GRAPHIC SYSTEM OF NOTATION] + +Numbers progress from unity to infinity, and return again to unity as +the soul, defined by Pythagoras as a self-moving number, goes forth +from, and returns to God. These two acts, one of projection and the +other of recall; these two forces, centrifugal and centripetal, are +symbolized in the operations of addition and subtraction. Within them +is embraced the whole of computation; but because every number, every +aggregation of units, is also a new unit capable of being added +or subtracted, there are also the operations of multiplication and +division, which consists in one case of the addition of several equal +numbers together, and in the other, of the subtraction of several +equal numbers from a greater until that is exhausted. In order to +think correctly it is necessary to consider the whole of numeration, +computation, and all mathematical processes whatsoever as _the +division of the unit_ into its component parts and the establishment +of relations between these parts. + +[Illustration 73] + +[Illustration 74] + +The progression and retrogression of numbers in groups expressed by +the multiplication table gives rise to what may be termed "numerical +conjunctions." These are analogous to astronomical conjunctions: the +planets, revolving around the sun at different rates of speed, and +in widely separated orbits, at certain times come into line with one +another and with the sun. They are then said to be in conjunction. +Similarly, numbers, advancing toward infinity singly and in groups +(expressed by the multiplication table), at certain stages of their +progression come into relation with one another. For example, an +important conjunction occurs in 12, for of a series of twos it is +the sixth, of threes the fourth, of fours the third, and of sixes the +second. It stands to 8 in the ratio of 3:2, and to 9, of 4:3. It is +related to 7 through being the product of 3 and 4, of which numbers 7 +is the sum. The numbers 11 and 13 are not conjunctive; 14 is so in +the series of twos, and sevens; 15 is so in the series of fives and +threes. The next conjunction after 12, of 3 and 4 and their first +multiples, is in 24, and the next following is in 36, which numbers +are respectively the two and three of a series of twelves, each end +being but a new beginning. + +[Illustration 75] + +It will be seen that this discovery of numerical conjunctions consists +merely of resolving numbers into their prime factors, and that a +conjunctive number is a common multiple; but by naming it so, to +dismiss the entire subject as known and exhausted, is to miss a +sense of the wonder, beauty and rhythm of it all: a mental impression +analogous to that made upon the eye by the swift-glancing balls of a +juggler, the evolutions of drilling troops, or the intricate figures +of a dance; for these things are number concrete and animate in time +and space. + +[Illustration 76] + +The truths of number are of all truths the most interior, abstract +and difficult of apprehension, and since knowledge becomes clear and +definite to the extent that it can be made to enter the mind through +the channels of physical sense, it is well to accustom oneself to +conceiving of number graphically, by means of geometrical symbols +(Illustration 72), rather than in terms of the familiar arabic +notation which though admirable for purposes of computation, is of +too condensed and arbitrary a character to reveal the properties of +individual numbers. To state, for example, that 4 is the first square, +and 8 the first cube, conveys but a vague idea to most persons, but if +4 be represented as a square enclosing four smaller squares, and 8 +as a cube containing eight smaller cubes, the idea is apprehended +immediately and without effort. The number 3 is of course the +triangle; the irregular and vital beauty of the number 5 appears +clearly in the heptalpha, or five-pointed star; the faultless symmetry +of 6, its relation to 3 and 2, and its regular division of the circle, +are portrayed in the familiar hexagram known as the Shield of David. +Seven, when represented as a compact group of circles reveals itself +as a number of singular beauty and perfection, worthy of the important +place accorded to it in all mystical philosophy (Illustration 73). It +is a curious fact that when asked to think of any number less than 10, +most persons will choose 7. + +[Illustration 77] + +Every form of art, though primarily a vehicle for the expression and +transmission of particular ideas and emotions, has subsidiary offices, +just as a musical tone has harmonics which render it more sweet. +Painting reveals the nature of color; music, of sound--in wood, +in brass, and in stretched strings; architecture shows forth the +qualities of light, and the strength and beauty of materials. All +of the arts, and particularly music and architecture, portray in +different manners and degrees the truths of number. Architecture does +this in two ways: esoterically as it were in the form of harmonic +proportions; and exoterically in the form of symbols which represent +numbers and groups of numbers. The fact that a series of threes and +a series of fours mutually conjoin in 12, finds an architectural +expression in the Tuscan, the Doric, and the Ionic orders according to +Vignole, for in them all the stylobate is four parts, the entablature +3, and the intermediate column 12 (Illustration 74). The affinity +between 4 and 7, revealed in the fact that they express (very nearly) +the ratio between the base and the altitude of the right-angled +triangle which forms half of an equilateral, and the musical interval +of the diminished seventh, is architecturally suggested in the Palazzo +Giraud, which is four stories in height with seven openings in each +story (Illustration 75). + +[Illustration 78] + +[Illustration 79] + +[Illustration 80] + +[Illustration 81] + +Every building is a symbol of some number or group of numbers, and +other things being equal the more perfect the numbers involved the +more beautiful will be the building (Illustrations 76-82). The numbers +5 and 7--those which occur oftenest--are the most satisfactory because +being of small quantity, they are easily grasped by the eye, and being +odd, they yield a center or axis, so necessary in every architectural +composition. Next in value are the lowest multiples of these numbers +and the least common multiples of any two of them, because the +eye, with a little assistance, is able to resolve them into their +constituent factors. It is part of the art of architecture to +render such assistance, for the eye counts always, consciously or +unconsciously, and when it is confronted with a number of units +greater than it can readily resolve, it is refreshed and rested if +these units are so grouped and arranged that they reveal themselves as +factors of some higher quantity. + +[Illustration 82] + +[Illustration 83: A NUMERICAL ANALYSIS OF GOTHIC TRACERY] + +There is a raison d'ĆŖtre for string courses other than to mark the +position of a floor on the interior of a building, and for quoins and +pilasters other than to indicate the presence of a transverse wall. +These sometimes serve the useful purpose of so subdividing a faƧade +that the eye estimates the number of its openings without conscious +effort and consequent fatigue (Illustration 82). The tracery of Gothic +windows forms perhaps the highest and finest architectural expression +of number (Illustration 83). Just as thirst makes water more sweet, so +does Gothic tracery confuse the eye with its complexity only the more +greatly to gratify the sight by revealing the inherent simplicity in +which this complexity has its root. Sometimes, as in the case of +the Venetian Ducal Palace, the numbers involved are too great for +counting, but other and different arithmetical truths are portrayed; +for example, the multiplication of the first arcade by 2 in +the second, and this by 3 in the cusped arches, and by 4 in the +quatrefoils immediately above. + +[Illustration 84: NUMERATION IN GROUPS EXPRESSED ARCHITECTURALLY] + +[Illustration 85: ARCHITECTURAL ORNAMENT CONSIDERED AS THE +OBJECTIFICATION OF NUMBER. MULTIPLICATION IN GROUPS OF FIVE; TWO; +THREE; ALTERNATION OF THREE AND SEVEN] + +[Illustration 86] + +Seven is proverbially the perfect number. It is of a quantity +sufficiently complex to stimulate the eye to resolve it, and yet so +simple that it can be analyzed at a glance; as a center with two equal +sides, it is possessed of symmetry, and as the sum of an odd and even +number (3 and 4) it has vitality and variety. All these properties a +work of architecture can variously reveal (Illustration 77). Fifteen, +also, is a number of great perfection. It is possible to arrange the +first 9 numbers in the form of a "magic" square so that the sum of +each line, read vertically, horizontally or diagonally, will be 15. +Thus: + + 4 9 2 = 15 + 3 5 7 = 15 + 8 1 6 = 15 + -- -- -- + 15 15 15 + +Its beauty is portrayed geometrically in the accompanying figure which +expresses it, being 15 triangles in three groups of 5 (Illustration +86). Few arrangements of openings in a faƧade better satisfy the eye +than three superimposed groups of five (Illustrations 76-80). May not +one source of this satisfaction dwell in the intrinsic beauty of the +number 15? + +In conclusion, it is perhaps well that the reader be again reminded +that these are the by-ways, and not the highways of architecture: that +the highest beauty comes always, not from beautiful numbers, nor +from likenesses to Nature's eternal patterns of the world, but from +utility, fitness, economy, and the perfect adaptation of means to +ends. But along with this truth there goes another: that in every +excellent work of architecture, in addition to its obvious and +individual beauty, there dwells an esoteric and universal beauty, +following as it does the archetypal pattern laid down by the Great +Architect for the building of that temple which is the world wherein +we dwell. + + + + +VII + +FROZEN MUSIC + + +In the series of essays of which this is the final one, the author has +undertaken to enforce the truth that evolution on any plane and on +any scale proceeds according to certain laws which are in reality only +ramifications of one ubiquitous and ever operative law; that this law +registers itself in the thing evolved, leaving stamped thereon as it +were fossil footprints by means of which it may be known. In the arts +the creative spirit of man is at its freest and finest, and nowhere +among the arts is it so free and so fine as in music. In music +accordingly the universal law of becoming finds instant, direct +and perfect self-expression; music voices the inner nature of the +_will-to-live_ in all its moods and moments; in it form, content, +means and end are perfectly fused. It is this fact which gives +validity to the before quoted saying that all of the arts "aspire +toward the condition of music." All aspire to express the law, but +music, being least encumbered by the leaden burden of materiality, +expresses it most easily and adequately. This being so there is +nothing unreasonable in attempting to apply the known facts of musical +harmony and rhythm to any other art, and since these essays concern +themselves primarily with architecture, the final aspect in which +that art will be presented here is as "frozen music"--ponderable form +governed by musical law. + +Music depends primarily upon the equal and regular division of time +into beats, and of these beats into measures. Over this soundless and +invisible warp is woven an infinitely various melodic pattern, made +up of tones of different pitch and duration arithmetically related +and combined according to the laws of harmony. Architecture, +correspondingly, implies the rhythmical division of space, and +obedience to laws numerical and geometrical. A certain identity +therefore exists between simple harmony in music, and simple +proportion in architecture. By translating the consonant +tone-intervals into number, the common denominator, as it were, of +both arts, it is possible to give these intervals a spatial, and +hence an architectural, expression. Such expression, considered as +proportion only and divorced from ornament, will prove pleasing to +the eye in the same way that its correlative is pleasing to the ear, +because in either case it is not alone the special organ of sense +which is gratified, but the inner Self, in which all senses are one. +Containing within itself the mystery of number, it thrills responsive +to every audible or visible presentment of that mystery. + +[Illustration 87] + +If a vibrating string yielding a certain musical note be stopped in +its center, that is, divided by half, it will then sound the octave +of that note. The numerical ratio which expresses the interval of +the octave is therefore 1:2. If one-third instead of one-half of the +string be stopped, and the remaining two-thirds struck, it will yield +the musical fifth of the original note, which thus corresponds to the +ratio 2:3. The length represented by 3:4 yields the fourth; 4:5 the +major third; and 5:6 the minor third. These comprise the principal +consonant intervals within the range of one octave. The ratios of +inverted intervals, so called, are found by doubling the smaller +number of the original interval as given above: 2:3, the fifth, gives +3:4, the fourth; 4:5, the major third, gives 5:8, the minor sixth; +5:6, the minor third, gives 6:10, or 3:5, the major sixth. + +[Illustration 88: ARCHITECTURE AS HARMONY] + +Of these various consonant intervals the octave, fifth, and major +third are the most important, in the sense of being the most perfect, +and they are expressed by numbers of the smallest quantity, an odd +number and an even. It will be noted that all the intervals above +given are expressed by the numbers 1, 2, 3, 4, 5 and 6, except the +minor sixth (5:8), and this is the most imperfect of all consonant +intervals. The sub-minor seventh, expressed by the ratio 4:7 though +included among the dissonances, forms, according to Helmholtz, a more +perfect consonance with the tonic than does the minor sixth. + +A natural deduction from these facts is that relations of +architectural length and breadth, height and width, to be "musical" +should be capable of being expressed by ratios of quantitively small +numbers, preferably an odd number and an even. Although generally +speaking the simpler the numerical ratio the more perfect the +consonance, yet the intervals of the fifth and major third (2:3 and +4:5), are considered to be more pleasing than the octave (1:2), which +is too obviously a repetition of the original note. From this it is +reasonable to assume (and the assumption is borne out by experience), +that proportions, the numerical ratios of which the eye resolves too +readily, become at last wearisome. The relation should be felt rather +than fathomed. There should be a perception of identity, and also +of difference. As in music, where dissonances are introduced to give +value to consonances which follow them, so in architecture simple +ratios should be employed in connection with those more complex. + +[Illustration 89] + +Harmonics are those tones which sound with, and reinforce any musical +note when it is sounded. The distinguishable harmonics of the tonic +yield the ratios 1:2, 2:3, 3:4, 4:5, and 4:7. A note and its harmonics +form a natural chord. They may be compared to the widening circles +which appear in still water when a stone is dropped into it, for when +a musical sound disturbs the quietude of that pool of silence which +we call the air, it ripples into overtones, which becoming fainter +and fainter, die away into silence. It would seem reasonable to assume +that the combination of numbers which express these overtones, if +translated into terms of space, would yield proportions agreeable +to the eye, and such is the fact, as the accompanying examples +sufficiently indicate (Illustrations 87-90). + +The interval of the sub-minor seventh (4:7), used in this way, in +connection with the simpler intervals of the octave (1:2), and the +fifth (2:3), is particularly pleasing because it is neither too +obvious nor too subtle. This ratio of 4:7 is important for the reason +that it expresses the angle of sixty degrees, that is, the numbers 4 +and 7 represent (very nearly) the ratio between one-half the base and +the altitude of an equilateral triangle: also because they form part +of the numerical series 1, 4, 7, 10, etc. Both are "mystic" numbers, +and in Gothic architecture particularly, proportions were frequently +determined by numbers to which a mystic meaning was attached. +According to Gwilt, the Gothic chapels of Windsor and Oxford are +divided longitudinally by four, and transversely by seven equal parts. +The arcade above the roses in the faƧade of the cathedral of Tours +shows seven principal units across the front of the nave, and four in +each of the towers. + +A distinguishing characteristic of the series of ratios which +represent the consonant intervals within the compass of an octave is +that it advances by the addition of 1 to both terms: 1:2, 2:3, +3:4, 4:5, and 5:6. Such a series always approaches unity, just as, +represented graphically by means of parallelograms, it tends toward a +square. Alberti in his book presents a design for a tower showing his +idea for its general proportions. It consists of six stories, in a +sequence of orders. The lowest story is a perfect cube and each of the +other stories is 11-12ths of the story below, diminishing practically +in the proportion of 8, 7, 6, 5, 4, 3, allowing in each case for the +amount hidden by the projection of the cornice below; each order being +accurate as regards column, entablature, etc. It is of interest to +compare this with Ruskin's idea in his _Seven Lamps_, where he takes +the case of a plant called Alisma Plantago, in which the various +branches diminish in the proportion of 7, 6, 5, 4, 3, respectively, +and so carry out the same idea; on which Ruskin observes that +diminution in a building should be after the manner of Nature. + +[Illustration 90: ARCADE OF THE CANCELLERIA] + +It would be a profitless task to formulate exact rules of +architectural proportion based upon the laws of musical harmony. The +two arts are too different from each other for that, and moreover +the last appeal must always be to the eye, and not to a mathematical +formula, just as in music the last appeal is to the ear. Laws there +are, but they discover themselves to the artist as he proceeds, and +are for the most part incommunicable. Rules and formulƦ are useful and +valuable not as a substitute for inspiration, but as a guide: not as +wings, but as a tail. In this connection perhaps all that is necessary +for the architectural designer to bear in mind is that important +ratios of length and breadth, height and width, to be "musical" should +be expressed by quantitively small numbers, and that if possible they +should obey some simple law of numerical progression. From this basic +simplicity complexity will follow, but it will be an ordered and +harmonious complexity, like that of a tree, or of a symphony. + +[Illustration 91: THE PALAZZO VERZI AT VERONA (LOWER PORTION ONLY). +A COMPOSITION FOUNDED ON THE EQUAL AND REGULAR DIVISION OF SPACE, AS +MUSIC IS FOUNDED ON THE EQUAL AND REGULAR DIVISION OF TIME.] + +[Illustration 92: ARCHITECTURE AS RHYTHM. A DIVISION OF SPACE +CORRESPONDING TO 3/4 AND 4/4 TIME.] + +In the same way that a musical composition implies the division of +time into equal and regular beats, so a work of architecture should +have for its basis some unit of space. This unit should be nowhere too +obvious and may be varied within certain limits, just as musical time +is retarded or accelerated. The underlying rhythm and symmetry will +thus give value and distinction to such variation. Vasari tells how +Brunelleschi. Bramante and Leonardo da Vinci used to work on paper +ruled in squares, describing it as a "truly ingenious thing, and of +great utility in the work of design." By this means they developed +proportions according to a definite scheme. They set to work with a +division of space analogous to the musician's division of time. +The examples given herewith indicate how close a parallel may exist +between music and architecture in this matter of rhythm (Illustrations +91-93). + +[Illustration 93] + +It is a demonstrable fact that musical sounds weave invisible patterns +in the air. Architecture, correspondingly, in one of its aspects, +is geometric pattern made fixed and enduring. What could be more +essentially musical for example than the sea arcade of the Venetian +Ducal Palace? The sand forms traced by sound-waves on a musically +vibrating steel plate might easily suggest architectural ornament did +not the differences of scale and of material tend to confuse the mind. +The architect should occupy himself with identities, not differences. +If he will but bear in mind that architecture is pattern in space, +just as music is pattern in time, he will come to perceive the +essential identity between, say, a Greek rosette and a Gothic +rose-window; an arcade and an egg and dart moulding (Illustration 94). +All architectural forms and arrangements which give enduring pleasure +are in their essence musical. Every well composed faƧade makes harmony +in three dimensions; every good roof-line sings a melody against the +sky. + +[Illustration 94: ARCHITECTURE AS PATTERN] + + + + +CONCLUSION + + +In taking leave of the reader at the end of this excursion together +among the by-ways of a beautiful art, the author must needs add a +final word or two touching upon the purpose and scope of these essays. +Architecture (like everything else) has two aspects: it may be viewed +from the standpoint of utility, that is, as construction; or from the +standpoint of expressiveness, that is, as decoration. No attempt has +been made here to deal with its first aspect, and of the second +(which is again twofold), only the universal, not the particular +expressiveness has been sought. The literature of architecture is rich +in works dealing with the utilitarian and constructive side of the +art: indeed, it may be said that to this side that literature is +almost exclusively devoted. This being so, it has seemed worth while +to attempt to show the reverse of the medal, even though it be "tails" +instead of "heads." + +It will be noted that the inductive method has not, in these pages, +been honored by a due observance. It would have been easy to +have treated the subject inductively, amassing facts and drawing +conclusions, but to have done so the author would have been false +to the very principle about which the work came into being. With the +acceptance of the Ancient Wisdom, the inductive method becomes +no longer necessary. Facts are not useful in order to establish a +hypothesis, they are used rather to elucidate a known and accepted +truth. When theosophical ideas shall have permeated the thought of +mankind, this work, if it survives at all, will be chiefly--perhaps +solely--remarkable by reason of the fact that it was among the +first in which the attempt was made again to unify science, art and +religion, as they were unified in those ancient times and among those +ancient peoples when the Wisdom swayed the hearts and minds of men. + +*** END OF THE PROJECT GUTENBERG EBOOK 12648 *** diff --git a/LICENSE.txt b/LICENSE.txt new file mode 100644 index 0000000..6312041 --- /dev/null +++ b/LICENSE.txt @@ -0,0 +1,11 @@ +This eBook, including all associated images, markup, improvements, +metadata, and any other content or labor, has been confirmed to be +in the PUBLIC DOMAIN IN THE UNITED STATES. + +Procedures for determining public domain status are described in +the "Copyright How-To" at https://www.gutenberg.org. + +No investigation has been made concerning possible copyrights in +jurisdictions other than the United States. Anyone seeking to utilize +this eBook outside of the United States should confirm copyright +status under the laws that apply to them. diff --git a/README.md b/README.md new file mode 100644 index 0000000..93ab5a4 --- /dev/null +++ b/README.md @@ -0,0 +1,2 @@ +Project Gutenberg (https://www.gutenberg.org) public repository for +eBook #12648 (https://www.gutenberg.org/ebooks/12648) diff --git a/old/12648-8.txt b/old/12648-8.txt new file mode 100644 index 0000000..e8ab5f1 --- /dev/null +++ b/old/12648-8.txt @@ -0,0 +1,2881 @@ +The Project Gutenberg eBook, The Beautiful Necessity, by Claude Fayette +Bragdon + + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + + + + + +Title: The Beautiful Necessity + +Author: Claude Fayette Bragdon + +Release Date: June 18, 2004 [eBook #12648] + +Language: English + +Character set encoding: ISO-8859-1 + + +***START OF THE PROJECT GUTENBERG EBOOK THE BEAUTIFUL NECESSITY*** + + +E-text prepared by Leah Moser and the Project Gutenberg Online Distributed +Proofreading Team + + + +THE BEAUTIFUL NECESSITY + +Seven Essays on Theosophy and Architecture + +by CLAUDE BRAGDON, F.A.I.A. + +MCMXXII + + + + + + + + "Let us build altars to the Beautiful Necessity" + --EMERSON + + + +By the Same Author: + Episodes From An Unwritten History + The Golden Person In The Heart + Architecture And Democracy + A Primer Of Higher Space + Four Dimensional Vistas + Projective Ornament + Oracle + + + + +CONTENTS + + I THE ART OF ARCHITECTURE + + II UNITY AND POLARITY + + III CHANGELESS CHANGE + + IV THE BODILY TEMPLE + + V LATENT GEOMETRY + + VI THE ARITHMETIC OF BEAUTY + + VII FROZEN MUSIC + + CONCLUSION + + + + +PREFACE TO THE SECOND EDITION + + +_The Beautiful Necessity_ was first published in 1910. Save for a slim +volume of privately printed verse it was my first book. I worked hard +on it. Fifteen years elapsed between its beginning and completion; +it was twice published serially--written, rewritten and +tre-written--before it reached its ultimate incarnation in book form. + +Confronted now with the opportunity to revise the text again, I find +myself in the position of a surgeon who feels that the operation he +is called upon to perform may perhaps harm more than it can help. +Prudence therefore prevails over my passion for dissection: warned by +eminent examples, I fear that any injection of my more mature and less +cocksure consciousness into this book might impair its unity--that I +"never could recapture the first fine careless rapture." + +The text stands therefore as originally published save for a few +verbal changes, and whatever reservations I have about it shall +be stated in this preface. These are not many nor important: _The +Beautiful Necessity_ contains nothing that I need repudiate or care to +contradict. + +Its thesis, briefly stated, is that art in all its manifestations is +an expression of the cosmic life, and that its symbols constitute a +language by means of which this life is published and represented. Art +is at all times subject to the _Beautiful Necessity_ of proclaiming +the _world order_. + +In attempting to develop this thesis it was not necessary (nor as +I now think, desirable) to link it up in so definite a manner with +theosophy. The individual consciousness is colored by the particular +medium through which it receives truth, and for me that medium was +theosophy. Though the book might gain a more unprejudiced hearing, +and from a larger audience, by the removal of the theosophic +"color-screen," it shall remain, for its removal now might seem to +imply a loss of faith in the fundamental tenets of theosophy, and such +an implication would not be true. + +The ideas in regard to time and space are those commonly current +in the world until the advent of the Theory of Relativity. To a +generation brought up on Einstein and Ouspensky they are bound to +appear "lower dimensional." Merely to state this fact is to deal +with it to the extent it needs to be dealt with. The integrity of my +argument is not impaired by these new views. + +The one important influence that has operated to modify my opinions +concerning the mathematical basis of the arts of space has been the +discoveries of Mr. Jay Hambidge with regard to the practice of the +Greeks in these matters, as exemplified in their temples and their +ceramics, and named by him _Dynamic Symmetry_. + +In tracing everything back to the logarithmic spiral (which embodies +the principle of extreme and mean ratios) I consider that Mr. Hambidge +has made one of those generalizations which reorganizes the old +knowledge and organizes the new. It would be only natural if in his +immersion in his idea he overworks it, but Mr. Hambidge is a man of +such intellectual integrity and thoroughness of method that he may be +trusted not to warp the facts to fit his theories. The truth of the +matter is that the entire field of research into the mathematics of +Beauty is of such richness that wherever a man plants his metaphysical +spade he is sure to come upon "pay dirt." _The_ _Beautiful Necessity_ +represents the result of my own prospecting; _Dynamic Symmetry_ +represents the result of his. If at any point our findings appear to +conflict, it is less likely that one or the other of us is mistaken +than that each is right from his own point of view. Be that as it may, +I should be the last man in the world to differ from Mr. Hambidge, +for if he convicted me of every conceivable error his work would still +remain the greatest justification and confirmation of my fundamental +contention--that art is an expression of the _world order_ and +is therefore orderly, organic; subject to mathematical law, and +susceptible of mathematical analysis. + +CLAUDE BRAGDON + +Rochester, N.Y. + +April, 1922 + + + + +I + +THE ART OF ARCHITECTURE + + +One of the advantages of a thorough assimilation of what may be called +the theosophic idea is that it can be applied with advantage to every +department of knowledge and of human activity: like the key to a +cryptogram it renders clear and simple that which before seemed +intricate and obscure. Let us apply this key to the subject of art, +and to the art of architecture in particular, and see if by so +doing we may not learn more of art than we knew before, and more of +theosophy too. + +The theosophic idea is that everything is an expression of the +Self--or whatever other name one may choose to give to that immanent +unknown reality which forever hides behind all phenomenal life--but +because, immersed as we are in materiality, our chief avenue of +knowledge is sense perception, a more exact expression of the +theosophic idea would be: Everything is the expression of the Self +in terms of sense. Art, accordingly, is the expression of the Self in +terms of sense. Now though the Self is _one_, sense is not one, but +manifold: and therefore there are _arts_, each addressed to some +particular faculty or group of faculties, and each expressing some +particular quality or group of qualities of the Self. The white light +of Truth is thus broken up into a rainbow-tinted spectrum of Beauty, +in which the various arts are colors, each distinct, yet merging one +into another--poetry into music; painting into decoration; decoration +becoming sculpture; sculpture--architecture, and so on. + +In such a spectrum of the arts each one occupies a definite place, and +all together form a series of which music and architecture are the two +extremes. That such is their relative position may be demonstrated in +various ways. The theosophic explanation involving the familiar idea +of the "pairs of opposites" would be something as follows. According +to the Hindu-Aryan theory, Brahma, that the world might be born, fell +asunder into man and wife--became in other words _name and form_[A] +The two universal aspects of name and form are what philosophers call +the two "modes of consciousness," one of time, and the other of space. +These are the two gates through which ideas enter phenomenal life; the +two boxes, as it were, that contain all the toys with which we play. +Everything, were we only keen enough to perceive it, bears the mark of +one or the other of them, and may be classified accordingly. In such a +classification music is seen to be allied to time, and architecture to +space, because music is successive in its mode of manifestation, and +in time alone everything would occur successively, one thing following +another; while architecture, on the other hand, impresses itself upon +the beholder all at once, and in space alone all things would exist +simultaneously. Music, which is in time alone, without any relation to +space; and architecture, which is in space alone, without any relation +to time, are thus seen to stand at opposite ends of the art spectrum, +and to be, in a sense, the only "pure" arts, because in all the others +the elements of both time and space enter in varying proportion, +either actually or by implication. Poetry and the drama are allied to +music inasmuch as the ideas and images of which they are made up are +presented successively, yet these images are for the most part +forms of space. Sculpture on the other hand is clearly allied to +architecture, and so to space, but the element of _action_, suspended +though it be, affiliates it with the opposite or time pole. Painting +occupies a middle position, since in it space instead of being +actual has become ideal--three dimensions being expressed through +the mediumship of two--and time enters into it more largely than into +sculpture by reason of the greater ease with which complicated action +can be indicated: a picture being nearly always time arrested in +midcourse as it were--a moment transfixed. + +In order to form a just conception of the relation between music and +architecture it is necessary that the two should be conceived of not +as standing at opposite ends of a series represented by a straight +line, but rather in juxtaposition, as in the ancient Egyptian symbol +of a serpent holding its tail in its mouth, the head in this case +corresponding to music, and the tail to architecture; in other words, +though in one sense they are the most-widely separated of the arts, in +another they are the most closely related. + +Music being purely in time and architecture being purely in space, +each is, in a manner and to a degree not possible with any of +the other arts, convertible into the other, by reason of the +correspondence subsisting between intervals of time and intervals of +space. A perception of this may have inspired the famous saying +that architecture is _frozen music_, a poetical statement of a +philosophical truth, since that which in music is expressed by means +of harmonious intervals of time and pitch, successively, after the +manner of time, may be translated into corresponding intervals of +architectural void and solid, height and width. + +In another sense music and architecture are allied. They alone of +all the arts are purely creative, since in them is presented, not +a likeness of some known idea, but _a thing-in-itself_ brought to +a distinct and complete expression of its nature. Neither a musical +composition nor a work of architecture depends for its effectiveness +upon resemblances to natural sounds in the one case, or to natural +forms in the other. Of none of the other arts is this to such a degree +true: they are not so much creative as re-creative, for in them all +the artist takes his subject ready made from nature and presents it +anew according to the dictates of his genius. + +The characteristic differences between music and architecture are the +same as those which subsist between time and space. Now time and space +are such abstract ideas that they can be dealt with best through +their corresponding correlatives in the natural world, for it is a +fundamental theosophic tenet that nature everywhere abounds in such +correspondences; that nature, in its myriad forms, is indeed the +concrete presentment of abstract unities. The energy which everywhere +animates form is a type of time within space; the mind working in +and through the body is another expression of the same thing. +Correspondingly, music is dynamic, subjective, mental, of one +dimension; while architecture is static, objective, physical, of three +dimensions; sustaining the same relation to music and the other +arts as does the human body to the various organs which compose, and +consciousnesses which animate it (it being the reservatory of these +organs and the vehicle of these consciousnesses); and a work of +architecture in like manner may and sometimes does include all of the +other arts within itself. Sculpture accentuates and enriches, painting +adorns, works of literature are stored within it, poetry and the drama +awake its echoes, while music thrills to its uttermost recesses, like +the very spirit of life tingling through the body's fibres. + +Such being the relation between them, the difference in the nature of +the ideas bodied forth in music and in architecture becomes apparent. +Music is interior, abstract, subjective, speaking directly to the soul +in a simple and universal language whose meaning is made personal and +particular in the breast of each listener: "Music alone of all the +arts," says Balzac, "has power to make us live within ourselves." +A work of architecture is the exact opposite of this: existing +principally and primarily for the uses of the body, it is like the +body a concrete organism, attaining to esthetic expression only in +the reconciliation and fulfilment of many conflicting practical +requirements. Music is pure beauty, the voice of the unfettered +and perpetually vanishing soul of things; architecture is that soul +imprisoned in a form, become subject to the law of causality, beaten +upon by the elements, at war with gravity, the slave of man. One is +the Ariel of the arts; the other, Caliban. + +Coming now to the consideration of architecture in its historical +rather than its philosophical aspect, it will be shown how certain +theosophical concepts are applicable here. Of these none is more +familiar and none more fundamental than the idea of reincarnation. By +reincarnation more than mere physical re-birth is meant, for physical +re-birth is but a single manifestation of that universal law of +alternation of state, of animation of vehicles, and progression +through related planes, in accordance with which all things move, +and as it were make music--each cycle complete, yet part of a larger +cycle, the incarnate monad passing through correlated changes, +carrying along and bringing into manifestation in each successive arc +of the spiral the experience accumulated in all preceding states, +and at the same time unfolding that power of the Self peculiar to the +plane in which it is momentarily manifesting. + +This law finds exemplification in the history of architecture in the +orderly flow of the building impulse from one nation and one country +to a different nation and a different country: its new vehicle of +manifestation; also in the continuity and increasing complexity of +the development of that impulse in manifestation; each "incarnation" +summarizing all those which have gone before, and adding some new +factor peculiar to itself alone; each being a growth, a life, with +periods corresponding to childhood, youth, maturity and decadence; +each also typifying in its entirety some single one of these +life-periods, and revealing some special aspect or power of the Self. + +For the sake of clearness and brevity the consideration of only one +of several architectural evolutions will be attempted: that which, +arising in the north of Africa, spread to southern Europe, thence to +the northwest of Europe and to England--the architecture, in short, of +the so-called civilized world. + +This architecture, anterior to the Christian era, may be broadly +divided into three great periods, during which it was successively +practiced by three peoples: the Egyptians, the Greeks and the Romans. +Then intervened the Dark Ages, and a new art arose, the Gothic, which +was a flowering out in stone of the spirit of Christianity. This was +in turn succeeded by the Renaissance, the impulse of which remains +to-day unexhausted. In each of these architectures the peculiar genius +of a people and of a period attained to a beautiful, complete and +coherent utterance, and notwithstanding the considerable intervals +of time which sometimes separated them they succeeded one another +logically and inevitably, and each was related to the one which +preceded and which followed it in a particular and intimate manner. + +The power and wisdom of ancient Egypt was vested in its priesthood, +which was composed of individuals exceptionally qualified by birth +and training for their high office, tried by the severest ordeals +and bound by the most solemn oaths. The priests were honored and +privileged above all other men, and spent their lives dwelling +apart from the multitude in vast and magnificent temples, dedicating +themselves to the study and practice of religion, philosophy, science +and art--subjects then intimately related, not widely separated as +they are now. These men were the architects of ancient Egypt: theirs +the minds which directed the hands that built those time-defying +monuments. + +The rites that the priests practiced centered about what are known +as the Lesser and the Greater Mysteries. These consisted of +representations by means of symbol and allegory, under conditions +and amid surroundings the most awe-inspiring, of those great truths +concerning man's nature, origin and destiny of which the priests--in +reality a brotherhood of initiates and their pupils--were the +custodians. These ceremonies were made the occasion for the initiation +of neophytes into the order, and the advancement of the already +initiated into its successive degrees. For the practice of such rites, +and others designed to impress not the elect but the multitude, the +great temples of Egypt were constructed. Everything about them was +calculated to induce a deep seriousness of mind, and to inspire +feelings of awe, dread and even terror, so as to test the candidate's +fortitude of soul to the utmost. + +The avenue of approach to an Egyptian temple was flanked on both +sides, sometimes for a mile or more, with great stone sphinxes--that +emblem of man's dual nature, the god emerging from the beast. The +entrance was through a single high doorway between two towering +pylons, presenting a vast surface sculptured and painted over with +many strange and enigmatic figures, and flanked by aspiring obelisks +and seated colossi with faces austere and calm. The large court thus +entered was surrounded by high walls and colonnades, but was open +to the sky. Opposite the first doorway was another, admitting to a +somewhat smaller enclosure, a forest of enormous carved and painted +columns supporting a roof through the apertures of which sunshine +gleamed or dim light filtered down. Beyond this in turn were other +courts and apartments culminating in some inmost sacred sanctuary. + +Not alone in their temples, but in their tombs and pyramids and +all the sculptured monuments of the Egyptians, there is the same +insistence upon the sublimity, mystery and awefulness of life, +which they seem to have felt so profoundly. But more than this, the +conscious thought of the masters who conceived them, the buildings of +Egypt give utterance also to the toil and suffering of the thousands +of slaves and captives which hewed the stones out of the heart of the +rock, dragged them long distances and placed them one upon another, so +that these buildings oppress while they inspire, for there is in them +no freedom, no spontaneity, no individuality, but everywhere the felt +presence of an iron conventionality, of a stern immutable law. + +In Egyptian architecture is symbolized the condition of the human soul +awakened from its long sleep in nature, and become conscious at once +of its divine source and of the leaden burden of its fleshy envelope. +Egypt is humanity new-born, bound still with an umbilical cord to +nature, and strong not so much with its own strength as with the +strength of its mother. This idea is aptly symbolized in those +gigantic colossi flanking the entrance to some rock-cut temple, which +though entire are yet part of the living cliff out of which they were +fashioned. + +In the architecture of Greece the note of dread and mystery yields to +one of pure joyousness and freedom. The terrors of childhood have been +outgrown, and man revels in the indulgence of his unjaded appetites +and in the exercise of his awakened reasoning faculties. In Greek art +is preserved that evanescent beauty of youth which, coming but once +and continuing but for a short interval in every human life, is yet +that for which all antecedent states seem a preparation, and of +which all subsequent ones are in some sort an effect. Greece typifies +adolescence, the love age, and so throughout the centuries humanity +has turned to the contemplation of her, just as a man all his life +long secretly cherishes the memory of his first love. + +An impassioned sense of beauty and an enlightened reason characterize +the productions of Greek architecture during its best period. The +perfection then attained was possible only in a nation whereof the +citizens were themselves critics and amateurs of art, one wherein +the artist was honored and his work appreciated in all its beauty +and subtlety. The Greek architect was less bound by tradition and +precedent than was the Egyptian, and he worked unhampered by any +restrictions save such as, like the laws of harmony in music, helped +rather than hindered his genius to express itself--restrictions +founded on sound reason, the value of which had been proved by +experience. + +The Doric order was employed for all large temples, since it possessed +in fullest measure the qualities of simplicity and dignity, the +attributes appropriate to greatness. Quite properly also its formulas +were more fixed than those of any other style. The Ionic order, +the feminine of which the Doric may be considered the corresponding +masculine, was employed for smaller temples; like a woman it was more +supple and adaptable than the Doric, its proportions were more slender +and graceful, its lines more flowing, and its ornament more delicate +and profuse. A freer and more elaborate style than either of these, +infinitely various, seeming to obey no law save that of beauty, was +used sometimes for small monuments and temples, such as the Tower of +the Winds, and the monument of Lysicrates at Athens. + +[Illustration 1] + +Because the Greek architect was at liberty to improve upon the work of +his predecessors if he could, no temple was just like any other, +and they form an ascending scale of excellence, culminating in the +Acropolis group. Every detail was considered not only with relation +to its position and function, but in regard to its intrinsic beauty as +well, so that the merest fragment, detached from the building of which +it formed a part, is found worthy of being treasured in our museums +for its own sake. + +Just as every detail of a Greek temple was adjusted to its position +and expressed its office, so the building itself was made to fit +its site and to show forth its purpose, forming with the surrounding +buildings a unit of a larger whole. The Athenian Acropolis is an +illustration of this: it is an irregular fortified hill, bearing +diverse monuments in various styles, at unequal levels and at +different angles with one another, yet the whole arrangement seems as +organic and inevitable as the disposition of the features of a face. +The Acropolis is an example of the ideal architectural republic +wherein each individual contributes to the welfare of all, and at the +same time enjoys the utmost personal liberty (Illustration 1). + +Very different is the spirit bodied forth in the architecture of +Imperial Rome. The iron hand of its sovereignty encased within the +silken glove of its luxury finds its prototype in buildings which were +stupendous crude brute masses of brick and concrete, hidden within a +covering of rich marbles and mosaics, wrought in beautiful but often +meaningless forms by clever degenerate Greeks. The genius of Rome +finds its most characteristic expression, not in temples to the high +gods, but rather in those vast and complicated structures--basilicas, +amphitheatres, baths--built for the amusement and purely temporal +needs of the people. + +If Egypt typifies the childhood of the race and Greece its beautiful +youth, Republican Rome represents its strong manhood--a soldier filled +with the lust of war and the love of glory--and Imperial Rome its +degeneracy: that soldier become conqueror, decked out in plundered +finery and sunk in sensuality, tolerant of all who minister to his +pleasures but terrible to all who interfere with them. + +The fall of Rome marked the end of the ancient Pagan world. Above +its ruin Christian civilization in the course of time arose. Gothic +architecture is an expression of the Christian spirit; in it is +manifest the reaction from licentiousness to asceticism. Man's +spiritual nature, awakening in a body worn and weakened by +debaucheries, longs ardently and tries vainly to escape. Of some such +mood a Gothic cathedral is the expression: its vaulting, marvelously +supported upon slender shafts by reason of a nicely adjusted +equilibrium of forces; its restless, upward-reaching pinnacles and +spires; its ornament, intricate and enigmatic--all these suggest the +over-strained organism of an ascetic; while its vast shadowy interior +lit by marvelously traceried and jeweled windows, which hold the eyes +in a hypnotic thrall, is like his soul: filled with world sadness, +dead to the bright brief joys of sense, seeing only heavenly visions, +knowing none but mystic raptures. + +Thus it is that the history of architecture illustrates and enforces +the theosophical teaching that everything of man's creating is made in +his own image. Architecture mirrors the life of the individual and of +the race, which is the life of the individual written large in time +and space. The terrors of childhood; the keen interests and appetites +of youth; the strong stern joy of conflict which comes with manhood; +the lust, the greed, the cruelty of a materialized old age--all these +serve but as a preparation for the life of the spirit, in which the +man becomes again as a little child, going over the whole round, but +on a higher arc of the spiral. + +The final, or fourth state being only in some sort a repetition of +the first, it would be reasonable to look for a certain correspondence +between Egyptian and Gothic architecture, and such a correspondence +there is, though it is more easily divined than demonstrated. In +both there is the same deeply religious spirit; both convey, in some +obscure yet potent manner, a sense of the soul being near the surface +of life. There is the same love of mystery and of symbolism; and in +both may be observed the tendency to create strange composite figures +to typify transcendental ideas, the sphinx seeming a blood-brother to +the gargoyle. The conditions under which each architecture flourished +were not dissimilar, for each was formulated and controlled by small +well-organized bodies of sincerely religious and highly enlightened +men--the priesthood in the one case, the masonic guilds in the +other--working together toward the consummation of great undertakings +amid a populace for the most part oblivious of the profound and subtle +meanings of which their work was full. In Medięval Europe, as in +ancient Egypt, fragments of the Ancient Wisdom--transmitted in the +symbols and secrets of the cathedral builders--determined much of +Gothic architecture. + +The architecture of the Renaissance period, which succeeded the +Gothic, corresponds again, in the spirit which animates it, to Greek +architecture, which succeeded the Egyptian, for the Renaissance as +the name implies was nothing other than an attempt to revive Classical +antiquity. Scholars writing in what they conceived to be a Classical +style, sculptors modeling Pagan deities, and architects building +according to their understanding of Vitruvian methods succeeded +in producing works like, yet different from the originals they +followed--different because, animated by a spirit unknown to the +ancients, they embodied a new ideal. + +In all the productions of the early Renaissance, "that first +transcendent springtide of the modern world," there is the evanescent +grace and beauty of youth which was seen to have pervaded Greek art, +but it is a grace and beauty of a different sort. The Greek artist +sought to attain to a certain abstract perfection of type; to build +a temple which should combine all the excellencies of every similar +temple, to carve a figure, impersonal in the highest sense, which +should embody every beauty. The artist of the Renaissance on the other +hand delighted not so much in the type as in the variation from it. +Preoccupied with the unique mystery of the individual soul--a sense of +which was Christianity's gift to Christendom--he endeavored to portray +that wherein a particular person is unique and singular. Acutely +conscious also of his own individuality, instead of effacing it he +made his work the vehicle and expression of that individuality. The +history of Renaissance architecture, as Symonds has pointed out, +is the history of a few eminent individuals, each one moulding and +modifying the style in a manner peculiar to himself alone. In the +hands of Brunelleschi it was stern and powerful; Bramante made +it chaste, elegant and graceful; Palladio made it formal, cold, +symmetrical; while with Sansovino and Sammichele it became sumptuous +and bombastic. + +As the Renaissance ripened to decay its architecture assumed more and +more the characteristics which distinguished that of Rome during the +decadence. In both there is the same lack of simplicity and sincerity, +the same profusion of debased and meaningless ornament, and there is +an increasing disposition to conceal and falsify the construction by +surface decoration. + +The final part of this second or modern architectural cycle lies still +in the future. It is not unreasonable to believe that the movement +toward mysticism, of which modern theosophy is a phase and the +spiritualization of science an episode, will flower out into an +architecture which will be in some sort a reincarnation of and a +return to the Gothic spirit, employing new materials, new methods, +and developing new forms to show forth the spirit of the modern world, +without violating ancient verities. + +In studying these crucial periods in the history of European +architecture it is possible to trace a gradual growth or unfolding +as of a plant. It is a fact fairly well established that the Greeks +derived their architecture and ornament from Egypt; the Romans in +turn borrowed from the Greeks; while a Gothic cathedral is a lineal +descendant from a Roman basilica. + +[Illustration 2] + +[Illustration 3] + +The Egyptians in their constructions did little more than to place +enormous stones on end, and pile one huge block upon another. They +used many columns placed close together: the spaces which they spanned +were inconsiderable. The upright or supporting member may be said to +have been in Egyptian architecture the predominant one. A vertical +line therefore may be taken as the simplest and most abstract symbol +of Egyptian architecture (Illustration 2). It remained for the Greeks +fully to develop the lintel. In their architecture the vertical +member, or column, existed solely for the sake of the horizontal +member, or lintel; it rarely stood alone as in the case of an Egyptian +obelisk. The columns of the Greek temples were reduced to those +proportions most consistent with strength and beauty, and the +intercolumnations were relatively greater than in Egyptian examples. +It may truly be said that Greek architecture exhibits the perfect +equality and equipoise of vertical and horizontal elements and these +only, no other factor entering in. Its graphic symbol would therefore +be composed of a vertical and a horizontal line (Illustration 3). The +Romans, while retaining the column and lintel of the Greeks, deprived +them of their structural significance and subordinated them to the +semicircular arch and the semi-cylindrical and hemispherical vault, +the truly characteristic and determining forms of Roman architecture. +Our symbol grows therefore by the addition of the arc of a circle +(Illustration 4). In Gothic architecture column, lintel, arch and +vault are all retained in changed form, but that which more than +anything else differentiates Gothic architecture from any style which +preceded it is the introduction of the principle of an equilibrium of +forces, of a state of balance rather than a state of rest, arrived at +by the opposition of one thrust with another contrary to it. This fact +can be indicated graphically by two opposing inclined lines, and +these united to the preceding symbol yield an accurate abstract of the +elements of Gothic architecture (Illustration 5). + +[Illustration 4] + +[Illustration 5] + +All this is but an unusual application of a familiar theosophic +teaching, namely, that it is the method of nature on every plane and +in every department not to omit anything that has gone before, but to +store it up and carry it along and bring it into manifestation later. +Nature everywhere proceeds like the jingle of _The House that Jack +Built_: she repeats each time all she has learned, and adds another +line for subsequent repetition. + +[Footnote A: The quaint Oriental imagery here employed should not +blind the reader to the precise scientific accuracy of the idea of +which this imagery is the vehicle. Schopenhauer says: "Polarity, or +the sundering of a force into two quantitively different and opposed +activities striving after re-union,... is a fundamental type of almost +all the phenomena of nature, from the magnet and the crystal to man +himself."] + + + + +II + +UNITY AND POLARITY + + +Theosophy, both as a philosophy, or system of thought, which discovers +correlations between things apparently unrelated, and as a life, +or system of training whereby it is possible to gain the power to +perceive and use these correlations for worthy ends, is of great value +to the creative artist, whose success depends on the extent to which +he works organically, conforming to the cosmic pattern, proceeding +rationally and rhythmically to some predetermined end. It is of value +no less to the layman, the critic, the art amateur--to anyone in +fact who would come to an accurate and intimate understanding and +appreciation of every variety of esthetic endeavor. For the benefit of +such I shall try to trace some of those correlations which theosophy +affirms, and indicate their bearing upon art, and upon the art of +architecture in particular. + +One of the things which theosophy teaches is that those transcendent +glimpses of a divine order and harmony throughout the universe +vouchsafed the poet and the mystic in their moments of vision are not +the paradoxes--the paronomasia as it were--of an intoxicated state of +consciousness, but glimpses of reality. We are all of us participators +in a world of concrete music, geometry and number--a world of +sounds, odors, forms, motions, colors, so mathematically related and +coordinated that our pigmy bodies, equally with the farthest star, +vibrate to the music of the spheres. There is a _Beautiful Necessity_ +which rules the world, which is a law of nature and equally a law of +art, for art is idealized creation: nature carried to a higher power +by reason of its passage through a human consciousness. Thought and +emotion tend to crystallize into forms of beauty as inevitably as does +the frost on a window pane. Art therefore in one of its aspects is the +weaving of a pattern, the communication of an order and a method to +the material or medium employed. Although no masterpiece was ever +created by the conscious following to set rules, for the true artist +works unconsciously, instinctively, as the bird sings or as the bee +builds its honey-cell, yet an analysis of any masterpiece reveals the +fact that its author (like the bird and the bee) has "followed the +rules without knowing them." + +Helmholtz says, "No doubt is now entertained that beauty is subject +to laws and rules dependent on the nature of human intelligence. The +difficulty consists in the fact that these laws and rules, on whose +fulfilment beauty depends, are not consciously present in the mind of +the artist who creates the work, or of the observer who contemplates +it." Nevertheless they are discoverable, and can be formulated, +after a fashion. We have only to read aright the lessons everywhere +portrayed in the vast picture-books of nature and of art. + +The first truth therein published is the law of _Unity_--oneness; for +there is one Self, one Life, which, myriad in manifestation, is yet +in essence ever _one_. Atom and universe, man and the world--each is +a unit, an organic and coherent whole. The application of this law to +art is so obvious as to be almost unnecessary of elucidation, for to +say that a work of art must possess unity, must seem to proceed from a +single impulse and be the embodiment of one dominant idea, is to state +a truism. In a work of architecture the coördination of its various +parts with one another is almost the measure of its success. We +remember any masterpiece--the cathedral of Paris no less than the +pyramids of Egypt--by the singleness of its appeal; complex it may be, +but it is a coordinated complexity; variety it may possess, but it is +a variety in an all-embracing unity. + +The second law, not contradicting but supplementing the first is the +law of _Polarity_, i.e., duality. All things have sex, are either +masculine or feminine. This too is the reflection on a lower plane +of one of those transcendental truths taught by the Ancient Wisdom, +namely that the Logos, in his voluntarily circumscribing his infinite +life in order that he may manifest, encloses himself within his +limiting veil, _maya_, and that his life appears as spirit (male), and +his _maya_ as matter (female), the two being never disjoined during +manifestation. The two terms of this polarity are endlessly repeated +throughout nature: in sun and moon, day and night, fire and water, man +and woman--and so on. A close inter-relation is always seen to subsist +between corresponding members of such pairs of opposites: sun, day, +fire, man express and embody the primal and active aspect of the +manifesting deity; moon, night, water, woman, its secondary and +passive aspect. Moreover, each implies or brings to mind the others +of its class: man, like the sun, is lord of day; he is like fire, a +devastating force; woman is subject to the lunar rhythm; like water, +she is soft, sinuous, fecund. + +The part which this polarity plays in the arts is important, and the +constant and characteristic distinction between the two terms is a +thing far beyond mere contrast. + +In music they are the major and minor modes: the typical, or +representative chords of the dominant seventh, and of the tonic (the +two chords into which Schopenhauer says all music can be resolved): a +partial dissonance, and a consonance: a chord of suspense, and a chord +of satisfaction. In speech the two are vowel, and consonant sounds: +the type of the first being _a_, a sound of suspense, made with the +mouth open; and of the second _m_, a sound of satisfaction, made by +closing the mouth; their combination forms the sacred syllable Om +(_Aum_). In painting they are warm colors, and cold: the pole of +the first being in red, the color of fire, which excites; and of the +second in blue, the color of water, which calms; in the Arts of design +they are lines straight (like fire), and flowing (like water); masses +light (like the day), and dark (like night). In architecture they are +the column, or vertical member, which resists the force of gravity; +and the lintel, or horizontal member, which succumbs to it; they are +vertical lines, which are aspiring, effortful; and horizontal lines, +which are restful to the eye and mind. + +It is desirable to have an instant and keen realization of this sex +quality, and to make this easier some sort of classification and +analysis must be attempted. Those things which are allied to and +partake of the nature of _time_ are masculine, and those which are +allied to and partake of the nature of _space_ are feminine: as +motion, and matter; mind, and body; etc. The English words "masculine" +and "feminine" are too intimately associated with the idea of physical +sex properly to designate the terms of this polarity. In Japanese +philosophy and art (derived from the Chinese) the two are called _In_ +and _Yo_ (In, feminine; Yo, masculine); and these little words, being +free from the limitations of their English correlatives, will be found +convenient, Yo to designate that which is simple, direct, primary, +active, positive; and In, that which is complex, indirect, derivative, +passive, negative. Things hard, straight, fixed, vertical, are Yo; +things soft, curved, horizontal, fluctuating, are In--and so on. + +[Illustration 6: WILD CHERRY; MAPLE LEAF] + +[Illustration 7: CALLAS IN YO] + +In passing it may be said that the superiority of the line, mass, and +color composition of Japanese prints and kakemonos to that exhibited +in the vastly more pretentious easel pictures of modern Occidental +artists--a superiority now generally acknowledged by connoisseurs--is +largely due to the conscious following, on the part of the Japanese, +of this principle of sex-complementaries. + +Nowhere are In and Yo more simply and adequately imaged than in the +vegetable kingdom. The trunk of a tree is Yo, its foliage, In; and +in each stem and leaf the two are repeated. A calla, consisting of +a single straight and rigid spadix embraced by a soft and tenderly +curved spathe, affords an almost perfect expression of the +characteristic differences between Yo and In and their reciprocal +relation to each other. The two are not often combined in such +simplicity and perfection in a single form. The straight, vertical +reeds which so often grow in still, shallow water, find their +complement in the curved lily-pads which lie horizontally on its +surface. Trees such as pine and hemlock, which are excurrent--those in +which the branches start successively (i.e., after the manner of time) +from a straight and vertical central stem--are Yo; trees such as +the elm and willow, which are deliquescent--those in which the trunk +dissolves as it were simultaneously (after the manner of space) into +its branches--are In. All tree forms lie in or between these two +extremes, and leaves are susceptible of a similar classification. It +will be seen to be a classification according to time and space, +for the characteristic of time is _succession_, and of space, +_simultaneousness_: the first is expressed symbolically by elements +arranged with relation to axial lines; the second, by elements +arranged with relation to focal points (Illustrations 6,7). + +The student should train himself to recognize In and Yo in all +their Protean presentments throughout nature--in the cloud upon the +mountain, the wave against the cliff, in the tracery of trees against +the sky--that he may the more readily recognize them in his chosen +art, whatever that art may be. If it happens to be painting, he will +endeavor to discern this law of duality in the composition of every +masterpiece, recognizing an instinctive obedience to it in that +favorite device of the great Renaissance masters of making an +architectural setting for their groups of figures, and he will +delight to trace the law in all its ramifications of contrast between +complementaries in line, color, and mass (Illustration 8). + +[Illustration 8: THE LAW OF POLARITY CLEOPATRA MELTING THE PEARL. BY +TIEPOLO] + +With reference to architecture, it is true, generally speaking, +that architectural forms have been developed through necessity, the +function seeking and finding its appropriate form. For example, the +buttress of a Gothic cathedral was developed by the necessity of +resisting the thrust of the interior vaulting without encroaching upon +the nave; the main lines of a buttress conform to the direction of the +thrust, and the pinnacle with which it terminates is a logical shape +for the masonry necessary to hold the top in position (Illustration +9). Research along these lines is interesting and fruitful of result, +but there remains a certain number of architectural forms whose origin +cannot be explained in any such manner. The secret of their undying +charm lies in the fact that in them In and Yo stand symbolized and +contrasted. They no longer obey a law of utility, but an abstract +law of beauty, for in becoming sexually expressive as it were, the +construction itself is sometimes weakened or falsified. The familiar +classic console or modillion is an example: although in general +contour it is well adapted to its function as a supporting bracket, +embedded in, and projecting from a wall, yet the scroll-like ornament +with which its sides are embellished gives it the appearance of +not entering the wall at all, but of being stuck against it in some +miraculous manner. This defect in functional expressiveness is +more than compensated for by the perfection with which feminine +and masculine characteristics are expressed and contrasted in the +exquisite double spiral, opposed to the straight lines of the moulding +which it subtends (Illustration 10). Again, by fluting the shaft of a +column its area of cross-section is diminished but the appearance of +strength is enhanced because its masculine character--as a supporting +member resisting the force of gravity--is emphasized. + +[Illustration 9: CROSS SECTION OF BUTTRESS.] + +The importance of the so-called "orders" lies in the fact that they +are architecture epitomized as it were. A building consists of a wall +upholding a roof: support and weight. The type of the first is the +column, which may be conceived of as a condensed section of wall; and +of the second, the lintel, which may be conceived of as a condensed +section of roof. The column, being vertical, is Yo; the lintel, being +horizontal, is In. To mark an entablature with horizontal lines in the +form of mouldings, and the columns with vertical lines in the form +of flutes, as is done in all the "classic orders," is a gain +in functional and sex expressiveness, and consequently in art +(Illustration 11). + +[Illustration 10: CORINTHIAN MODILLION; CLASSIC CONSOLE; IONIC CAP] + +The column is again divided into the shaft, which is Yo; and the +capital, which is In. The capital is itself twofold, consisting of a +curved member and an angular member. These two appear in their utmost +simplicity in the _echinus_ (In) and the _abacus_ (Yo) of a +Greek Doric cap. The former was adorned with painted leaf forms, +characteristically feminine, and the latter with the angular fret +and meander (Illustration 12). The Ionic capital, belonging to a more +feminine style, exhibits the abacus subordinated to that beautiful +cushion-shaped member with its two spirally marked volutes. This, +though a less rational and expressive form for its particular office +than is the echinus of the Doric cap, is a far more perfect symbol of +the feminine element in nature. There is an essential identity between +the Ionic cap and the classic console before referred to--although +superficially the two do not resemble each other--for a straight line +and a double spiral are elements common to both (Illustration 10). +The Corinthian capital consists of an ordered mass of delicately +sculptured leaf and scroll forms sustaining an abacus which though +relatively masculine is yet more curved and feminine than that of any +other style. In the caulicole of a Corinthian cap In and Yo are again +contrasted. In the unique and exquisite capital from the Tower of the +Winds at Athens, the two are well suggested in the simple, erect, and +pointed leaf forms of the upper part, contrasted with the complex, +deliquescent, rounded ones from which they spring. The essential +identity of principle subsisting between this cap and the Renaissance +baluster by San Gallo is easily seen (Illustration 13). + +[Illustration 11] + +[Illustration 12] + +This law of sex-expressiveness is of such universality that it can +be made the basis of an analysis of the architectural ornament of any +style or period. It is more than mere opposition and contrast. The egg +and tongue motif, which has persisted throughout so many centuries and +survived so many styles, exhibits an alternation of forms resembling +phallic emblems. Yo and In are well suggested in the channeled +triglyphs and the sculptured metopes of a Doric frieze, in the +straight and vertical mullions and the flowing tracery of Gothic +windows, in the banded torus, the bead and reel, and other familiar +ornamented mouldings (Illustrations 14, 15, 16). + +There are indications that at some time during the development +of Gothic architecture in France, this sex-distinction became a +recognized principle, moulding and modifying the design of a cathedral +in much the same way that sex modifies bodily structure. The masonic +guilds of the Middle Ages were custodians of the esoteric--which is +the theosophic--side of the Christian faith, and every student of +esotericism knows how fundamental and how far-reaching is this idea of +sex. + +[Illustration 13: CAPITAL FROM THE TOWER OF THE WINDS, ATHENS; +CORINTHIAN CAP FROM HADRIAN BUILDINGS, ATHENS; ROSETTE FROM TEMPLE OF +MARS, ROME; CAULICULUS OF CORINTHIAN CAP; BULUSTER BY SAN GALLO] + +[Illustration 14: EGG AND TONGUE; BEAD AND REEL; BANDED TORUS] + +The entire cathedral symbolized the crucified body of Christ; its two +towers, man and woman--that Adam and that Eve for whose redemption +according to current teaching Christ suffered and was crucified. The +north or right-hand tower ("the man's side") was called the sacred +male pillar, Jachin; and the south, or left-hand tower ("the woman's +side"), the sacred female pillar, Boaz, from the two columns flanking +the gate to Solomon's Temple--itself an allegory to the bodily temple. +In only a few of the French cathedrals is this distinction clearly +and consistently maintained, and of these Tours forms perhaps the most +remarkable example, for in its flamboyant faēade, over and above the +difference in actual breadth and apparent sturdiness of the two towers +(the south being the more slender and delicate), there is a clearly +marked distinction in the character of the ornamentation, that of the +north tower being more salient, angular, radial--more masculine in +point of fact (Illustration 17). In Notre Dame, the cathedral of +Paris, as in the cathedral of Tours, the north tower is perceptibly +broader than the south. The only other important difference appears to +be in the angular label-mould above the north entrance: whatever may +have been its original function or significance, it serves to define +the tower sexually, so to speak, as effectively as does the beard on +a man's face. In Amiens the north tower is taller than the south, and +more massive in its upper stages. The only traceable indication of +sex in the ornamentation occurs in the spandrels at the sides of the +entrance arches: those of the north tower containing single circles, +and those of the south tower containing two in one. This difference, +small as it may seem, is significant, for in Europe during the Middle +Ages, just as anciently in Egypt and again in Greece--in fact wherever +and whenever the Secret Doctrine was known--sex was attributed to +numbers, odd numbers being conceived of as masculine, and even, as +feminine. Two, the first feminine number, thus became a symbol of +femininity, accepted as such so universally at the time the cathedrals +were built, that two strokes of a bell announced the death of a woman, +three, the death of a man. + +[Illustration 15: FRIEZE OF THE FARNESE PALACE; ROMAN CONSOLE. VATICAN +MUSEUM; FRIEZE IN THE EMPIRE STYLE BY PERCIER AND FONTAINE. +FRIEZE FROM THE TEMPLE OF VESTA AT TIVOLI. (ROMAN); ROMAN DORIC +FRIEZE--VIGNOLE] + +[Illustration 16] + +[Illustration 17] + +The vital, organic quality so conspicuous in the best Gothic +architecture has been attributed to the fact that necessity determined +its characteristic forms. Professor Goodyear has demonstrated that +it may be due also in part to certain subtle vertical leans and +horizontal bends; and to nicely calculated variations from strict +uniformity, which find their analogue in nature, where structure is +seldom rigidly geometrical. The author hazards the theory that still +another reason why a Gothic cathedral seems so living a thing is +because it abounds in contrasts between what, for lack of more +descriptive adjectives, he is forced to call masculine and feminine +forms. + +[Illustration 18] + +[Illustration 19] + +Ruskin says, in _Stones of Venice_, "All good Gothic is nothing more +than the development, in various ways, and on every conceivable scale, +of the group formed by the pointed arch for the bearing line below, +and the gable for the protecting line above, and from the huge, gray, +shaly slope of the cathedral roof, with its elastic pointed vaults +beneath, to the crown-like points that enrich the smallest niche of +its doorway, one law and one expression will be found in all. The +modes of support and of decoration are infinitely various, but the +real character of the building, in all good Gothic, depends on the +single lines of the gable over the pointed arch endlessly rearranged +and repeated." These two, an angular and a curved form, like the +everywhere recurring column and lintel of classic architecture, +are but presentments of Yo and In (Illustration 18). Every Gothic +traceried window, with straight and vertical mullions in the +rectangle, losing themselves in the intricate foliations of the arch, +celebrates the marriage of this ever diverse pair. The circle and the +triangle are the In and Yo of Gothic tracery, its Eve and Adam, as +it were, for from their union springs that progeny of trefoil, +quatrefoil, cinquefoil, of shapes flowing like water, and shapes +darting like flame, which makes such visible music to the entranced +ear. + +[Illustration 20: SAN GIMIGNANO S. JACOPO.] + +By seeking to discover In and Yo in their myriad manifestations, by +learning to discriminate between them, and by attempting to express +their characteristic qualities in new forms of beauty--from +the disposition of a faēade to the shaping of a moulding--the +architectural designer will charge his work with that esoteric +significance, that excess of beauty, by which architecture rises +to the dignity of a "fine" art (Illustrations 19, 20). In so doing, +however, he should never forget, and the layman also should ever +remember, that the supreme architectural excellence is fitness, +appropriateness, the perfect adaptation of means to ends, and the +adequate expression of both means and ends. These two aims, the one +abstract and universal, the other concrete and individual, can always +be combined, just as in every human countenance are combined a type, +which is universal, and a character, which is individual. + + + + +III + +CHANGELESS CHANGE + +TRINITY, CONSONANCE, DIVERSITY IN MONOTONY, BALANCE, RHYTHMIC CHANGE, +RADIATION + + +The preceding essay was devoted for the most part to that "inevitable +duality" which finds concrete expression in countless pairs of +opposites, such as day and night, fire and water, man and woman; +in the art of music by two chords, one of suspense and the other of +fulfilment; in speech by vowel and consonant sounds, epitomized in _a_ +and in _m_; in painting by warm colors and cold, epitomized in red +and blue; in architecture by the vertical column and the horizontal +lintel, by void and solid--and so on. + + +TRINITY + +This concept should now be modified by another, namely, that in every +duality a third is latent; that two implies three, for each sex so +to speak is in process of becoming the other, and this alternation +engenders and is accomplished by means of a third term or neuter, +which is like neither of the original two but partakes of the nature +of them both, just as a child may resemble both its parents. Twilight +comes between day and night; earth is the child of fire and water; +in music, besides the chord of longing and striving, and the chord of +rest and satisfaction (the dominant seventh and the tonic), there is +a third or resolving chord in which the two are reconciled. In the +sacred syllable Om (_Aum_), which epitomizes all speech, the _u_ sound +effects a transition between the _a_ sound and the _m_; among the +so-called primary colors yellow comes between red and blue; and in +architecture the arch, which is both weight and support, which is +neither vertical nor horizontal, may be considered the neuter of the +group of which the column and the lintel are respectively masculine +and feminine. "These are the three," says Mr. Louis Sullivan, "the +only three letters from which has been expanded the architectural art, +as a great and superb language wherewith man has expressed, through +the generations, the changing drift of his thoughts." + +[Illustration 21: THE LAW OF TRINITY. A ROMAN IONIC ARCADE, BY +VIGNOLE.--THE COLUMN, THE ENTABLATURE, AND THE ARCH CORRESPOND TO LINES +VERTICAL, HORIZONTAL AND CURVED.] + +It would be supererogatory to dwell at any length on this "trinity +of manifestation" as the concrete expression of that unmanifest and +mystical trinity, that _three-in-one_ which under various names occurs +in every world-religion, where, defying definition, it was wont +to find expression symbolically in some combination of vertical, +horizontal and curved lines. The anstated cross of the Egyptians +is such a symbol, the Buddhist wheel, and the fylfot or swastika +inscribed within a circle, also those numerous Christian symbols +combining the circle and the cross. Such ideographs have spelled +profound meaning to the thinkers of past ages. We of to-day are not +given to discovering anything wonderful in three strokes of a pen, +but every artist in the weaving of his pattern must needs employ these +mystic symbols in one form or another, and if he employs them with +a full sense of their hidden meaning his work will be apt to gain +in originality and beauty--for originality is a new and personal +perception of beauty, and beauty is the name we give to truth we +cannot understand. + +In architecture, this trinity of vertical, horizontal and curved +lines finds admirable illustration in the application of columns and +entablature to an arch and impost construction, so common in Roman and +Renaissance work. This is a redundancy, and finds no justification in +reason, because the weight is sustained by the arch, and the "order" +is an appendage merely; yet the combination, illogical as it is, +satisfies the sense of beauty because the arch effects a transition +between the columns and the entablature, and completes the trinity +of vertical, horizontal and curved lines (Illustration 21). In the +entrances to many of the Gothic cathedrals and churches the same +elements are better because more logically disposed. Here the +horizontal lintel and its vertical supports are not decorative merely, +but really perform their proper functions, while the arch, too, has +a raison d'źtre in that it serves to relieve the lintel of the +superincumbent weight of masonry. The same arrangement sometimes +occurs in classic architecture also, as when an opening spanned by a +single arch is subdivided by means of an order (Illustration 22). + +Three is pre-eminently the number of architecture, because it is the +number of space, which for us is three-dimensional, and of all the +arts architecture is most concerned with the expression of spatial +relations. The division of a composition into three related parts is +so universal that it would seem to be the result of an instinctive +action of the human mind. The twin pylons of an Egyptian temple with +its entrance between, for a third division, has its correspondence in +the two towers of a Gothic cathedral and the intervening screen +wall of the nave. In the palaces of the Renaissance a threefold +division--vertically by means of quoins or pilasters, and horizontally +by means of cornices or string courses--was common, as was also the +division into a principal and two subordinate masses (Illustration +23). + +[Illustration 22: THE LAW OF TRINITY. THE TRINITY OF HORIZONTAL VERTICAL +AND CURVED LINES.] + +The architectural "orders" are divided threefold into pedestal or +stylobate, column and entablature; and each of these is again divided +threefold: the first into plinth, die and cornice; the second into +base, shaft and capital; the third into architrave, frieze and +cornice. In many cases these again lend themselves to a threefold +subdivision. A more detailed analysis of the capitals already shown to +be twofold reveals a third member: in the Greek Doric this consists +of the annulets immediately below the abacus; in the other orders, the +necking which divides the shaft from the cap. + + +CONSONANCE + +"As is the small, so is the great" is a perpetually recurring phrase +in the literature of theosophy, and naturally so, for it is a succinct +statement of a fundamental and far-reaching truth. The scientist +recognizes it now and then and here and there, but the occultist +trusts it always and utterly. To him the microcosm and the macrocosm +are one and the same in essence, and the forth-going impulse +which calls a universe into being and the indrawing impulse which +extinguishes it again, each lasting millions of years, are echoed and +repeated in the inflow and outflow of the breath through the nostrils, +in nutrition and excretion, in daily activity and nightly rest, in +that longer day which we name a lifetime, and that longer rest in +_Devachan_--and so on until time itself is transcended. + +[Illustration 23] + +In the same way, in nature, a thing is echoed and repeated throughout +its parts. Each leaf on a tree is itself a tree in miniature, each +blossom a modified leaf; every vertebrate animal is a complicated +system of spines; the ripple is the wave of a larger wave, and that +larger wave is a part of the ebbing and flowing tide. In music this +law is illustrated in the return of the tonic to itself in the octave, +and its partial return in the dominant; also in a more extended sense +in the repetition of a major theme in the minor, or in the treble and +again in the bass, with modifications perhaps of time and key. In +the art of painting the law is exemplified in the repetition with +variation of certain colors and combinations of lines in different +parts of the same picture, so disposed as to lead the eye to some +focal point. Every painter knows that any important color in his +picture must be echoed, as it were, in different places, for harmony +of the whole. + +[Illustration 24] + +In the drama the repetition of a speech or of an entire scene, but +under circumstances which give it a different meaning, is often most +effective, as when Gratiano, in the trial scene of _The Merchant +of Venice_ taunts Shylock with his own words, "A Daniel come to +judgment!" or, as when in one of the later scenes of _As You Like It_ +an earlier scene is repeated, but with Rosalind speaking in her proper +person and no longer as the boy Ganymede. + +These recurrences, these inner consonances, these repetitions with +variations are common in architecture also. The channeled triglyphs of +a Greek Doric frieze echo the fluted columns below (Illustration 24). +The balustrade which crowns a colonnade is a repetition, in some sort, +of the colonnade itself. The modillions of a Corinthian cornice are +but elaborated and embellished dentils. Each pinnacle of a Gothic +cathedral is a little tower with its spire. As Ruskin has pointed out, +the great vault of the cathedral nave, together with the pointed roof +above it, is repeated in the entrance arch with its gable, and the +same two elements appear in every statue-enshrining niche of the +doorway. In classic architecture, as has been shown, instead of the +arch and gable, the column and entablature everywhere recur under +different forms. The minor domes which flank the great dome of the +cathedral of Florence enhance and reinforce the latter, and prepare +the eye for a climax which would otherwise be too abrupt. The central +pavilion of the Chāteau Maintenon, with its two turrets, echoes the +entire faēade with its two towers. Like the overture to an opera, it +introduces themes which find a more extended development elsewhere +(Illustration 26). + +[Illustration 25] + +[Illustration 26] + +[Illustration 27] + +This law of Consonance is operative in architecture more obscurely +in the form of recurring numerical ratios, identical geometrical +determining figures, parallel diagonals and the like, which will be +discussed in a subsequent essay. It has also to do with style and +scale, the adherence to substantially one method of construction and +manner of ornament, just as in music the key, or chosen series of +notes, may not be departed from except through proper modulations, or +in a specific manner. + +Thus it is seen that in a work of art, as in a piece of tapestry, +the same thread runs through the web, but goes to make up different +figures. The idea is deeply theosophic: one life, many manifestations; +hence, inevitably, echoes, resemblances--_Consonance_. + + +DIVERSITY IN MONOTONY + +Another principle of natural beauty, closely allied to the foregoing, +its complement as it were, is that of _Diversity in Monotony_--not +identity, but difference. It shows itself for the most part as a +perceptible and piquant variation between individual units belonging +to the same class, type, or species. + +No two trees put forth their branches in just the same manner, and no +two leaves from the same tree exactly correspond; no two persons +look alike, though they have similiar members and features; even the +markings on the skin of the thumb are different in every human hand. +Browning says, + + "As like as a hand to another hand! + Whoever said that foolish thing, + Could not have studied to understand--" + +Now every principle of natural beauty is but the presentment of some +occult law, some theosophical truth; and this law of Diversity in +Monotony is the presentment of the truth that identity does not +exclude difference. The law is binding, yet the will is free: all men +are brothers united by the ties of brotherhood, yet each is unique, a +free agent, and never so free as when most bound by the Good Law. This +truth nature beautifully proclaims, and art also. In architecture it +is admirably exemplified in the metopes of the Parthenon frieze: seen +at a distance these must have presented a scarcely distinguishable +texture of sunlit marble and cool shadow, yet in reality each is +a separate work of art. So with the capitals of the columns of the +wonderful sea-arcade of the Venetian Ducal palace: alike in general +contour they differ widely in detail, and unfold a Bible story. +In Gothic cathedrals, in Romanesque monastery cloisters, a teeming +variety of invention is hidden beneath apparent uniformity. The +gargoyles of Notre Dame make similiar silhouettes against the sky, +but seen near at hand what a menagerie of monsters! The same spirit of +controlled individuality, of liberty subservient to the law of all, is +exemplified in the bases of the columns of the temple of Apollo near +Miletus--each one a separate masterpiece of various ornamentation +adorning an established architectural form (Illustration 28). + +[Illustration 28] + +[Illustration 29] + +The builders of the early Italian churches, instinctively obeying this +law of Diversity in Monotony, varied the size of the arches in the +same arcade (Illustration 29), and that this was an effect of art and +not of accident or carelessness Ruskin long ago discovered, and the +Brooklyn Institute surveys have amply confirmed his view. Although +by these means the builders of that day produced effects of deceptive +perspective, of subtle concord and contrast, their sheer hatred of +monotony and meaningless repetition may have led them to diversify +their arcades in the manner described, for a rigidly equal and regular +division lacks interest and vitality. + + +BALANCE + +If one were to establish an axial plane vertically through the center +of a tree, in most cases it would be found that the masses of foliage, +however irregularly shaped on either side of such an axis, just about +balanced each other. Similarly, in all our bodily movements, for every +change of equilibrium there occurs an opposition and adjustment of +members of such a nature that an axial plane through the center of +gravity would divide the body into two substantially equal masses, +as in the case of the tree. This physical plane law of Balance +shows itself for the most part on the human plane as the law of +Compensation, whereby, to the vision of the occultist, all accounts +are "squared," so to speak. It is in effect the law of Justice, aptly +symbolized by the scales. + +The law of Balance finds abundant illustration in art: in music by +the opposition, the answering, of one phrase by another of the same +elements and the same length, but involving a different sequence of +intervals; in painting by the disposition of masses in such a way that +they about equalize one another, so that there is no sense of "strain" +in the composition. + +In architecture the common and obvious recognition of the law of +Balance is in the symmetrical disposition of the elements, whether of +plan or of elevation, on either side of axial lines. A far more subtle +and vital illustration of the law occurs when the opposed elements do +not exactly match, but differ from each other, as in the case of the +two towers of Amiens, for example. This sort of balance may be said to +be characteristic of Gothic, as symmetry is characteristic of Classic, +architecture. + + +RHYTHMIC CHANGE + +There is in nature a universal tendency toward refinement and +compactness of form in space, or contrariwise, toward increment +and diffusion; and this manifests itself in time as acceleration or +retardation. It is governed, in either case, by an exact mathematical +law, like the law of falling bodies. It shows itself in the widening +circles which appear when one drops a stone into still water, in the +convolutions of shells, in the branching of trees and the veining +of leaves; the diminution in the size of the pipes of an organ +illustrates it, and the spacing of the frets of a guitar. More and +more science is coming to recognize, what theosophy affirms, that the +spiral vortex, which so beautifully illustrates this law, both in its +time and its space aspects is the universal archetype, the pattern of +all that is, has been, or will be, since it is the form assumed by the +ultimate physical atom, and the ultimate physical atom is the physical +cosmos in miniature. + +This Rhythmic Diminution is everywhere: it is in the eye itself, for +any series of mathematically equal units, such for example as the +columns and intercolumnations of a colonnade, become when seen +in perspective rhythmically unequal, diminishing according to the +universal law. The entasis of a Classic column is determined by this +law, the spirals of the Ionic volute, the annulets of the Parthenon +cap, obey it (Illustration 30). + +In recognition of the same principle of Rhythmic Diminution a building +is often made to grow, or appear to grow lighter, more intricate, +finer, from the ground upward, an end attained by various devices, +one of the most common being the employment of the more attenuated +and highly ornamented orders above the simpler and sturdier, as in the +Roman Colosseum, or in the Palazzo Uguccioni, in Florence--to mention +only two examples out of a great number. In the Riccardi Palace +an effect of increasing refinement is obtained by diminishing the +boldness of the rustication of the ashlar in successive stories; in +the Farnese, by the gradual reduction of the size of the angle quoins +(Illustration 30). In an Egyptian pylon it is achieved most simply by +battering the wall; in a Gothic cathedral most elaborately by a +kind of segregation, or breaking up, analogous to that which a tree +undergoes--the strong, relatively unbroken base corresponding to +the trunk, the diminishing buttresses to the tapering limbs, and +the multitude of delicate pinnacles and crockets, to the outermost +branches and twigs, seen against the sky. + + +RADIATION + +The final principle of natural beauty to which the author would call +attention is the law of _Radiation_, which is in a manner a return +to the first, the law of _Unity_. The various parts of any organism +radiate from, or otherwise refer back to common centers, or foci, +and these to centers of their own. The law is represented in its +simplicity in the star-fish, in its complexity in the body of man; a +tree springs from a seed, the solar system centers in the sun. + +The idea here expressed by the term "radiation" is a familiar one +to all students of theosophy. The Logos radiates his life and light +throughout his universe, bringing into activity a host of entities +which become themselves radial centers; these generate still others, +and so on endlessly. This principle, like every other, patiently +publishes itself to us, unheeding, everywhere in nature, and in +all great art as well; it is a law of optics, for example, that all +straight lines having a common direction if sufficiently prolonged +appear to meet in a point, i.e., radiate from it (Illustration 31). +Leonardo da Vinci employed this principle of perspective in his Last +Supper to draw the spectator's eye to the picture's central figure, +the point of sight toward which the lines of the walls and ceiling +converge centering in the head of Christ. Puvis de Chavannes, in his +Boston Library decoration, leads the eye by a system of triangulation +to the small figure of the Genius of Enlightenment above the central +door (Illustration 32); and Ruskin, in his _Elements of Drawing_, has +shown how artfully Turner arranged some of his compositions to attract +attention to a focal point. + +This law of Radiation enters largely into architecture. The Colosseum, +based upon the ellipse, a figure generated from two points or foci, +and the Pantheon, based upon the circle, a figure generated from a +central point, are familiar examples. The distinctive characteristic +of Gothic construction, the concentration or focalization of the +weight of the vaults and arches at certain points, is another +illustration of the same principle applied to architecture, +beautifully exemplified in the semicircular apse of a cathedral, where +the lines of the plan converge to a common center, and the ribs of the +vaulting meet upon the capitals of the piers and columns, seeming +to radiate thence to still other centers in the loftier vaults which +finally meet in a center common to all. + +[Illustration 30] + +[Illustration 31] + +[Illustration 32] + +The tracery of the great roses, high up in the faēades of the +cathedrals of Paris and of Amiens, illustrate Radiation, in the one +case masculine: straight, angular, direct; in the feminine: curved, +flowing, sinuous. The same _Beautiful Necessity_ determined the +characteristics of much of the ornament of widely separated styles +and periods: the Egyptian lotus, the Greek honeysuckle, the Roman +acanthus, Gothic leaf work--to snatch at random four blossoms from +the sheaf of time. The radial principle still inherent in the debased +ornament of the late Renaissance gives that ornament a unity, a +coherence, and a kind of beauty all its own (Illustration 35). + +[Illustration 33] + +[Illustration 34] + +Such are a few of the more obvious laws of natural beauty and their +application to the art of architecture. The list is by no means +exhausted, but it is not the multiplicity and diversity of these laws +which is important to keep in mind, so much as their relatedness and +coördination, for they are but different aspects of the One Law, that +whereby the Logos manifests in time and space. A brief recapitulation +will serve to make this correlation plain, and at the same time fix +what has been written more firmly in the reader's mind. + +[Illustration 35] + +[Illustration 36] + +First comes the law of _Unity_; then, since every unit is in its +essence twofold, there is the law of _Polarity_; but this duality is +not static but dynamic, the two parts acting and reacting upon one +another to produce a third--hence the law of _Trinity_. Given this +third term, and the innumerable combinations made possible by +its relations to and reactions upon the original pair, the law +of _Multiplicity in Unity_ naturally follows, as does the law +of _Consonance_, or repetition, since the primal process of +differentiation tends to repeat itself, and the original combinations +to reappear--but to reappear in changed form, hence the law of +_Diversity in Monotony_. The law of _Balance_ is seen to be but a +modification of the law of Polarity, and since all things are waxing +and waning, there is the law whereby they wax and wane, that of +_Rhythmic Change_. _Radiation_ rediscovers and reaffirms, even in the +utmost complexity, that essential and fundamental unity from which +complexity was wrought. + +Everything, beautiful or ugly, obeys and illustrates one or another of +these laws, so universal are they, so inseparably attendant upon every +kind of manifestation in time and space. It is the number of them +which finds illustration within small compass, and the aptness and +completeness of such illustration, which makes for beauty, because +beauty is the fine flower of a sort of sublime ingenuity. A work of +art is nothing if not _artful_: like an acrostic, the more different +ways it can be read--up, down, across, from right to left and from +left to right--the better it is, other things being equal. This +statement, of course, may be construed in such a way as to appear +absurd; what is meant is simply that the more a work of art is +freighted and fraught with meaning beyond meaning, the more secure its +immortality, the more powerful its appeal. For enjoyment, it is not +necessary that all these meanings should be fathomed, it is only +necessary that they should be felt. + +Consider for a moment the manner in which Leonardo da Vinci's Last +Supper, an acknowledged masterpiece, conforms to everyone of the laws +of beauty enumerated above (Illustration 32). It illustrates the law +of Unity in that it movingly portrays a single significant episode in +the life of Christ. The eye is led to dwell upon the central personage +of this drama by many artful expedients: the visible part of the +figure of Christ conforms to the lines of an equilateral triangle +placed exactly in the center of the picture; the figure is separated +by a considerable space from the groups of the disciples on either +hand, and stands relieved against the largest parallelogram of light, +and the vanishing point of the perspective is in the head of Christ, +at the apex, therefore, of the triangle. The law of Polarity finds +fulfilment in the complex and flowing lines of the draped figures +contrasted with the simple parallelogram of the cloth-covered table, +and the severe architecture of the room. The law of Trinity is +exemplified in the three windows, and in the subdivision of the twelve +figures of the disciples into four groups of three figures each. The +law of Consonance appears in the repetition of the horizontal lines +of the table in the ceiling above; and in the central triangle before +referred to, continued and echoed, as it were, in the triangular +supports of the table visible underneath the cloth. The law of +Diversity in Monotony is illustrated in the varying disposition of the +heads of the figures in the four groups of three; the law of Balance +in the essential symmetry of the entire composition; the law of +Rhythmic Change in the diminishing of the wall and ceiling spaces; and +the law of Radiation in the convergence of all the perspective lines +to a single significant point. + +To illustrate further the universality of these laws, consider now +their application to a single work of architecture: the Taj Mahal, one +of the most beautiful buildings of the world (Illustration 36). It is +a unit, but twofold, for it consists of a curved part and an angular +part, roughly figured as an inverted cup upon a cube; each of these +(seen in parallel perspective, at the end of the principal vista) is +threefold, for there are two sides and a central parallelogram, and +two lesser domes flank the great dome. The composition is rich in +consonances, for the side arches echo the central one, the subordinate +domes the great dome, and the lanterns of the outstanding minarets +repeat the principal motif. Diversity in Monotony appears abundantly +in the ornament, which is intricate and infinitely various; the law of +Balance is everywhere operative in the symmetry of the entire design. +Rhythmic Change appears in the tapering of the minarets, the outlines +of the domes and their mass relations to one another; and finally, +the whole effect is of radiation from a central point, of elements +disposed on radial lines. + +It would be fatuous to contend that the prime object of a work of +architecture is to obey and illustrate these laws. The prime object of +a work of architecture is to fulfill certain definite conditions in a +practical, economical, and admirable way, and in fulfilling to express +as far as possible these conditions, making the form express the +function. The architect who is also an artist however will do this +and something beyond: working for the most part unconsciously, +harmoniously, joyously, his building will obey and illustrate natural +laws--these laws of beauty--and to the extent it does so it will be a +work of art; for art is the method of nature carried into those higher +regions of thought and feeling which man alone inhabits: regions which +it is one of the purposes of theosophy to explore. + + + + +IV + +THE BODILY TEMPLE + + +Carlyle says: "There is but one temple in the world, and that is the +body of man." If the body is, as he declares, a temple, it is not less +true that a temple or any work of architectural art is a larger body +which man has created for his uses, just as the individual self is +housed within its stronghold of flesh and bones. Architectural beauty +like human beauty depends upon the proper subordination of parts +to the whole, the harmonious interrelation between these parts, the +expressiveness of each of its function or functions, and when these +are many and diverse, their reconcilement one with another. This being +so, a study of the human figure with a view to analyzing the sources +of its beauty cannot fail to be profitable. Pursued intelligently, +such a study will stimulate the mind to a perception of those simple +yet subtle laws according to which nature everywhere works, and +it will educate the eye in the finest known school of proportion, +training it to distinguish minute differences, in the same way that +the hearing of good music cultivates the ear. + +Those principles of natural beauty which formed the subject of the +two preceding essays are all exemplified in the ideally perfect human +figure. Though essentially a unit, there is a well marked division +into right and left--"Hands to hands, and feet to feet, in one body +grooms and brides." There are two arms, two legs, two ears, two eyes, +and two lids to each eye; the nose has two nostrils, the mouth has +two lips. Moreover, the terms of such pairs are masculine and feminine +with respect to each other, one being active and the other passive. +Owing to the great size and one-sided position of the liver, the right +half of the body is heavier than the left; the right arm is usually +longer and more muscular than the left; the right eye is slightly +higher than its fellow. In speaking and eating the lower jaw and under +lip are active and mobile with relation to the upper; in winking it is +the upper eyelid which is the more active. That "inevitable duality" +which is exhibited in the form of the body characterizes its motions +also. In the act of walking for example, a forward movement is +attained by means of a forward and a backward movement of the thighs +on the axis of the hips; this leg movement becomes twofold again below +the knee, and the feet move up and down independently on the axis of +the ankle. A similar progression is followed in raising the arm and +hand: motion is communicated first to the larger parts, through them +to the smaller and thence to the extremities, becoming more rapid and +complex as it progresses, so that all free and natural movements of +the limbs describe invisible lines of beauty in the air. Coexistent +with this pervasive duality there is a threefold division of the +figure into trunk, head and limbs: a superior trinity of head and +arms, and an inferior trinity of trunk and legs. The limbs are divided +threefold into upper-arm, forearm and hand; thigh, leg and foot. The +hand flowers out into fingers and the foot into toes, each with a +threefold articulation; and in this way is effected that transition +from unity to multiplicity, from simplicity to complexity, which +appears to be so universal throughout nature, and of which a tree is +the perfect symbol. + +[Illustration 37: THE LAW OF RHYTHMIC DIMINUTION ILLUSTRATED IN THE +TAPERING BODY, LIMBS, FINGERS & TOES.] + +[Illustration 38] + +[Illustration 39] + +The body is rich in veiled repetitions, echoes, _consonances_. The +head and arms are in a sense a refinement upon the trunk and legs, +there being a clearly traceable correspondence between their various +parts. The hand is the body in little--_"Your soft hand is a woman of +itself"_--the palm, the trunk; the four fingers, the four limbs; and +the thumb, the head;-each finger is a little arm, each finger tip a +little palm. The lips are the lids of the mouth, the lids are the +lips of the eyes--and so on. The law of _Rhythmic Diminution_ is +illustrated in the tapering of the entire body and of the limbs, in +the graduated sizes and lengths of the palm and the toes, and in +the successively decreasing length of the palm and the joints of the +fingers, so that in closing the hand the fingers describe natural +spirals (Illustrations 37, 38). Finally, the limbs radiate as it were +from the trunk, the fingers from a point in the wrist, the toes from +a point in the ankle. The ribs radiate from the spinal column like the +veins of a leaf from its midrib (Illustration 39). + +[Illustration 40] + +The relation of these laws of beauty to the art of architecture has +been shown already. They are reiterated here only to show that man is +indeed the microcosm--a little world fashioned from the same elements +and in accordance with the same _Beautiful Necessity_ as is the +greater world in which he dwells. When he builds a house or temple he +builds it not literally in his own image, but according to the laws of +his own being, and there are correspondences not altogether fanciful +between the animate body of flesh and the inanimate body of stone. Do +we not all of us, consciously or unconsciously, recognize the fact +of character and physiognomy in buildings? Are they not, to our +imagination, masculine or feminine, winning or forbidding--_human_, +in point of fact--to a greater degree than anything else of man's +creating? They are this certainly to a true lover and student of +architecture. Seen from a distance the great French cathedrals appear +like crouching monsters, half beast, half human: the two towers stand +like a man and a woman, mysterious and gigantic, looking out over city +and plain. The campaniles of Italy rise above the churches and houses +like the sentinels of a sleeping camp--nor is their strangely human +aspect wholly imaginary: these giants of mountain and campagna have +eyes and brazen tongues; rising four square, story above story, with +a belfry or lookout, like a head, atop, their likeness to a man is not +infrequently enhanced by a certain identity of proportion--of ratio, +that is, of height to width: Giotto's beautiful tower is an example. +The caryatid is a supporting member in the form of a woman; in the +Ionic column we discern her stiffened, like Lot's wife, into a pillar, +with nothing to show her feminine but the spirals of her beautiful +hair. The columns which uphold the pediment of the Parthenon are +unmistakably masculine: the ratio of their breadth to their height is +the ratio of the breadth to the height of a man (Illustration 40). + +[Illustration 41: THE BODY THE ARCHETYPE OF SACRED EDIFICES.] + +[Illustration 42: THE VESICA PISCIS AND THE PLAN OF CHARTRES.] + +At certain periods of the world's history, periods of mystical +enlightenment, men have been wont to use the human figure, the soul's +temple, as a sort of archetype for sacred edifices (Illustration 41). +The colossi, with calm inscrutable faces, which flank the entrance to +Egyptian temples; the great bronze Buddha of Japan, with its dreaming +eyes; the little known colossal figures of India and China--all these +belong scarcely less to the domain of architecture than of sculpture. +The relation above referred to however is a matter more subtle and +occult than mere obvious imitation on a large scale, being based upon +some correspondence of parts, or similarity of proportions, or both. +The correspondence between the innermost sanctuary or shrine of a +temple and the heart of a man, and between the gates of that temple +and the organs of sense is sufficiently obvious, and a relation once +established, the idea is susceptible of almost infinite development. +That the ancients proportioned their temples from the human figure +is no new idea, nor is it at all surprising. The sculpture of the +Egyptians and the Greeks reveals the fact that they studied the body +abstractly, in its exterior presentment. It is clear that the rules +of its proportions must have been established for sculpture, and it is +not unreasonable to suppose that they became canonical in architecture +also. Vitruvius and Alberti both lay stress on the fact that all +sacred buildings should be founded on the proportions of the human +body. + +[Illustration 43: A GOTHIC CATHEDRAL THE SYMBOL OF THE BODY OF JESUS +CHRIST] + +[Illustration 44: THE SYMBOLISM OF A GOTHIC CATHEDRAL FROM THE +ROSICRUCIANS: HARGRAVE JENNINGS] + +In France, during the Middle Ages, a Gothic cathedral became, at the +hands of the secret masonic guilds, a glorified symbol of the body +of Christ. To practical-minded students of architectural history, +familiar with the slow and halting evolution of a Gothic cathedral +from a Roman basilica, such an idea may seem to be only the +maunderings of a mystical imagination, a theory evolved from the inner +consciousness, entitled to no more consideration than the familiar +fallacy that vaulted nave of a Gothic church was an attempt to imitate +the green aisles of a forest. It should be remembered however that the +habit of the thought of that time was mystical, as that of our own age +is utilitarian and scientific; and the chosen language of mysticism is +always an elaborate and involved symbolism. What could be more natural +than that a building devoted to the worship of a crucified Savior +should be made a symbol, not of the cross only, but of the body +crucified? + +[Illustration 45: THE GEOMETRICAL BASIS OF THE HUMAN FIGURE] + +[Illustration 46] + +The _vesica piscis_ (a figure formed by the developing arcs of two +equilateral triangles having a common side) which in so many cases +seems to have determined the main proportion of a cathedral plan--the +interior length and width across the transepts--appears as an aureole +around the figure of Christ in early representations, a fact which +certainly points to a relation between the two (Illustrations 42, +43). A curious little book, _The Rosicrucians_, by Hargrave Jennings, +contains an interesting diagram which well illustrates this conception +of the symbolism of a cathedral. A copy of it is here given. The apse +is seen to correspond to the head of Christ, the north transept to his +right hand, the south transept to the left hand, the nave to the body, +and the north and south towers to the right and left feet respectively +(Illustration 44). + +[Illustration 47] + +The cathedral builders excelled all others in the artfulness with +which they established and maintained a relation between their +architecture and the stature of a man. This is perhaps one reason why +the French and English cathedrals, even those of moderate dimensions +are more truly impressive than even the largest of the great +Renaissance structures, such as St. Peter's in Rome. A gigantic order +furnishes no true measure for the eye: its vastness is revealed +only by the accident of some human presence which forms a basis +of comparison. That architecture is not necessarily the most +awe-inspiring which gives the impression of having been built by +giants for the abode of pigmies; like the other arts, architecture is +highest when it is most human. The medięval builders, true to this +dictum, employed stones of a size proportionate to the strength of +a man working without unusual mechanical aids; the great piers and +columns, built up of many such stones, were commonly subdivided +into clusters, and the circumference of each shaft of such a cluster +approximated the girth of a man; by this device the moulding of the +base and the foliation of the caps were easily kept in scale. Wherever +a balustrade occurred it was proportioned not with relation to the +height of the wall or the column below, as in classic architecture, +but with relation to a man's stature. + +[Illustration 48: FIGURE DIVIDED ACCORDING TO THE EGYPTIAN CANON] + +It may be stated as a general rule that every work of architecture, +of whatever style, should have somewhere about it something fixed and +enduring to relate it to the human figure, if it be only a flight of +steps in which each one is the measure of a stride. In the Farnese, +the Riccardi, the Strozzi, and many another Italian palace, the stone +seat about the base gives scale to the building because the beholder +knows instinctively that the height of such a seat must have some +relation to the length of a man's leg. In the Pitti palace the +balustrade which crowns each story answers a similar purpose: it +stands in no intimate relation to the gigantic arches below, but is +of a height convenient for lounging elbows. The door to Giotto's +campanile reveals the true size of the tower as nothing else could, +because it is so evidently related to the human figure and not to the +great windows higher up in the shaft. + +[Illustration 49: THE MEDIĘVAL METHOD OF DRAWING THE FIGURE] + +The geometrical plane figures which play the most important part in +architectural proportion are the square, the circle and the triangle; +and the human figure is intimately related to these elementary forms. +If a man stand with heels together, and arms outstretched horizontally +in opposite directions, he will be inscribed, as it were, within a +square; and his arms will mark, with fair accuracy, the base of an +inverted equilateral triangle, the apex of which will touch the ground +at his feet. If the arms be extended upward at an angle, and the +legs correspondingly separated, the extremities will touch +the circumferences of a circle having its center in the navel +(Illustrations 45, 46). + +[Illustration 50] + +The figure has been variously analyzed with a view to establishing +numerical ratios between its parts (Illustrations 47, 48, 49). Some +of these are so simple and easily remembered that they have obtained +a certain popular currency; such as that the length of the hand equals +the length of the face; that the span of the horizontally extended +arms equals the height; and the well known rule that twice around +the wrist is once around the neck, and twice around the neck is once +around the waist. The Roman architect Vitruvius, writing in the age of +Augustus Cęsar, formulated the important proportions of the statues +of classical antiquity, and except that he makes the head smaller than +the normal (as it should be in heroic statuary), the ratios which +he gives are those to which the ideally perfect male figure should +conform. Among the ancients the foot was probably the standard of all +large measurements, being a more determinate length than that of the +head or face, and the height was six lengths of the foot. If the head +be taken as a unit, the ratio becomes 1:8, and if the face--1:10. + +Doctor Rimmer, in his _Art Anatomy_, divides the figure into four +parts, three of which are equal, and correspond to the lengths of +the leg, the thigh and the trunk; while the fourth part, which is +two-thirds of one of these thirds, extends from the sternum to the +crown of the head. One excellence of such a division aside from its +simplicity, consists in the fact that it may be applied to the face as +well. The lowest of the three major divisions extends from the tip of +the chin to the base of the nose, the next coincides with the height +of the nose (its top being level with the eyebrows), and the last with +the height of the forehead, while the remaining two-thirds of one of +these thirds represents the horizontal projection from the beginning +of the hair on the forehead to the crown of the head. The middle of +the three larger divisions locates the ears, which are the same height +as the nose (Illustrations 45, 47). + +Such analyses of the figure, however conducted, reveals an +all-pervasive harmony of parts, between which definite numerical +relations are traceable, and an apprehension of these should assist +the architectural designer to arrive at beauty of proportion by +methods of his own, not perhaps in the shape of rigid formulę, but +present in the consciousness as a restraining influence, acting and +reacting upon the mind with a conscious intention toward rhythm and +harmony. By means of such exercises, he will approach nearer to an +understanding of that great mystery, the beauty and significance of +numbers, of which mystery music, architecture, and the human figure +are equally presentments--considered, that is, from the standpoint of +the occultist. + + + + +V + +LATENT GEOMETRY + + +[Illustration 51: THE HEXAGRAM AND EQUILATERAL TRIANGLE IN NATURE] + +It is a well known fact that in the microscopically minute of nature, +units everywhere tend to arrange themselves with relation to certain +simple geometrical solids, among which are the tetrahedron, the cube, +and the sphere. This process gives rise to harmony, which may be +defined as the relation between parts and unity, the simplicity latent +in the infinitely complex, the potential complexity of that which is +simple. Proceeding to things visible and tangible, this indwelling +harmony, rhythm, proportion, which has its basis in geometry and +number, is seen to exist in crystals, flower forms, leaf groups, and +the like, where it is obvious; and in the more highly organized world +of the animal kingdom also; though here the geometry is latent rather +than patent, eluding though not quite defying analysis, and thus +augmenting beauty, which like a woman is alluring in proportion as she +eludes (Illustrations 51, 52, 53). + +[Illustration 52: PROPORTIONS OF THE HORSE] + +[Illustration 53] + +By the true artist, in the crystal mirror of whose mind the universal +harmony is focused and reflected, this secret of the cause and source +of rhythm--that it dwells in a correlation of parts based on an +ultimate simplicity--is instinctively apprehended. A knowledge of it +formed part of the equipment of the painters who made glorious the +golden noon of pictorial art in Italy during the Renaissance. The +problem which preoccupied them was, as Symonds says of Leonardo, +"to submit the freest play of form to simple figures of geometry in +grouping." Alberti held that the painter should above all things have +mastered geometry, and it is known that the study of perspective and +kindred subjects was widespread and popular. + +[Illustration 54] + +The first painter who deliberately rather than instinctively based +his compositions on geometrical principles seems to have been Fra +Bartolommeo, in his Last Judgment, in the church of St. Maria Nuova, +in Florence. Symonds says of this picture, "Simple figures--the +pyramid and triangle, upright, inverted, and interwoven like the +rhymes of a sonnet--form the basis of the composition. This system was +adhered to by the Fratre in all his subsequent works" (Illustration +54). Raphael, with that power of assimilation which distinguishes +him among men of genius, learned from Fra Bartolommeo this method +of disposing figures and combining them in masses with almost +mathematical precision. It would have been indeed surprising if +Leonardo da Vinci, in whom the artist and the man of science were +so wonderfully united, had not been greatly preoccupied with the +mathematics of the art of painting. His Madonna of the Rocks, and +Virgin on the Lap of Saint Anne, in the Louvre, exhibit the very +perfection of pyramidal composition. It is however in his masterpiece, +The Last Supper, that he combines geometrical symmetry and precision +with perfect naturalness and freedom in the grouping of individually +interesting and dramatic figures. Michael Angelo, Andrea del Sarto, +and the great Venetians, in whose work the art of painting may be said +to have culminated, recognized and obeyed those mathematical laws of +composition known to their immediate predecessors, and the decadence +of the art in the ensuing period may be traced not alone to the false +sentiment and affectation of the times, but also in the abandonment by +the artists of those obscurely geometrical arrangements and groupings +which in the works of the greatest masters so satisfy the eye and +haunt the memory of the beholder (Illustrations 55, 56). + +[Illustration 55: THE EMPLOYMENT OF THE EQUILATERAL TRIANGLE IN +RENAISSANCE PAINTING] + +[Illustration 56: GEOMETRICAL BASIS OF THE SISTINE CEILING PAINTINGS] + +[Illustration 57: ASSYRIAN; GREEK] + +[Illustration 58: THE GEOMETRICAL BASIS OF THE PLAN IN ARCHITECTURAL +DESIGN] + +[Illustration 59] + +Sculpture, even more than painting, is based on geometry. The colossi +of Egypt, the bas-reliefs of Assyria, the figured pediments and +metopes of the temples of Greece, the carved tombs of Revenna, +the Della Robbia lunettes, the sculptured tympani of Gothic church +portals, all alike lend themselves in greater or less degree to a +geometrical synopsis (Illustration 57). Whenever sculpture suffered +divorce from architecture the geometrical element became less +prominent, doubtless because of all the arts architecture is the most +clearly and closely related to geometry. Indeed, it may be said that +architecture is geometry made visible, in the same sense that music +is number made audible. A building is an aggregation of the commonest +geometrical forms: parallelograms, prisms, pyramids and cones--the +cylinder appearing in the column, and the hemisphere in the dome. +The plans likewise of the world's famous buildings reduced to their +simplest expression are discovered to resolve themselves into a few +simple geometrical figures. (Illustration 58). This is the "bed rock" +of all excellent design. + +[Illustration 60: EGYPTIAN; GREEK; ROMAN; MEDIĘVAL] + +[Illustration 61: JEFFERSON'S PEN SKETCH FOR THE ROTUNDA OF THE +UNIVERSITY OF VIRGINIA] + +[Illustration 62: APPLICATION OF THE EQUILATERAL TRIANGLE TO THE +ERECHTHEUM AT ATHENS] + +[Illustration 63] + +[Illustration 64: THE EQUILATERAL TRIANGLE IN ROMAN ARCHITECTURE] + +But architecture is geometrical in another and a higher sense than +this. Emerson says: "The pleasure a palace or a temple gives the eye +is that an order and a method has been communicated to stones, so that +they speak and geometrize, become tender or sublime with expression." +All truly great and beautiful works of architecture from the Egyptian +pyramids to the cathedrals of Ile-de-France--are harmoniously +proportioned, their principal and subsidiary masses being related, +sometimes obviously, more often obscurely, to certain symmetrical +figures of geometry, which though invisible to the sight and not +consciously present in the mind of the beholder, yet perform the +important function of coördinating the entire fabric into one easily +remembered whole. Upon some such principle is surely founded what +Symonds calls "that severe and lofty art of composition which seeks +the highest beauty of design in architectural harmony supreme, above +the melodies of gracefulness of detail." + +[Illustration 65: THE EQUILATERAL TRIANGLE IN ITALIAN ARCHITECTURE] + +[Illustration 66: THE HEXAGRAM IN GOTHIC ARCHITECTURE] + +There is abundant evidence in support of the theory that the +builders of antiquity, the masonic guilds of the Middle Ages, and +the architects of the Italian Renaissance, knew and followed certain +rules, but though this theory be denied or even disproved--if after +all these men obtained their results unconsciously--their creations +so lend themselves to a geometrical analysis that the claim for the +existence of certain canons of proportion, based on geometry, remains +unimpeached. + +[Illustration 67] + +[Illustration 68] + +The plane figures principally employed in determining architectural +proportion are the circle, the equilateral triangle, and the +square--which also yields the right angled isosceles triangle. It +will be noted that these are the two dimensional correlatives of the +sphere, the tetrahedron and the cube, mentioned as being among the +determining forms in molecular structure. The question naturally +arises, why the circle, the equilateral triangle and the square? +Because, aside from the fact that they are of all plane figures the +most elementary, they are intimately related to the body of man, as +has been shown (Illustration 45), and the body of man is as it were +the architectural archetype. But this simply removes the inquiry to +a different field, it is not an answer. Why is the body of man so +constructed and related? This leads us, as does every question, to +the threshold of a mystery upon which theosophy alone is able to throw +light. Any extended elucidation would be out of place here: it is +sufficient to remind the reader that the circle is the symbol of the +universe; the equilateral triangle, of the higher trinity (_atma, +buddhi, manas_); and the square, of the lower quaternary of man's +sevenfold nature. + +[Illustration 69] + +[Illustration 70] + +The square is principally used in preliminary plotting: it is the +determining figure in many of the palaces of the Italian Renaissance; +the Arc de Triomphe, in Paris is a modern example of its use +(Illustrations 59, 60). The circle is often employed in conjunction +with the square and the triangle. In Thomas Jefferson's Rotunda for +the University of Virginia, a single great circle was the determining +figure, as his original pen sketch of the building shows (Illustration +61). Some of the best Roman triumphal arches submit themselves to a +circular synopsis, and a system of double intersecting circles has +been applied, with interesting results, to faēades as widely different +as those of the Parthenon and the Farnese Palace in Rome, though +it would be fatuous to claim that these figures determined the +proportions of the faēades. + +By far the most important figure in architectural proportion, +considered from the standpoint of geometry, is the equilateral +triangle. It would seem that the eye has an especial fondness for +this figure, just as the ear has for certain related sounds. Indeed it +might not be too fanciful to assert that the common chord of any key +(the tonic with its third and fifth) is the musical equivalent of +the equilateral triangle. It is scarcely necessary to dwell upon +the properties and unique perfection of this figure. Of all regular +polygons it is the simplest: its three equal sides subtend equal +angles, each of 60 degrees; it trisects the circumference of a circle; +it is the graphic symbol of the number three, and hence of every +threefold thing; doubled, its generating arcs form the _vesica +piscis_, of so frequent occurrence in early Christian art; two +symmetrically intersecting equilateral triangles yield the figure +known as "Solomon's Seal," or the "Shield of David," to which mystic +properties have always been ascribed. + +It may be stated as a general rule that whenever three important +points in any architectural composition coincide (approximately or +exactly) with the three extremities of an equilateral triangle, it +makes for beauty of proportion. An ancient and notable example occurs +in the pyramids of Egypt, the sides of which, in their original +condition, are believed to have been equilateral triangles. It is a +demonstrable fact that certain geometrical intersections yield the +important proportions of Greek architecture. The perfect little +Erechtheum would seem to have been proportioned by means of the +equilateral triangle and the angle of 60 degrees, both in general and +in detail (Illustration 62). The same angle, erected from the central +axis of a column at the point where it intersects the architrave, +determines both the projection of the cornice and the height of +the architrave in many of the finest Greek and Roman temples +(Illustrations 67-70). The equilateral triangle used in conjunction +with the circle and the square was employed by the Romans in +determining the proportions of triumphal arches, basilicas and +baths. That the same figure was a factor in the designing of Gothic +cathedrals is sufficiently indicated in the accompanying facsimile +reproductions of an illustration from the Como Vitruvius, published in +Milan in 1521, which shows a vertical section of the Milan cathedral +and the system of equilateral triangles which determined its various +parts (Illustration 71). The _vesica piscis_ was often used to +establish the two main internal dimensions of the cathedral plan: the +greatest diameter of the figure corresponding with the width across +the transepts, the upper apex marking the limit of the apse, and the +lower, the termination of the nave. Such a proportion is seen to be +both subtle and simple, and possesses the advantage of being easily +laid out. The architects of the Italian Renaissance doubtless +inherited certain of the Roman canons of architectural proportion, +for they seem very generally to have recognized them as an essential +principle of design. + +[Illustration 71] + +Nevertheless, when all is said, it is easy to exaggerate the +importance of this matter of geometrical proportion. The designer +who seeks the ultimate secret of architectural harmony in mathematics +rather than in the trained eye, is following the wrong road to +success. A happy inspiration is worth all the formulę in the world--if +it be really happy, the artist will probably find that he has +"followed the rules without knowing them." Even while formulating +concepts of art, the author must reiterate Schopenhauer's dictum +that the _concept_ is unfruitful in art. The mathematical analysis +of spatial beauty is an interesting study, and a useful one to the +artist; but it can never take the place of the creative faculty, it +can only supplement, restrain, direct it. The study of proportion is +to the architect what the study of harmony is to a musician--it helps +his genius adequately to express itself. + + + + +VI + +THE ARITHMETIC OF BEAUTY + + +Although architecture is based primarily upon geometry, it is possible +to express all spatial relations numerically: for arithmetic, not +geometry, is the universal science of quantity. The relation of masses +one to another--of voids to solids, and of heights and lengths to +widths--forms ratios; and when such ratios are simple and harmonious, +architecture may be said, in Walter Pater's famous phrase, to +"aspire towards the condition of music." The trained eye, and not an +arithmetical formula, determines what is, and what is not, beautiful +proportion. Nevertheless the fact that the eye instinctively rejects +certain proportions as unpleasing, and accepts others as satisfactory, +is an indication of the existence of laws of space, based upon number, +not unlike those which govern musical harmony. The secret of the deep +reasonableness of such selection by the senses lies hidden in the very +nature of number itself, for number is the invisible thread on which +the worlds are strung--the universe abstractly symbolized. + +Number is the within of all things--the "first form of Brahman." It +is the measure of time and space; it lurks in the heart-beat and is +blazoned upon the starred canopy of night. Substance, in a state of +vibration, in other words conditioned by number, ceaselessly undergoes +the myriad transmutations which produce phenomenal life. Elements +separate and combine chemically according to numerical ratios: +"Moon, plant, gas, crystal, are concrete geometry and number." By +the Pythagoreans and by the ancient Egyptians sex was attributed to +numbers, odd numbers being conceived of as masculine or generating, +and even numbers as feminine or parturitive, on account of their +infinite divisibility. Harmonious combinations were those +involving the marriage of a masculine and a feminine--an odd and an +even--number. + +[Illustration 72: A GRAPHIC SYSTEM OF NOTATION] + +Numbers progress from unity to infinity, and return again to unity as +the soul, defined by Pythagoras as a self-moving number, goes forth +from, and returns to God. These two acts, one of projection and the +other of recall; these two forces, centrifugal and centripetal, are +symbolized in the operations of addition and subtraction. Within them +is embraced the whole of computation; but because every number, every +aggregation of units, is also a new unit capable of being added +or subtracted, there are also the operations of multiplication and +division, which consists in one case of the addition of several equal +numbers together, and in the other, of the subtraction of several +equal numbers from a greater until that is exhausted. In order to +think correctly it is necessary to consider the whole of numeration, +computation, and all mathematical processes whatsoever as _the +division of the unit_ into its component parts and the establishment +of relations between these parts. + +[Illustration 73] + +[Illustration 74] + +The progression and retrogression of numbers in groups expressed by +the multiplication table gives rise to what may be termed "numerical +conjunctions." These are analogous to astronomical conjunctions: the +planets, revolving around the sun at different rates of speed, and +in widely separated orbits, at certain times come into line with one +another and with the sun. They are then said to be in conjunction. +Similarly, numbers, advancing toward infinity singly and in groups +(expressed by the multiplication table), at certain stages of their +progression come into relation with one another. For example, an +important conjunction occurs in 12, for of a series of twos it is +the sixth, of threes the fourth, of fours the third, and of sixes the +second. It stands to 8 in the ratio of 3:2, and to 9, of 4:3. It is +related to 7 through being the product of 3 and 4, of which numbers 7 +is the sum. The numbers 11 and 13 are not conjunctive; 14 is so in +the series of twos, and sevens; 15 is so in the series of fives and +threes. The next conjunction after 12, of 3 and 4 and their first +multiples, is in 24, and the next following is in 36, which numbers +are respectively the two and three of a series of twelves, each end +being but a new beginning. + +[Illustration 75] + +It will be seen that this discovery of numerical conjunctions consists +merely of resolving numbers into their prime factors, and that a +conjunctive number is a common multiple; but by naming it so, to +dismiss the entire subject as known and exhausted, is to miss a +sense of the wonder, beauty and rhythm of it all: a mental impression +analogous to that made upon the eye by the swift-glancing balls of a +juggler, the evolutions of drilling troops, or the intricate figures +of a dance; for these things are number concrete and animate in time +and space. + +[Illustration 76] + +The truths of number are of all truths the most interior, abstract +and difficult of apprehension, and since knowledge becomes clear and +definite to the extent that it can be made to enter the mind through +the channels of physical sense, it is well to accustom oneself to +conceiving of number graphically, by means of geometrical symbols +(Illustration 72), rather than in terms of the familiar arabic +notation which though admirable for purposes of computation, is of +too condensed and arbitrary a character to reveal the properties of +individual numbers. To state, for example, that 4 is the first square, +and 8 the first cube, conveys but a vague idea to most persons, but if +4 be represented as a square enclosing four smaller squares, and 8 +as a cube containing eight smaller cubes, the idea is apprehended +immediately and without effort. The number 3 is of course the +triangle; the irregular and vital beauty of the number 5 appears +clearly in the heptalpha, or five-pointed star; the faultless symmetry +of 6, its relation to 3 and 2, and its regular division of the circle, +are portrayed in the familiar hexagram known as the Shield of David. +Seven, when represented as a compact group of circles reveals itself +as a number of singular beauty and perfection, worthy of the important +place accorded to it in all mystical philosophy (Illustration 73). It +is a curious fact that when asked to think of any number less than 10, +most persons will choose 7. + +[Illustration 77] + +Every form of art, though primarily a vehicle for the expression and +transmission of particular ideas and emotions, has subsidiary offices, +just as a musical tone has harmonics which render it more sweet. +Painting reveals the nature of color; music, of sound--in wood, +in brass, and in stretched strings; architecture shows forth the +qualities of light, and the strength and beauty of materials. All +of the arts, and particularly music and architecture, portray in +different manners and degrees the truths of number. Architecture does +this in two ways: esoterically as it were in the form of harmonic +proportions; and exoterically in the form of symbols which represent +numbers and groups of numbers. The fact that a series of threes and +a series of fours mutually conjoin in 12, finds an architectural +expression in the Tuscan, the Doric, and the Ionic orders according to +Vignole, for in them all the stylobate is four parts, the entablature +3, and the intermediate column 12 (Illustration 74). The affinity +between 4 and 7, revealed in the fact that they express (very nearly) +the ratio between the base and the altitude of the right-angled +triangle which forms half of an equilateral, and the musical interval +of the diminished seventh, is architecturally suggested in the Palazzo +Giraud, which is four stories in height with seven openings in each +story (Illustration 75). + +[Illustration 78] + +[Illustration 79] + +[Illustration 80] + +[Illustration 81] + +Every building is a symbol of some number or group of numbers, and +other things being equal the more perfect the numbers involved the +more beautiful will be the building (Illustrations 76-82). The numbers +5 and 7--those which occur oftenest--are the most satisfactory because +being of small quantity, they are easily grasped by the eye, and being +odd, they yield a center or axis, so necessary in every architectural +composition. Next in value are the lowest multiples of these numbers +and the least common multiples of any two of them, because the +eye, with a little assistance, is able to resolve them into their +constituent factors. It is part of the art of architecture to +render such assistance, for the eye counts always, consciously or +unconsciously, and when it is confronted with a number of units +greater than it can readily resolve, it is refreshed and rested if +these units are so grouped and arranged that they reveal themselves as +factors of some higher quantity. + +[Illustration 82] + +[Illustration 83: A NUMERICAL ANALYSIS OF GOTHIC TRACERY] + +There is a raison d'źtre for string courses other than to mark the +position of a floor on the interior of a building, and for quoins and +pilasters other than to indicate the presence of a transverse wall. +These sometimes serve the useful purpose of so subdividing a faēade +that the eye estimates the number of its openings without conscious +effort and consequent fatigue (Illustration 82). The tracery of Gothic +windows forms perhaps the highest and finest architectural expression +of number (Illustration 83). Just as thirst makes water more sweet, so +does Gothic tracery confuse the eye with its complexity only the more +greatly to gratify the sight by revealing the inherent simplicity in +which this complexity has its root. Sometimes, as in the case of +the Venetian Ducal Palace, the numbers involved are too great for +counting, but other and different arithmetical truths are portrayed; +for example, the multiplication of the first arcade by 2 in +the second, and this by 3 in the cusped arches, and by 4 in the +quatrefoils immediately above. + +[Illustration 84: NUMERATION IN GROUPS EXPRESSED ARCHITECTURALLY] + +[Illustration 85: ARCHITECTURAL ORNAMENT CONSIDERED AS THE +OBJECTIFICATION OF NUMBER. MULTIPLICATION IN GROUPS OF FIVE; TWO; +THREE; ALTERNATION OF THREE AND SEVEN] + +[Illustration 86] + +Seven is proverbially the perfect number. It is of a quantity +sufficiently complex to stimulate the eye to resolve it, and yet so +simple that it can be analyzed at a glance; as a center with two equal +sides, it is possessed of symmetry, and as the sum of an odd and even +number (3 and 4) it has vitality and variety. All these properties a +work of architecture can variously reveal (Illustration 77). Fifteen, +also, is a number of great perfection. It is possible to arrange the +first 9 numbers in the form of a "magic" square so that the sum of +each line, read vertically, horizontally or diagonally, will be 15. +Thus: + + 4 9 2 = 15 + 3 5 7 = 15 + 8 1 6 = 15 + -- -- -- + 15 15 15 + +Its beauty is portrayed geometrically in the accompanying figure which +expresses it, being 15 triangles in three groups of 5 (Illustration +86). Few arrangements of openings in a faēade better satisfy the eye +than three superimposed groups of five (Illustrations 76-80). May not +one source of this satisfaction dwell in the intrinsic beauty of the +number 15? + +In conclusion, it is perhaps well that the reader be again reminded +that these are the by-ways, and not the highways of architecture: that +the highest beauty comes always, not from beautiful numbers, nor +from likenesses to Nature's eternal patterns of the world, but from +utility, fitness, economy, and the perfect adaptation of means to +ends. But along with this truth there goes another: that in every +excellent work of architecture, in addition to its obvious and +individual beauty, there dwells an esoteric and universal beauty, +following as it does the archetypal pattern laid down by the Great +Architect for the building of that temple which is the world wherein +we dwell. + + + + +VII + +FROZEN MUSIC + + +In the series of essays of which this is the final one, the author has +undertaken to enforce the truth that evolution on any plane and on +any scale proceeds according to certain laws which are in reality only +ramifications of one ubiquitous and ever operative law; that this law +registers itself in the thing evolved, leaving stamped thereon as it +were fossil footprints by means of which it may be known. In the arts +the creative spirit of man is at its freest and finest, and nowhere +among the arts is it so free and so fine as in music. In music +accordingly the universal law of becoming finds instant, direct +and perfect self-expression; music voices the inner nature of the +_will-to-live_ in all its moods and moments; in it form, content, +means and end are perfectly fused. It is this fact which gives +validity to the before quoted saying that all of the arts "aspire +toward the condition of music." All aspire to express the law, but +music, being least encumbered by the leaden burden of materiality, +expresses it most easily and adequately. This being so there is +nothing unreasonable in attempting to apply the known facts of musical +harmony and rhythm to any other art, and since these essays concern +themselves primarily with architecture, the final aspect in which +that art will be presented here is as "frozen music"--ponderable form +governed by musical law. + +Music depends primarily upon the equal and regular division of time +into beats, and of these beats into measures. Over this soundless and +invisible warp is woven an infinitely various melodic pattern, made +up of tones of different pitch and duration arithmetically related +and combined according to the laws of harmony. Architecture, +correspondingly, implies the rhythmical division of space, and +obedience to laws numerical and geometrical. A certain identity +therefore exists between simple harmony in music, and simple +proportion in architecture. By translating the consonant +tone-intervals into number, the common denominator, as it were, of +both arts, it is possible to give these intervals a spatial, and +hence an architectural, expression. Such expression, considered as +proportion only and divorced from ornament, will prove pleasing to +the eye in the same way that its correlative is pleasing to the ear, +because in either case it is not alone the special organ of sense +which is gratified, but the inner Self, in which all senses are one. +Containing within itself the mystery of number, it thrills responsive +to every audible or visible presentment of that mystery. + +[Illustration 87] + +If a vibrating string yielding a certain musical note be stopped in +its center, that is, divided by half, it will then sound the octave +of that note. The numerical ratio which expresses the interval of +the octave is therefore 1:2. If one-third instead of one-half of the +string be stopped, and the remaining two-thirds struck, it will yield +the musical fifth of the original note, which thus corresponds to the +ratio 2:3. The length represented by 3:4 yields the fourth; 4:5 the +major third; and 5:6 the minor third. These comprise the principal +consonant intervals within the range of one octave. The ratios of +inverted intervals, so called, are found by doubling the smaller +number of the original interval as given above: 2:3, the fifth, gives +3:4, the fourth; 4:5, the major third, gives 5:8, the minor sixth; +5:6, the minor third, gives 6:10, or 3:5, the major sixth. + +[Illustration 88: ARCHITECTURE AS HARMONY] + +Of these various consonant intervals the octave, fifth, and major +third are the most important, in the sense of being the most perfect, +and they are expressed by numbers of the smallest quantity, an odd +number and an even. It will be noted that all the intervals above +given are expressed by the numbers 1, 2, 3, 4, 5 and 6, except the +minor sixth (5:8), and this is the most imperfect of all consonant +intervals. The sub-minor seventh, expressed by the ratio 4:7 though +included among the dissonances, forms, according to Helmholtz, a more +perfect consonance with the tonic than does the minor sixth. + +A natural deduction from these facts is that relations of +architectural length and breadth, height and width, to be "musical" +should be capable of being expressed by ratios of quantitively small +numbers, preferably an odd number and an even. Although generally +speaking the simpler the numerical ratio the more perfect the +consonance, yet the intervals of the fifth and major third (2:3 and +4:5), are considered to be more pleasing than the octave (1:2), which +is too obviously a repetition of the original note. From this it is +reasonable to assume (and the assumption is borne out by experience), +that proportions, the numerical ratios of which the eye resolves too +readily, become at last wearisome. The relation should be felt rather +than fathomed. There should be a perception of identity, and also +of difference. As in music, where dissonances are introduced to give +value to consonances which follow them, so in architecture simple +ratios should be employed in connection with those more complex. + +[Illustration 89] + +Harmonics are those tones which sound with, and reinforce any musical +note when it is sounded. The distinguishable harmonics of the tonic +yield the ratios 1:2, 2:3, 3:4, 4:5, and 4:7. A note and its harmonics +form a natural chord. They may be compared to the widening circles +which appear in still water when a stone is dropped into it, for when +a musical sound disturbs the quietude of that pool of silence which +we call the air, it ripples into overtones, which becoming fainter +and fainter, die away into silence. It would seem reasonable to assume +that the combination of numbers which express these overtones, if +translated into terms of space, would yield proportions agreeable +to the eye, and such is the fact, as the accompanying examples +sufficiently indicate (Illustrations 87-90). + +The interval of the sub-minor seventh (4:7), used in this way, in +connection with the simpler intervals of the octave (1:2), and the +fifth (2:3), is particularly pleasing because it is neither too +obvious nor too subtle. This ratio of 4:7 is important for the reason +that it expresses the angle of sixty degrees, that is, the numbers 4 +and 7 represent (very nearly) the ratio between one-half the base and +the altitude of an equilateral triangle: also because they form part +of the numerical series 1, 4, 7, 10, etc. Both are "mystic" numbers, +and in Gothic architecture particularly, proportions were frequently +determined by numbers to which a mystic meaning was attached. +According to Gwilt, the Gothic chapels of Windsor and Oxford are +divided longitudinally by four, and transversely by seven equal parts. +The arcade above the roses in the faēade of the cathedral of Tours +shows seven principal units across the front of the nave, and four in +each of the towers. + +A distinguishing characteristic of the series of ratios which +represent the consonant intervals within the compass of an octave is +that it advances by the addition of 1 to both terms: 1:2, 2:3, +3:4, 4:5, and 5:6. Such a series always approaches unity, just as, +represented graphically by means of parallelograms, it tends toward a +square. Alberti in his book presents a design for a tower showing his +idea for its general proportions. It consists of six stories, in a +sequence of orders. The lowest story is a perfect cube and each of the +other stories is 11-12ths of the story below, diminishing practically +in the proportion of 8, 7, 6, 5, 4, 3, allowing in each case for the +amount hidden by the projection of the cornice below; each order being +accurate as regards column, entablature, etc. It is of interest to +compare this with Ruskin's idea in his _Seven Lamps_, where he takes +the case of a plant called Alisma Plantago, in which the various +branches diminish in the proportion of 7, 6, 5, 4, 3, respectively, +and so carry out the same idea; on which Ruskin observes that +diminution in a building should be after the manner of Nature. + +[Illustration 90: ARCADE OF THE CANCELLERIA] + +It would be a profitless task to formulate exact rules of +architectural proportion based upon the laws of musical harmony. The +two arts are too different from each other for that, and moreover +the last appeal must always be to the eye, and not to a mathematical +formula, just as in music the last appeal is to the ear. Laws there +are, but they discover themselves to the artist as he proceeds, and +are for the most part incommunicable. Rules and formulę are useful and +valuable not as a substitute for inspiration, but as a guide: not as +wings, but as a tail. In this connection perhaps all that is necessary +for the architectural designer to bear in mind is that important +ratios of length and breadth, height and width, to be "musical" should +be expressed by quantitively small numbers, and that if possible they +should obey some simple law of numerical progression. From this basic +simplicity complexity will follow, but it will be an ordered and +harmonious complexity, like that of a tree, or of a symphony. + +[Illustration 91: THE PALAZZO VERZI AT VERONA (LOWER PORTION ONLY). +A COMPOSITION FOUNDED ON THE EQUAL AND REGULAR DIVISION OF SPACE, AS +MUSIC IS FOUNDED ON THE EQUAL AND REGULAR DIVISION OF TIME.] + +[Illustration 92: ARCHITECTURE AS RHYTHM. A DIVISION OF SPACE +CORRESPONDING TO 3/4 AND 4/4 TIME.] + +In the same way that a musical composition implies the division of +time into equal and regular beats, so a work of architecture should +have for its basis some unit of space. This unit should be nowhere too +obvious and may be varied within certain limits, just as musical time +is retarded or accelerated. The underlying rhythm and symmetry will +thus give value and distinction to such variation. Vasari tells how +Brunelleschi. Bramante and Leonardo da Vinci used to work on paper +ruled in squares, describing it as a "truly ingenious thing, and of +great utility in the work of design." By this means they developed +proportions according to a definite scheme. They set to work with a +division of space analogous to the musician's division of time. +The examples given herewith indicate how close a parallel may exist +between music and architecture in this matter of rhythm (Illustrations +91-93). + +[Illustration 93] + +It is a demonstrable fact that musical sounds weave invisible patterns +in the air. Architecture, correspondingly, in one of its aspects, +is geometric pattern made fixed and enduring. What could be more +essentially musical for example than the sea arcade of the Venetian +Ducal Palace? The sand forms traced by sound-waves on a musically +vibrating steel plate might easily suggest architectural ornament did +not the differences of scale and of material tend to confuse the mind. +The architect should occupy himself with identities, not differences. +If he will but bear in mind that architecture is pattern in space, +just as music is pattern in time, he will come to perceive the +essential identity between, say, a Greek rosette and a Gothic +rose-window; an arcade and an egg and dart moulding (Illustration 94). +All architectural forms and arrangements which give enduring pleasure +are in their essence musical. Every well composed faēade makes harmony +in three dimensions; every good roof-line sings a melody against the +sky. + +[Illustration 94: ARCHITECTURE AS PATTERN] + + + + +CONCLUSION + + +In taking leave of the reader at the end of this excursion together +among the by-ways of a beautiful art, the author must needs add a +final word or two touching upon the purpose and scope of these essays. +Architecture (like everything else) has two aspects: it may be viewed +from the standpoint of utility, that is, as construction; or from the +standpoint of expressiveness, that is, as decoration. No attempt has +been made here to deal with its first aspect, and of the second +(which is again twofold), only the universal, not the particular +expressiveness has been sought. The literature of architecture is rich +in works dealing with the utilitarian and constructive side of the +art: indeed, it may be said that to this side that literature is +almost exclusively devoted. This being so, it has seemed worth while +to attempt to show the reverse of the medal, even though it be "tails" +instead of "heads." + +It will be noted that the inductive method has not, in these pages, +been honored by a due observance. It would have been easy to +have treated the subject inductively, amassing facts and drawing +conclusions, but to have done so the author would have been false +to the very principle about which the work came into being. With the +acceptance of the Ancient Wisdom, the inductive method becomes +no longer necessary. Facts are not useful in order to establish a +hypothesis, they are used rather to elucidate a known and accepted +truth. When theosophical ideas shall have permeated the thought of +mankind, this work, if it survives at all, will be chiefly--perhaps +solely--remarkable by reason of the fact that it was among the +first in which the attempt was made again to unify science, art and +religion, as they were unified in those ancient times and among those +ancient peoples when the Wisdom swayed the hearts and minds of men. + + + +***END OF THE PROJECT GUTENBERG EBOOK THE BEAUTIFUL NECESSITY*** + + +******* This file should be named 12648-8.txt or 12648-8.zip ******* + + +This and all associated files of various formats will be found in: +https://www.gutenberg.org/1/2/6/4/12648 + + + +Updated editions will replace the previous one--the old editions +will be renamed. + +Creating the works from public domain print editions means that no +one owns a United States copyright in these works, so the Foundation +(and you!) can copy and distribute it in the United States without +permission and without paying copyright royalties. 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Thus, we do not necessarily +keep eBooks in compliance with any particular paper edition. + +Most people start at our Web site which has the main PG search facility: + + https://www.gutenberg.org + +This Web site includes information about Project Gutenberg-tm, +including how to make donations to the Project Gutenberg Literary +Archive Foundation, how to help produce our new eBooks, and how to +subscribe to our email newsletter to hear about new eBooks. + diff --git a/old/12648-8.zip b/old/12648-8.zip Binary files differnew file mode 100644 index 0000000..372a786 --- /dev/null +++ b/old/12648-8.zip diff --git a/old/12648.txt b/old/12648.txt new file mode 100644 index 0000000..482ae16 --- /dev/null +++ b/old/12648.txt @@ -0,0 +1,2881 @@ +The Project Gutenberg eBook, The Beautiful Necessity, by Claude Fayette +Bragdon + + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + + + + + +Title: The Beautiful Necessity + +Author: Claude Fayette Bragdon + +Release Date: June 18, 2004 [eBook #12648] + +Language: English + +Character set encoding: US-ASCII + + +***START OF THE PROJECT GUTENBERG EBOOK THE BEAUTIFUL NECESSITY*** + + +E-text prepared by Leah Moser and the Project Gutenberg Online Distributed +Proofreading Team + + + +THE BEAUTIFUL NECESSITY + +Seven Essays on Theosophy and Architecture + +by CLAUDE BRAGDON, F.A.I.A. + +MCMXXII + + + + + + + + "Let us build altars to the Beautiful Necessity" + --EMERSON + + + +By the Same Author: + Episodes From An Unwritten History + The Golden Person In The Heart + Architecture And Democracy + A Primer Of Higher Space + Four Dimensional Vistas + Projective Ornament + Oracle + + + + +CONTENTS + + I THE ART OF ARCHITECTURE + + II UNITY AND POLARITY + + III CHANGELESS CHANGE + + IV THE BODILY TEMPLE + + V LATENT GEOMETRY + + VI THE ARITHMETIC OF BEAUTY + + VII FROZEN MUSIC + + CONCLUSION + + + + +PREFACE TO THE SECOND EDITION + + +_The Beautiful Necessity_ was first published in 1910. Save for a slim +volume of privately printed verse it was my first book. I worked hard +on it. Fifteen years elapsed between its beginning and completion; +it was twice published serially--written, rewritten and +tre-written--before it reached its ultimate incarnation in book form. + +Confronted now with the opportunity to revise the text again, I find +myself in the position of a surgeon who feels that the operation he +is called upon to perform may perhaps harm more than it can help. +Prudence therefore prevails over my passion for dissection: warned by +eminent examples, I fear that any injection of my more mature and less +cocksure consciousness into this book might impair its unity--that I +"never could recapture the first fine careless rapture." + +The text stands therefore as originally published save for a few +verbal changes, and whatever reservations I have about it shall +be stated in this preface. These are not many nor important: _The +Beautiful Necessity_ contains nothing that I need repudiate or care to +contradict. + +Its thesis, briefly stated, is that art in all its manifestations is +an expression of the cosmic life, and that its symbols constitute a +language by means of which this life is published and represented. Art +is at all times subject to the _Beautiful Necessity_ of proclaiming +the _world order_. + +In attempting to develop this thesis it was not necessary (nor as +I now think, desirable) to link it up in so definite a manner with +theosophy. The individual consciousness is colored by the particular +medium through which it receives truth, and for me that medium was +theosophy. Though the book might gain a more unprejudiced hearing, +and from a larger audience, by the removal of the theosophic +"color-screen," it shall remain, for its removal now might seem to +imply a loss of faith in the fundamental tenets of theosophy, and such +an implication would not be true. + +The ideas in regard to time and space are those commonly current +in the world until the advent of the Theory of Relativity. To a +generation brought up on Einstein and Ouspensky they are bound to +appear "lower dimensional." Merely to state this fact is to deal +with it to the extent it needs to be dealt with. The integrity of my +argument is not impaired by these new views. + +The one important influence that has operated to modify my opinions +concerning the mathematical basis of the arts of space has been the +discoveries of Mr. Jay Hambidge with regard to the practice of the +Greeks in these matters, as exemplified in their temples and their +ceramics, and named by him _Dynamic Symmetry_. + +In tracing everything back to the logarithmic spiral (which embodies +the principle of extreme and mean ratios) I consider that Mr. Hambidge +has made one of those generalizations which reorganizes the old +knowledge and organizes the new. It would be only natural if in his +immersion in his idea he overworks it, but Mr. Hambidge is a man of +such intellectual integrity and thoroughness of method that he may be +trusted not to warp the facts to fit his theories. The truth of the +matter is that the entire field of research into the mathematics of +Beauty is of such richness that wherever a man plants his metaphysical +spade he is sure to come upon "pay dirt." _The_ _Beautiful Necessity_ +represents the result of my own prospecting; _Dynamic Symmetry_ +represents the result of his. If at any point our findings appear to +conflict, it is less likely that one or the other of us is mistaken +than that each is right from his own point of view. Be that as it may, +I should be the last man in the world to differ from Mr. Hambidge, +for if he convicted me of every conceivable error his work would still +remain the greatest justification and confirmation of my fundamental +contention--that art is an expression of the _world order_ and +is therefore orderly, organic; subject to mathematical law, and +susceptible of mathematical analysis. + +CLAUDE BRAGDON + +Rochester, N.Y. + +April, 1922 + + + + +I + +THE ART OF ARCHITECTURE + + +One of the advantages of a thorough assimilation of what may be called +the theosophic idea is that it can be applied with advantage to every +department of knowledge and of human activity: like the key to a +cryptogram it renders clear and simple that which before seemed +intricate and obscure. Let us apply this key to the subject of art, +and to the art of architecture in particular, and see if by so +doing we may not learn more of art than we knew before, and more of +theosophy too. + +The theosophic idea is that everything is an expression of the +Self--or whatever other name one may choose to give to that immanent +unknown reality which forever hides behind all phenomenal life--but +because, immersed as we are in materiality, our chief avenue of +knowledge is sense perception, a more exact expression of the +theosophic idea would be: Everything is the expression of the Self +in terms of sense. Art, accordingly, is the expression of the Self in +terms of sense. Now though the Self is _one_, sense is not one, but +manifold: and therefore there are _arts_, each addressed to some +particular faculty or group of faculties, and each expressing some +particular quality or group of qualities of the Self. The white light +of Truth is thus broken up into a rainbow-tinted spectrum of Beauty, +in which the various arts are colors, each distinct, yet merging one +into another--poetry into music; painting into decoration; decoration +becoming sculpture; sculpture--architecture, and so on. + +In such a spectrum of the arts each one occupies a definite place, and +all together form a series of which music and architecture are the two +extremes. That such is their relative position may be demonstrated in +various ways. The theosophic explanation involving the familiar idea +of the "pairs of opposites" would be something as follows. According +to the Hindu-Aryan theory, Brahma, that the world might be born, fell +asunder into man and wife--became in other words _name and form_[A] +The two universal aspects of name and form are what philosophers call +the two "modes of consciousness," one of time, and the other of space. +These are the two gates through which ideas enter phenomenal life; the +two boxes, as it were, that contain all the toys with which we play. +Everything, were we only keen enough to perceive it, bears the mark of +one or the other of them, and may be classified accordingly. In such a +classification music is seen to be allied to time, and architecture to +space, because music is successive in its mode of manifestation, and +in time alone everything would occur successively, one thing following +another; while architecture, on the other hand, impresses itself upon +the beholder all at once, and in space alone all things would exist +simultaneously. Music, which is in time alone, without any relation to +space; and architecture, which is in space alone, without any relation +to time, are thus seen to stand at opposite ends of the art spectrum, +and to be, in a sense, the only "pure" arts, because in all the others +the elements of both time and space enter in varying proportion, +either actually or by implication. Poetry and the drama are allied to +music inasmuch as the ideas and images of which they are made up are +presented successively, yet these images are for the most part +forms of space. Sculpture on the other hand is clearly allied to +architecture, and so to space, but the element of _action_, suspended +though it be, affiliates it with the opposite or time pole. Painting +occupies a middle position, since in it space instead of being +actual has become ideal--three dimensions being expressed through +the mediumship of two--and time enters into it more largely than into +sculpture by reason of the greater ease with which complicated action +can be indicated: a picture being nearly always time arrested in +midcourse as it were--a moment transfixed. + +In order to form a just conception of the relation between music and +architecture it is necessary that the two should be conceived of not +as standing at opposite ends of a series represented by a straight +line, but rather in juxtaposition, as in the ancient Egyptian symbol +of a serpent holding its tail in its mouth, the head in this case +corresponding to music, and the tail to architecture; in other words, +though in one sense they are the most-widely separated of the arts, in +another they are the most closely related. + +Music being purely in time and architecture being purely in space, +each is, in a manner and to a degree not possible with any of +the other arts, convertible into the other, by reason of the +correspondence subsisting between intervals of time and intervals of +space. A perception of this may have inspired the famous saying +that architecture is _frozen music_, a poetical statement of a +philosophical truth, since that which in music is expressed by means +of harmonious intervals of time and pitch, successively, after the +manner of time, may be translated into corresponding intervals of +architectural void and solid, height and width. + +In another sense music and architecture are allied. They alone of +all the arts are purely creative, since in them is presented, not +a likeness of some known idea, but _a thing-in-itself_ brought to +a distinct and complete expression of its nature. Neither a musical +composition nor a work of architecture depends for its effectiveness +upon resemblances to natural sounds in the one case, or to natural +forms in the other. Of none of the other arts is this to such a degree +true: they are not so much creative as re-creative, for in them all +the artist takes his subject ready made from nature and presents it +anew according to the dictates of his genius. + +The characteristic differences between music and architecture are the +same as those which subsist between time and space. Now time and space +are such abstract ideas that they can be dealt with best through +their corresponding correlatives in the natural world, for it is a +fundamental theosophic tenet that nature everywhere abounds in such +correspondences; that nature, in its myriad forms, is indeed the +concrete presentment of abstract unities. The energy which everywhere +animates form is a type of time within space; the mind working in +and through the body is another expression of the same thing. +Correspondingly, music is dynamic, subjective, mental, of one +dimension; while architecture is static, objective, physical, of three +dimensions; sustaining the same relation to music and the other +arts as does the human body to the various organs which compose, and +consciousnesses which animate it (it being the reservatory of these +organs and the vehicle of these consciousnesses); and a work of +architecture in like manner may and sometimes does include all of the +other arts within itself. Sculpture accentuates and enriches, painting +adorns, works of literature are stored within it, poetry and the drama +awake its echoes, while music thrills to its uttermost recesses, like +the very spirit of life tingling through the body's fibres. + +Such being the relation between them, the difference in the nature of +the ideas bodied forth in music and in architecture becomes apparent. +Music is interior, abstract, subjective, speaking directly to the soul +in a simple and universal language whose meaning is made personal and +particular in the breast of each listener: "Music alone of all the +arts," says Balzac, "has power to make us live within ourselves." +A work of architecture is the exact opposite of this: existing +principally and primarily for the uses of the body, it is like the +body a concrete organism, attaining to esthetic expression only in +the reconciliation and fulfilment of many conflicting practical +requirements. Music is pure beauty, the voice of the unfettered +and perpetually vanishing soul of things; architecture is that soul +imprisoned in a form, become subject to the law of causality, beaten +upon by the elements, at war with gravity, the slave of man. One is +the Ariel of the arts; the other, Caliban. + +Coming now to the consideration of architecture in its historical +rather than its philosophical aspect, it will be shown how certain +theosophical concepts are applicable here. Of these none is more +familiar and none more fundamental than the idea of reincarnation. By +reincarnation more than mere physical re-birth is meant, for physical +re-birth is but a single manifestation of that universal law of +alternation of state, of animation of vehicles, and progression +through related planes, in accordance with which all things move, +and as it were make music--each cycle complete, yet part of a larger +cycle, the incarnate monad passing through correlated changes, +carrying along and bringing into manifestation in each successive arc +of the spiral the experience accumulated in all preceding states, +and at the same time unfolding that power of the Self peculiar to the +plane in which it is momentarily manifesting. + +This law finds exemplification in the history of architecture in the +orderly flow of the building impulse from one nation and one country +to a different nation and a different country: its new vehicle of +manifestation; also in the continuity and increasing complexity of +the development of that impulse in manifestation; each "incarnation" +summarizing all those which have gone before, and adding some new +factor peculiar to itself alone; each being a growth, a life, with +periods corresponding to childhood, youth, maturity and decadence; +each also typifying in its entirety some single one of these +life-periods, and revealing some special aspect or power of the Self. + +For the sake of clearness and brevity the consideration of only one +of several architectural evolutions will be attempted: that which, +arising in the north of Africa, spread to southern Europe, thence to +the northwest of Europe and to England--the architecture, in short, of +the so-called civilized world. + +This architecture, anterior to the Christian era, may be broadly +divided into three great periods, during which it was successively +practiced by three peoples: the Egyptians, the Greeks and the Romans. +Then intervened the Dark Ages, and a new art arose, the Gothic, which +was a flowering out in stone of the spirit of Christianity. This was +in turn succeeded by the Renaissance, the impulse of which remains +to-day unexhausted. In each of these architectures the peculiar genius +of a people and of a period attained to a beautiful, complete and +coherent utterance, and notwithstanding the considerable intervals +of time which sometimes separated them they succeeded one another +logically and inevitably, and each was related to the one which +preceded and which followed it in a particular and intimate manner. + +The power and wisdom of ancient Egypt was vested in its priesthood, +which was composed of individuals exceptionally qualified by birth +and training for their high office, tried by the severest ordeals +and bound by the most solemn oaths. The priests were honored and +privileged above all other men, and spent their lives dwelling +apart from the multitude in vast and magnificent temples, dedicating +themselves to the study and practice of religion, philosophy, science +and art--subjects then intimately related, not widely separated as +they are now. These men were the architects of ancient Egypt: theirs +the minds which directed the hands that built those time-defying +monuments. + +The rites that the priests practiced centered about what are known +as the Lesser and the Greater Mysteries. These consisted of +representations by means of symbol and allegory, under conditions +and amid surroundings the most awe-inspiring, of those great truths +concerning man's nature, origin and destiny of which the priests--in +reality a brotherhood of initiates and their pupils--were the +custodians. These ceremonies were made the occasion for the initiation +of neophytes into the order, and the advancement of the already +initiated into its successive degrees. For the practice of such rites, +and others designed to impress not the elect but the multitude, the +great temples of Egypt were constructed. Everything about them was +calculated to induce a deep seriousness of mind, and to inspire +feelings of awe, dread and even terror, so as to test the candidate's +fortitude of soul to the utmost. + +The avenue of approach to an Egyptian temple was flanked on both +sides, sometimes for a mile or more, with great stone sphinxes--that +emblem of man's dual nature, the god emerging from the beast. The +entrance was through a single high doorway between two towering +pylons, presenting a vast surface sculptured and painted over with +many strange and enigmatic figures, and flanked by aspiring obelisks +and seated colossi with faces austere and calm. The large court thus +entered was surrounded by high walls and colonnades, but was open +to the sky. Opposite the first doorway was another, admitting to a +somewhat smaller enclosure, a forest of enormous carved and painted +columns supporting a roof through the apertures of which sunshine +gleamed or dim light filtered down. Beyond this in turn were other +courts and apartments culminating in some inmost sacred sanctuary. + +Not alone in their temples, but in their tombs and pyramids and +all the sculptured monuments of the Egyptians, there is the same +insistence upon the sublimity, mystery and awefulness of life, +which they seem to have felt so profoundly. But more than this, the +conscious thought of the masters who conceived them, the buildings of +Egypt give utterance also to the toil and suffering of the thousands +of slaves and captives which hewed the stones out of the heart of the +rock, dragged them long distances and placed them one upon another, so +that these buildings oppress while they inspire, for there is in them +no freedom, no spontaneity, no individuality, but everywhere the felt +presence of an iron conventionality, of a stern immutable law. + +In Egyptian architecture is symbolized the condition of the human soul +awakened from its long sleep in nature, and become conscious at once +of its divine source and of the leaden burden of its fleshy envelope. +Egypt is humanity new-born, bound still with an umbilical cord to +nature, and strong not so much with its own strength as with the +strength of its mother. This idea is aptly symbolized in those +gigantic colossi flanking the entrance to some rock-cut temple, which +though entire are yet part of the living cliff out of which they were +fashioned. + +In the architecture of Greece the note of dread and mystery yields to +one of pure joyousness and freedom. The terrors of childhood have been +outgrown, and man revels in the indulgence of his unjaded appetites +and in the exercise of his awakened reasoning faculties. In Greek art +is preserved that evanescent beauty of youth which, coming but once +and continuing but for a short interval in every human life, is yet +that for which all antecedent states seem a preparation, and of +which all subsequent ones are in some sort an effect. Greece typifies +adolescence, the love age, and so throughout the centuries humanity +has turned to the contemplation of her, just as a man all his life +long secretly cherishes the memory of his first love. + +An impassioned sense of beauty and an enlightened reason characterize +the productions of Greek architecture during its best period. The +perfection then attained was possible only in a nation whereof the +citizens were themselves critics and amateurs of art, one wherein +the artist was honored and his work appreciated in all its beauty +and subtlety. The Greek architect was less bound by tradition and +precedent than was the Egyptian, and he worked unhampered by any +restrictions save such as, like the laws of harmony in music, helped +rather than hindered his genius to express itself--restrictions +founded on sound reason, the value of which had been proved by +experience. + +The Doric order was employed for all large temples, since it possessed +in fullest measure the qualities of simplicity and dignity, the +attributes appropriate to greatness. Quite properly also its formulas +were more fixed than those of any other style. The Ionic order, +the feminine of which the Doric may be considered the corresponding +masculine, was employed for smaller temples; like a woman it was more +supple and adaptable than the Doric, its proportions were more slender +and graceful, its lines more flowing, and its ornament more delicate +and profuse. A freer and more elaborate style than either of these, +infinitely various, seeming to obey no law save that of beauty, was +used sometimes for small monuments and temples, such as the Tower of +the Winds, and the monument of Lysicrates at Athens. + +[Illustration 1] + +Because the Greek architect was at liberty to improve upon the work of +his predecessors if he could, no temple was just like any other, +and they form an ascending scale of excellence, culminating in the +Acropolis group. Every detail was considered not only with relation +to its position and function, but in regard to its intrinsic beauty as +well, so that the merest fragment, detached from the building of which +it formed a part, is found worthy of being treasured in our museums +for its own sake. + +Just as every detail of a Greek temple was adjusted to its position +and expressed its office, so the building itself was made to fit +its site and to show forth its purpose, forming with the surrounding +buildings a unit of a larger whole. The Athenian Acropolis is an +illustration of this: it is an irregular fortified hill, bearing +diverse monuments in various styles, at unequal levels and at +different angles with one another, yet the whole arrangement seems as +organic and inevitable as the disposition of the features of a face. +The Acropolis is an example of the ideal architectural republic +wherein each individual contributes to the welfare of all, and at the +same time enjoys the utmost personal liberty (Illustration 1). + +Very different is the spirit bodied forth in the architecture of +Imperial Rome. The iron hand of its sovereignty encased within the +silken glove of its luxury finds its prototype in buildings which were +stupendous crude brute masses of brick and concrete, hidden within a +covering of rich marbles and mosaics, wrought in beautiful but often +meaningless forms by clever degenerate Greeks. The genius of Rome +finds its most characteristic expression, not in temples to the high +gods, but rather in those vast and complicated structures--basilicas, +amphitheatres, baths--built for the amusement and purely temporal +needs of the people. + +If Egypt typifies the childhood of the race and Greece its beautiful +youth, Republican Rome represents its strong manhood--a soldier filled +with the lust of war and the love of glory--and Imperial Rome its +degeneracy: that soldier become conqueror, decked out in plundered +finery and sunk in sensuality, tolerant of all who minister to his +pleasures but terrible to all who interfere with them. + +The fall of Rome marked the end of the ancient Pagan world. Above +its ruin Christian civilization in the course of time arose. Gothic +architecture is an expression of the Christian spirit; in it is +manifest the reaction from licentiousness to asceticism. Man's +spiritual nature, awakening in a body worn and weakened by +debaucheries, longs ardently and tries vainly to escape. Of some such +mood a Gothic cathedral is the expression: its vaulting, marvelously +supported upon slender shafts by reason of a nicely adjusted +equilibrium of forces; its restless, upward-reaching pinnacles and +spires; its ornament, intricate and enigmatic--all these suggest the +over-strained organism of an ascetic; while its vast shadowy interior +lit by marvelously traceried and jeweled windows, which hold the eyes +in a hypnotic thrall, is like his soul: filled with world sadness, +dead to the bright brief joys of sense, seeing only heavenly visions, +knowing none but mystic raptures. + +Thus it is that the history of architecture illustrates and enforces +the theosophical teaching that everything of man's creating is made in +his own image. Architecture mirrors the life of the individual and of +the race, which is the life of the individual written large in time +and space. The terrors of childhood; the keen interests and appetites +of youth; the strong stern joy of conflict which comes with manhood; +the lust, the greed, the cruelty of a materialized old age--all these +serve but as a preparation for the life of the spirit, in which the +man becomes again as a little child, going over the whole round, but +on a higher arc of the spiral. + +The final, or fourth state being only in some sort a repetition of +the first, it would be reasonable to look for a certain correspondence +between Egyptian and Gothic architecture, and such a correspondence +there is, though it is more easily divined than demonstrated. In +both there is the same deeply religious spirit; both convey, in some +obscure yet potent manner, a sense of the soul being near the surface +of life. There is the same love of mystery and of symbolism; and in +both may be observed the tendency to create strange composite figures +to typify transcendental ideas, the sphinx seeming a blood-brother to +the gargoyle. The conditions under which each architecture flourished +were not dissimilar, for each was formulated and controlled by small +well-organized bodies of sincerely religious and highly enlightened +men--the priesthood in the one case, the masonic guilds in the +other--working together toward the consummation of great undertakings +amid a populace for the most part oblivious of the profound and subtle +meanings of which their work was full. In Mediaeval Europe, as in +ancient Egypt, fragments of the Ancient Wisdom--transmitted in the +symbols and secrets of the cathedral builders--determined much of +Gothic architecture. + +The architecture of the Renaissance period, which succeeded the +Gothic, corresponds again, in the spirit which animates it, to Greek +architecture, which succeeded the Egyptian, for the Renaissance as +the name implies was nothing other than an attempt to revive Classical +antiquity. Scholars writing in what they conceived to be a Classical +style, sculptors modeling Pagan deities, and architects building +according to their understanding of Vitruvian methods succeeded +in producing works like, yet different from the originals they +followed--different because, animated by a spirit unknown to the +ancients, they embodied a new ideal. + +In all the productions of the early Renaissance, "that first +transcendent springtide of the modern world," there is the evanescent +grace and beauty of youth which was seen to have pervaded Greek art, +but it is a grace and beauty of a different sort. The Greek artist +sought to attain to a certain abstract perfection of type; to build +a temple which should combine all the excellencies of every similar +temple, to carve a figure, impersonal in the highest sense, which +should embody every beauty. The artist of the Renaissance on the other +hand delighted not so much in the type as in the variation from it. +Preoccupied with the unique mystery of the individual soul--a sense of +which was Christianity's gift to Christendom--he endeavored to portray +that wherein a particular person is unique and singular. Acutely +conscious also of his own individuality, instead of effacing it he +made his work the vehicle and expression of that individuality. The +history of Renaissance architecture, as Symonds has pointed out, +is the history of a few eminent individuals, each one moulding and +modifying the style in a manner peculiar to himself alone. In the +hands of Brunelleschi it was stern and powerful; Bramante made +it chaste, elegant and graceful; Palladio made it formal, cold, +symmetrical; while with Sansovino and Sammichele it became sumptuous +and bombastic. + +As the Renaissance ripened to decay its architecture assumed more and +more the characteristics which distinguished that of Rome during the +decadence. In both there is the same lack of simplicity and sincerity, +the same profusion of debased and meaningless ornament, and there is +an increasing disposition to conceal and falsify the construction by +surface decoration. + +The final part of this second or modern architectural cycle lies still +in the future. It is not unreasonable to believe that the movement +toward mysticism, of which modern theosophy is a phase and the +spiritualization of science an episode, will flower out into an +architecture which will be in some sort a reincarnation of and a +return to the Gothic spirit, employing new materials, new methods, +and developing new forms to show forth the spirit of the modern world, +without violating ancient verities. + +In studying these crucial periods in the history of European +architecture it is possible to trace a gradual growth or unfolding +as of a plant. It is a fact fairly well established that the Greeks +derived their architecture and ornament from Egypt; the Romans in +turn borrowed from the Greeks; while a Gothic cathedral is a lineal +descendant from a Roman basilica. + +[Illustration 2] + +[Illustration 3] + +The Egyptians in their constructions did little more than to place +enormous stones on end, and pile one huge block upon another. They +used many columns placed close together: the spaces which they spanned +were inconsiderable. The upright or supporting member may be said to +have been in Egyptian architecture the predominant one. A vertical +line therefore may be taken as the simplest and most abstract symbol +of Egyptian architecture (Illustration 2). It remained for the Greeks +fully to develop the lintel. In their architecture the vertical +member, or column, existed solely for the sake of the horizontal +member, or lintel; it rarely stood alone as in the case of an Egyptian +obelisk. The columns of the Greek temples were reduced to those +proportions most consistent with strength and beauty, and the +intercolumnations were relatively greater than in Egyptian examples. +It may truly be said that Greek architecture exhibits the perfect +equality and equipoise of vertical and horizontal elements and these +only, no other factor entering in. Its graphic symbol would therefore +be composed of a vertical and a horizontal line (Illustration 3). The +Romans, while retaining the column and lintel of the Greeks, deprived +them of their structural significance and subordinated them to the +semicircular arch and the semi-cylindrical and hemispherical vault, +the truly characteristic and determining forms of Roman architecture. +Our symbol grows therefore by the addition of the arc of a circle +(Illustration 4). In Gothic architecture column, lintel, arch and +vault are all retained in changed form, but that which more than +anything else differentiates Gothic architecture from any style which +preceded it is the introduction of the principle of an equilibrium of +forces, of a state of balance rather than a state of rest, arrived at +by the opposition of one thrust with another contrary to it. This fact +can be indicated graphically by two opposing inclined lines, and +these united to the preceding symbol yield an accurate abstract of the +elements of Gothic architecture (Illustration 5). + +[Illustration 4] + +[Illustration 5] + +All this is but an unusual application of a familiar theosophic +teaching, namely, that it is the method of nature on every plane and +in every department not to omit anything that has gone before, but to +store it up and carry it along and bring it into manifestation later. +Nature everywhere proceeds like the jingle of _The House that Jack +Built_: she repeats each time all she has learned, and adds another +line for subsequent repetition. + +[Footnote A: The quaint Oriental imagery here employed should not +blind the reader to the precise scientific accuracy of the idea of +which this imagery is the vehicle. Schopenhauer says: "Polarity, or +the sundering of a force into two quantitively different and opposed +activities striving after re-union,... is a fundamental type of almost +all the phenomena of nature, from the magnet and the crystal to man +himself."] + + + + +II + +UNITY AND POLARITY + + +Theosophy, both as a philosophy, or system of thought, which discovers +correlations between things apparently unrelated, and as a life, +or system of training whereby it is possible to gain the power to +perceive and use these correlations for worthy ends, is of great value +to the creative artist, whose success depends on the extent to which +he works organically, conforming to the cosmic pattern, proceeding +rationally and rhythmically to some predetermined end. It is of value +no less to the layman, the critic, the art amateur--to anyone in +fact who would come to an accurate and intimate understanding and +appreciation of every variety of esthetic endeavor. For the benefit of +such I shall try to trace some of those correlations which theosophy +affirms, and indicate their bearing upon art, and upon the art of +architecture in particular. + +One of the things which theosophy teaches is that those transcendent +glimpses of a divine order and harmony throughout the universe +vouchsafed the poet and the mystic in their moments of vision are not +the paradoxes--the paronomasia as it were--of an intoxicated state of +consciousness, but glimpses of reality. We are all of us participators +in a world of concrete music, geometry and number--a world of +sounds, odors, forms, motions, colors, so mathematically related and +coordinated that our pigmy bodies, equally with the farthest star, +vibrate to the music of the spheres. There is a _Beautiful Necessity_ +which rules the world, which is a law of nature and equally a law of +art, for art is idealized creation: nature carried to a higher power +by reason of its passage through a human consciousness. Thought and +emotion tend to crystallize into forms of beauty as inevitably as does +the frost on a window pane. Art therefore in one of its aspects is the +weaving of a pattern, the communication of an order and a method to +the material or medium employed. Although no masterpiece was ever +created by the conscious following to set rules, for the true artist +works unconsciously, instinctively, as the bird sings or as the bee +builds its honey-cell, yet an analysis of any masterpiece reveals the +fact that its author (like the bird and the bee) has "followed the +rules without knowing them." + +Helmholtz says, "No doubt is now entertained that beauty is subject +to laws and rules dependent on the nature of human intelligence. The +difficulty consists in the fact that these laws and rules, on whose +fulfilment beauty depends, are not consciously present in the mind of +the artist who creates the work, or of the observer who contemplates +it." Nevertheless they are discoverable, and can be formulated, +after a fashion. We have only to read aright the lessons everywhere +portrayed in the vast picture-books of nature and of art. + +The first truth therein published is the law of _Unity_--oneness; for +there is one Self, one Life, which, myriad in manifestation, is yet +in essence ever _one_. Atom and universe, man and the world--each is +a unit, an organic and coherent whole. The application of this law to +art is so obvious as to be almost unnecessary of elucidation, for to +say that a work of art must possess unity, must seem to proceed from a +single impulse and be the embodiment of one dominant idea, is to state +a truism. In a work of architecture the cooerdination of its various +parts with one another is almost the measure of its success. We +remember any masterpiece--the cathedral of Paris no less than the +pyramids of Egypt--by the singleness of its appeal; complex it may be, +but it is a coordinated complexity; variety it may possess, but it is +a variety in an all-embracing unity. + +The second law, not contradicting but supplementing the first is the +law of _Polarity_, i.e., duality. All things have sex, are either +masculine or feminine. This too is the reflection on a lower plane +of one of those transcendental truths taught by the Ancient Wisdom, +namely that the Logos, in his voluntarily circumscribing his infinite +life in order that he may manifest, encloses himself within his +limiting veil, _maya_, and that his life appears as spirit (male), and +his _maya_ as matter (female), the two being never disjoined during +manifestation. The two terms of this polarity are endlessly repeated +throughout nature: in sun and moon, day and night, fire and water, man +and woman--and so on. A close inter-relation is always seen to subsist +between corresponding members of such pairs of opposites: sun, day, +fire, man express and embody the primal and active aspect of the +manifesting deity; moon, night, water, woman, its secondary and +passive aspect. Moreover, each implies or brings to mind the others +of its class: man, like the sun, is lord of day; he is like fire, a +devastating force; woman is subject to the lunar rhythm; like water, +she is soft, sinuous, fecund. + +The part which this polarity plays in the arts is important, and the +constant and characteristic distinction between the two terms is a +thing far beyond mere contrast. + +In music they are the major and minor modes: the typical, or +representative chords of the dominant seventh, and of the tonic (the +two chords into which Schopenhauer says all music can be resolved): a +partial dissonance, and a consonance: a chord of suspense, and a chord +of satisfaction. In speech the two are vowel, and consonant sounds: +the type of the first being _a_, a sound of suspense, made with the +mouth open; and of the second _m_, a sound of satisfaction, made by +closing the mouth; their combination forms the sacred syllable Om +(_Aum_). In painting they are warm colors, and cold: the pole of +the first being in red, the color of fire, which excites; and of the +second in blue, the color of water, which calms; in the Arts of design +they are lines straight (like fire), and flowing (like water); masses +light (like the day), and dark (like night). In architecture they are +the column, or vertical member, which resists the force of gravity; +and the lintel, or horizontal member, which succumbs to it; they are +vertical lines, which are aspiring, effortful; and horizontal lines, +which are restful to the eye and mind. + +It is desirable to have an instant and keen realization of this sex +quality, and to make this easier some sort of classification and +analysis must be attempted. Those things which are allied to and +partake of the nature of _time_ are masculine, and those which are +allied to and partake of the nature of _space_ are feminine: as +motion, and matter; mind, and body; etc. The English words "masculine" +and "feminine" are too intimately associated with the idea of physical +sex properly to designate the terms of this polarity. In Japanese +philosophy and art (derived from the Chinese) the two are called _In_ +and _Yo_ (In, feminine; Yo, masculine); and these little words, being +free from the limitations of their English correlatives, will be found +convenient, Yo to designate that which is simple, direct, primary, +active, positive; and In, that which is complex, indirect, derivative, +passive, negative. Things hard, straight, fixed, vertical, are Yo; +things soft, curved, horizontal, fluctuating, are In--and so on. + +[Illustration 6: WILD CHERRY; MAPLE LEAF] + +[Illustration 7: CALLAS IN YO] + +In passing it may be said that the superiority of the line, mass, and +color composition of Japanese prints and kakemonos to that exhibited +in the vastly more pretentious easel pictures of modern Occidental +artists--a superiority now generally acknowledged by connoisseurs--is +largely due to the conscious following, on the part of the Japanese, +of this principle of sex-complementaries. + +Nowhere are In and Yo more simply and adequately imaged than in the +vegetable kingdom. The trunk of a tree is Yo, its foliage, In; and +in each stem and leaf the two are repeated. A calla, consisting of +a single straight and rigid spadix embraced by a soft and tenderly +curved spathe, affords an almost perfect expression of the +characteristic differences between Yo and In and their reciprocal +relation to each other. The two are not often combined in such +simplicity and perfection in a single form. The straight, vertical +reeds which so often grow in still, shallow water, find their +complement in the curved lily-pads which lie horizontally on its +surface. Trees such as pine and hemlock, which are excurrent--those in +which the branches start successively (i.e., after the manner of time) +from a straight and vertical central stem--are Yo; trees such as +the elm and willow, which are deliquescent--those in which the trunk +dissolves as it were simultaneously (after the manner of space) into +its branches--are In. All tree forms lie in or between these two +extremes, and leaves are susceptible of a similar classification. It +will be seen to be a classification according to time and space, +for the characteristic of time is _succession_, and of space, +_simultaneousness_: the first is expressed symbolically by elements +arranged with relation to axial lines; the second, by elements +arranged with relation to focal points (Illustrations 6,7). + +The student should train himself to recognize In and Yo in all +their Protean presentments throughout nature--in the cloud upon the +mountain, the wave against the cliff, in the tracery of trees against +the sky--that he may the more readily recognize them in his chosen +art, whatever that art may be. If it happens to be painting, he will +endeavor to discern this law of duality in the composition of every +masterpiece, recognizing an instinctive obedience to it in that +favorite device of the great Renaissance masters of making an +architectural setting for their groups of figures, and he will +delight to trace the law in all its ramifications of contrast between +complementaries in line, color, and mass (Illustration 8). + +[Illustration 8: THE LAW OF POLARITY CLEOPATRA MELTING THE PEARL. BY +TIEPOLO] + +With reference to architecture, it is true, generally speaking, +that architectural forms have been developed through necessity, the +function seeking and finding its appropriate form. For example, the +buttress of a Gothic cathedral was developed by the necessity of +resisting the thrust of the interior vaulting without encroaching upon +the nave; the main lines of a buttress conform to the direction of the +thrust, and the pinnacle with which it terminates is a logical shape +for the masonry necessary to hold the top in position (Illustration +9). Research along these lines is interesting and fruitful of result, +but there remains a certain number of architectural forms whose origin +cannot be explained in any such manner. The secret of their undying +charm lies in the fact that in them In and Yo stand symbolized and +contrasted. They no longer obey a law of utility, but an abstract +law of beauty, for in becoming sexually expressive as it were, the +construction itself is sometimes weakened or falsified. The familiar +classic console or modillion is an example: although in general +contour it is well adapted to its function as a supporting bracket, +embedded in, and projecting from a wall, yet the scroll-like ornament +with which its sides are embellished gives it the appearance of +not entering the wall at all, but of being stuck against it in some +miraculous manner. This defect in functional expressiveness is +more than compensated for by the perfection with which feminine +and masculine characteristics are expressed and contrasted in the +exquisite double spiral, opposed to the straight lines of the moulding +which it subtends (Illustration 10). Again, by fluting the shaft of a +column its area of cross-section is diminished but the appearance of +strength is enhanced because its masculine character--as a supporting +member resisting the force of gravity--is emphasized. + +[Illustration 9: CROSS SECTION OF BUTTRESS.] + +The importance of the so-called "orders" lies in the fact that they +are architecture epitomized as it were. A building consists of a wall +upholding a roof: support and weight. The type of the first is the +column, which may be conceived of as a condensed section of wall; and +of the second, the lintel, which may be conceived of as a condensed +section of roof. The column, being vertical, is Yo; the lintel, being +horizontal, is In. To mark an entablature with horizontal lines in the +form of mouldings, and the columns with vertical lines in the form +of flutes, as is done in all the "classic orders," is a gain +in functional and sex expressiveness, and consequently in art +(Illustration 11). + +[Illustration 10: CORINTHIAN MODILLION; CLASSIC CONSOLE; IONIC CAP] + +The column is again divided into the shaft, which is Yo; and the +capital, which is In. The capital is itself twofold, consisting of a +curved member and an angular member. These two appear in their utmost +simplicity in the _echinus_ (In) and the _abacus_ (Yo) of a +Greek Doric cap. The former was adorned with painted leaf forms, +characteristically feminine, and the latter with the angular fret +and meander (Illustration 12). The Ionic capital, belonging to a more +feminine style, exhibits the abacus subordinated to that beautiful +cushion-shaped member with its two spirally marked volutes. This, +though a less rational and expressive form for its particular office +than is the echinus of the Doric cap, is a far more perfect symbol of +the feminine element in nature. There is an essential identity between +the Ionic cap and the classic console before referred to--although +superficially the two do not resemble each other--for a straight line +and a double spiral are elements common to both (Illustration 10). +The Corinthian capital consists of an ordered mass of delicately +sculptured leaf and scroll forms sustaining an abacus which though +relatively masculine is yet more curved and feminine than that of any +other style. In the caulicole of a Corinthian cap In and Yo are again +contrasted. In the unique and exquisite capital from the Tower of the +Winds at Athens, the two are well suggested in the simple, erect, and +pointed leaf forms of the upper part, contrasted with the complex, +deliquescent, rounded ones from which they spring. The essential +identity of principle subsisting between this cap and the Renaissance +baluster by San Gallo is easily seen (Illustration 13). + +[Illustration 11] + +[Illustration 12] + +This law of sex-expressiveness is of such universality that it can +be made the basis of an analysis of the architectural ornament of any +style or period. It is more than mere opposition and contrast. The egg +and tongue motif, which has persisted throughout so many centuries and +survived so many styles, exhibits an alternation of forms resembling +phallic emblems. Yo and In are well suggested in the channeled +triglyphs and the sculptured metopes of a Doric frieze, in the +straight and vertical mullions and the flowing tracery of Gothic +windows, in the banded torus, the bead and reel, and other familiar +ornamented mouldings (Illustrations 14, 15, 16). + +There are indications that at some time during the development +of Gothic architecture in France, this sex-distinction became a +recognized principle, moulding and modifying the design of a cathedral +in much the same way that sex modifies bodily structure. The masonic +guilds of the Middle Ages were custodians of the esoteric--which is +the theosophic--side of the Christian faith, and every student of +esotericism knows how fundamental and how far-reaching is this idea of +sex. + +[Illustration 13: CAPITAL FROM THE TOWER OF THE WINDS, ATHENS; +CORINTHIAN CAP FROM HADRIAN BUILDINGS, ATHENS; ROSETTE FROM TEMPLE OF +MARS, ROME; CAULICULUS OF CORINTHIAN CAP; BULUSTER BY SAN GALLO] + +[Illustration 14: EGG AND TONGUE; BEAD AND REEL; BANDED TORUS] + +The entire cathedral symbolized the crucified body of Christ; its two +towers, man and woman--that Adam and that Eve for whose redemption +according to current teaching Christ suffered and was crucified. The +north or right-hand tower ("the man's side") was called the sacred +male pillar, Jachin; and the south, or left-hand tower ("the woman's +side"), the sacred female pillar, Boaz, from the two columns flanking +the gate to Solomon's Temple--itself an allegory to the bodily temple. +In only a few of the French cathedrals is this distinction clearly +and consistently maintained, and of these Tours forms perhaps the most +remarkable example, for in its flamboyant facade, over and above the +difference in actual breadth and apparent sturdiness of the two towers +(the south being the more slender and delicate), there is a clearly +marked distinction in the character of the ornamentation, that of the +north tower being more salient, angular, radial--more masculine in +point of fact (Illustration 17). In Notre Dame, the cathedral of +Paris, as in the cathedral of Tours, the north tower is perceptibly +broader than the south. The only other important difference appears to +be in the angular label-mould above the north entrance: whatever may +have been its original function or significance, it serves to define +the tower sexually, so to speak, as effectively as does the beard on +a man's face. In Amiens the north tower is taller than the south, and +more massive in its upper stages. The only traceable indication of +sex in the ornamentation occurs in the spandrels at the sides of the +entrance arches: those of the north tower containing single circles, +and those of the south tower containing two in one. This difference, +small as it may seem, is significant, for in Europe during the Middle +Ages, just as anciently in Egypt and again in Greece--in fact wherever +and whenever the Secret Doctrine was known--sex was attributed to +numbers, odd numbers being conceived of as masculine, and even, as +feminine. Two, the first feminine number, thus became a symbol of +femininity, accepted as such so universally at the time the cathedrals +were built, that two strokes of a bell announced the death of a woman, +three, the death of a man. + +[Illustration 15: FRIEZE OF THE FARNESE PALACE; ROMAN CONSOLE. VATICAN +MUSEUM; FRIEZE IN THE EMPIRE STYLE BY PERCIER AND FONTAINE. +FRIEZE FROM THE TEMPLE OF VESTA AT TIVOLI. (ROMAN); ROMAN DORIC +FRIEZE--VIGNOLE] + +[Illustration 16] + +[Illustration 17] + +The vital, organic quality so conspicuous in the best Gothic +architecture has been attributed to the fact that necessity determined +its characteristic forms. Professor Goodyear has demonstrated that +it may be due also in part to certain subtle vertical leans and +horizontal bends; and to nicely calculated variations from strict +uniformity, which find their analogue in nature, where structure is +seldom rigidly geometrical. The author hazards the theory that still +another reason why a Gothic cathedral seems so living a thing is +because it abounds in contrasts between what, for lack of more +descriptive adjectives, he is forced to call masculine and feminine +forms. + +[Illustration 18] + +[Illustration 19] + +Ruskin says, in _Stones of Venice_, "All good Gothic is nothing more +than the development, in various ways, and on every conceivable scale, +of the group formed by the pointed arch for the bearing line below, +and the gable for the protecting line above, and from the huge, gray, +shaly slope of the cathedral roof, with its elastic pointed vaults +beneath, to the crown-like points that enrich the smallest niche of +its doorway, one law and one expression will be found in all. The +modes of support and of decoration are infinitely various, but the +real character of the building, in all good Gothic, depends on the +single lines of the gable over the pointed arch endlessly rearranged +and repeated." These two, an angular and a curved form, like the +everywhere recurring column and lintel of classic architecture, +are but presentments of Yo and In (Illustration 18). Every Gothic +traceried window, with straight and vertical mullions in the +rectangle, losing themselves in the intricate foliations of the arch, +celebrates the marriage of this ever diverse pair. The circle and the +triangle are the In and Yo of Gothic tracery, its Eve and Adam, as +it were, for from their union springs that progeny of trefoil, +quatrefoil, cinquefoil, of shapes flowing like water, and shapes +darting like flame, which makes such visible music to the entranced +ear. + +[Illustration 20: SAN GIMIGNANO S. JACOPO.] + +By seeking to discover In and Yo in their myriad manifestations, by +learning to discriminate between them, and by attempting to express +their characteristic qualities in new forms of beauty--from +the disposition of a facade to the shaping of a moulding--the +architectural designer will charge his work with that esoteric +significance, that excess of beauty, by which architecture rises +to the dignity of a "fine" art (Illustrations 19, 20). In so doing, +however, he should never forget, and the layman also should ever +remember, that the supreme architectural excellence is fitness, +appropriateness, the perfect adaptation of means to ends, and the +adequate expression of both means and ends. These two aims, the one +abstract and universal, the other concrete and individual, can always +be combined, just as in every human countenance are combined a type, +which is universal, and a character, which is individual. + + + + +III + +CHANGELESS CHANGE + +TRINITY, CONSONANCE, DIVERSITY IN MONOTONY, BALANCE, RHYTHMIC CHANGE, +RADIATION + + +The preceding essay was devoted for the most part to that "inevitable +duality" which finds concrete expression in countless pairs of +opposites, such as day and night, fire and water, man and woman; +in the art of music by two chords, one of suspense and the other of +fulfilment; in speech by vowel and consonant sounds, epitomized in _a_ +and in _m_; in painting by warm colors and cold, epitomized in red +and blue; in architecture by the vertical column and the horizontal +lintel, by void and solid--and so on. + + +TRINITY + +This concept should now be modified by another, namely, that in every +duality a third is latent; that two implies three, for each sex so +to speak is in process of becoming the other, and this alternation +engenders and is accomplished by means of a third term or neuter, +which is like neither of the original two but partakes of the nature +of them both, just as a child may resemble both its parents. Twilight +comes between day and night; earth is the child of fire and water; +in music, besides the chord of longing and striving, and the chord of +rest and satisfaction (the dominant seventh and the tonic), there is +a third or resolving chord in which the two are reconciled. In the +sacred syllable Om (_Aum_), which epitomizes all speech, the _u_ sound +effects a transition between the _a_ sound and the _m_; among the +so-called primary colors yellow comes between red and blue; and in +architecture the arch, which is both weight and support, which is +neither vertical nor horizontal, may be considered the neuter of the +group of which the column and the lintel are respectively masculine +and feminine. "These are the three," says Mr. Louis Sullivan, "the +only three letters from which has been expanded the architectural art, +as a great and superb language wherewith man has expressed, through +the generations, the changing drift of his thoughts." + +[Illustration 21: THE LAW OF TRINITY. A ROMAN IONIC ARCADE, BY +VIGNOLE.--THE COLUMN, THE ENTABLATURE, AND THE ARCH CORRESPOND TO LINES +VERTICAL, HORIZONTAL AND CURVED.] + +It would be supererogatory to dwell at any length on this "trinity +of manifestation" as the concrete expression of that unmanifest and +mystical trinity, that _three-in-one_ which under various names occurs +in every world-religion, where, defying definition, it was wont +to find expression symbolically in some combination of vertical, +horizontal and curved lines. The anstated cross of the Egyptians +is such a symbol, the Buddhist wheel, and the fylfot or swastika +inscribed within a circle, also those numerous Christian symbols +combining the circle and the cross. Such ideographs have spelled +profound meaning to the thinkers of past ages. We of to-day are not +given to discovering anything wonderful in three strokes of a pen, +but every artist in the weaving of his pattern must needs employ these +mystic symbols in one form or another, and if he employs them with +a full sense of their hidden meaning his work will be apt to gain +in originality and beauty--for originality is a new and personal +perception of beauty, and beauty is the name we give to truth we +cannot understand. + +In architecture, this trinity of vertical, horizontal and curved +lines finds admirable illustration in the application of columns and +entablature to an arch and impost construction, so common in Roman and +Renaissance work. This is a redundancy, and finds no justification in +reason, because the weight is sustained by the arch, and the "order" +is an appendage merely; yet the combination, illogical as it is, +satisfies the sense of beauty because the arch effects a transition +between the columns and the entablature, and completes the trinity +of vertical, horizontal and curved lines (Illustration 21). In the +entrances to many of the Gothic cathedrals and churches the same +elements are better because more logically disposed. Here the +horizontal lintel and its vertical supports are not decorative merely, +but really perform their proper functions, while the arch, too, has +a raison d'etre in that it serves to relieve the lintel of the +superincumbent weight of masonry. The same arrangement sometimes +occurs in classic architecture also, as when an opening spanned by a +single arch is subdivided by means of an order (Illustration 22). + +Three is pre-eminently the number of architecture, because it is the +number of space, which for us is three-dimensional, and of all the +arts architecture is most concerned with the expression of spatial +relations. The division of a composition into three related parts is +so universal that it would seem to be the result of an instinctive +action of the human mind. The twin pylons of an Egyptian temple with +its entrance between, for a third division, has its correspondence in +the two towers of a Gothic cathedral and the intervening screen +wall of the nave. In the palaces of the Renaissance a threefold +division--vertically by means of quoins or pilasters, and horizontally +by means of cornices or string courses--was common, as was also the +division into a principal and two subordinate masses (Illustration +23). + +[Illustration 22: THE LAW OF TRINITY. THE TRINITY OF HORIZONTAL VERTICAL +AND CURVED LINES.] + +The architectural "orders" are divided threefold into pedestal or +stylobate, column and entablature; and each of these is again divided +threefold: the first into plinth, die and cornice; the second into +base, shaft and capital; the third into architrave, frieze and +cornice. In many cases these again lend themselves to a threefold +subdivision. A more detailed analysis of the capitals already shown to +be twofold reveals a third member: in the Greek Doric this consists +of the annulets immediately below the abacus; in the other orders, the +necking which divides the shaft from the cap. + + +CONSONANCE + +"As is the small, so is the great" is a perpetually recurring phrase +in the literature of theosophy, and naturally so, for it is a succinct +statement of a fundamental and far-reaching truth. The scientist +recognizes it now and then and here and there, but the occultist +trusts it always and utterly. To him the microcosm and the macrocosm +are one and the same in essence, and the forth-going impulse +which calls a universe into being and the indrawing impulse which +extinguishes it again, each lasting millions of years, are echoed and +repeated in the inflow and outflow of the breath through the nostrils, +in nutrition and excretion, in daily activity and nightly rest, in +that longer day which we name a lifetime, and that longer rest in +_Devachan_--and so on until time itself is transcended. + +[Illustration 23] + +In the same way, in nature, a thing is echoed and repeated throughout +its parts. Each leaf on a tree is itself a tree in miniature, each +blossom a modified leaf; every vertebrate animal is a complicated +system of spines; the ripple is the wave of a larger wave, and that +larger wave is a part of the ebbing and flowing tide. In music this +law is illustrated in the return of the tonic to itself in the octave, +and its partial return in the dominant; also in a more extended sense +in the repetition of a major theme in the minor, or in the treble and +again in the bass, with modifications perhaps of time and key. In +the art of painting the law is exemplified in the repetition with +variation of certain colors and combinations of lines in different +parts of the same picture, so disposed as to lead the eye to some +focal point. Every painter knows that any important color in his +picture must be echoed, as it were, in different places, for harmony +of the whole. + +[Illustration 24] + +In the drama the repetition of a speech or of an entire scene, but +under circumstances which give it a different meaning, is often most +effective, as when Gratiano, in the trial scene of _The Merchant +of Venice_ taunts Shylock with his own words, "A Daniel come to +judgment!" or, as when in one of the later scenes of _As You Like It_ +an earlier scene is repeated, but with Rosalind speaking in her proper +person and no longer as the boy Ganymede. + +These recurrences, these inner consonances, these repetitions with +variations are common in architecture also. The channeled triglyphs of +a Greek Doric frieze echo the fluted columns below (Illustration 24). +The balustrade which crowns a colonnade is a repetition, in some sort, +of the colonnade itself. The modillions of a Corinthian cornice are +but elaborated and embellished dentils. Each pinnacle of a Gothic +cathedral is a little tower with its spire. As Ruskin has pointed out, +the great vault of the cathedral nave, together with the pointed roof +above it, is repeated in the entrance arch with its gable, and the +same two elements appear in every statue-enshrining niche of the +doorway. In classic architecture, as has been shown, instead of the +arch and gable, the column and entablature everywhere recur under +different forms. The minor domes which flank the great dome of the +cathedral of Florence enhance and reinforce the latter, and prepare +the eye for a climax which would otherwise be too abrupt. The central +pavilion of the Chateau Maintenon, with its two turrets, echoes the +entire facade with its two towers. Like the overture to an opera, it +introduces themes which find a more extended development elsewhere +(Illustration 26). + +[Illustration 25] + +[Illustration 26] + +[Illustration 27] + +This law of Consonance is operative in architecture more obscurely +in the form of recurring numerical ratios, identical geometrical +determining figures, parallel diagonals and the like, which will be +discussed in a subsequent essay. It has also to do with style and +scale, the adherence to substantially one method of construction and +manner of ornament, just as in music the key, or chosen series of +notes, may not be departed from except through proper modulations, or +in a specific manner. + +Thus it is seen that in a work of art, as in a piece of tapestry, +the same thread runs through the web, but goes to make up different +figures. The idea is deeply theosophic: one life, many manifestations; +hence, inevitably, echoes, resemblances--_Consonance_. + + +DIVERSITY IN MONOTONY + +Another principle of natural beauty, closely allied to the foregoing, +its complement as it were, is that of _Diversity in Monotony_--not +identity, but difference. It shows itself for the most part as a +perceptible and piquant variation between individual units belonging +to the same class, type, or species. + +No two trees put forth their branches in just the same manner, and no +two leaves from the same tree exactly correspond; no two persons +look alike, though they have similiar members and features; even the +markings on the skin of the thumb are different in every human hand. +Browning says, + + "As like as a hand to another hand! + Whoever said that foolish thing, + Could not have studied to understand--" + +Now every principle of natural beauty is but the presentment of some +occult law, some theosophical truth; and this law of Diversity in +Monotony is the presentment of the truth that identity does not +exclude difference. The law is binding, yet the will is free: all men +are brothers united by the ties of brotherhood, yet each is unique, a +free agent, and never so free as when most bound by the Good Law. This +truth nature beautifully proclaims, and art also. In architecture it +is admirably exemplified in the metopes of the Parthenon frieze: seen +at a distance these must have presented a scarcely distinguishable +texture of sunlit marble and cool shadow, yet in reality each is +a separate work of art. So with the capitals of the columns of the +wonderful sea-arcade of the Venetian Ducal palace: alike in general +contour they differ widely in detail, and unfold a Bible story. +In Gothic cathedrals, in Romanesque monastery cloisters, a teeming +variety of invention is hidden beneath apparent uniformity. The +gargoyles of Notre Dame make similiar silhouettes against the sky, +but seen near at hand what a menagerie of monsters! The same spirit of +controlled individuality, of liberty subservient to the law of all, is +exemplified in the bases of the columns of the temple of Apollo near +Miletus--each one a separate masterpiece of various ornamentation +adorning an established architectural form (Illustration 28). + +[Illustration 28] + +[Illustration 29] + +The builders of the early Italian churches, instinctively obeying this +law of Diversity in Monotony, varied the size of the arches in the +same arcade (Illustration 29), and that this was an effect of art and +not of accident or carelessness Ruskin long ago discovered, and the +Brooklyn Institute surveys have amply confirmed his view. Although +by these means the builders of that day produced effects of deceptive +perspective, of subtle concord and contrast, their sheer hatred of +monotony and meaningless repetition may have led them to diversify +their arcades in the manner described, for a rigidly equal and regular +division lacks interest and vitality. + + +BALANCE + +If one were to establish an axial plane vertically through the center +of a tree, in most cases it would be found that the masses of foliage, +however irregularly shaped on either side of such an axis, just about +balanced each other. Similarly, in all our bodily movements, for every +change of equilibrium there occurs an opposition and adjustment of +members of such a nature that an axial plane through the center of +gravity would divide the body into two substantially equal masses, +as in the case of the tree. This physical plane law of Balance +shows itself for the most part on the human plane as the law of +Compensation, whereby, to the vision of the occultist, all accounts +are "squared," so to speak. It is in effect the law of Justice, aptly +symbolized by the scales. + +The law of Balance finds abundant illustration in art: in music by +the opposition, the answering, of one phrase by another of the same +elements and the same length, but involving a different sequence of +intervals; in painting by the disposition of masses in such a way that +they about equalize one another, so that there is no sense of "strain" +in the composition. + +In architecture the common and obvious recognition of the law of +Balance is in the symmetrical disposition of the elements, whether of +plan or of elevation, on either side of axial lines. A far more subtle +and vital illustration of the law occurs when the opposed elements do +not exactly match, but differ from each other, as in the case of the +two towers of Amiens, for example. This sort of balance may be said to +be characteristic of Gothic, as symmetry is characteristic of Classic, +architecture. + + +RHYTHMIC CHANGE + +There is in nature a universal tendency toward refinement and +compactness of form in space, or contrariwise, toward increment +and diffusion; and this manifests itself in time as acceleration or +retardation. It is governed, in either case, by an exact mathematical +law, like the law of falling bodies. It shows itself in the widening +circles which appear when one drops a stone into still water, in the +convolutions of shells, in the branching of trees and the veining +of leaves; the diminution in the size of the pipes of an organ +illustrates it, and the spacing of the frets of a guitar. More and +more science is coming to recognize, what theosophy affirms, that the +spiral vortex, which so beautifully illustrates this law, both in its +time and its space aspects is the universal archetype, the pattern of +all that is, has been, or will be, since it is the form assumed by the +ultimate physical atom, and the ultimate physical atom is the physical +cosmos in miniature. + +This Rhythmic Diminution is everywhere: it is in the eye itself, for +any series of mathematically equal units, such for example as the +columns and intercolumnations of a colonnade, become when seen +in perspective rhythmically unequal, diminishing according to the +universal law. The entasis of a Classic column is determined by this +law, the spirals of the Ionic volute, the annulets of the Parthenon +cap, obey it (Illustration 30). + +In recognition of the same principle of Rhythmic Diminution a building +is often made to grow, or appear to grow lighter, more intricate, +finer, from the ground upward, an end attained by various devices, +one of the most common being the employment of the more attenuated +and highly ornamented orders above the simpler and sturdier, as in the +Roman Colosseum, or in the Palazzo Uguccioni, in Florence--to mention +only two examples out of a great number. In the Riccardi Palace +an effect of increasing refinement is obtained by diminishing the +boldness of the rustication of the ashlar in successive stories; in +the Farnese, by the gradual reduction of the size of the angle quoins +(Illustration 30). In an Egyptian pylon it is achieved most simply by +battering the wall; in a Gothic cathedral most elaborately by a +kind of segregation, or breaking up, analogous to that which a tree +undergoes--the strong, relatively unbroken base corresponding to +the trunk, the diminishing buttresses to the tapering limbs, and +the multitude of delicate pinnacles and crockets, to the outermost +branches and twigs, seen against the sky. + + +RADIATION + +The final principle of natural beauty to which the author would call +attention is the law of _Radiation_, which is in a manner a return +to the first, the law of _Unity_. The various parts of any organism +radiate from, or otherwise refer back to common centers, or foci, +and these to centers of their own. The law is represented in its +simplicity in the star-fish, in its complexity in the body of man; a +tree springs from a seed, the solar system centers in the sun. + +The idea here expressed by the term "radiation" is a familiar one +to all students of theosophy. The Logos radiates his life and light +throughout his universe, bringing into activity a host of entities +which become themselves radial centers; these generate still others, +and so on endlessly. This principle, like every other, patiently +publishes itself to us, unheeding, everywhere in nature, and in +all great art as well; it is a law of optics, for example, that all +straight lines having a common direction if sufficiently prolonged +appear to meet in a point, i.e., radiate from it (Illustration 31). +Leonardo da Vinci employed this principle of perspective in his Last +Supper to draw the spectator's eye to the picture's central figure, +the point of sight toward which the lines of the walls and ceiling +converge centering in the head of Christ. Puvis de Chavannes, in his +Boston Library decoration, leads the eye by a system of triangulation +to the small figure of the Genius of Enlightenment above the central +door (Illustration 32); and Ruskin, in his _Elements of Drawing_, has +shown how artfully Turner arranged some of his compositions to attract +attention to a focal point. + +This law of Radiation enters largely into architecture. The Colosseum, +based upon the ellipse, a figure generated from two points or foci, +and the Pantheon, based upon the circle, a figure generated from a +central point, are familiar examples. The distinctive characteristic +of Gothic construction, the concentration or focalization of the +weight of the vaults and arches at certain points, is another +illustration of the same principle applied to architecture, +beautifully exemplified in the semicircular apse of a cathedral, where +the lines of the plan converge to a common center, and the ribs of the +vaulting meet upon the capitals of the piers and columns, seeming +to radiate thence to still other centers in the loftier vaults which +finally meet in a center common to all. + +[Illustration 30] + +[Illustration 31] + +[Illustration 32] + +The tracery of the great roses, high up in the facades of the +cathedrals of Paris and of Amiens, illustrate Radiation, in the one +case masculine: straight, angular, direct; in the feminine: curved, +flowing, sinuous. The same _Beautiful Necessity_ determined the +characteristics of much of the ornament of widely separated styles +and periods: the Egyptian lotus, the Greek honeysuckle, the Roman +acanthus, Gothic leaf work--to snatch at random four blossoms from +the sheaf of time. The radial principle still inherent in the debased +ornament of the late Renaissance gives that ornament a unity, a +coherence, and a kind of beauty all its own (Illustration 35). + +[Illustration 33] + +[Illustration 34] + +Such are a few of the more obvious laws of natural beauty and their +application to the art of architecture. The list is by no means +exhausted, but it is not the multiplicity and diversity of these laws +which is important to keep in mind, so much as their relatedness and +cooerdination, for they are but different aspects of the One Law, that +whereby the Logos manifests in time and space. A brief recapitulation +will serve to make this correlation plain, and at the same time fix +what has been written more firmly in the reader's mind. + +[Illustration 35] + +[Illustration 36] + +First comes the law of _Unity_; then, since every unit is in its +essence twofold, there is the law of _Polarity_; but this duality is +not static but dynamic, the two parts acting and reacting upon one +another to produce a third--hence the law of _Trinity_. Given this +third term, and the innumerable combinations made possible by +its relations to and reactions upon the original pair, the law +of _Multiplicity in Unity_ naturally follows, as does the law +of _Consonance_, or repetition, since the primal process of +differentiation tends to repeat itself, and the original combinations +to reappear--but to reappear in changed form, hence the law of +_Diversity in Monotony_. The law of _Balance_ is seen to be but a +modification of the law of Polarity, and since all things are waxing +and waning, there is the law whereby they wax and wane, that of +_Rhythmic Change_. _Radiation_ rediscovers and reaffirms, even in the +utmost complexity, that essential and fundamental unity from which +complexity was wrought. + +Everything, beautiful or ugly, obeys and illustrates one or another of +these laws, so universal are they, so inseparably attendant upon every +kind of manifestation in time and space. It is the number of them +which finds illustration within small compass, and the aptness and +completeness of such illustration, which makes for beauty, because +beauty is the fine flower of a sort of sublime ingenuity. A work of +art is nothing if not _artful_: like an acrostic, the more different +ways it can be read--up, down, across, from right to left and from +left to right--the better it is, other things being equal. This +statement, of course, may be construed in such a way as to appear +absurd; what is meant is simply that the more a work of art is +freighted and fraught with meaning beyond meaning, the more secure its +immortality, the more powerful its appeal. For enjoyment, it is not +necessary that all these meanings should be fathomed, it is only +necessary that they should be felt. + +Consider for a moment the manner in which Leonardo da Vinci's Last +Supper, an acknowledged masterpiece, conforms to everyone of the laws +of beauty enumerated above (Illustration 32). It illustrates the law +of Unity in that it movingly portrays a single significant episode in +the life of Christ. The eye is led to dwell upon the central personage +of this drama by many artful expedients: the visible part of the +figure of Christ conforms to the lines of an equilateral triangle +placed exactly in the center of the picture; the figure is separated +by a considerable space from the groups of the disciples on either +hand, and stands relieved against the largest parallelogram of light, +and the vanishing point of the perspective is in the head of Christ, +at the apex, therefore, of the triangle. The law of Polarity finds +fulfilment in the complex and flowing lines of the draped figures +contrasted with the simple parallelogram of the cloth-covered table, +and the severe architecture of the room. The law of Trinity is +exemplified in the three windows, and in the subdivision of the twelve +figures of the disciples into four groups of three figures each. The +law of Consonance appears in the repetition of the horizontal lines +of the table in the ceiling above; and in the central triangle before +referred to, continued and echoed, as it were, in the triangular +supports of the table visible underneath the cloth. The law of +Diversity in Monotony is illustrated in the varying disposition of the +heads of the figures in the four groups of three; the law of Balance +in the essential symmetry of the entire composition; the law of +Rhythmic Change in the diminishing of the wall and ceiling spaces; and +the law of Radiation in the convergence of all the perspective lines +to a single significant point. + +To illustrate further the universality of these laws, consider now +their application to a single work of architecture: the Taj Mahal, one +of the most beautiful buildings of the world (Illustration 36). It is +a unit, but twofold, for it consists of a curved part and an angular +part, roughly figured as an inverted cup upon a cube; each of these +(seen in parallel perspective, at the end of the principal vista) is +threefold, for there are two sides and a central parallelogram, and +two lesser domes flank the great dome. The composition is rich in +consonances, for the side arches echo the central one, the subordinate +domes the great dome, and the lanterns of the outstanding minarets +repeat the principal motif. Diversity in Monotony appears abundantly +in the ornament, which is intricate and infinitely various; the law of +Balance is everywhere operative in the symmetry of the entire design. +Rhythmic Change appears in the tapering of the minarets, the outlines +of the domes and their mass relations to one another; and finally, +the whole effect is of radiation from a central point, of elements +disposed on radial lines. + +It would be fatuous to contend that the prime object of a work of +architecture is to obey and illustrate these laws. The prime object of +a work of architecture is to fulfill certain definite conditions in a +practical, economical, and admirable way, and in fulfilling to express +as far as possible these conditions, making the form express the +function. The architect who is also an artist however will do this +and something beyond: working for the most part unconsciously, +harmoniously, joyously, his building will obey and illustrate natural +laws--these laws of beauty--and to the extent it does so it will be a +work of art; for art is the method of nature carried into those higher +regions of thought and feeling which man alone inhabits: regions which +it is one of the purposes of theosophy to explore. + + + + +IV + +THE BODILY TEMPLE + + +Carlyle says: "There is but one temple in the world, and that is the +body of man." If the body is, as he declares, a temple, it is not less +true that a temple or any work of architectural art is a larger body +which man has created for his uses, just as the individual self is +housed within its stronghold of flesh and bones. Architectural beauty +like human beauty depends upon the proper subordination of parts +to the whole, the harmonious interrelation between these parts, the +expressiveness of each of its function or functions, and when these +are many and diverse, their reconcilement one with another. This being +so, a study of the human figure with a view to analyzing the sources +of its beauty cannot fail to be profitable. Pursued intelligently, +such a study will stimulate the mind to a perception of those simple +yet subtle laws according to which nature everywhere works, and +it will educate the eye in the finest known school of proportion, +training it to distinguish minute differences, in the same way that +the hearing of good music cultivates the ear. + +Those principles of natural beauty which formed the subject of the +two preceding essays are all exemplified in the ideally perfect human +figure. Though essentially a unit, there is a well marked division +into right and left--"Hands to hands, and feet to feet, in one body +grooms and brides." There are two arms, two legs, two ears, two eyes, +and two lids to each eye; the nose has two nostrils, the mouth has +two lips. Moreover, the terms of such pairs are masculine and feminine +with respect to each other, one being active and the other passive. +Owing to the great size and one-sided position of the liver, the right +half of the body is heavier than the left; the right arm is usually +longer and more muscular than the left; the right eye is slightly +higher than its fellow. In speaking and eating the lower jaw and under +lip are active and mobile with relation to the upper; in winking it is +the upper eyelid which is the more active. That "inevitable duality" +which is exhibited in the form of the body characterizes its motions +also. In the act of walking for example, a forward movement is +attained by means of a forward and a backward movement of the thighs +on the axis of the hips; this leg movement becomes twofold again below +the knee, and the feet move up and down independently on the axis of +the ankle. A similar progression is followed in raising the arm and +hand: motion is communicated first to the larger parts, through them +to the smaller and thence to the extremities, becoming more rapid and +complex as it progresses, so that all free and natural movements of +the limbs describe invisible lines of beauty in the air. Coexistent +with this pervasive duality there is a threefold division of the +figure into trunk, head and limbs: a superior trinity of head and +arms, and an inferior trinity of trunk and legs. The limbs are divided +threefold into upper-arm, forearm and hand; thigh, leg and foot. The +hand flowers out into fingers and the foot into toes, each with a +threefold articulation; and in this way is effected that transition +from unity to multiplicity, from simplicity to complexity, which +appears to be so universal throughout nature, and of which a tree is +the perfect symbol. + +[Illustration 37: THE LAW OF RHYTHMIC DIMINUTION ILLUSTRATED IN THE +TAPERING BODY, LIMBS, FINGERS & TOES.] + +[Illustration 38] + +[Illustration 39] + +The body is rich in veiled repetitions, echoes, _consonances_. The +head and arms are in a sense a refinement upon the trunk and legs, +there being a clearly traceable correspondence between their various +parts. The hand is the body in little--_"Your soft hand is a woman of +itself"_--the palm, the trunk; the four fingers, the four limbs; and +the thumb, the head;-each finger is a little arm, each finger tip a +little palm. The lips are the lids of the mouth, the lids are the +lips of the eyes--and so on. The law of _Rhythmic Diminution_ is +illustrated in the tapering of the entire body and of the limbs, in +the graduated sizes and lengths of the palm and the toes, and in +the successively decreasing length of the palm and the joints of the +fingers, so that in closing the hand the fingers describe natural +spirals (Illustrations 37, 38). Finally, the limbs radiate as it were +from the trunk, the fingers from a point in the wrist, the toes from +a point in the ankle. The ribs radiate from the spinal column like the +veins of a leaf from its midrib (Illustration 39). + +[Illustration 40] + +The relation of these laws of beauty to the art of architecture has +been shown already. They are reiterated here only to show that man is +indeed the microcosm--a little world fashioned from the same elements +and in accordance with the same _Beautiful Necessity_ as is the +greater world in which he dwells. When he builds a house or temple he +builds it not literally in his own image, but according to the laws of +his own being, and there are correspondences not altogether fanciful +between the animate body of flesh and the inanimate body of stone. Do +we not all of us, consciously or unconsciously, recognize the fact +of character and physiognomy in buildings? Are they not, to our +imagination, masculine or feminine, winning or forbidding--_human_, +in point of fact--to a greater degree than anything else of man's +creating? They are this certainly to a true lover and student of +architecture. Seen from a distance the great French cathedrals appear +like crouching monsters, half beast, half human: the two towers stand +like a man and a woman, mysterious and gigantic, looking out over city +and plain. The campaniles of Italy rise above the churches and houses +like the sentinels of a sleeping camp--nor is their strangely human +aspect wholly imaginary: these giants of mountain and campagna have +eyes and brazen tongues; rising four square, story above story, with +a belfry or lookout, like a head, atop, their likeness to a man is not +infrequently enhanced by a certain identity of proportion--of ratio, +that is, of height to width: Giotto's beautiful tower is an example. +The caryatid is a supporting member in the form of a woman; in the +Ionic column we discern her stiffened, like Lot's wife, into a pillar, +with nothing to show her feminine but the spirals of her beautiful +hair. The columns which uphold the pediment of the Parthenon are +unmistakably masculine: the ratio of their breadth to their height is +the ratio of the breadth to the height of a man (Illustration 40). + +[Illustration 41: THE BODY THE ARCHETYPE OF SACRED EDIFICES.] + +[Illustration 42: THE VESICA PISCIS AND THE PLAN OF CHARTRES.] + +At certain periods of the world's history, periods of mystical +enlightenment, men have been wont to use the human figure, the soul's +temple, as a sort of archetype for sacred edifices (Illustration 41). +The colossi, with calm inscrutable faces, which flank the entrance to +Egyptian temples; the great bronze Buddha of Japan, with its dreaming +eyes; the little known colossal figures of India and China--all these +belong scarcely less to the domain of architecture than of sculpture. +The relation above referred to however is a matter more subtle and +occult than mere obvious imitation on a large scale, being based upon +some correspondence of parts, or similarity of proportions, or both. +The correspondence between the innermost sanctuary or shrine of a +temple and the heart of a man, and between the gates of that temple +and the organs of sense is sufficiently obvious, and a relation once +established, the idea is susceptible of almost infinite development. +That the ancients proportioned their temples from the human figure +is no new idea, nor is it at all surprising. The sculpture of the +Egyptians and the Greeks reveals the fact that they studied the body +abstractly, in its exterior presentment. It is clear that the rules +of its proportions must have been established for sculpture, and it is +not unreasonable to suppose that they became canonical in architecture +also. Vitruvius and Alberti both lay stress on the fact that all +sacred buildings should be founded on the proportions of the human +body. + +[Illustration 43: A GOTHIC CATHEDRAL THE SYMBOL OF THE BODY OF JESUS +CHRIST] + +[Illustration 44: THE SYMBOLISM OF A GOTHIC CATHEDRAL FROM THE +ROSICRUCIANS: HARGRAVE JENNINGS] + +In France, during the Middle Ages, a Gothic cathedral became, at the +hands of the secret masonic guilds, a glorified symbol of the body +of Christ. To practical-minded students of architectural history, +familiar with the slow and halting evolution of a Gothic cathedral +from a Roman basilica, such an idea may seem to be only the +maunderings of a mystical imagination, a theory evolved from the inner +consciousness, entitled to no more consideration than the familiar +fallacy that vaulted nave of a Gothic church was an attempt to imitate +the green aisles of a forest. It should be remembered however that the +habit of the thought of that time was mystical, as that of our own age +is utilitarian and scientific; and the chosen language of mysticism is +always an elaborate and involved symbolism. What could be more natural +than that a building devoted to the worship of a crucified Savior +should be made a symbol, not of the cross only, but of the body +crucified? + +[Illustration 45: THE GEOMETRICAL BASIS OF THE HUMAN FIGURE] + +[Illustration 46] + +The _vesica piscis_ (a figure formed by the developing arcs of two +equilateral triangles having a common side) which in so many cases +seems to have determined the main proportion of a cathedral plan--the +interior length and width across the transepts--appears as an aureole +around the figure of Christ in early representations, a fact which +certainly points to a relation between the two (Illustrations 42, +43). A curious little book, _The Rosicrucians_, by Hargrave Jennings, +contains an interesting diagram which well illustrates this conception +of the symbolism of a cathedral. A copy of it is here given. The apse +is seen to correspond to the head of Christ, the north transept to his +right hand, the south transept to the left hand, the nave to the body, +and the north and south towers to the right and left feet respectively +(Illustration 44). + +[Illustration 47] + +The cathedral builders excelled all others in the artfulness with +which they established and maintained a relation between their +architecture and the stature of a man. This is perhaps one reason why +the French and English cathedrals, even those of moderate dimensions +are more truly impressive than even the largest of the great +Renaissance structures, such as St. Peter's in Rome. A gigantic order +furnishes no true measure for the eye: its vastness is revealed +only by the accident of some human presence which forms a basis +of comparison. That architecture is not necessarily the most +awe-inspiring which gives the impression of having been built by +giants for the abode of pigmies; like the other arts, architecture is +highest when it is most human. The mediaeval builders, true to this +dictum, employed stones of a size proportionate to the strength of +a man working without unusual mechanical aids; the great piers and +columns, built up of many such stones, were commonly subdivided +into clusters, and the circumference of each shaft of such a cluster +approximated the girth of a man; by this device the moulding of the +base and the foliation of the caps were easily kept in scale. Wherever +a balustrade occurred it was proportioned not with relation to the +height of the wall or the column below, as in classic architecture, +but with relation to a man's stature. + +[Illustration 48: FIGURE DIVIDED ACCORDING TO THE EGYPTIAN CANON] + +It may be stated as a general rule that every work of architecture, +of whatever style, should have somewhere about it something fixed and +enduring to relate it to the human figure, if it be only a flight of +steps in which each one is the measure of a stride. In the Farnese, +the Riccardi, the Strozzi, and many another Italian palace, the stone +seat about the base gives scale to the building because the beholder +knows instinctively that the height of such a seat must have some +relation to the length of a man's leg. In the Pitti palace the +balustrade which crowns each story answers a similar purpose: it +stands in no intimate relation to the gigantic arches below, but is +of a height convenient for lounging elbows. The door to Giotto's +campanile reveals the true size of the tower as nothing else could, +because it is so evidently related to the human figure and not to the +great windows higher up in the shaft. + +[Illustration 49: THE MEDIAEVAL METHOD OF DRAWING THE FIGURE] + +The geometrical plane figures which play the most important part in +architectural proportion are the square, the circle and the triangle; +and the human figure is intimately related to these elementary forms. +If a man stand with heels together, and arms outstretched horizontally +in opposite directions, he will be inscribed, as it were, within a +square; and his arms will mark, with fair accuracy, the base of an +inverted equilateral triangle, the apex of which will touch the ground +at his feet. If the arms be extended upward at an angle, and the +legs correspondingly separated, the extremities will touch +the circumferences of a circle having its center in the navel +(Illustrations 45, 46). + +[Illustration 50] + +The figure has been variously analyzed with a view to establishing +numerical ratios between its parts (Illustrations 47, 48, 49). Some +of these are so simple and easily remembered that they have obtained +a certain popular currency; such as that the length of the hand equals +the length of the face; that the span of the horizontally extended +arms equals the height; and the well known rule that twice around +the wrist is once around the neck, and twice around the neck is once +around the waist. The Roman architect Vitruvius, writing in the age of +Augustus Caesar, formulated the important proportions of the statues +of classical antiquity, and except that he makes the head smaller than +the normal (as it should be in heroic statuary), the ratios which +he gives are those to which the ideally perfect male figure should +conform. Among the ancients the foot was probably the standard of all +large measurements, being a more determinate length than that of the +head or face, and the height was six lengths of the foot. If the head +be taken as a unit, the ratio becomes 1:8, and if the face--1:10. + +Doctor Rimmer, in his _Art Anatomy_, divides the figure into four +parts, three of which are equal, and correspond to the lengths of +the leg, the thigh and the trunk; while the fourth part, which is +two-thirds of one of these thirds, extends from the sternum to the +crown of the head. One excellence of such a division aside from its +simplicity, consists in the fact that it may be applied to the face as +well. The lowest of the three major divisions extends from the tip of +the chin to the base of the nose, the next coincides with the height +of the nose (its top being level with the eyebrows), and the last with +the height of the forehead, while the remaining two-thirds of one of +these thirds represents the horizontal projection from the beginning +of the hair on the forehead to the crown of the head. The middle of +the three larger divisions locates the ears, which are the same height +as the nose (Illustrations 45, 47). + +Such analyses of the figure, however conducted, reveals an +all-pervasive harmony of parts, between which definite numerical +relations are traceable, and an apprehension of these should assist +the architectural designer to arrive at beauty of proportion by +methods of his own, not perhaps in the shape of rigid formulae, but +present in the consciousness as a restraining influence, acting and +reacting upon the mind with a conscious intention toward rhythm and +harmony. By means of such exercises, he will approach nearer to an +understanding of that great mystery, the beauty and significance of +numbers, of which mystery music, architecture, and the human figure +are equally presentments--considered, that is, from the standpoint of +the occultist. + + + + +V + +LATENT GEOMETRY + + +[Illustration 51: THE HEXAGRAM AND EQUILATERAL TRIANGLE IN NATURE] + +It is a well known fact that in the microscopically minute of nature, +units everywhere tend to arrange themselves with relation to certain +simple geometrical solids, among which are the tetrahedron, the cube, +and the sphere. This process gives rise to harmony, which may be +defined as the relation between parts and unity, the simplicity latent +in the infinitely complex, the potential complexity of that which is +simple. Proceeding to things visible and tangible, this indwelling +harmony, rhythm, proportion, which has its basis in geometry and +number, is seen to exist in crystals, flower forms, leaf groups, and +the like, where it is obvious; and in the more highly organized world +of the animal kingdom also; though here the geometry is latent rather +than patent, eluding though not quite defying analysis, and thus +augmenting beauty, which like a woman is alluring in proportion as she +eludes (Illustrations 51, 52, 53). + +[Illustration 52: PROPORTIONS OF THE HORSE] + +[Illustration 53] + +By the true artist, in the crystal mirror of whose mind the universal +harmony is focused and reflected, this secret of the cause and source +of rhythm--that it dwells in a correlation of parts based on an +ultimate simplicity--is instinctively apprehended. A knowledge of it +formed part of the equipment of the painters who made glorious the +golden noon of pictorial art in Italy during the Renaissance. The +problem which preoccupied them was, as Symonds says of Leonardo, +"to submit the freest play of form to simple figures of geometry in +grouping." Alberti held that the painter should above all things have +mastered geometry, and it is known that the study of perspective and +kindred subjects was widespread and popular. + +[Illustration 54] + +The first painter who deliberately rather than instinctively based +his compositions on geometrical principles seems to have been Fra +Bartolommeo, in his Last Judgment, in the church of St. Maria Nuova, +in Florence. Symonds says of this picture, "Simple figures--the +pyramid and triangle, upright, inverted, and interwoven like the +rhymes of a sonnet--form the basis of the composition. This system was +adhered to by the Fratre in all his subsequent works" (Illustration +54). Raphael, with that power of assimilation which distinguishes +him among men of genius, learned from Fra Bartolommeo this method +of disposing figures and combining them in masses with almost +mathematical precision. It would have been indeed surprising if +Leonardo da Vinci, in whom the artist and the man of science were +so wonderfully united, had not been greatly preoccupied with the +mathematics of the art of painting. His Madonna of the Rocks, and +Virgin on the Lap of Saint Anne, in the Louvre, exhibit the very +perfection of pyramidal composition. It is however in his masterpiece, +The Last Supper, that he combines geometrical symmetry and precision +with perfect naturalness and freedom in the grouping of individually +interesting and dramatic figures. Michael Angelo, Andrea del Sarto, +and the great Venetians, in whose work the art of painting may be said +to have culminated, recognized and obeyed those mathematical laws of +composition known to their immediate predecessors, and the decadence +of the art in the ensuing period may be traced not alone to the false +sentiment and affectation of the times, but also in the abandonment by +the artists of those obscurely geometrical arrangements and groupings +which in the works of the greatest masters so satisfy the eye and +haunt the memory of the beholder (Illustrations 55, 56). + +[Illustration 55: THE EMPLOYMENT OF THE EQUILATERAL TRIANGLE IN +RENAISSANCE PAINTING] + +[Illustration 56: GEOMETRICAL BASIS OF THE SISTINE CEILING PAINTINGS] + +[Illustration 57: ASSYRIAN; GREEK] + +[Illustration 58: THE GEOMETRICAL BASIS OF THE PLAN IN ARCHITECTURAL +DESIGN] + +[Illustration 59] + +Sculpture, even more than painting, is based on geometry. The colossi +of Egypt, the bas-reliefs of Assyria, the figured pediments and +metopes of the temples of Greece, the carved tombs of Revenna, +the Della Robbia lunettes, the sculptured tympani of Gothic church +portals, all alike lend themselves in greater or less degree to a +geometrical synopsis (Illustration 57). Whenever sculpture suffered +divorce from architecture the geometrical element became less +prominent, doubtless because of all the arts architecture is the most +clearly and closely related to geometry. Indeed, it may be said that +architecture is geometry made visible, in the same sense that music +is number made audible. A building is an aggregation of the commonest +geometrical forms: parallelograms, prisms, pyramids and cones--the +cylinder appearing in the column, and the hemisphere in the dome. +The plans likewise of the world's famous buildings reduced to their +simplest expression are discovered to resolve themselves into a few +simple geometrical figures. (Illustration 58). This is the "bed rock" +of all excellent design. + +[Illustration 60: EGYPTIAN; GREEK; ROMAN; MEDIAEVAL] + +[Illustration 61: JEFFERSON'S PEN SKETCH FOR THE ROTUNDA OF THE +UNIVERSITY OF VIRGINIA] + +[Illustration 62: APPLICATION OF THE EQUILATERAL TRIANGLE TO THE +ERECHTHEUM AT ATHENS] + +[Illustration 63] + +[Illustration 64: THE EQUILATERAL TRIANGLE IN ROMAN ARCHITECTURE] + +But architecture is geometrical in another and a higher sense than +this. Emerson says: "The pleasure a palace or a temple gives the eye +is that an order and a method has been communicated to stones, so that +they speak and geometrize, become tender or sublime with expression." +All truly great and beautiful works of architecture from the Egyptian +pyramids to the cathedrals of Ile-de-France--are harmoniously +proportioned, their principal and subsidiary masses being related, +sometimes obviously, more often obscurely, to certain symmetrical +figures of geometry, which though invisible to the sight and not +consciously present in the mind of the beholder, yet perform the +important function of cooerdinating the entire fabric into one easily +remembered whole. Upon some such principle is surely founded what +Symonds calls "that severe and lofty art of composition which seeks +the highest beauty of design in architectural harmony supreme, above +the melodies of gracefulness of detail." + +[Illustration 65: THE EQUILATERAL TRIANGLE IN ITALIAN ARCHITECTURE] + +[Illustration 66: THE HEXAGRAM IN GOTHIC ARCHITECTURE] + +There is abundant evidence in support of the theory that the +builders of antiquity, the masonic guilds of the Middle Ages, and +the architects of the Italian Renaissance, knew and followed certain +rules, but though this theory be denied or even disproved--if after +all these men obtained their results unconsciously--their creations +so lend themselves to a geometrical analysis that the claim for the +existence of certain canons of proportion, based on geometry, remains +unimpeached. + +[Illustration 67] + +[Illustration 68] + +The plane figures principally employed in determining architectural +proportion are the circle, the equilateral triangle, and the +square--which also yields the right angled isosceles triangle. It +will be noted that these are the two dimensional correlatives of the +sphere, the tetrahedron and the cube, mentioned as being among the +determining forms in molecular structure. The question naturally +arises, why the circle, the equilateral triangle and the square? +Because, aside from the fact that they are of all plane figures the +most elementary, they are intimately related to the body of man, as +has been shown (Illustration 45), and the body of man is as it were +the architectural archetype. But this simply removes the inquiry to +a different field, it is not an answer. Why is the body of man so +constructed and related? This leads us, as does every question, to +the threshold of a mystery upon which theosophy alone is able to throw +light. Any extended elucidation would be out of place here: it is +sufficient to remind the reader that the circle is the symbol of the +universe; the equilateral triangle, of the higher trinity (_atma, +buddhi, manas_); and the square, of the lower quaternary of man's +sevenfold nature. + +[Illustration 69] + +[Illustration 70] + +The square is principally used in preliminary plotting: it is the +determining figure in many of the palaces of the Italian Renaissance; +the Arc de Triomphe, in Paris is a modern example of its use +(Illustrations 59, 60). The circle is often employed in conjunction +with the square and the triangle. In Thomas Jefferson's Rotunda for +the University of Virginia, a single great circle was the determining +figure, as his original pen sketch of the building shows (Illustration +61). Some of the best Roman triumphal arches submit themselves to a +circular synopsis, and a system of double intersecting circles has +been applied, with interesting results, to facades as widely different +as those of the Parthenon and the Farnese Palace in Rome, though +it would be fatuous to claim that these figures determined the +proportions of the facades. + +By far the most important figure in architectural proportion, +considered from the standpoint of geometry, is the equilateral +triangle. It would seem that the eye has an especial fondness for +this figure, just as the ear has for certain related sounds. Indeed it +might not be too fanciful to assert that the common chord of any key +(the tonic with its third and fifth) is the musical equivalent of +the equilateral triangle. It is scarcely necessary to dwell upon +the properties and unique perfection of this figure. Of all regular +polygons it is the simplest: its three equal sides subtend equal +angles, each of 60 degrees; it trisects the circumference of a circle; +it is the graphic symbol of the number three, and hence of every +threefold thing; doubled, its generating arcs form the _vesica +piscis_, of so frequent occurrence in early Christian art; two +symmetrically intersecting equilateral triangles yield the figure +known as "Solomon's Seal," or the "Shield of David," to which mystic +properties have always been ascribed. + +It may be stated as a general rule that whenever three important +points in any architectural composition coincide (approximately or +exactly) with the three extremities of an equilateral triangle, it +makes for beauty of proportion. An ancient and notable example occurs +in the pyramids of Egypt, the sides of which, in their original +condition, are believed to have been equilateral triangles. It is a +demonstrable fact that certain geometrical intersections yield the +important proportions of Greek architecture. The perfect little +Erechtheum would seem to have been proportioned by means of the +equilateral triangle and the angle of 60 degrees, both in general and +in detail (Illustration 62). The same angle, erected from the central +axis of a column at the point where it intersects the architrave, +determines both the projection of the cornice and the height of +the architrave in many of the finest Greek and Roman temples +(Illustrations 67-70). The equilateral triangle used in conjunction +with the circle and the square was employed by the Romans in +determining the proportions of triumphal arches, basilicas and +baths. That the same figure was a factor in the designing of Gothic +cathedrals is sufficiently indicated in the accompanying facsimile +reproductions of an illustration from the Como Vitruvius, published in +Milan in 1521, which shows a vertical section of the Milan cathedral +and the system of equilateral triangles which determined its various +parts (Illustration 71). The _vesica piscis_ was often used to +establish the two main internal dimensions of the cathedral plan: the +greatest diameter of the figure corresponding with the width across +the transepts, the upper apex marking the limit of the apse, and the +lower, the termination of the nave. Such a proportion is seen to be +both subtle and simple, and possesses the advantage of being easily +laid out. The architects of the Italian Renaissance doubtless +inherited certain of the Roman canons of architectural proportion, +for they seem very generally to have recognized them as an essential +principle of design. + +[Illustration 71] + +Nevertheless, when all is said, it is easy to exaggerate the +importance of this matter of geometrical proportion. The designer +who seeks the ultimate secret of architectural harmony in mathematics +rather than in the trained eye, is following the wrong road to +success. A happy inspiration is worth all the formulae in the world--if +it be really happy, the artist will probably find that he has +"followed the rules without knowing them." Even while formulating +concepts of art, the author must reiterate Schopenhauer's dictum +that the _concept_ is unfruitful in art. The mathematical analysis +of spatial beauty is an interesting study, and a useful one to the +artist; but it can never take the place of the creative faculty, it +can only supplement, restrain, direct it. The study of proportion is +to the architect what the study of harmony is to a musician--it helps +his genius adequately to express itself. + + + + +VI + +THE ARITHMETIC OF BEAUTY + + +Although architecture is based primarily upon geometry, it is possible +to express all spatial relations numerically: for arithmetic, not +geometry, is the universal science of quantity. The relation of masses +one to another--of voids to solids, and of heights and lengths to +widths--forms ratios; and when such ratios are simple and harmonious, +architecture may be said, in Walter Pater's famous phrase, to +"aspire towards the condition of music." The trained eye, and not an +arithmetical formula, determines what is, and what is not, beautiful +proportion. Nevertheless the fact that the eye instinctively rejects +certain proportions as unpleasing, and accepts others as satisfactory, +is an indication of the existence of laws of space, based upon number, +not unlike those which govern musical harmony. The secret of the deep +reasonableness of such selection by the senses lies hidden in the very +nature of number itself, for number is the invisible thread on which +the worlds are strung--the universe abstractly symbolized. + +Number is the within of all things--the "first form of Brahman." It +is the measure of time and space; it lurks in the heart-beat and is +blazoned upon the starred canopy of night. Substance, in a state of +vibration, in other words conditioned by number, ceaselessly undergoes +the myriad transmutations which produce phenomenal life. Elements +separate and combine chemically according to numerical ratios: +"Moon, plant, gas, crystal, are concrete geometry and number." By +the Pythagoreans and by the ancient Egyptians sex was attributed to +numbers, odd numbers being conceived of as masculine or generating, +and even numbers as feminine or parturitive, on account of their +infinite divisibility. Harmonious combinations were those +involving the marriage of a masculine and a feminine--an odd and an +even--number. + +[Illustration 72: A GRAPHIC SYSTEM OF NOTATION] + +Numbers progress from unity to infinity, and return again to unity as +the soul, defined by Pythagoras as a self-moving number, goes forth +from, and returns to God. These two acts, one of projection and the +other of recall; these two forces, centrifugal and centripetal, are +symbolized in the operations of addition and subtraction. Within them +is embraced the whole of computation; but because every number, every +aggregation of units, is also a new unit capable of being added +or subtracted, there are also the operations of multiplication and +division, which consists in one case of the addition of several equal +numbers together, and in the other, of the subtraction of several +equal numbers from a greater until that is exhausted. In order to +think correctly it is necessary to consider the whole of numeration, +computation, and all mathematical processes whatsoever as _the +division of the unit_ into its component parts and the establishment +of relations between these parts. + +[Illustration 73] + +[Illustration 74] + +The progression and retrogression of numbers in groups expressed by +the multiplication table gives rise to what may be termed "numerical +conjunctions." These are analogous to astronomical conjunctions: the +planets, revolving around the sun at different rates of speed, and +in widely separated orbits, at certain times come into line with one +another and with the sun. They are then said to be in conjunction. +Similarly, numbers, advancing toward infinity singly and in groups +(expressed by the multiplication table), at certain stages of their +progression come into relation with one another. For example, an +important conjunction occurs in 12, for of a series of twos it is +the sixth, of threes the fourth, of fours the third, and of sixes the +second. It stands to 8 in the ratio of 3:2, and to 9, of 4:3. It is +related to 7 through being the product of 3 and 4, of which numbers 7 +is the sum. The numbers 11 and 13 are not conjunctive; 14 is so in +the series of twos, and sevens; 15 is so in the series of fives and +threes. The next conjunction after 12, of 3 and 4 and their first +multiples, is in 24, and the next following is in 36, which numbers +are respectively the two and three of a series of twelves, each end +being but a new beginning. + +[Illustration 75] + +It will be seen that this discovery of numerical conjunctions consists +merely of resolving numbers into their prime factors, and that a +conjunctive number is a common multiple; but by naming it so, to +dismiss the entire subject as known and exhausted, is to miss a +sense of the wonder, beauty and rhythm of it all: a mental impression +analogous to that made upon the eye by the swift-glancing balls of a +juggler, the evolutions of drilling troops, or the intricate figures +of a dance; for these things are number concrete and animate in time +and space. + +[Illustration 76] + +The truths of number are of all truths the most interior, abstract +and difficult of apprehension, and since knowledge becomes clear and +definite to the extent that it can be made to enter the mind through +the channels of physical sense, it is well to accustom oneself to +conceiving of number graphically, by means of geometrical symbols +(Illustration 72), rather than in terms of the familiar arabic +notation which though admirable for purposes of computation, is of +too condensed and arbitrary a character to reveal the properties of +individual numbers. To state, for example, that 4 is the first square, +and 8 the first cube, conveys but a vague idea to most persons, but if +4 be represented as a square enclosing four smaller squares, and 8 +as a cube containing eight smaller cubes, the idea is apprehended +immediately and without effort. The number 3 is of course the +triangle; the irregular and vital beauty of the number 5 appears +clearly in the heptalpha, or five-pointed star; the faultless symmetry +of 6, its relation to 3 and 2, and its regular division of the circle, +are portrayed in the familiar hexagram known as the Shield of David. +Seven, when represented as a compact group of circles reveals itself +as a number of singular beauty and perfection, worthy of the important +place accorded to it in all mystical philosophy (Illustration 73). It +is a curious fact that when asked to think of any number less than 10, +most persons will choose 7. + +[Illustration 77] + +Every form of art, though primarily a vehicle for the expression and +transmission of particular ideas and emotions, has subsidiary offices, +just as a musical tone has harmonics which render it more sweet. +Painting reveals the nature of color; music, of sound--in wood, +in brass, and in stretched strings; architecture shows forth the +qualities of light, and the strength and beauty of materials. All +of the arts, and particularly music and architecture, portray in +different manners and degrees the truths of number. Architecture does +this in two ways: esoterically as it were in the form of harmonic +proportions; and exoterically in the form of symbols which represent +numbers and groups of numbers. The fact that a series of threes and +a series of fours mutually conjoin in 12, finds an architectural +expression in the Tuscan, the Doric, and the Ionic orders according to +Vignole, for in them all the stylobate is four parts, the entablature +3, and the intermediate column 12 (Illustration 74). The affinity +between 4 and 7, revealed in the fact that they express (very nearly) +the ratio between the base and the altitude of the right-angled +triangle which forms half of an equilateral, and the musical interval +of the diminished seventh, is architecturally suggested in the Palazzo +Giraud, which is four stories in height with seven openings in each +story (Illustration 75). + +[Illustration 78] + +[Illustration 79] + +[Illustration 80] + +[Illustration 81] + +Every building is a symbol of some number or group of numbers, and +other things being equal the more perfect the numbers involved the +more beautiful will be the building (Illustrations 76-82). The numbers +5 and 7--those which occur oftenest--are the most satisfactory because +being of small quantity, they are easily grasped by the eye, and being +odd, they yield a center or axis, so necessary in every architectural +composition. Next in value are the lowest multiples of these numbers +and the least common multiples of any two of them, because the +eye, with a little assistance, is able to resolve them into their +constituent factors. It is part of the art of architecture to +render such assistance, for the eye counts always, consciously or +unconsciously, and when it is confronted with a number of units +greater than it can readily resolve, it is refreshed and rested if +these units are so grouped and arranged that they reveal themselves as +factors of some higher quantity. + +[Illustration 82] + +[Illustration 83: A NUMERICAL ANALYSIS OF GOTHIC TRACERY] + +There is a raison d'etre for string courses other than to mark the +position of a floor on the interior of a building, and for quoins and +pilasters other than to indicate the presence of a transverse wall. +These sometimes serve the useful purpose of so subdividing a facade +that the eye estimates the number of its openings without conscious +effort and consequent fatigue (Illustration 82). The tracery of Gothic +windows forms perhaps the highest and finest architectural expression +of number (Illustration 83). Just as thirst makes water more sweet, so +does Gothic tracery confuse the eye with its complexity only the more +greatly to gratify the sight by revealing the inherent simplicity in +which this complexity has its root. Sometimes, as in the case of +the Venetian Ducal Palace, the numbers involved are too great for +counting, but other and different arithmetical truths are portrayed; +for example, the multiplication of the first arcade by 2 in +the second, and this by 3 in the cusped arches, and by 4 in the +quatrefoils immediately above. + +[Illustration 84: NUMERATION IN GROUPS EXPRESSED ARCHITECTURALLY] + +[Illustration 85: ARCHITECTURAL ORNAMENT CONSIDERED AS THE +OBJECTIFICATION OF NUMBER. MULTIPLICATION IN GROUPS OF FIVE; TWO; +THREE; ALTERNATION OF THREE AND SEVEN] + +[Illustration 86] + +Seven is proverbially the perfect number. It is of a quantity +sufficiently complex to stimulate the eye to resolve it, and yet so +simple that it can be analyzed at a glance; as a center with two equal +sides, it is possessed of symmetry, and as the sum of an odd and even +number (3 and 4) it has vitality and variety. All these properties a +work of architecture can variously reveal (Illustration 77). Fifteen, +also, is a number of great perfection. It is possible to arrange the +first 9 numbers in the form of a "magic" square so that the sum of +each line, read vertically, horizontally or diagonally, will be 15. +Thus: + + 4 9 2 = 15 + 3 5 7 = 15 + 8 1 6 = 15 + -- -- -- + 15 15 15 + +Its beauty is portrayed geometrically in the accompanying figure which +expresses it, being 15 triangles in three groups of 5 (Illustration +86). Few arrangements of openings in a facade better satisfy the eye +than three superimposed groups of five (Illustrations 76-80). May not +one source of this satisfaction dwell in the intrinsic beauty of the +number 15? + +In conclusion, it is perhaps well that the reader be again reminded +that these are the by-ways, and not the highways of architecture: that +the highest beauty comes always, not from beautiful numbers, nor +from likenesses to Nature's eternal patterns of the world, but from +utility, fitness, economy, and the perfect adaptation of means to +ends. But along with this truth there goes another: that in every +excellent work of architecture, in addition to its obvious and +individual beauty, there dwells an esoteric and universal beauty, +following as it does the archetypal pattern laid down by the Great +Architect for the building of that temple which is the world wherein +we dwell. + + + + +VII + +FROZEN MUSIC + + +In the series of essays of which this is the final one, the author has +undertaken to enforce the truth that evolution on any plane and on +any scale proceeds according to certain laws which are in reality only +ramifications of one ubiquitous and ever operative law; that this law +registers itself in the thing evolved, leaving stamped thereon as it +were fossil footprints by means of which it may be known. In the arts +the creative spirit of man is at its freest and finest, and nowhere +among the arts is it so free and so fine as in music. In music +accordingly the universal law of becoming finds instant, direct +and perfect self-expression; music voices the inner nature of the +_will-to-live_ in all its moods and moments; in it form, content, +means and end are perfectly fused. It is this fact which gives +validity to the before quoted saying that all of the arts "aspire +toward the condition of music." All aspire to express the law, but +music, being least encumbered by the leaden burden of materiality, +expresses it most easily and adequately. This being so there is +nothing unreasonable in attempting to apply the known facts of musical +harmony and rhythm to any other art, and since these essays concern +themselves primarily with architecture, the final aspect in which +that art will be presented here is as "frozen music"--ponderable form +governed by musical law. + +Music depends primarily upon the equal and regular division of time +into beats, and of these beats into measures. Over this soundless and +invisible warp is woven an infinitely various melodic pattern, made +up of tones of different pitch and duration arithmetically related +and combined according to the laws of harmony. Architecture, +correspondingly, implies the rhythmical division of space, and +obedience to laws numerical and geometrical. A certain identity +therefore exists between simple harmony in music, and simple +proportion in architecture. By translating the consonant +tone-intervals into number, the common denominator, as it were, of +both arts, it is possible to give these intervals a spatial, and +hence an architectural, expression. Such expression, considered as +proportion only and divorced from ornament, will prove pleasing to +the eye in the same way that its correlative is pleasing to the ear, +because in either case it is not alone the special organ of sense +which is gratified, but the inner Self, in which all senses are one. +Containing within itself the mystery of number, it thrills responsive +to every audible or visible presentment of that mystery. + +[Illustration 87] + +If a vibrating string yielding a certain musical note be stopped in +its center, that is, divided by half, it will then sound the octave +of that note. The numerical ratio which expresses the interval of +the octave is therefore 1:2. If one-third instead of one-half of the +string be stopped, and the remaining two-thirds struck, it will yield +the musical fifth of the original note, which thus corresponds to the +ratio 2:3. The length represented by 3:4 yields the fourth; 4:5 the +major third; and 5:6 the minor third. These comprise the principal +consonant intervals within the range of one octave. The ratios of +inverted intervals, so called, are found by doubling the smaller +number of the original interval as given above: 2:3, the fifth, gives +3:4, the fourth; 4:5, the major third, gives 5:8, the minor sixth; +5:6, the minor third, gives 6:10, or 3:5, the major sixth. + +[Illustration 88: ARCHITECTURE AS HARMONY] + +Of these various consonant intervals the octave, fifth, and major +third are the most important, in the sense of being the most perfect, +and they are expressed by numbers of the smallest quantity, an odd +number and an even. It will be noted that all the intervals above +given are expressed by the numbers 1, 2, 3, 4, 5 and 6, except the +minor sixth (5:8), and this is the most imperfect of all consonant +intervals. The sub-minor seventh, expressed by the ratio 4:7 though +included among the dissonances, forms, according to Helmholtz, a more +perfect consonance with the tonic than does the minor sixth. + +A natural deduction from these facts is that relations of +architectural length and breadth, height and width, to be "musical" +should be capable of being expressed by ratios of quantitively small +numbers, preferably an odd number and an even. Although generally +speaking the simpler the numerical ratio the more perfect the +consonance, yet the intervals of the fifth and major third (2:3 and +4:5), are considered to be more pleasing than the octave (1:2), which +is too obviously a repetition of the original note. From this it is +reasonable to assume (and the assumption is borne out by experience), +that proportions, the numerical ratios of which the eye resolves too +readily, become at last wearisome. The relation should be felt rather +than fathomed. There should be a perception of identity, and also +of difference. As in music, where dissonances are introduced to give +value to consonances which follow them, so in architecture simple +ratios should be employed in connection with those more complex. + +[Illustration 89] + +Harmonics are those tones which sound with, and reinforce any musical +note when it is sounded. The distinguishable harmonics of the tonic +yield the ratios 1:2, 2:3, 3:4, 4:5, and 4:7. A note and its harmonics +form a natural chord. They may be compared to the widening circles +which appear in still water when a stone is dropped into it, for when +a musical sound disturbs the quietude of that pool of silence which +we call the air, it ripples into overtones, which becoming fainter +and fainter, die away into silence. It would seem reasonable to assume +that the combination of numbers which express these overtones, if +translated into terms of space, would yield proportions agreeable +to the eye, and such is the fact, as the accompanying examples +sufficiently indicate (Illustrations 87-90). + +The interval of the sub-minor seventh (4:7), used in this way, in +connection with the simpler intervals of the octave (1:2), and the +fifth (2:3), is particularly pleasing because it is neither too +obvious nor too subtle. This ratio of 4:7 is important for the reason +that it expresses the angle of sixty degrees, that is, the numbers 4 +and 7 represent (very nearly) the ratio between one-half the base and +the altitude of an equilateral triangle: also because they form part +of the numerical series 1, 4, 7, 10, etc. Both are "mystic" numbers, +and in Gothic architecture particularly, proportions were frequently +determined by numbers to which a mystic meaning was attached. +According to Gwilt, the Gothic chapels of Windsor and Oxford are +divided longitudinally by four, and transversely by seven equal parts. +The arcade above the roses in the facade of the cathedral of Tours +shows seven principal units across the front of the nave, and four in +each of the towers. + +A distinguishing characteristic of the series of ratios which +represent the consonant intervals within the compass of an octave is +that it advances by the addition of 1 to both terms: 1:2, 2:3, +3:4, 4:5, and 5:6. Such a series always approaches unity, just as, +represented graphically by means of parallelograms, it tends toward a +square. Alberti in his book presents a design for a tower showing his +idea for its general proportions. It consists of six stories, in a +sequence of orders. The lowest story is a perfect cube and each of the +other stories is 11-12ths of the story below, diminishing practically +in the proportion of 8, 7, 6, 5, 4, 3, allowing in each case for the +amount hidden by the projection of the cornice below; each order being +accurate as regards column, entablature, etc. It is of interest to +compare this with Ruskin's idea in his _Seven Lamps_, where he takes +the case of a plant called Alisma Plantago, in which the various +branches diminish in the proportion of 7, 6, 5, 4, 3, respectively, +and so carry out the same idea; on which Ruskin observes that +diminution in a building should be after the manner of Nature. + +[Illustration 90: ARCADE OF THE CANCELLERIA] + +It would be a profitless task to formulate exact rules of +architectural proportion based upon the laws of musical harmony. The +two arts are too different from each other for that, and moreover +the last appeal must always be to the eye, and not to a mathematical +formula, just as in music the last appeal is to the ear. Laws there +are, but they discover themselves to the artist as he proceeds, and +are for the most part incommunicable. Rules and formulae are useful and +valuable not as a substitute for inspiration, but as a guide: not as +wings, but as a tail. In this connection perhaps all that is necessary +for the architectural designer to bear in mind is that important +ratios of length and breadth, height and width, to be "musical" should +be expressed by quantitively small numbers, and that if possible they +should obey some simple law of numerical progression. From this basic +simplicity complexity will follow, but it will be an ordered and +harmonious complexity, like that of a tree, or of a symphony. + +[Illustration 91: THE PALAZZO VERZI AT VERONA (LOWER PORTION ONLY). +A COMPOSITION FOUNDED ON THE EQUAL AND REGULAR DIVISION OF SPACE, AS +MUSIC IS FOUNDED ON THE EQUAL AND REGULAR DIVISION OF TIME.] + +[Illustration 92: ARCHITECTURE AS RHYTHM. A DIVISION OF SPACE +CORRESPONDING TO 3/4 AND 4/4 TIME.] + +In the same way that a musical composition implies the division of +time into equal and regular beats, so a work of architecture should +have for its basis some unit of space. This unit should be nowhere too +obvious and may be varied within certain limits, just as musical time +is retarded or accelerated. The underlying rhythm and symmetry will +thus give value and distinction to such variation. Vasari tells how +Brunelleschi. Bramante and Leonardo da Vinci used to work on paper +ruled in squares, describing it as a "truly ingenious thing, and of +great utility in the work of design." By this means they developed +proportions according to a definite scheme. They set to work with a +division of space analogous to the musician's division of time. +The examples given herewith indicate how close a parallel may exist +between music and architecture in this matter of rhythm (Illustrations +91-93). + +[Illustration 93] + +It is a demonstrable fact that musical sounds weave invisible patterns +in the air. Architecture, correspondingly, in one of its aspects, +is geometric pattern made fixed and enduring. What could be more +essentially musical for example than the sea arcade of the Venetian +Ducal Palace? The sand forms traced by sound-waves on a musically +vibrating steel plate might easily suggest architectural ornament did +not the differences of scale and of material tend to confuse the mind. +The architect should occupy himself with identities, not differences. +If he will but bear in mind that architecture is pattern in space, +just as music is pattern in time, he will come to perceive the +essential identity between, say, a Greek rosette and a Gothic +rose-window; an arcade and an egg and dart moulding (Illustration 94). +All architectural forms and arrangements which give enduring pleasure +are in their essence musical. Every well composed facade makes harmony +in three dimensions; every good roof-line sings a melody against the +sky. + +[Illustration 94: ARCHITECTURE AS PATTERN] + + + + +CONCLUSION + + +In taking leave of the reader at the end of this excursion together +among the by-ways of a beautiful art, the author must needs add a +final word or two touching upon the purpose and scope of these essays. +Architecture (like everything else) has two aspects: it may be viewed +from the standpoint of utility, that is, as construction; or from the +standpoint of expressiveness, that is, as decoration. No attempt has +been made here to deal with its first aspect, and of the second +(which is again twofold), only the universal, not the particular +expressiveness has been sought. The literature of architecture is rich +in works dealing with the utilitarian and constructive side of the +art: indeed, it may be said that to this side that literature is +almost exclusively devoted. This being so, it has seemed worth while +to attempt to show the reverse of the medal, even though it be "tails" +instead of "heads." + +It will be noted that the inductive method has not, in these pages, +been honored by a due observance. It would have been easy to +have treated the subject inductively, amassing facts and drawing +conclusions, but to have done so the author would have been false +to the very principle about which the work came into being. With the +acceptance of the Ancient Wisdom, the inductive method becomes +no longer necessary. Facts are not useful in order to establish a +hypothesis, they are used rather to elucidate a known and accepted +truth. When theosophical ideas shall have permeated the thought of +mankind, this work, if it survives at all, will be chiefly--perhaps +solely--remarkable by reason of the fact that it was among the +first in which the attempt was made again to unify science, art and +religion, as they were unified in those ancient times and among those +ancient peoples when the Wisdom swayed the hearts and minds of men. + + + +***END OF THE PROJECT GUTENBERG EBOOK THE BEAUTIFUL NECESSITY*** + + +******* This file should be named 12648.txt or 12648.zip ******* + + +This and all associated files of various formats will be found in: +https://www.gutenberg.org/1/2/6/4/12648 + + + +Updated editions will replace the previous one--the old editions +will be renamed. + +Creating the works from public domain print editions means that no +one owns a United States copyright in these works, so the Foundation +(and you!) can copy and distribute it in the United States without +permission and without paying copyright royalties. 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