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+The Project Gutenberg EBook of Was the Beginning Day of the Maya Month
+Numbered Zero (or Twenty) or One?, by Charles P. Bowditch
+
+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: Was the Beginning Day of the Maya Month Numbered Zero (or Twenty) or One?
+
+Author: Charles P. Bowditch
+
+Release Date: March 25, 2012 [EBook #39259]
+
+Language: English
+
+Character set encoding: ISO-8859-1
+
+*** START OF THIS PROJECT GUTENBERG EBOOK BEGINNING DAY OF THE MAYA MONTH ***
+
+
+
+
+Produced by Julia Miller, Diane Monico, and the Online
+Distributed Proofreading Team at http://www.pgdp.net (This
+file was produced from images generously made available
+by The Internet Archive)
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+
+
+
+WAS THE BEGINNING DAY OF THE
+MAYA MONTH NUMBERED ZERO
+(OR TWENTY) OR ONE?
+
+
+BY
+
+CHARLES P. BOWDITCH
+
+
+CAMBRIDGE
+THE UNIVERSITY PRESS
+1901
+
+
+
+
+WAS THE BEGINNING DAY OF THE MAYA MONTH NUMBERED ZERO (OR TWENTY) OR
+ONE?
+
+
+Goodman, in his elaborate and valuable book on the Maya Inscriptions,
+has made up his Tables on the supposition that the beginning day of the
+month was not called Day 1, but Day 20, giving the day this number
+because in his view the Mayas counted the number of days which had
+passed and not the current or passing day. That is, the Mayas,
+according to Goodman, used the same plan in counting their days which
+we use in counting our minutes and hours and which we depart from in
+counting our days. Thus, when we speak of January 1, we do not mean
+that one day has passed since January came in, but that the month of
+December has passed and that we are living in the day which when
+completed will be the first day of January. But when we say that it is
+one o'clock, we do not mean that we are living in the hour which when
+passed will be the first hour of the day or half-day, but we mean that
+one whole hour of the day or half-day has fully passed. Goodman's idea
+is that the Mayas used this system in counting their days of the month,
+their kins, uinals, tuns, katuns, and cycles. In other words he
+considers that the beginning day of the month Pop was not 1 Pop, but 20
+Pop, the beginning day of Uo was 20 Uo; that the beginning kin of a
+uinal was Kin 20, the beginning uinal of a tun was Uinal 18, the
+beginning tun of a katun was Tun 20, that the beginning katun of a
+cycle was Katun 20, and that the beginning cycle of a grand cycle was
+Cycle 13. The reason why Goodman substitutes 18 and 13 for 20 in the
+case of the uinals and cycles respectively is that these are the
+numbers of uinals and cycles which are needed to make one of the next
+higher units in his scale of numeration.
+
+Without considering the truth or error of his view in regard to the
+cycles, katuns, etc., let us try to solve the following questions:
+
+1st. Did the Mayas count the days of their month by the day which had
+passed, as we count our hours?
+
+2d. Was the number which they gave to the beginning day of the month 0
+or 20?
+
+For our answers to these questions, let us turn to pages 46-50 of the
+Dresden Codex. These pages contain three rows of twenty month dates
+each, and each of these dates is reached with but two exceptions by
+counting forward from the preceding date the number of days specified
+in red at the bottom of the pages, the first date of each row on page
+46 being the regular number of days distant from the last date of the
+same row on page 50.
+
+In the first row of dates, we find that the third date on page 48 is 12
+Chen. The number of days at the bottom of the page which need to be
+counted forward in order to reach the fourth date is 8. If the
+beginning day of the month were marked by the Mayas with 1, then the
+last day would be marked with 20, and by adding 8 days to 12 Chen, we
+should reach 20 Chen. But the date is not 20 Chen. The month is
+Yax,--the month immediately following Chen,--and the glyph which takes
+the place of the number has a form resembling two half-circles placed
+side by side. In other words, in this case 8 days from 12 Chen reach ?
+Yax, and as far as the first proposition is concerned, it is immaterial
+whether the form above given is called 0 or 20. Eight days have taken
+us out of the month Chen into the next month Yax, and to a day of that
+month which is not 1 Yax, but must be a day preceding 1 Yax, whether
+that is called 0 Yax or 20 Yax.
+
+Again, the first date of the first row of month dates on page 50 is 10
+Kankin, and the number at the bottom of the page to be added in order
+to reach the second date is 90. Counting forward 90 days from 10 Kankin
+we should reach 20 Cumhu, if the beginning day of the month is 1
+Cumhu. But the month is not Cumhu nor is it Pop, but it is undoubtedly
+the glyph for the five supplementary days, Uayeb. The glyph which takes
+the place of the number is the same as that which has just been found
+before Yax. This is additional evidence that the months began with 0 or
+20 and not with 1.
+
+Again, on the first date of the second row of page 50 is 15 Cumhu, and
+the number of days to be added in order to reach the next date is 90,
+which appears at the bottom of the page. Counting forward this number
+of days from 15 Cumhu, we should reach 20 Zotz if the beginning day of
+the month were 1 Zotz. But the month is clearly Tzec, and the number is
+that which we have already found twice before as meaning 0 or 20.
+
+These cases would seem to show that after passing day 19 of any month,
+we reach the beginning day of the next month, and that this day is
+found with the glyph which means 0 or 20.
+
+Against this is the evidence of the last month date of the third row of
+page 49, which is clearly 9 Mac, and the number to be added at the
+bottom of the page is 236. This would take us to 20 Xul, if the
+beginning day of Xul is 1 Xul, but to 0 or 20 Yaxkin if the beginning
+day of Xul is 0 or 20. The first month date of the third row of page 50
+is 0 or 20 Xul. This, I think, is clear, although the Xul glyph is not
+exactly like the other glyphs of this month.
+
+Here then are three cases which support Goodman's view and one against
+it. The weight of evidence is therefore in favor of his system so far.
+
+In the Inscriptions there are not very many cases where the month has
+the zero or twenty sign attached to it, and there are still fewer cases
+where this occurs in a position where the question can be decided from
+the context as to whether the 0 or 20 is the last day of one month or
+the beginning day of the next month.
+
+On the inscription of the Temple of the Cross at Palenque, however, we
+have a month date which is 5 Ahau 3 Tzec. This is on R S 10. On R 8 to
+9 we find 1.16.7.17., if the thumb with the katun glyph means 1, as it
+almost surely does. Counting forward this number of days from 5 Ahau 3
+Tzec, we should reach 5 Caban 20 Zip if the month begins with 1, or 5
+Caban 0 or 20 Zotz if the beginning day is 0 or 20. On S 12 R 13 is 5
+Caban 0 or 20 Zotz. The form of the number glyph cannot fail to recall
+that of the similar glyphs in the Dresden Codex.
+
+De Rosny has given in his "Compte-Rendu d'une Mission Scientifique,"
+published in the "Mémoires de la Société d'Ethnographie," an admirable
+reproduction of the wooden inscription which came from Tikal. On Plate
+12 of this work we find on A B 1, 3 Ahau 3 Mol, and on B 2 A 3, we have
+2.11.12. By counting forward this number of days from 3 Ahau 3 Mol we
+reach 6 Eb 0 or 20 Pop, if the month begins with 0 or 20, but 6 Eb 5
+Uayeb if the month begins with 1. This is a particularly strong case,
+for the month is surely Pop and the number is certainly not 5, and is
+like those of the manuscripts and of the Temple of the Cross, which we
+have just commented on and which are in all probability 0 or 20.
+
+Again, on a part of a doorway in El Cayo, on C D 3 we find 13 Cimi 19
+Zotz; on H 3 G 4 is a number which seems to be 8.18.6. Counting forward
+we reach 9 Eb 20 Uo, if the month begins with 1, or 9 Eb 0 or 20 Zip,
+if the months begin with 0 or 20. Although the glyphs for Uo and Zip
+resemble each other, yet the date on I J 1 is clearly 9 Eb 0 or 20 Zip.
+It should be said, however, that the number on H 3 G 4 is somewhat
+effaced and very unusual, in showing 18 uinals, and that there is
+another date 5 ? 3 Yaxkin on E F 3.
+
+On the other hand the inscription of the Temple of the Cross shows us
+on D 3 C 4, 4 Ahau 8 Cumhu, and on D 5 C 6, is 1.9.2., which is equal
+to 1 year 177 days. Counting forward this number of days from 4 Ahau 8
+Cumhu we reach 13 Ik 20 Mol, if the month begins with 1, or 0 or 20
+Chen, if the month begins with 0 or 20. On C D 9 we find 13 Ik ? Mol.
+However, on D 13 to C 15 we have the long number 1.18.3.12.0., which
+counted forward from 13 Ik 20 Mol brings us to 9 Ik 15 Zac, which is
+not found anywhere near by. But if we count forward this number from 13
+Ik 0 or 20 Chen, we should reach 9 Ik 15 Ceh, which is found on E F 1.
+It would seem, therefore, that the glyph for Mol had been carved in
+error for that of Chen.
+
+Other cases where 0 or 20 probably occur before the month sign are the
+following:
+
+Copan,         Altar U,  1 to  2     2 Caban 0 or 20 Pop.
+  "              "   U, 51 to 52     3 Eb    0 or 20 Pop.
+Temple of the Cross, Q   2 P   3    11 Caban 0 or 20 Pop.
+  "    "  "    "     F  12 E  13     9 Ik    0 or 20 Chen (J.T.G.)
+  "    "  "    "     E F 9           9 Ik    0 or 20 Yax or Zac.
+
+The month glyph of the last example looks like Zac. If it is Yax it
+proves Goodman's theory by calculation.
+
+Thus we see that in three out of four cases in the Dresden Codex and in
+three cases out of four in the Inscriptions where the context is such
+as to throw light on the question, the evidence is in favor of
+concluding that the months began with a day 0 or 20 and not with a day
+1. Moreover in the single case in the Codex which tends to prove the
+contrary, it is interesting to see that the month glyph, Xul, is
+somewhat different from the other Xul glyphs, while in the doubtful
+case in the inscriptions, if the month glyph had been Chen and not Mol,
+it would have agreed with the dates before and after it. In other
+words, the calculations both before and after the date in question
+would be quite accurate if the month were Chen and if, therefore, the
+beginning day were 0 or 20, while the glyph of Mol makes the
+calculation after that date inaccurate.
+
+All the evidence taken gives a very strong presumption in favor of
+Goodman's theory that the month began with 0 or 20.
+
+It is also interesting to notice that of the other dates given above
+where the calculation does not help us, three of these are 0 or 20 Pop
+(provided we have identified the number glyph correctly, which is
+certainly none of the known glyphs for any of the numbers 1 to 19).
+This date would not be significant if 20 Pop were the last day of the
+month, but it would be very significant if it were the beginning day of
+the month, that is the beginning day of the New Year. I think,
+therefore, that it is safe to assume as a good working hypothesis that
+the beginning days of the month were designated as 0 or 20, and the
+last day of the month as 19.
+
+The second of our questions,--namely, whether this beginning day was
+called Day 0 or Day 20,--must now be taken up. Of course if we had
+decided that those cases which we have been considering represented the
+last days of the month, there would have been no question that the
+number glyphs which were not any of the numbers from 1 to 19 must be
+the number 20. It would have been very improbable that after having
+numbered the days of a month from 1 to 19 they would have called the
+last day 0. But it is not as certain that they might not have called
+the beginning day of a month 20, considering that twenty days had
+passed of the preceding month, and that their count was regulated by
+the number of days which had passed. As far as the month dates are
+concerned, however, it is absolutely unimportant whether the beginning
+day is called 0 or 20. Goodman says that the Mayas had no need of a
+zero (following the Romans in this respect), since zero was of no use
+as a multiplier. This is hardly conclusive. It may be true, as Goodman
+says, that the Mayas in their month dates spoke of the twenty days
+which had passed in the preceding month; but it is equally true that
+they may have expressed this idea by attaching the number zero to the
+beginning day on the ground that no days of the current month had
+elapsed. Indeed the latter explanation is the more credible, since, if
+they had spoken of the twenty days of the preceding month as having
+elapsed, it would seem possible at least, and perhaps probable, that
+they would have used the name of the preceding month as well, and would
+have called the beginning day of Yaxkin, for instance, 20 Xul and not
+20 Yaxkin. But this it seems they did not do, unless the instance on
+the Temple of the Cross and that of the Dresden Codex, already cited,
+would bear this construction. These instances, however, are
+contradicted by all the other cases and are themselves capable of a
+different interpretation. It would seem as if the Mayas probably called
+the beginning day of a month by the name of the current month, and that
+they attached the zero to it, meaning that no days of that month had
+elapsed. Moreover such a plan is very much easier for calculation and
+there is less liability to error; for it is natural to think of a day
+with the number 20 as following a day with the number 19 and as being
+the last day of a month containing 20 days, rather than the beginning
+day of a month. I do not place too much reliance on this, however, for
+it is hardly safe to argue back from what we at this time would
+consider the best thing to do, in order to find out what some other
+nation at some other time would have done.
+
+The chief evidence in favor of giving the 0 or 20 glyph the meaning of
+20 is, that this glyph is often drawn with a hand stretching across its
+lower part, especially when the main part of the glyph is a face. Now
+the face glyphs which represent the cycle of 144,000 days and the katun
+of 7,200 days are very similar, except that the cycle glyph has also a
+hand across its lower part, and the cycle is equal to 20 katuns; but
+this evidence is somewhat weak, since it is clear that even if the 0
+or 20 glyph should be decided to mean 20, in all calculations it is to
+be treated as 0, as is proved by many of the inscriptions of Palenque,
+Piedras Negras, Copan, and elsewhere.
+
+On the whole, therefore, I think the weight of evidence is in favor of
+the hypothesis that the Mayas called the beginning days of their month
+Day 0 and numbered the days of their month from 0 to 19.
+
+
+
+
+
+End of the Project Gutenberg EBook of Was the Beginning Day of the Maya
+Month Numbered Zero (or Twenty) or One?, by Charles P. Bowditch
+
+*** END OF THIS PROJECT GUTENBERG EBOOK BEGINNING DAY OF THE MAYA MONTH ***
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+Maya Month Numbered Zero (Or Twenty) Or One?, by Charles P. Bowditch.
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+<pre>
+
+The Project Gutenberg EBook of Was the Beginning Day of the Maya Month
+Numbered Zero (or Twenty) or One?, by Charles P. Bowditch
+
+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: Was the Beginning Day of the Maya Month Numbered Zero (or Twenty) or One?
+
+Author: Charles P. Bowditch
+
+Release Date: March 25, 2012 [EBook #39259]
+
+Language: English
+
+Character set encoding: ISO-8859-1
+
+*** START OF THIS PROJECT GUTENBERG EBOOK BEGINNING DAY OF THE MAYA MONTH ***
+
+
+
+
+Produced by Julia Miller, Diane Monico, and the Online
+Distributed Proofreading Team at http://www.pgdp.net (This
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+</pre>
+
+
+
+
+
+
+<h1>
+WAS THE BEGINNING DAY OF THE<br />
+MAYA MONTH NUMBERED ZERO<br />
+(OR TWENTY) OR ONE?</h1>
+
+
+<p class="title"><small>BY</small><br />
+
+CHARLES P. BOWDITCH<br /><br />
+
+
+<small>CAMBRIDGE</small><br />
+THE UNIVERSITY PRESS<br />
+1901
+</p>
+
+
+
+
+<hr class="chap" /><p><span class="pagenum"><a name="Page_1" id="Page_1">[Pg 1]</a></span></p>
+<h2>WAS THE BEGINNING DAY OF THE MAYA MONTH
+NUMBERED ZERO (OR TWENTY) OR ONE?</h2>
+
+
+<p>Goodman, in his elaborate and valuable book on the Maya Inscriptions,
+has made up his Tables on the supposition that the beginning day of the
+month was not called Day 1, but Day 20, giving the day this number
+because in his view the Mayas counted the number of days which had
+passed and not the current or passing day. That is, the Mayas,
+according to Goodman, used the same plan in counting their days which
+we use in counting our minutes and hours and which we depart from in
+counting our days. Thus, when we speak of January 1, we do not mean
+that one day has passed since January came in, but that the month of
+December has passed and that we are living in the day which when
+completed will be the first day of January. But when we say that it is
+one o'clock, we do not mean that we are living in the hour which when
+passed will be the first hour of the day or half-day, but we mean that
+one whole hour of the day or half-day has fully passed. Goodman's idea
+is that the Mayas used this system in counting their days of the month,
+their kins, uinals, tuns, katuns, and cycles. In other words he
+considers that the beginning day of the month Pop was not 1 Pop, but 20
+Pop, the beginning day of Uo was 20 Uo; that the beginning kin of a
+uinal was Kin 20, the beginning uinal of a tun was Uinal 18, the
+beginning tun of a katun was Tun 20, that the beginning katun of a
+cycle was Katun 20, and that the beginning cycle of a grand cycle was
+Cycle 13. The reason why Goodman substitutes 18 and 13 for 20 in the
+case of the uinals and cycles respectively is that these are the
+numbers of uinals and cycles which are needed to make one of the next
+higher units in his scale of numeration.</p><p><span class="pagenum"><a name="Page_2" id="Page_2">[Pg 2]</a></span></p>
+
+<p>Without considering the truth or error of his view in regard to the
+cycles, katuns, etc., let us try to solve the following questions:</p>
+
+<p>1st. Did the Mayas count the days of their month by the day which had
+passed, as we count our hours?</p>
+
+<p>2d. Was the number which they gave to the beginning day of the month 0
+or 20?</p>
+
+<p>For our answers to these questions, let us turn to pages 46-50 of the
+Dresden Codex. These pages contain three rows of twenty month dates
+each, and each of these dates is reached with but two exceptions by
+counting forward from the preceding date the number of days specified
+in red at the bottom of the pages, the first date of each row on page
+46 being the regular number of days distant from the last date of the
+same row on page 50.</p>
+
+<p>In the first row of dates, we find that the third date on page 48 is 12
+Chen. The number of days at the bottom of the page which need to be
+counted forward in order to reach the fourth date is 8. If the
+beginning day of the month were marked by the Mayas with 1, then the
+last day would be marked with 20, and by adding 8 days to 12 Chen, we
+should reach 20 Chen. But the date is not 20 Chen. The month is
+Yax,&mdash;the month immediately following Chen,&mdash;and the glyph which takes
+the place of the number has a form resembling two half-circles placed
+side by side. In other words, in this case 8 days from 12 Chen reach ?
+Yax, and as far as the first proposition is concerned, it is immaterial
+whether the form above given is called 0 or 20. Eight days have taken
+us out of the month Chen into the next month Yax, and to a day of that
+month which is not 1 Yax, but must be a day preceding 1 Yax, whether
+that is called 0 Yax or 20 Yax.</p>
+
+<p>Again, the first date of the first row of month dates on page 50 is 10
+Kankin, and the number at the bottom of the page to be added in order
+to reach the second date is 90. Counting forward 90 days from 10 Kankin
+we should reach 20 Cumhu, if the beginning<span class="pagenum"><a name="Page_3" id="Page_3">[Pg 3]</a></span> day of the month is 1
+Cumhu. But the month is not Cumhu nor is it Pop, but it is undoubtedly
+the glyph for the five supplementary days, Uayeb. The glyph which takes
+the place of the number is the same as that which has just been found
+before Yax. This is additional evidence that the months began with 0 or
+20 and not with 1.</p>
+
+<p>Again, on the first date of the second row of page 50 is 15 Cumhu, and
+the number of days to be added in order to reach the next date is 90,
+which appears at the bottom of the page. Counting forward this number
+of days from 15 Cumhu, we should reach 20 Zotz if the beginning day of
+the month were 1 Zotz. But the month is clearly Tzec, and the number is
+that which we have already found twice before as meaning 0 or 20.</p>
+
+<p>These cases would seem to show that after passing day 19 of any month,
+we reach the beginning day of the next month, and that this day is
+found with the glyph which means 0 or 20.</p>
+
+<p>Against this is the evidence of the last month date of the third row of
+page 49, which is clearly 9 Mac, and the number to be added at the
+bottom of the page is 236. This would take us to 20 Xul, if the
+beginning day of Xul is 1 Xul, but to 0 or 20 Yaxkin if the beginning
+day of Xul is 0 or 20. The first month date of the third row of page 50
+is 0 or 20 Xul. This, I think, is clear, although the Xul glyph is not
+exactly like the other glyphs of this month.</p>
+
+<p>Here then are three cases which support Goodman's view and one against
+it. The weight of evidence is therefore in favor of his system so far.</p>
+
+<p>In the Inscriptions there are not very many cases where the month has
+the zero or twenty sign attached to it, and there are still fewer cases
+where this occurs in a position where the question can be decided from
+the context as to whether the 0 or 20 is the last day of one month or
+the beginning day of the next month.</p><p><span class="pagenum"><a name="Page_4" id="Page_4">[Pg 4]</a></span></p>
+
+<p>On the inscription of the Temple of the Cross at Palenque, however, we
+have a month date which is 5 Ahau 3 Tzec. This is on R S 10. On R 8 to
+9 we find 1.16.7.17., if the thumb with the katun glyph means 1, as it
+almost surely does. Counting forward this number of days from 5 Ahau 3
+Tzec, we should reach 5 Caban 20 Zip if the month begins with 1, or 5
+Caban 0 or 20 Zotz if the beginning day is 0 or 20. On S 12 R 13 is 5
+Caban 0 or 20 Zotz. The form of the number glyph cannot fail to recall
+that of the similar glyphs in the Dresden Codex.</p>
+
+<p>De Rosny has given in his "Compte-Rendu d'une Mission Scientifique,"
+published in the "Mémoires de la Société d'Ethnographie," an admirable
+reproduction of the wooden inscription which came from Tikal. On Plate
+12 of this work we find on A B 1, 3 Ahau 3 Mol, and on B 2 A 3, we have
+2.11.12. By counting forward this number of days from 3 Ahau 3 Mol we
+reach 6 Eb 0 or 20 Pop, if the month begins with 0 or 20, but 6 Eb 5
+Uayeb if the month begins with 1. This is a particularly strong case,
+for the month is surely Pop and the number is certainly not 5, and is
+like those of the manuscripts and of the Temple of the Cross, which we
+have just commented on and which are in all probability 0 or 20.</p>
+
+<p>Again, on a part of a doorway in El Cayo, on C D 3 we find 13 Cimi 19
+Zotz; on H 3 G 4 is a number which seems to be 8.18.6. Counting forward
+we reach 9 Eb 20 Uo, if the month begins with 1, or 9 Eb 0 or 20 Zip,
+if the months begin with 0 or 20. Although the glyphs for Uo and Zip
+resemble each other, yet the date on I J 1 is clearly 9 Eb 0 or 20 Zip.
+It should be said, however, that the number on H 3 G 4 is somewhat
+effaced and very unusual, in showing 18 uinals, and that there is
+another date 5 ? 3 Yaxkin on E F 3.</p>
+
+<p>On the other hand the inscription of the Temple of the Cross shows us
+on D 3 C 4, 4 Ahau 8 Cumhu, and on D 5 C 6, is 1.9.2.,<span class="pagenum"><a name="Page_5" id="Page_5">[Pg 5]</a></span> which is equal
+to 1 year 177 days. Counting forward this number of days from 4 Ahau 8
+Cumhu we reach 13 Ik 20 Mol, if the month begins with 1, or 0 or 20
+Chen, if the month begins with 0 or 20. On C D 9 we find 13 Ik ? Mol.
+However, on D 13 to C 15 we have the long number 1.18.3.12.0., which
+counted forward from 13 Ik 20 Mol brings us to 9 Ik 15 Zac, which is
+not found anywhere near by. But if we count forward this number from 13
+Ik 0 or 20 Chen, we should reach 9 Ik 15 Ceh, which is found on E F 1.
+It would seem, therefore, that the glyph for Mol had been carved in
+error for that of Chen.</p>
+
+<p>Other cases where 0 or 20 probably occur before the month sign are the
+following:</p>
+
+
+
+<div class="center">
+<table border="1" cellpadding="4" cellspacing="0" summary="cases">
+<tr><td align="left">Copan,&nbsp;&nbsp;&nbsp; Altar</td><td align="left"> U,&nbsp;&nbsp;1&nbsp; to&nbsp;&nbsp; 2</td><td align="left">2 Caban</td><td align="left"> 0 or 20 Pop.</td></tr>
+<tr><td align="left"><span style="margin-left: 1em;">"&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; "</span></td><td align="left">U, 51 to 52</td><td align="left">3 Eb</td><td align="left">0 or 20 Pop.</td></tr>
+<tr><td align="left">Temple of the Cross,</td><td align="left">Q&nbsp;&nbsp; 2&nbsp; P&nbsp;&nbsp;&nbsp; 3</td><td align="left">11 Caban</td><td align="left"> 0 or 20 Pop.</td></tr>
+<tr><td align="left"><span style="margin-left: 1em;">"&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; "&nbsp;&nbsp; "&nbsp;&nbsp; &nbsp;&nbsp; "</span></td><td align="left">F&nbsp; 12&nbsp; E&nbsp; 13</td><td align="left">9 Ik</td><td align="left">0 or 20 Chen (J.T.G.)</td></tr>
+<tr><td align="left"><span style="margin-left: 1em;">"&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; "&nbsp;&nbsp; "&nbsp;&nbsp;&nbsp; &nbsp; "</span></td><td align="left">E F 9</td><td align="left">9 Ik</td><td align="left"> 0 or 20 Yax or Zac.</td></tr>
+</table></div>
+
+<p>The month glyph of the last example looks like Zac. If it is Yax it
+proves Goodman's theory by calculation.</p>
+
+<p>Thus we see that in three out of four cases in the Dresden Codex and in
+three cases out of four in the Inscriptions where the context is such
+as to throw light on the question, the evidence is in favor of
+concluding that the months began with a day 0 or 20 and not with a day
+1. Moreover in the single case in the Codex which tends to prove the
+contrary, it is interesting to see that the month glyph, Xul, is
+somewhat different from the other Xul glyphs, while in the doubtful
+case in the inscriptions, if the month glyph had been Chen and not Mol,
+it would have agreed with the dates before and after it. In other
+words, the calculations both before and after the date in question
+would be quite accurate if the month were Chen and if, therefore, the
+beginning day were 0 or 20,<span class="pagenum"><a name="Page_6" id="Page_6">[Pg 6]</a></span> while the glyph of Mol makes the
+calculation after that date inaccurate.</p>
+
+<p>All the evidence taken gives a very strong presumption in favor of
+Goodman's theory that the month began with 0 or 20.</p>
+
+<p>It is also interesting to notice that of the other dates given above
+where the calculation does not help us, three of these are 0 or 20 Pop
+(provided we have identified the number glyph correctly, which is
+certainly none of the known glyphs for any of the numbers 1 to 19).
+This date would not be significant if 20 Pop were the last day of the
+month, but it would be very significant if it were the beginning day of
+the month, that is the beginning day of the New Year. I think,
+therefore, that it is safe to assume as a good working hypothesis that
+the beginning days of the month were designated as 0 or 20, and the
+last day of the month as 19.</p>
+
+<p>The second of our questions,&mdash;namely, whether this beginning day was
+called Day 0 or Day 20,&mdash;must now be taken up. Of course if we had
+decided that those cases which we have been considering represented the
+last days of the month, there would have been no question that the
+number glyphs which were not any of the numbers from 1 to 19 must be
+the number 20. It would have been very improbable that after having
+numbered the days of a month from 1 to 19 they would have called the
+last day 0. But it is not as certain that they might not have called
+the beginning day of a month 20, considering that twenty days had
+passed of the preceding month, and that their count was regulated by
+the number of days which had passed. As far as the month dates are
+concerned, however, it is absolutely unimportant whether the beginning
+day is called 0 or 20. Goodman says that the Mayas had no need of a
+zero (following the Romans in this respect), since zero was of no use
+as a multiplier. This is hardly conclusive. It may be true, as Goodman
+says, that the Mayas in their month<span class="pagenum"><a name="Page_7" id="Page_7">[Pg 7]</a></span> dates spoke of the twenty days
+which had passed in the preceding month; but it is equally true that
+they may have expressed this idea by attaching the number zero to the
+beginning day on the ground that no days of the current month had
+elapsed. Indeed the latter explanation is the more credible, since, if
+they had spoken of the twenty days of the preceding month as having
+elapsed, it would seem possible at least, and perhaps probable, that
+they would have used the name of the preceding month as well, and would
+have called the beginning day of Yaxkin, for instance, 20 Xul and not
+20 Yaxkin. But this it seems they did not do, unless the instance on
+the Temple of the Cross and that of the Dresden Codex, already cited,
+would bear this construction. These instances, however, are
+contradicted by all the other cases and are themselves capable of a
+different interpretation. It would seem as if the Mayas probably called
+the beginning day of a month by the name of the current month, and that
+they attached the zero to it, meaning that no days of that month had
+elapsed. Moreover such a plan is very much easier for calculation and
+there is less liability to error; for it is natural to think of a day
+with the number 20 as following a day with the number 19 and as being
+the last day of a month containing 20 days, rather than the beginning
+day of a month. I do not place too much reliance on this, however, for
+it is hardly safe to argue back from what we at this time would
+consider the best thing to do, in order to find out what some other
+nation at some other time would have done.</p>
+
+<p>The chief evidence in favor of giving the 0 or 20 glyph the meaning of
+20 is, that this glyph is often drawn with a hand stretching across its
+lower part, especially when the main part of the glyph is a face. Now
+the face glyphs which represent the cycle of 144,000 days and the katun
+of 7,200 days are very similar, except that the cycle glyph has also a
+hand across its lower part, and the cycle is equal to 20 katuns; but
+this evidence<span class="pagenum"><a name="Page_8" id="Page_8">[Pg 8]</a></span> is somewhat weak, since it is clear that even if the 0
+or 20 glyph should be decided to mean 20, in all calculations it is to
+be treated as 0, as is proved by many of the inscriptions of Palenque,
+Piedras Negras, Copan, and elsewhere.</p>
+
+<p>On the whole, therefore, I think the weight of evidence is in favor of
+the hypothesis that the Mayas called the beginning days of their month
+Day 0 and numbered the days of their month from 0 to 19.</p>
+
+
+
+
+
+
+
+
+<pre>
+
+
+
+
+
+End of the Project Gutenberg EBook of Was the Beginning Day of the Maya
+Month Numbered Zero (or Twenty) or One?, by Charles P. Bowditch
+
+*** END OF THIS PROJECT GUTENBERG EBOOK BEGINNING DAY OF THE MAYA MONTH ***
+
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+The Project Gutenberg EBook of Was the Beginning Day of the Maya Month
+Numbered Zero (or Twenty) or One?, by Charles P. Bowditch
+
+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: Was the Beginning Day of the Maya Month Numbered Zero (or Twenty) or One?
+
+Author: Charles P. Bowditch
+
+Release Date: March 25, 2012 [EBook #39259]
+
+Language: English
+
+Character set encoding: ASCII
+
+*** START OF THIS PROJECT GUTENBERG EBOOK BEGINNING DAY OF THE MAYA MONTH ***
+
+
+
+
+Produced by Julia Miller, Diane Monico, and the Online
+Distributed Proofreading Team at http://www.pgdp.net (This
+file was produced from images generously made available
+by The Internet Archive)
+
+
+
+
+
+
+
+
+
+
+
+WAS THE BEGINNING DAY OF THE
+MAYA MONTH NUMBERED ZERO
+(OR TWENTY) OR ONE?
+
+
+BY
+
+CHARLES P. BOWDITCH
+
+
+CAMBRIDGE
+THE UNIVERSITY PRESS
+1901
+
+
+
+
+WAS THE BEGINNING DAY OF THE MAYA MONTH NUMBERED ZERO (OR TWENTY) OR
+ONE?
+
+
+Goodman, in his elaborate and valuable book on the Maya Inscriptions,
+has made up his Tables on the supposition that the beginning day of the
+month was not called Day 1, but Day 20, giving the day this number
+because in his view the Mayas counted the number of days which had
+passed and not the current or passing day. That is, the Mayas,
+according to Goodman, used the same plan in counting their days which
+we use in counting our minutes and hours and which we depart from in
+counting our days. Thus, when we speak of January 1, we do not mean
+that one day has passed since January came in, but that the month of
+December has passed and that we are living in the day which when
+completed will be the first day of January. But when we say that it is
+one o'clock, we do not mean that we are living in the hour which when
+passed will be the first hour of the day or half-day, but we mean that
+one whole hour of the day or half-day has fully passed. Goodman's idea
+is that the Mayas used this system in counting their days of the month,
+their kins, uinals, tuns, katuns, and cycles. In other words he
+considers that the beginning day of the month Pop was not 1 Pop, but 20
+Pop, the beginning day of Uo was 20 Uo; that the beginning kin of a
+uinal was Kin 20, the beginning uinal of a tun was Uinal 18, the
+beginning tun of a katun was Tun 20, that the beginning katun of a
+cycle was Katun 20, and that the beginning cycle of a grand cycle was
+Cycle 13. The reason why Goodman substitutes 18 and 13 for 20 in the
+case of the uinals and cycles respectively is that these are the
+numbers of uinals and cycles which are needed to make one of the next
+higher units in his scale of numeration.
+
+Without considering the truth or error of his view in regard to the
+cycles, katuns, etc., let us try to solve the following questions:
+
+1st. Did the Mayas count the days of their month by the day which had
+passed, as we count our hours?
+
+2d. Was the number which they gave to the beginning day of the month 0
+or 20?
+
+For our answers to these questions, let us turn to pages 46-50 of the
+Dresden Codex. These pages contain three rows of twenty month dates
+each, and each of these dates is reached with but two exceptions by
+counting forward from the preceding date the number of days specified
+in red at the bottom of the pages, the first date of each row on page
+46 being the regular number of days distant from the last date of the
+same row on page 50.
+
+In the first row of dates, we find that the third date on page 48 is 12
+Chen. The number of days at the bottom of the page which need to be
+counted forward in order to reach the fourth date is 8. If the
+beginning day of the month were marked by the Mayas with 1, then the
+last day would be marked with 20, and by adding 8 days to 12 Chen, we
+should reach 20 Chen. But the date is not 20 Chen. The month is
+Yax,--the month immediately following Chen,--and the glyph which takes
+the place of the number has a form resembling two half-circles placed
+side by side. In other words, in this case 8 days from 12 Chen reach ?
+Yax, and as far as the first proposition is concerned, it is immaterial
+whether the form above given is called 0 or 20. Eight days have taken
+us out of the month Chen into the next month Yax, and to a day of that
+month which is not 1 Yax, but must be a day preceding 1 Yax, whether
+that is called 0 Yax or 20 Yax.
+
+Again, the first date of the first row of month dates on page 50 is 10
+Kankin, and the number at the bottom of the page to be added in order
+to reach the second date is 90. Counting forward 90 days from 10 Kankin
+we should reach 20 Cumhu, if the beginning day of the month is 1
+Cumhu. But the month is not Cumhu nor is it Pop, but it is undoubtedly
+the glyph for the five supplementary days, Uayeb. The glyph which takes
+the place of the number is the same as that which has just been found
+before Yax. This is additional evidence that the months began with 0 or
+20 and not with 1.
+
+Again, on the first date of the second row of page 50 is 15 Cumhu, and
+the number of days to be added in order to reach the next date is 90,
+which appears at the bottom of the page. Counting forward this number
+of days from 15 Cumhu, we should reach 20 Zotz if the beginning day of
+the month were 1 Zotz. But the month is clearly Tzec, and the number is
+that which we have already found twice before as meaning 0 or 20.
+
+These cases would seem to show that after passing day 19 of any month,
+we reach the beginning day of the next month, and that this day is
+found with the glyph which means 0 or 20.
+
+Against this is the evidence of the last month date of the third row of
+page 49, which is clearly 9 Mac, and the number to be added at the
+bottom of the page is 236. This would take us to 20 Xul, if the
+beginning day of Xul is 1 Xul, but to 0 or 20 Yaxkin if the beginning
+day of Xul is 0 or 20. The first month date of the third row of page 50
+is 0 or 20 Xul. This, I think, is clear, although the Xul glyph is not
+exactly like the other glyphs of this month.
+
+Here then are three cases which support Goodman's view and one against
+it. The weight of evidence is therefore in favor of his system so far.
+
+In the Inscriptions there are not very many cases where the month has
+the zero or twenty sign attached to it, and there are still fewer cases
+where this occurs in a position where the question can be decided from
+the context as to whether the 0 or 20 is the last day of one month or
+the beginning day of the next month.
+
+On the inscription of the Temple of the Cross at Palenque, however, we
+have a month date which is 5 Ahau 3 Tzec. This is on R S 10. On R 8 to
+9 we find 1.16.7.17., if the thumb with the katun glyph means 1, as it
+almost surely does. Counting forward this number of days from 5 Ahau 3
+Tzec, we should reach 5 Caban 20 Zip if the month begins with 1, or 5
+Caban 0 or 20 Zotz if the beginning day is 0 or 20. On S 12 R 13 is 5
+Caban 0 or 20 Zotz. The form of the number glyph cannot fail to recall
+that of the similar glyphs in the Dresden Codex.
+
+De Rosny has given in his "Compte-Rendu d'une Mission Scientifique,"
+published in the "Memoires de la Societe d'Ethnographie," an admirable
+reproduction of the wooden inscription which came from Tikal. On Plate
+12 of this work we find on A B 1, 3 Ahau 3 Mol, and on B 2 A 3, we have
+2.11.12. By counting forward this number of days from 3 Ahau 3 Mol we
+reach 6 Eb 0 or 20 Pop, if the month begins with 0 or 20, but 6 Eb 5
+Uayeb if the month begins with 1. This is a particularly strong case,
+for the month is surely Pop and the number is certainly not 5, and is
+like those of the manuscripts and of the Temple of the Cross, which we
+have just commented on and which are in all probability 0 or 20.
+
+Again, on a part of a doorway in El Cayo, on C D 3 we find 13 Cimi 19
+Zotz; on H 3 G 4 is a number which seems to be 8.18.6. Counting forward
+we reach 9 Eb 20 Uo, if the month begins with 1, or 9 Eb 0 or 20 Zip,
+if the months begin with 0 or 20. Although the glyphs for Uo and Zip
+resemble each other, yet the date on I J 1 is clearly 9 Eb 0 or 20 Zip.
+It should be said, however, that the number on H 3 G 4 is somewhat
+effaced and very unusual, in showing 18 uinals, and that there is
+another date 5 ? 3 Yaxkin on E F 3.
+
+On the other hand the inscription of the Temple of the Cross shows us
+on D 3 C 4, 4 Ahau 8 Cumhu, and on D 5 C 6, is 1.9.2., which is equal
+to 1 year 177 days. Counting forward this number of days from 4 Ahau 8
+Cumhu we reach 13 Ik 20 Mol, if the month begins with 1, or 0 or 20
+Chen, if the month begins with 0 or 20. On C D 9 we find 13 Ik ? Mol.
+However, on D 13 to C 15 we have the long number 1.18.3.12.0., which
+counted forward from 13 Ik 20 Mol brings us to 9 Ik 15 Zac, which is
+not found anywhere near by. But if we count forward this number from 13
+Ik 0 or 20 Chen, we should reach 9 Ik 15 Ceh, which is found on E F 1.
+It would seem, therefore, that the glyph for Mol had been carved in
+error for that of Chen.
+
+Other cases where 0 or 20 probably occur before the month sign are the
+following:
+
+Copan,         Altar U,  1 to  2     2 Caban 0 or 20 Pop.
+  "              "   U, 51 to 52     3 Eb    0 or 20 Pop.
+Temple of the Cross, Q   2 P   3    11 Caban 0 or 20 Pop.
+  "    "  "    "     F  12 E  13     9 Ik    0 or 20 Chen (J.T.G.)
+  "    "  "    "     E F 9           9 Ik    0 or 20 Yax or Zac.
+
+The month glyph of the last example looks like Zac. If it is Yax it
+proves Goodman's theory by calculation.
+
+Thus we see that in three out of four cases in the Dresden Codex and in
+three cases out of four in the Inscriptions where the context is such
+as to throw light on the question, the evidence is in favor of
+concluding that the months began with a day 0 or 20 and not with a day
+1. Moreover in the single case in the Codex which tends to prove the
+contrary, it is interesting to see that the month glyph, Xul, is
+somewhat different from the other Xul glyphs, while in the doubtful
+case in the inscriptions, if the month glyph had been Chen and not Mol,
+it would have agreed with the dates before and after it. In other
+words, the calculations both before and after the date in question
+would be quite accurate if the month were Chen and if, therefore, the
+beginning day were 0 or 20, while the glyph of Mol makes the
+calculation after that date inaccurate.
+
+All the evidence taken gives a very strong presumption in favor of
+Goodman's theory that the month began with 0 or 20.
+
+It is also interesting to notice that of the other dates given above
+where the calculation does not help us, three of these are 0 or 20 Pop
+(provided we have identified the number glyph correctly, which is
+certainly none of the known glyphs for any of the numbers 1 to 19).
+This date would not be significant if 20 Pop were the last day of the
+month, but it would be very significant if it were the beginning day of
+the month, that is the beginning day of the New Year. I think,
+therefore, that it is safe to assume as a good working hypothesis that
+the beginning days of the month were designated as 0 or 20, and the
+last day of the month as 19.
+
+The second of our questions,--namely, whether this beginning day was
+called Day 0 or Day 20,--must now be taken up. Of course if we had
+decided that those cases which we have been considering represented the
+last days of the month, there would have been no question that the
+number glyphs which were not any of the numbers from 1 to 19 must be
+the number 20. It would have been very improbable that after having
+numbered the days of a month from 1 to 19 they would have called the
+last day 0. But it is not as certain that they might not have called
+the beginning day of a month 20, considering that twenty days had
+passed of the preceding month, and that their count was regulated by
+the number of days which had passed. As far as the month dates are
+concerned, however, it is absolutely unimportant whether the beginning
+day is called 0 or 20. Goodman says that the Mayas had no need of a
+zero (following the Romans in this respect), since zero was of no use
+as a multiplier. This is hardly conclusive. It may be true, as Goodman
+says, that the Mayas in their month dates spoke of the twenty days
+which had passed in the preceding month; but it is equally true that
+they may have expressed this idea by attaching the number zero to the
+beginning day on the ground that no days of the current month had
+elapsed. Indeed the latter explanation is the more credible, since, if
+they had spoken of the twenty days of the preceding month as having
+elapsed, it would seem possible at least, and perhaps probable, that
+they would have used the name of the preceding month as well, and would
+have called the beginning day of Yaxkin, for instance, 20 Xul and not
+20 Yaxkin. But this it seems they did not do, unless the instance on
+the Temple of the Cross and that of the Dresden Codex, already cited,
+would bear this construction. These instances, however, are
+contradicted by all the other cases and are themselves capable of a
+different interpretation. It would seem as if the Mayas probably called
+the beginning day of a month by the name of the current month, and that
+they attached the zero to it, meaning that no days of that month had
+elapsed. Moreover such a plan is very much easier for calculation and
+there is less liability to error; for it is natural to think of a day
+with the number 20 as following a day with the number 19 and as being
+the last day of a month containing 20 days, rather than the beginning
+day of a month. I do not place too much reliance on this, however, for
+it is hardly safe to argue back from what we at this time would
+consider the best thing to do, in order to find out what some other
+nation at some other time would have done.
+
+The chief evidence in favor of giving the 0 or 20 glyph the meaning of
+20 is, that this glyph is often drawn with a hand stretching across its
+lower part, especially when the main part of the glyph is a face. Now
+the face glyphs which represent the cycle of 144,000 days and the katun
+of 7,200 days are very similar, except that the cycle glyph has also a
+hand across its lower part, and the cycle is equal to 20 katuns; but
+this evidence is somewhat weak, since it is clear that even if the 0
+or 20 glyph should be decided to mean 20, in all calculations it is to
+be treated as 0, as is proved by many of the inscriptions of Palenque,
+Piedras Negras, Copan, and elsewhere.
+
+On the whole, therefore, I think the weight of evidence is in favor of
+the hypothesis that the Mayas called the beginning days of their month
+Day 0 and numbered the days of their month from 0 to 19.
+
+
+
+
+
+End of the Project Gutenberg EBook of Was the Beginning Day of the Maya
+Month Numbered Zero (or Twenty) or One?, by Charles P. Bowditch
+
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