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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.