[Aztlan] Dresden 4 Ajaw 8 Cumk'u, Palenque House E

Tue Jul 22 11:25:10 CDT 2008

Dear Lloyd and Friends,

Thank you for your very careful analysis of my words, phrasings and speculations. I believe research not debated is research dead!. I put forth these two examples (one relating to "Zero Day" and the the other relating to a deep time mythical event) to show that there is still much to understand and explore about myth and associated Maya mathematics. Not only have the "Zero Day" events from the Dresden Codex been largely overlooked (in my opinion) but there has not been a complete analysis of the source data on the subject. For instance, just look the text and iconography of the 7 and 11 Gods (K2796 and K7750). The differences and similarities between these two extraordinary (Lloyd I hope the e-word is permissible here) vases reveal additional insights about the true identity of the gods depicted, associated cyclic renewal rites, as well asthe gods and their relationship to the Naranjo rulers mentioned in the vase Dedicatory Text.

 Also numerouspassages
yield accounts of what transpired during this most sacred of all
days and from this data we know that several events took place on "Zero Day." Are these events part of a shared mythology? If the Classic Maya did share a core mythos of the day's events then how should  the day’s events be organized? Today they
remain a jumbled bag of gods, actions and place names. In my humble estimation, there is much work to be done concerning the gods, actions and places of  "Zero Day." 

The data concerning the Palenque House E Text is tentative at best since parts of the opening LC and the DN that directly follows are cracked away and are difficult to reconstruct. Yet enough remains to speculate on certain values. You are correct in noting that internal math does not agree with the shown values of a few of the cycles. I look forward to sharing the new composite photos of this beautiful text

All the Best,

Carl

----- Original Message ----
From: "ECOLING at aol.com" <ECOLING at aol.com>
To: aztlan at lists.famsi.org
Sent: Monday, July 21, 2008 9:58:38 PM
Subject: [Aztlan] Dresden 4 Ajaw 8 Cumk'u, Palenque House E

Here some commentary on content items in Carl Calloway's posting:

<<In the Dresden Codex,   the day appears no less that 24 times and it is the 
benchmark for denoting the position of various cycles and the footsteps of 
gods.>>

4 Ajaw 8 Cumk'u is the calendar round of the starting point of the current 
5-place long count,
very closely analogous to our "zero".   (We do not normally refer to the 
starting point
of our common calendar as a "zero" either -- How about the end of 31st 
December of
the year 1 BCE / BC, or the beginning of the day 1 January of the year 1 CE / 
AD?
Do we have a name for that? If we do, would it be usable for the Mayan 
near-analog?
(In the sentence just above of course I'm using historical not astronomical 
dating.)

The 4 Ajaw 8 Cumk'u date is the base for a number of date specifications 
in the Dresden.   Understood rarely by the notation <13.0.0.0.0>,
but a few times 13 Baktuns is implied by a notation 12.x.x.x.x
where the distance is small to a date in the current long count.

This includes several specialized "long reckonings",
in which a distance number greater than the long-count date referred to
is counted from a base which *precedes* the 4 Ajaw 8 Cumk'u, 
by an amount specified in a "ring number" (likely referring to the part of
the larger distance number which was already completed by 4 Ajaw 8 Cumk'u).

It also includes some which take a date *after* 4 Ajaw 8 Cumk'u 
and start a distance number from that latter date.
I'll get back to that after a couple of quotations from Carl Calloway.

<<For instance, see Dresden page 51 Section A which is the start of the lunar 
tables. Column 1 begins with the 4 Ajaw 8 Kumk'u Era date and is followed imme
diately by a 12 Lamat day- a date that serves as one of four 'lubs' by which 
eclipses are reckoned from. Following the day 12 Lamat there is "8 k'in ti 
ha'". If one counts forward 8 days from Era date one will indeed fall upon the 
day 12 Lamat (we'll leave what "ti ha" means for a future discussion).
>>

[I think it means approximately "8 days above that", in the sense of later 
than that.]

<<Now, turn to page 52, Section A, Column 4. David Stuart first pointed out 
this odd LC/DN to me. This is a very strange passage that incorporates a giant 
DN? of 13 x 13 cycles (or is the column acting as a giant LC??) that leads to 
the Era date that begins the start of Column 5. 
>>

[It may not be a Distance Number at all.   So then it would not "lead to" the 
Calendar Round
at the top of the next column.   Rather it appears to be a long count whose 
value is the same 
if one eliminates that series of "13"s.   Just as is true on the Yaxchilan 
lintel 
with a series of "13"s followed by a long count in the 9th Baktun.   Also 
there not a DN.
This is one way of looking at it which allows the series of "13"s to simply 
signal
completion of larger units, without implying any mathematics.

<<Back to the top of Column 4-Here, the first glyph is effaced but seems be 
the head of a skull or death head. Next is " 8 k'ins 1 winal 5 ti haab' 2 ti 
ha'" and is followed by the DN of 13 x 13.   If one counts forward from Era Day 
a DN 5.1.8 days they do indeed land upon 12 Lamat 11 Kumk'u-another 12 Lamat 
lub.
>>

This second "do indeed" is misleading, as it implies in normal English
that landing upon that date was somehow predicted, which it was not.  
It is simply observed as in the text.  
The first "will indeed" in the preceding paragraph is marginally justified 
if by that one means merely that the DN of 8 days leads to a Tzolk'in value 
of 12 Lamat, so that the two are *consistent*.   (Nothing more yet, at 
least.)

This can all be phrased a bit more accurately.  
First, 8 days after 4 Ajaw 8 Cumk'u is 12 Lamat 16 Cumk'u.
The additional 5 TUUNs and 1 WINAL is 5 x (360 + 4), 
and that number of days 1820 is also divisible by 260, 7 x 260 = 1820.
So it yields the same Tzolk'in day but is 5 days short of an even number of 36
5-day years.
So from 12 Lamat 16 Cumk'u with an interval 5.1.0 
we arrive at a date 12 Lamat 11 Cumk'u.

More specifically, the date (13).0.0.0.8      12 Lamat (16 Cumk'u)
may *not* be one of the Lub's of the Eclipse table, it may be rather a base 
date after
4 Ajaw 8 Cumk'u which is analogous to the dates preceding 4 Ajaw 8 Cumk'u,
reached by ring numbers in the other kind of long reckoning.
>From that base date, Distance Numbers lead to possible Lub's.
Here
   0.   0.   0.   0.   8   (Long count reached on p.51A) (not a Lub?)
+9.16.   4.10.   0   (yields)
(9.16.   4.10.   8)   12 Lamat (16 Cumk'u).  

[Astronomical references in the Eclipse Table to positions or motions of
planets confirm this last as the principal Lub of the Table.
This is one principal topic in a forthcoming book on planetary references
in the Dresden.]

***

If Carl's transcriptions of Palenque House E notations are correct, he may 
have an 
argument for use of "13" in a mathematical computation with higher units.
I repeat it below with the long counts and distance number spaced so the 
subtraction operation can be more easily scanned.
There are two kinds of caveats I would have for his argument
(which does not mean I think it is wrong, just that I am being careful).
First, there is no position in the place-notation string for which
values in all three numbers are certain.  
Second, the date "9 IK' 0 Sak" is associated with a problem
in calculations as pointed out already by Linda Schele.   My solution is
different from hers, because I take the "9 IK' " to be a symbolic reference
to the simultaneous passage of Mercury and Venus through inferior 
conjunction,
their paths almost coinciding for some time.   (9 Wind is the Mixtec name
of the wind god, Ehecatl, Venus, etc.)   This is also discussed in the book
referred to shortly above.

But it will be very interesting if Carl is correct in reconstructing the 
numbers
in this way.   At least then we would have a case of "13" being used in
calculations for larger units,
something more than the starting point of the current 5-place long count
being taken as 13 Baktuns, so dates shortly before that are notated 
12.x.x.x.x
Whether this was abstract play or manifested a deeper belief in
13 Baktuns = 1 Pictun is a somewhat different question.

<<I also would like to point out that there is preliminary evidence to sugge
st that the scribes at Palenque were calculating deep time, past events with 
the higher periods set at 13. The internal math of the Palenque House E Painted 
Inscription implies (if my analysis of the recorded LC and DN is correct) that 
the Piktuns and the Kalb'tuns   must be   counting to 13. Below is my 
plausible and partial reconstruction given the information so far (by the way the 
entire paper of the Palenque House E Painted Text will be posted online in August 
2008, until then, I'm happy to send it to you upon request): (Note: numbers 
within parentheses (#) equal mathematically reconstructed values):

<<
(13.) (13.)    2.        0.      0.    10.       2.      9 IK' 0 Sak 
(Accession of Triad Progenitor)

    1.       2. (17.?) (17.) 11.    13.        6?               (subtract) 
(Distance Number)

(11?.) 10.    (4.?)     2.    (8?)(14.?)(16?)    (? KIB) (Haab?) (Opening LC 
Date)

<<What I find fascinating here is the the values for the Piktuns cycles of 
the DN (2) and the opening LC (10) are known recorded values (that are clearly 
painted) so that X - 2 = 10.   In this case   X can not   possibly   equal   20 
but must   hold a value of 13. So it   is very, very tentatively SEEMS that 
the Palenque scribes in this instance, were calculating the higher periods 
above a B'aktun up to a value of 13. We have so few of these deep time events 
recorded and a full analysis of their calculations in connection with Era Day 
calcs. is badly needed before we can come to any real firm conclusions.  
>>

So far, this appears good on the surface (without examinining drawings or 
photos of the originals).
But notice that if 17 Baktuns is subtracted from a long count with "2" in the 
Baktuns position
(reduced to "1" by the subtraction of 17 K'atuns from 0 K'atuns),
then we can get 4? Baktuns as the result only if there are 20, not 13, 
Baktuns in a Pictun.
If there were only 13, then 17 should not even occur in the Baktuns position 
of the
Distance Number being subtracted (
it should be not 17.17.11.13.6 but rather 1.4.17.11.13.6)
And if despite that it did occur, the result in the bottom line should have 
been

(11?.)    9.    [10.]     2.    (8?)(14.?)(16?)    (? KIB) (Haab?) (Opening 
LC Date)

Note that subtracting 17 from 2 Baktuns requires carrying *2* not *1* from
the Pictuns position, since 1+13 = 14 which is still less than 17.
Carrying 2 Pictuns, 1+26 = 27 less 17 = [10], the entry given just above.
So 13 - 2 - 2 (last from carrying to Baktuns place) = 9.

If the Calabtuns long count entry is 13 and the DN Calabtuns is 1,
the resulting Calabtuns should be [12] not (11?.).

So we have the oddity that for the Palenque House E text in Carl Calloway's
     reading of partly missing and damaged glyphs,
Calabtuns go up to 13 ?
Pictuns go up to 13 ?
Baktuns go up to 20 ! (unlike the Dresden examples 
        where Baktuns going up to 13 is implied by several calculations)

So problems remain of several kinds.
But it remains very interesting.

***

However, the following is not directly related to it.  

<<It is fascinating to look at how Classic and Post Classic scribes treat 
this most important day both mathematically and mythologically.   If "Past is 
Prologue" then one wonders if the Era Day events of the past will repeat 
themselves in 2012.   If so, it   is then important to understand fully those events 
of Era Day and the gods and actions surrounding them.
>>

The House E calculation is not about the data 4 Ajaw 8 Cumk'u.
And there is nothing in the specifics which Carl has presented
which justify using either the term "Era Day" or the speculation
about "the era events of the past" repeating themselves in 2012.
The date 4 Ajaw 8 Cumk'u is very rarely the subject of discussion
of events occurring *on that date*.   Rather, it is a base point for
calculating to dates before it or after it.   It would be interesting in
fact to tally those occasions on which events *at* that date are
the subject of discussion.   Is the "vase of the Seven Gods" one such?
Or are those events *preceding* 4 Ajaw 8 Cumk'u ?
I don't remember offhand, but no doubt others have already
looked at this in some detail.

Best wishes,
Lloyd

Lloyd Anderson
Ecological Linguistics
PO Box 15156
Washington DC 20003
ecoling at aol.com
202-547-7683

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