[Aztlan] Perhaps Calendrics, architecture

Thu May 11 10:09:57 CDT 2006

Listeros in order to understand why there is a sacred calendar of 260 
days, one must understand its function. Its function has to fulfill 
certain requirements or otherwise it is meaningles. The answer to some 
of this issues raised in this e-mail is to be found not in the Maya 
calendaric system but in the Mesoamerican calendaric system, that is in 
the whole of which the Mayan system is only a part . So when looking at 
the whole of the Calendaric system and putting their different 
particularities behind, (names of days, beginings of yearly cycles 
which vary according to the culture, etc,) One can look at the whole 
mechanism of the calendar and undertsand why there is a 260 system.  
I'm now finishing my text on the calendar and in it you will find that 
the 260 day calendar is a function of a 26,000 (and change since it is 
a venusian calendar) Wey Tonatiuh or great sun. If the Wey Tonatiuh was 
in the order of say 28,000 years then the sacred calendar would have 
been designd as a 280 day calendar. This Wei Tonatiuh composed of five 
suns is derived from knowing an accurate number for the tropic year and 
an accurate number for synodic cycles of venus up to the tenth, no more 
(583.9), which is also the estimated number for sinodic cyles in the 
LC.  for those who are interested, here is a link to the spanish 
version and in it is also a brief chapter devoted to the present 
Oxlakatun.
http://homepage.mac.com/villas1/Calendario/index.html

for an english version which is not as complete as the spanish 
http://homepage.mac.com/villas1/Calendar/index.html

either version it is not finished and I need to make several changes 
but the system is clear. One does not require higher mathematics to 
come up with this calendar, one requires centuries of careful 
observations with the naked eye.

Marco Villaseñor

On May 10, 2006, at 6:33 PM, Michael Finley wrote:

> Sid, I think you have pointed to the principal  problem with many of 
> the speculative theories about the calendar. For example, it seems to 
> me that  neither astronomy nor archeology stand in the way of  the 
> hypothesis that the long count was contrived to end (or complete a 
> Great Cycle of 13 baktuns) on a solstice, or even that it was 
> contrived to end on a solstice  at a time when the solstice point was 
> near the centre line of Milky Way (a popular idea of course among New 
> Age admirers of the Maya, of course). The biggest problem  with such 
> views (apart from clear confirmation from the Classical Maya 
> themselves) is trying to imagine (much less find evidence for) the 
> logistics of the development of such a calendar.  The key to accurate 
> observational astronomy is observation over long periods of time. As 
> Ptolemy wrote of the moon "It is not proper, we think, to be haphazard 
> in the use of observations for this purpose.  For a general 
> understanding of the Moon it is best to use methods which cover a long 
> period of time"  --- and the Maya observers who carried out the  
> eclipse table in the Dresden Codex to 405 lunar months would no doubt 
> have agreed.  But , as you suggest, how do you do it before you have a 
> good calendar?
>
> Having said that, in the spirit of speculation you invite,  I'd 
> suggest that neither the 13 piles of 20 (or 20 piles of 13) days that 
> became the 260 day count, nor the year of 360-365 days require 
> exceptional mathematical or astronomical acumen (compared to similar 
> cultures) --- Why 13 and 20 is a mystery, of course, but not a 
> deal-breaker.   The peculiar genius of  Mesoamerican calendar makers 
> may have begun with the notion of combining these cycles into the 
> calendar round.  I don't think any other calendrical system has tried 
> to solve the problem of fitting cycles together by finding common 
> multiples rather than by adjusting the cycles by intercalating leap 
> days etc. But novel as this is, it  seems to require good mathematical 
> imagination rather than  a developed "higher math."  Given that 20 is 
> a basic unit in Mesoamerican counting, why not also record 20 year 
> periods?  Then it's only necessary to notice that  katun end dates 
> cycle through the 13 days Ahaw, and you have the u kahlay katanob of 
> 13 katuns, which is commensurate with the tzolk'in.  This may have 
> been sufficient to record a lot of long term astronomical 
> observations. Note we still don't  need place-holding arithmetic at 
> this stage.  So I guess it is possible to plausibly imagine that the 
> calendar developed in such a way that when the long count was 
> "invented," any number of complicated numerological or astronomical  
> features could have been embedded in it.  Whether any such features 
> were imbedded is of course another question. I'm far from being 
> convinced myself.
>
> Michael Finley
>
> Sid Hollander wrote:
>
>> Perhaps *Calendrics, architecture*
>>
>> Some (the ancient among you)will recall the early 60's, Sputnik and
>> Yale's  answer
>> to our civilizations' math decline - SMSG (School Mathematics Study
>> Group-sometimes referred to as Some Math, Some Garbage). As a 
>> beginning math
>> teacher I was enthralled by it. I taught various number bases and 
>> historical
>> numeration systems (but not the Maya). Imagine my surprise when on 
>> vacation
>> in the Yucatan I discovered the Maya and thus began my Maya calendar
>> studies.  So much for the background.
>>
>>
>>
>>> From that time I have been trying (w/o success) to piece together a 
>>> possible
>>
>> chronological sequence of events that would trace development  of  
>> the Maya
>> Calendar within their mathematical and astronomical knowledge. Of 
>> course,
>> this sequence would need to be:
>>
>>
>>
>>   - Mathematically and otherwise reasonable
>>   - Not conflict with current historical and/or archaeological 'fact'
>>
>>
>>
>>
>>
>> I am NOT trying to create a time line, merely a hypothetical sequence.
>>
>>
>>
>> I am inspired by the current thread  *Re: [Aztlan] Calendrics, 
>> architecture
>> *because, it appears to me, that those speaking to the subject take 
>> the
>> whole calendar as if it was unveiled in its entirety one bright day 
>> by the
>> calendar committee in a neat packaged. If you believe this, what has
>> happened to the system used before this.  There had to be one!  
>> Certainly
>> the data had to be recorded and I mean recorded for many, MANY 
>> centuries.
>> Doesn't that in itself call for some type of calendar/recording 
>> system?  What
>> was it?  Surely, to follow the current thread one must believe the CR 
>> etc.
>> is as it is because to be otherwise would not fit the ideas being 
>> presented
>> (i.e. solar tracking, solstices, beginning of long counts and these 
>> use of
>> all to 'track' tropical years to umpteen digits past the decimal 
>> point.  We
>> all love the Maya but I think that some are trying to reverse 
>> engineer their
>> calendar to fit your hypothesis.
>>
>>
>>
>> So, where does it all begin?
>>
>>
>>
>> No doubt with a limited counting system where by the Maya made a 1 to 
>> 1
>> correspondence with their digits. Without numerals perhaps they did  
>> some
>> kind of 'signing' I imagine them extending fingers on one hand 
>> towards the
>> listener.  The listener sees the ends of the fingers as small circles.
>> Perhaps when the signer extended his hand in a hand shaking manner 
>> five
>> circles (one on top the other) in a 'bar'. Well it doesn't take too 
>> much to
>> imagine pictographs developing to make 20 different digits (namely 1 
>> thru
>> 20!) in a bars-dots system.
>>
>>
>>
>> We are at a critical point here.   We have no Zero, we have no 
>> positional
>> notation (i.e. a LC).  But what 'calendar' development capacity do we 
>> have?
>> If we had 20 gods we could number them at least.  If we did, I doubt 
>> that we
>> would be ready to combine them with 13 for the lack of easy counting 
>> (but
>> doable with just plain stacking of 20's and perhaps this eventually 
>> leads to
>> a positional number system based on perhaps 20 but I need to be 
>> convinced of
>> this.  We (sorry that I say we but I am trying to imagine myself 
>> there) also
>> with this 1 to 1 correspondence could easily track lunations (after 
>> all a 29
>> or 30 count is not difficult to imagine) and throw in a C, D and E 
>> glyph
>> without more math sophistication.  Goodness we could even handle 
>> Lords of
>> the Night!. So, where are we?  It is easier to ask, "Where aren't 
>> we?"  We
>> are not at the point where we can collect large numbers to record 
>> lengthy
>> astronomical data.   It is very, very difficult to record LONG 
>> periods of
>> astronomical phenomena with piles of twenties. It would be like 
>> trying to
>> record Bill Gates net worth with stacks of 4 nickels!
>>
>> Are some of you on this list willing to develop this hypothetical 
>> sequence
>> at greater length?
>>
>>
>> -- 
>> Sid Hollander
>> Merida, Yucatan
>> Mexico CP 97310
>> 52-999-941.OO.21
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