[Aztlan] Perhaps Calendrics, architecture

[Michael Finley]

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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