[Aztlan] Calendrics, architecture
vgray (gotsky)
vgray at gotsky.com
Mon May 1 12:53:16 CDT 2006
David,
Egypt adopted a leap year adjustment methodology in the early 3rd century
BCE or late 4th BCE, and this development occurred rather late, not because
the astronomy of the time was lacking, but rather certain superstitions
regarding calendars prevented an earlier adoption. Similar practices around
the world delayed calendar developments, and the existence of but a single
calendric base period tended to focus attention on a 360 or 365-day
calendar, where invariably the two did not coexist peaceably - the one
tended to preempt the other. In other words there existed no tendency to use
a multiplicity of tropical calendars, and the lunar and tropical calendars
were difficult to align to each other over the course of time. The 360-day
calendar makes a very nice tropical calendar, all as much accomplished as a
365-day variant, but this is often lost on the secular authorities ordained
to institute a calendar, and so earlier calendric endeavors adopted a narrow
focus. This tendency around the world led to the use of but a single
calendric base period, which naturally developed into a Julian style
calendar, with a periodic calendric base period adjustment every 4y, thus
preempting the importance of the lunar calendar to some extent. Further the
lunar calendar as an independent effort was also periodically intercalated
with whole lunar months to keep some semblance of alignment between the
tropical and lunar calendars, as in for example in the Middle East. The
astronomy necessary to characterize the tropical year was usually developed
several centuries before this knowledge was applied to developing a change
to the calendar, and there appears to have been societal pressure against
making any changes. The 364 day Enoch calendar was an attempt to synchronize
3 conventional or calculational years (1092 days) with 37 lunations,
accepting an almost 4-day tropical station divergence between the
calculational year and tropical year, in order to accommodate lunar orbital
behavior, but most efforts usually gravitated towards a more accurately
orchestrated tropical calendar, with lunar month intercalations accommodated
as a separate effort. Certain parts of the Middle East to this very day even
favor a primarily lunar based calendar of 354-days, with less emphasis on
the tropical calendar. All these efforts have one theme in common - a
limitation in the number of calendric base periods adopted to gauge orbital
behavior, in association with a decision to develop a fixed tropical
calendar (i.e. where individual dates have a fixed alignment to the
heavens). Most of the world perceived the leap year phenomenon as a problem
that needed to be eliminated, and once eliminated, there was no longer any
need to study the phenomenon any further.
Developments around the world followed similar practices, but the
Mesoamerican experience is unique, and I believe the Olmecs developed their
astronomy quite early too, aligning their citadels to the primary celestial
sphere events. From San Lorenzo ca 1200 BCE and La Venta ca. 1000 BCE, to
the waning years of the Olmec civilization in the 4th century BCE, over 800y
of astronomical observations persisted, and this is not counting the earlier
centuries leading up to 1200 BCE which likely yielded the initial discovery
of the leap year phenomenon. In this regard Mesoamerican experience is
similar to the rest of the world, with a long history of astronomical
observation in support of calendric endeavors. So in answer to David's
question, about how long the Mayans took to develop a calendar, it would
appear it took Mesoamericans (Olmecs and/or Zoques) just as long to develop
a calendar as in other parts of the world. But in the case of the Mayans,
they stood on the shoulders of giants with a huge legacy from the Olmecs,
and changed the calendar very little from the variant that the Olmecs
developed. But it is David's second question that is more interesting -
"Could the other ancient civilizations of the period around the globe have
perfected their calendars in the same amount of time?" The answer to this is
NO, because it is a choice about what constitutes a perfected calendar.
It is not so much a question of the time required to develop a calendar, but
rather the decisions made about how best to apply the knowledge that
astronomy affords an accomplished calendric endeavor. The practice around
the world used a limited number of calendric base period alternatives on the
one hand, and quickly resorted to a Julian style solution, which effectively
eliminates the leap year phenomenon from the calendar, and thereby thwarts a
deeper ongoing appreciation of the phenomenon. In other words, once the
"true" tropical calendar is adopted by implementing a "haab" adjustment
methodology, there is little incentive to develop the calendar any further,
because the sole remaining problem is a pesky lunar calendar that must be
periodically aligned to the tropical stations. It is this attitude that
calendric endeavor has reached its pinnacle of achievement with a leap year
adjustment methodology, that thwarts further development, and therefore more
advanced (or more exotic) calendars are not forthcoming, no matter how much
time is available to them. The Gregorian calendar is a rather miserable
artifact, as the legacy of an aborted calendric endeavor, but the
foundations of organized calendrics and commerce are very different or even
incompatible. Today, for example, we prefer commercial elegance in our
calendar, and do not wish to mix arcane calendric lore with the convenience
of commercial features. But just because the Gregorian calendar is a
commercial marvel, does not mean that it is also a wise calendric structure,
because there are better ways of organizing the music of the spheres into
calendric structures of various kinds, which offer an elegant categorization
of calendric information or orbital behavior. There are the needs of
astronomy which go beyond calendrics, and there are the needs of commercial
endeavor which also go beyond the needs of proper calendric design. So
David's question should have read: "Did Mesoamericans make different
calendric decisions which explains how their calendar became differentiated
from the variants used elsewhere in the world?" Indeed,YES.
David asks if these advanced theories could have indicated something more
basic concerning humanity as a whole? Well, decisions made early in a
calendric endeavor changes the character of what is developed within that
endeavor over time. But the idea of an advanced calendric theory is possibly
overstating the situation - more accomplished certainly, but it is merely a
different series of decisions taken in an early calendric endeavor, which
leads to a deeper appreciation of the leap year phenomenon, where others
merely implemented a calendar adjustment methodology that thwarted further
development. So the lack of a haab adjustment methodology really points to a
more accomplished achievement, which is not obvious on the surface, until
the calendric foundations underpinning that achievement is articulated. A
civilization pays a price for the decisions it makes along the way.
Buried deep in Mesoamerican history is an initial endeavor that combined the
365-day and 260-day calendars into a synchronized whole, as a 73 tzolkin/52
haab calendar round (CR) combination, reaching at least as far back as the
6th century BCE and possibly as far back as 1000 BCE. This should
immediately alert scholars to an overt decision made long ago, to expressly
ignore one important solution to the leap year phenomenon in preference for
another, where a calendar round combination largely made the issue of
celestial calendar alignments moot, by increasing the effect length of the
calendar's dating system to 18,980-days. Or rather the migration of tropical
stations within one calendric base period was not considered more
significant than that same phenomenon within another base period. There was
a question about making adjustments in several calendric base periods (365,
360, 260), which was unpalatable, and there was a strong tendency not to
resort to just a single calendric base period to express the behavior of
various orbital phenomena. This approach, or rather the CR resultant, would
forever shun the haab adjustment methodology, and it is this that ultimately
led to a better appreciation of the leap year phenomenon, because each
calendric base period was maintained in its pure calendric state, which
offered a better means of inspecting orbital migration phenomena within the
calendar. There was a tendency to resolve the astronomy by resorting to
longer periods of time, and this is also evidenced in the Lunar Series for
example, where a tracking mechanism over 18 lunar months is implemented
rather than just an approximate tropical year span, showing a preference for
resolving calendric phenomena over longer spans of time. The earlier
Mesoamericans understood that a calendric period adjustment methodology not
only gave rise to arithmetic complications, but also left unresolved many
calendric migration phenomena, and therefore not a wise solution in terms of
harmonizing calendric efforts overall. This coupled with the use of tropical
/ lunar conjunctions as a means of harnessing the precision of astronomy,
yielded an accomplished tropical calendar rendition, that is embedded within
the dates themselves that describe the underlying heuristics of orbital
calibration spans generally. When it came time to erect the great cycle a
long calendric history already prevailed, that expressly shunned the haab
adjustment solution, and as a consequence has already garnered a wealth of
calendric knowledge as regards orbital migration phenomena. This is why it
is not correct to apply simplistic Eurocentric calendric concepts in trying
to understand the Mesoamerican experience, because their earliest calendric
decisions led them down a different and more accomplished path.
So when did the Olmecs develop their Long Count calendar system? This
subject I address in a paper currently unpublished, where I revisit Sylvanus
Morley's 1931 reading of a (7.5.0.0.0) 13-Ahaw 13-K'ank'in Initial Series
inscription on a Uaxactun cylindrical polychrome vase, and place that date
within the context of an actual celestial observation ca. -255 BCE. Using
the '83-GMT correlate allows a valid moon age derivation, that differs from
a Mayan moon age specification, which supports the case for an actual
celestial observation, and I show how the leap year phenomenon is used to
derive the apparently anomalous haab basis associated with that inscription,
and further how this date is used as an observational focus to erect the
13-baktun-cycle. The 4-day divergence between a winter solstice station and
(7.5.0.0.0) katun ending, with a Full Moon positioned midway in this zone,
was expressly chosen to orient the great cycle. I interpret the image on
that vase as an ancient 3rd century BCE historical scene, depicted on an 8th
century CE Mayan vase, where Olmec dignitaries are presenting the gift of
the Long Count to a Mayan king. An accomplished Mesoamerican calendric
science relied on a deeper appreciation of the leap year phenomenon to
precisely align the great cycle.
So when did the Mayans accept the Olmec legacy as a foundation to their Long
Count calendar system? 220y later, memorialized on a Chiapa de Corzo stela
2, with a (7.16.3.2.13 ) Initial Series ca. -35 BCE, which points to another
winter solstice & Full Moon conjunction event, as a secondary observational
focus for erecting the great cycle. The interval between the Olmec and
proto-Mayan Initial Series dates is 220y between their corresponding winter
solstice stations which is also exactly 2,721 lunations. The Mayan Classic
Period would not begin until some three centuries later.
I hope I have conveyed to David that this is a matter of a more accomplished
calendric endeavor, rooted in a better understanding of the leap year
phenomenon, and not so much the subject of an advanced theory, but rather
the result of a series of decisions taken by Mesoamericans which led to a
different final calendric resultant. Making choices about what constituted
bad calendric science, led the Olmecs to designing different calendric
structures, and a haab adjustment methodology was considered an
inappropriate method for orchestrating the astronomical results.
Cheers Cliff
----- Original Message -----
From: <wakinyaska at bellsouth.net>
To: "vgray (gotsky)" <vgray at gotsky.com>
Sent: Sunday, April 30, 2006 8:03 PM
Subject: Re: Re: [Aztlan] Calendrics, architecture
> So, in your opinion, how long did it take the Mayans to perfect their
> calender? Could the other ancient civilizations of the period around the
> globe have perfected their calendars in the same amount of time? Could
> these advanced theories have indicated something more basic concerning
> humanity as a whole?
> David
>>
>> From: "vgray \(gotsky\)" <vgray at gotsky.com>
>> Date: 2006/04/30 Sun PM 04:02:59 EDT
>> To: <calendar.message at gmail.com>, "'Aztlan'" <aztlan at lists.famsi.org>
>> Subject: Re: [Aztlan] Calendrics, architecture
>>
>> I have read part of Vladimir Pakhomov's work, and this largely describes
>> calendars that are structured relative to the heavens. I must point out
>> there is a difference between structured calendars and dating systems.
>> Dating systems simply describe the passage of time by decorating the
>> time-line with a continuous series of dates, while structured calendars
>> attempt to orient the dates themselves to the celestial sphere. The
>> Julian
>> calendar is expressly contrived to convert the "haab" into a fixed
>> tropical
>> calendar, while the Mayan calendar is merely a dating system for the
>> purpose
>> of decorating the passage of time with a series of continuous dates,
>> without
>> modifying the system of dating to fit the celestial sphere. Or at least
>> the
>> Mayan calendar does not periodically adjust the dating system in some
>> manner
>> as to fix it's divergence relative to the celestial sphere - the true
>> tropical calendar is distinct from the dating system itself. This
>> difference
>> is not obvious, and scholars often confuse a "series of dates" with a
>> "structured tropical calendar", and extrapolate that lack of a date
>> adjustment methodology implies a tropical calendar solution does not
>> exist.
>> The underlying heuristics of the Mayan calendar cannot be understood in
>> the
>> terms usually associated with a structured calendar solution, as Vladimir
>> Pakhomov suggests, and the leap year phenomenon must be addressed in
>> different terms.
>>
>> Actually the Mayan calendar does not contain the leap year phenomenon at
>> all, in terms of the three calendric periods used in its construction
>> (I.e.
>> 365, 360, 260 days), but rather uses an entirely different and unique
>> leap
>> year solution, while keeping the calendric base periods fixed. The Julian
>> calendar periodically adjusts the calendric period to fix alignment of
>> the
>> calendar's dates to the tropical stations (approximately), but the Mayan
>> calendar expressly shuns period adjustments (to simplify calendric
>> arithmetic), and rather fixes two different elements: (a) the time-line's
>> orientation to specific tropical events, and (b) uses fixed orbital
>> calibration spans to describe tropical/lunar orbital behavior outside the
>> dating system itself. In other words the Julian calendar uses periodic
>> adjustments, while the Mayan calendar uses a one-time adjustment to fix
>> haab, tun, and tzolkin basis, and to align the 13-baktun-cycle to the
>> celestial sphere is a unique way. The Julian calendar attempts to create
>> a
>> fixed tropical calendar by periodic adjustments, while the Mayan calendar
>> fixes the alignment of a fixed cycle interval to the heavens at its
>> initial
>> inauguration, changes nothing thereafter, and describes the tropical
>> calendar by means of a pair of dates used to delineate a tropical
>> calibration span. The two systems are almost opposite in character,
>> fixing
>> different elements of the temporal equation, and it would be a mistake to
>> address the Mayan solution in Eurocentric terms.
>>
>> This difference in approach may be viewed as follows. The Julian calendar
>> fixes the calendar's orientation to the heavens, fixing the relationship
>> between solar calendar dates and tropical stations, so winter solstice
>> always appears on Dec 21st every year (diverging only very slowly 1-day
>> every 128y). But the Mayan calendar simply uses the dating system as a
>> fixed
>> unchanging means of decorating the time-line with dates, with no attempt
>> made at orienting the dates themselves to the celestial sphere, and
>> therefore in this sense there is no leap year solution incorporated into
>> the
>> dating system. In other words the Julian calendar converts the dating
>> system
>> to a tropical calendar, while the Mayan calendar expressly maintains the
>> tropical calendar outside the purview of the dating system itself in a
>> sense. This approach of differentiating the dating system from the
>> tropical
>> calendar is a uniquely Mesoamerican calendric technique, that other
>> civilizations around the world did not adopt, and indeed has primarily
>> misled scholars into believing the Mayan calendar does not incorporate a
>> leap year solution of any kind. It is becoming increasingly clear
>> Mesoamericans understood the tropical calendar to a greater depth than
>> their
>> contemporaries around the world.
>>
>> The Mayan tropical calendar exists in the form of a series of well
>> designed
>> tropical calibration spans, expressed using two dates to delineate the
>> span's extremities - so the underlying tropical orbital heuristics are
>> embedded within the span's makeup and not within the dating system
>> itself.
>> This is necessitated by the fact Mayans did not possess a numerical
>> fraction
>> notation, partitioning the interval between 0 and 1, but rather expressed
>> calendric factions using calendric period residuals as a means of
>> partitioning much larger numbers - for example a haab period residual of
>> 73-days is a 1/5th fraction of 365-days. In this way a high degree of
>> precision is obtainable where orbital circulation divergences are
>> accumulated over much larger expanses of time. The precision is really
>> quite
>> remarkable, as in an example given earlier, where a 206 year tropical
>> span
>> is equated with a 209 tun calendric interval, where it is plain that the
>> 52
>> Julian leap days that should have occurred over 208y did not materialize.
>> But rather only 50 leap days occurs in 206y expressing the fact that 1½
>> leap
>> days are missing, but also this interval of 209-tuns is also 3 complete
>> rounds of seasonal migration with the tun constituting 1,080 "tun leap
>> days" - equating 50 haab leap days with 1,080 tun leap days. Associated
>> with
>> this tropical calibration is also the span of 68y equated to a 69-tun
>> calendric interval, which is approximately one complete seasonal
>> migration
>> round within the tun, over an interval that is also expressive of 17 haab
>> leap days. This period is an important universal period, not just because
>> it
>> is one seasonal round within a tun calendric base period, but also
>> because
>> it defines a way for describing the divergence between the haab and tun
>> calendric period origins. Elsewhere I have made the claim a Mayan haab
>> basis
>> is derived using a one-time reorientation of an idealized 13-baktun-cycle
>> arising at 0-Pohp, where a great cycle is arranged to start at a TUN
>> PERIOD
>> ORIGIN 17-days before a HAAB PERIOD ORIGIN, and therefore the cycle
>> begins
>> at 0-Poph - 17 = 8-Kumku. This offers a one time orientation between the
>> haab, tun and tropical calendar that is rooted in the leap year
>> phenomenon,
>> as a relative period origin alignment.
>>
>> Another example is a 42y tropical span that equates to 59 tzolkin, and
>> this
>> is 1-day short of 519½ lunations, and also 43.5y equating to 538
>> lunations.
>> The latter tropical lunar calibration span measures the interval between
>> a
>> summer solstice & Full Moon conjunction event and a winter solstice &
>> Full
>> Moon conjunction event, and such calibration spans offer greater
>> flexibility
>> than the structured calendar approaches used in the Julian/Gregorian
>> calendars. Without the need for mutilating the dating system with
>> periodic
>> adjustments that complicate calendric arithmetic. But more than this,
>> identifies a technique where tropical/lunar conjunctions are used, as a
>> means of harnessing the precision of astronomy. It is not just a question
>> of
>> a 1,461 day leap year interval, but rather this interval in conjunction
>> with
>> the 1,462-day interval that describes a lunar calibration span of 49½
>> lunations, with a ¼-day lunar period residual. Far more significant than
>> the
>> tropical leap year phenomenon in isolation, is a tropical/lunar
>> conjunction
>> resultant - over just 4*1462 days (~16y) it is clear the interval must be
>> corrected by subtracting 1-day to describe 198 lunations, thus
>> establishing
>> a 3-day divergence between the tropical and lunar stations (and not
>> 4-days).
>> Seventeen such corrected spans must elapse over 272y before a further
>> +1-day
>> correction is needed, to give an integral lunar span of 3,366 lunations,
>> and
>> this predicts 17x3 + 1 = 52 days of tropical period residual must
>> persist,
>> but in reality two missing leap days increases the tropical period
>> residual
>> to 54-days. In other words 68 Julian leap days yields to 66 actual leap
>> days, and a computed 52-day tropical station divergence then also yields
>> to
>> a 54-day resultant. Such tropical/lunar calibration spans form the
>> foundations of the Mayan calendar, and also offers a deeper appreciation
>> of
>> both tropical and lunar phenomena than the leap year phenomenon alone,
>> and
>> further explains why a haab adjustment methodology, or a structured lunar
>> calendar aligned to the tropical calendar, was never instituted by the
>> Mayans. It is in these terms that the issue of orbital station migration
>> is
>> understood, and the precision achieved cognizable as a result of
>> harnessing
>> tropical/lunar conjunctions, and it seems quite likely that Mesoamericans
>> shunned a haab adjustment methodology, long before Julius Caesar adopted
>> the
>> Julian calendar.
>>
>> The Mayans adopted in my mind a superior system for studying the
>> phenomenon
>> of orbital station migration generally. I respectively submit that
>> Vladimir
>> Pakhomov's work is expressly primarily a structured calendar heuristic,
>> and
>> is not a sufficient basis for describing Mesoamerican calendric science,
>> which is quite unique in several important respects. In particular the
>> Mesoamerican technique of using tropical and lunar conjunctions to
>> harness
>> the precision of astronomy over the longer term, and as a means of
>> compensating for the lack of a numerical fraction notation system,
>> preempting the design of both tropical and lunar calendars. What the
>> Mayans
>> might have understood in terms of mathematics is unknown, because their
>> books were burnt, and also the question of exotic numerical structures is
>> largely unknown ill understood. Vladimir Pakhomov's work discusses exotic
>> numerical structures that do not appear to be particularly useful in
>> studying the Mayan calendar. Although I find his work interesting for
>> different reasons to do with structure theory generally.
>>
>> Cheers Cliff
>>
>>
>> ----- Original Message -----
>> From: "Vladimir Pakhomov" <calendar.message at gmail.com>
>> To: "'vgray (gotsky)'" <vgray at gotsky.com>; "'Jorge P?rez de Lara'"
>> <jorgepl at estudioelias.com>; "'Aztlan'" <aztlan at lists.famsi.org>
>> Sent: Saturday, April 29, 2006 1:34 PM
>> Subject: RE: [Aztlan] Calendrics, architecture and the "obvious"
>>
>>
>>
>> -----Original Message-----
>> From: aztlan-bounces at lists.famsi.org
>> [mailto:aztlan-bounces at lists.famsi.org]
>> On Behalf Of vgray (gotsky)
>> Sent: Monday, March 27, 2006 5:03 AM
>> ...
>> Counting leap days is not difficult, and given that tropical station
>> divergence can be tracked over 208y, as for instance by noticing that the
>> year-bearer system itself leaps ahead one day every 4y, as depicted in a
>> 208y table within the Madrid Codex...
>> -------------------------
>>
>> If the Mayan calendar has the leap days then my article
>> http://www.pakhomov.com/calendar.html
>> http://www.pakhomov.com/seals.html
>> will help us to understand the Mayan calendar.
>>
>> Vladimir Pakhomov
>>
>>
>>
>>
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