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The
unlikely starting date of the current epoch raises
questions that should be answered. If counting started at
the beginning of the 5,125-day epoch, the tzolk'in
should begin with 1 imix and
the haab' with
0 pop. If
counting started at any other time, it should theoretically
be possible to backtrack to the start of time (in the
counting sense). Simple backtracking shows immediately that
the starting dates cannot be made to align and so have been
generally dismissed as enigmatic decisions from a time we
cannot revisit for consultation.
Not
being content to accept that separate counting schemes were
independently initiated at different times, I set about
modeling the consequences of starting to count from a
hypothetical zero point on winter solstice 10,250 years
ago. Dividing two successive epochs of 1,872,000 days each
by the value of the tropical year provided the timing of
winter solstice, but left a gap of 97 days before the known
end date for the current epoch.
Some
simple calculations provide the means to appropriately
assemble the various components into a calendar. Although
as many as 17 cycles were tracked, only four will be
addressed here.
Dividing
the number of days in each time period shows by the decimal
remainder how many days are taken to complete the period
after an even cycle completion, and how many days are
counted at the start of the next time period. Once the end
of the current epoch is shifted by 97 days to match winter
solstice, the intervals can be placed in reverse to
position the starting date.
Registering
the components with winter solstice and the known end of
the calendar reveals some very interesting characteristics:
• Comparing
the hypothetical haab’
series
to the current epoch shows that the haab’
has
been displaced backward in the tropical year reckoning by
336 days. Amazingly, the first haab’
begins
with the same name as the first haab’
in
the initial epoch. Further, the day-naming convention has
been shifted backward in time by 170 days. The resulting
pattern in the final haab’
creates
a symmetrical 102 days from winter solstice to haab’
start,
263 days to epoch end, and then another 102 days to the
next winter solstice. Finally, the current epoch starts 134
days prior to a winter solstice while the first epoch ends
134 days after a winter solstice.
• Similar
inspection of the tzolk’in
shows
that shifting its placement in the tropical year 98 days
forward in time ended the epoch on the tzolk’in
break
and nearly matched the start of the final haab’.
At the same time, the day-naming convention of the tzolk’in
was
shifted backwards by 24 days.
• We
might reasonably expect tzolk’in
and
haab’
numbers
to be related by the 365 to 260 proportion, and three
equations demonstrate how:
335.7
haab’ shift in solar time minus 97.5 day
tzolk’in shift in time equals 238 days of
relative shift.
(170
day haab’ name shift) times 365/260 equals
239, or ten times the tzolk'in name shift.
(336-day
haab’ shift in solar time) times 260/365
equals 239, or ten times the tzolk'in name shift.
Granted,
the calculations have a numerological theme, but they are
sufficient to show that shifts of haab’ and
tzolk’in relative to solar time and in
day-naming convention are deliberately orchestrated to
honor the tzolk'in day-name shift.
• Subtracting
the ordinal position value for the starting and ending
haab’
names
leaves 85, which is the haab’
remainder
at the end of the first epoch. Subtracting the ordinal
position of the haab’
series
at the start of the second epoch from the length of a haab’
leaves
17, which is also the number of days to finish the first
haab’
of
the second epoch. Ordinal position tables (Aveni
2001:143,147) are useful tools for modern researchers, but
no such tables have been recovered from antiquity. The
ordinal position of the ending haab’
day
is 264, the same as the number of days since the last haab’
break.
• Skipping
98 days between epochs gave the calendar a seasonal
symmetry by starting the first epoch at winter solstice and
also ending the current epoch on winter solstice. Full moon
occurs 1 day before the first epoch, while the current
epoch begins 3 days before a full moon and ends 7 days
before a full moon.
• Finally,
combining all of the shifts demonstrates that the resulting
structure sets itself back in time just enough to make up
for the 134-day haab’
remainder
in an epoch without disturbing the relationship between
haab’
and
tzolk’in
naming
conventions.
-336
haab’ name shift
-
24 tzolk’in name shift
-170
haab’ shift in solar time
+
98 tzolk’in shift in solar time
----------------------------------------
-432
days + 365 = -67 days, times two equals 134 day haab’
remainder in an epoch.
Obviously,
a great deal of effort went into such an elaborate redesign
that managed to transform itself so thoroughly and still
leave enough vestiges of its previous incarnation that
reconstruction was still possible. Surely it would have
taken considerable time and broad involvement to bring it
about because there are no apparent competing schemes to
indicate dissension.
Only
by considering a winter solstice 10,250 years ago as the
start of counting time, can the inferred Maya equations
transform the count between epochs and reach winter
solstice on December 21, 2012 with the designation 4
ahau 3 kankin. Not only do the counting relationships
retain their mathematical relationship from the original
count, there are too many aesthetic properties of symmetry,
balance, and mirroring of critical intervals with ordinal
name positions to believe the outcome could occur by
chance. Using a single assumption to explain every feature
of the integrated calendar is compellingly simple, however,
the proposal implies far greater mathematical
sophistication, much earlier than generally expected.
So
what might be important about revealing a calendric
adjustment from 5,125 years ago? After all, there are no
known dates from the earlier epoch to require correction.
And, even if records could be located, the adjustments are
too minor to have impact on history that far back in time.
However, recognizing that the adjustment provides indirect
evidence that the calendar was in use from 10,250 years ago
forces us to look far deeper in time for physical traces of
its origins. Keep in mind that no extra data or construct
has been added to make the argument. Logical deduction,
using no more information than the known structure of the
calendar system, sets the likely date of its creation
because it is associated with the starting haab’
and tzolk’in counting cycles. We may also
deduce that the cycles have always been integrated.
The
proposed design criteria avoids an arbitrary start of the
current calendar to force the calendar to end on the winter
solstice. Because the starting position is a fact of
nature, there is no need to suppose that the originators of
the integrated calendar anticipated an adjustment to
force the calendar to close at a particular time. The
machinations of day-naming conventions may have been
intended as a message to the Creator that the designers of
the adjustment fully understood the workings of time.
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