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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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