Clifford Emeric
UPDATED 2023 Jan 26. Independent researcher of Mayan great cycle astronomy. Scholars assume Mayans did not possess proper fractions, and lacked a strong command of computational astronomy over protracted spans of time. This is a false perspective, and papers here address various elements that point to a different reality, best described as Zapotec/ Mayan calendric science. I infer here they surpassed foundations of the Gregorian calendar, to reach unheard of precision, using a different kind of proper fraction methodology, as a superior methodology harnessing embedded arithmetical derivations, well suited to tracking astronomical cycles. Gregorian temporal spans are aligned at day's-start, so by definition a span's ending-date lies outside this span, which aids span concatenations. A Long Count date is aligned at day's-ending, as in how our own clock time works, where days are not counted until they pass into history. A Long Count date continues to hold to the prior day's date, until the very moment of this day's ending point at sunset, sunrise or noon, which changes the notion of a day rollover. Span concatenation set the root date outside any given temporal span, so span concatenations and date subtractions are radically different between the two calendric disciplines; even extending to a hidden temporal paradox in the traditional Julian Day Number (JDN) notations, of the GMT correlation platform.
Of note modulo arithmetic forms the foundations of this calendric science, where modulo period residuals are referred back to a modulo calendric base period, as a means of conveying a fractional day. What has not been realized before, is modulo integer period residuals are inherently proper fractions in their own right, as numerator integers, where a modulo base period is an implied denominator. This is how tropical, lunar, Venus and other leap days were processed, but unfamiliarity with modulo arithmetic has led scholars to think leap days were not used. Leap days were not used to adjust a Haab 365d modulo base period, or any other base period for that matter, but were nevertheless used in computations. It is this facet, that modulo base periods of necessity must remain fixed by design, that scholars have totally missed and thus led astray. Such an act as this would totally destroy the adoption of modulo integer numerators, as calendric proper fractions. Author claims the earliest Zapotecs and Mayans were well aware of this arithmetical facet. Unraveling the underlying calendric science is the focus of all the author's papers, revealing a Long Count calendar and great cycle alignment was inaugurated, with a hitherto unknown astronomy, and identifies the earliest "inventor" citadels. This led to decoding Monte Alban stone tablets for the first time, as extensive records of various astronomical conjunctions (a pending publication). The stone tablets prove intent and methodology.
Integer numerators (modulo period residuals) of protracted spans, were combined with fixed modulo base periods in cyclic accumulations, yes, but the end result also incorporated an astronomical drift component, be it tropical, sidereal, Venus etc. Subtractions of the base period accumulations, must reveal the added perspective of this inherent astronomical drift - to wit, accumulation of astronomical divergences (leap days). This revealed not just Haab computational leap days, but also a missing Julian leap day every 128 yrs. A trivial tropical period residual arithmetic computation isolates this drift as: for x years, x*365/4 - x*365/128 = Julian leaps days - missing Julian leap days.
For a 1,872,000 cycle rounded to 5126y, yields: 5126/4 - 5126/128 = 1281.5 - 40 = 1241.5 mod (365) = 146.5 tropical leap days in 5126 yrs. An assumed 1536y Haab Round for 1536/4= 384d Julian leap days, with 1536/128 = 12d missing Julian leap days, or 384-12= 372 leap days, for a 7d residual to give a corrected 1536 - 7*4 = 1508 yr Haab round. Since 28y is nearly a missing 28/128 = ~0.25d Julian leap day, a Haab Seasonal Round is closer to 1507y. Applying this to a 1,872,000 cycle as a modulo base period, in subtracting 3 Haab Rounds, is thus 1241.5 mod (365) = 146.5 tropical leap days noted above. This formula is: (JULIAN PARTIAL YEAR RESIDUAL - TROPICAL LEAP DAYS) mod (365) = TROPICAL PARTIAL YEAR RESIDUAL.
Cycle's 280d Julian residual - 1241.5 mod (365) = 280 - 146.5 = 133.5d tropical residual. where 1872000 mod (365) = 280, and subtracting 3 Haab Rounds yields a 280d partial year residual, so cycle's tropical residual is 280 - 146.5 = ~133d, for a Dec 20 - 133d = Aug 9 date of creation at (0.0.0.0.0) [-3113 Aug 9 CE] sunset day's-ending, as the previous cycle's last day. The next cycle begins (0.0.0.0.1) [-3113 Aug 10] at 90W longitude sunset ending, or at same moment in time at Aug 11 Greenwich Midnight. This is a -12 hr correction to the Goodman/Martinez/Thompson 83-GMT JDN correlation. Or an 82.5-GMT JDN correlation constant.
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Phone: 1-208 290 9539
Address: PO Box 662 Clark Fork ID 83811. USA
Of note modulo arithmetic forms the foundations of this calendric science, where modulo period residuals are referred back to a modulo calendric base period, as a means of conveying a fractional day. What has not been realized before, is modulo integer period residuals are inherently proper fractions in their own right, as numerator integers, where a modulo base period is an implied denominator. This is how tropical, lunar, Venus and other leap days were processed, but unfamiliarity with modulo arithmetic has led scholars to think leap days were not used. Leap days were not used to adjust a Haab 365d modulo base period, or any other base period for that matter, but were nevertheless used in computations. It is this facet, that modulo base periods of necessity must remain fixed by design, that scholars have totally missed and thus led astray. Such an act as this would totally destroy the adoption of modulo integer numerators, as calendric proper fractions. Author claims the earliest Zapotecs and Mayans were well aware of this arithmetical facet. Unraveling the underlying calendric science is the focus of all the author's papers, revealing a Long Count calendar and great cycle alignment was inaugurated, with a hitherto unknown astronomy, and identifies the earliest "inventor" citadels. This led to decoding Monte Alban stone tablets for the first time, as extensive records of various astronomical conjunctions (a pending publication). The stone tablets prove intent and methodology.
Integer numerators (modulo period residuals) of protracted spans, were combined with fixed modulo base periods in cyclic accumulations, yes, but the end result also incorporated an astronomical drift component, be it tropical, sidereal, Venus etc. Subtractions of the base period accumulations, must reveal the added perspective of this inherent astronomical drift - to wit, accumulation of astronomical divergences (leap days). This revealed not just Haab computational leap days, but also a missing Julian leap day every 128 yrs. A trivial tropical period residual arithmetic computation isolates this drift as: for x years, x*365/4 - x*365/128 = Julian leaps days - missing Julian leap days.
For a 1,872,000 cycle rounded to 5126y, yields: 5126/4 - 5126/128 = 1281.5 - 40 = 1241.5 mod (365) = 146.5 tropical leap days in 5126 yrs. An assumed 1536y Haab Round for 1536/4= 384d Julian leap days, with 1536/128 = 12d missing Julian leap days, or 384-12= 372 leap days, for a 7d residual to give a corrected 1536 - 7*4 = 1508 yr Haab round. Since 28y is nearly a missing 28/128 = ~0.25d Julian leap day, a Haab Seasonal Round is closer to 1507y. Applying this to a 1,872,000 cycle as a modulo base period, in subtracting 3 Haab Rounds, is thus 1241.5 mod (365) = 146.5 tropical leap days noted above. This formula is: (JULIAN PARTIAL YEAR RESIDUAL - TROPICAL LEAP DAYS) mod (365) = TROPICAL PARTIAL YEAR RESIDUAL.
Cycle's 280d Julian residual - 1241.5 mod (365) = 280 - 146.5 = 133.5d tropical residual. where 1872000 mod (365) = 280, and subtracting 3 Haab Rounds yields a 280d partial year residual, so cycle's tropical residual is 280 - 146.5 = ~133d, for a Dec 20 - 133d = Aug 9 date of creation at (0.0.0.0.0) [-3113 Aug 9 CE] sunset day's-ending, as the previous cycle's last day. The next cycle begins (0.0.0.0.1) [-3113 Aug 10] at 90W longitude sunset ending, or at same moment in time at Aug 11 Greenwich Midnight. This is a -12 hr correction to the Goodman/Martinez/Thompson 83-GMT JDN correlation. Or an 82.5-GMT JDN correlation constant.
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Phone: 1-208 290 9539
Address: PO Box 662 Clark Fork ID 83811. USA
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Tulum’s Diving God suggests Monte Alban’s upside down heads are not deposed rulers of subjugated places but rather a diving deity, and the entire Citadel is now cognized as an astronomical observatory implicated in Long Count’s inaugural launch. Venus astronomy played a commanding role in the Long Count’s inauguration, and this paper presents the simplicity deriving from Venus leap days in computations.
This entry is left only for historical purposes (rather than deleting it). See the uploaded newly titled paper for further reading of the updated sections.
A revised period residual analysis of Tikal incised bone fragments focuses on an embedded proper fraction methodology, giving broader mathematical credence to Grofe's analysis, and explains why Mesoamericans shunned haab calendar adjustments of necessity.
Tonina cognizes an astronomical structure with 5 Saros lunar eclipses aligned at 4½y and 9y vertical sun transits, at {May 30 , Jun 9 , Jun 21, Jul 2 , Jul 13}, and being sub cycles of Tonina's 18 haab TLZ equation solution, marker dates at 18 haab intervals define a companion structure in celebration of this astronomy. Tonina's 18 haab spans highlight a snapshot in time when 5 Saros lunar eclipses, progressed across 9y and 4½y solar transits of the TLZ equation construct, interlocked to the sequence of 18 haab spans aligned at ¼ and ¾ lunar cycle stations. A chinstrap glyph associated with the 18 haab span markers may well refer to the TLZ equation, in context of Tonina's latitude, where vertical sun transits are bound to Saros lunar eclipses as sub cycles of Tonina's TLZ equation construct.
This paper uses a revised 82½ GMT correlation preempting the '83 GMT variant, in adopting a 90ºW longitude correlation authority using day's ending date subtraction heuristics, which corrects a 1d Long Count aberration in the traditional '83 GMT correlation, and Tonina's astro-calendric structures are thus more precisely discernible as a result.
Tulum’s Diving God suggests Monte Alban’s upside down heads are not deposed rulers of subjugated places but rather a diving deity, and the entire Citadel is now cognized as an astronomical observatory implicated in Long Count’s inaugural launch. Venus astronomy played a commanding role in the Long Count’s inauguration, and this paper presents the simplicity deriving from Venus leap days in computations.
This entry is left only for historical purposes (rather than deleting it). See the uploaded newly titled paper for further reading of the updated sections.
A revised period residual analysis of Tikal incised bone fragments focuses on an embedded proper fraction methodology, giving broader mathematical credence to Grofe's analysis, and explains why Mesoamericans shunned haab calendar adjustments of necessity.
Tonina cognizes an astronomical structure with 5 Saros lunar eclipses aligned at 4½y and 9y vertical sun transits, at {May 30 , Jun 9 , Jun 21, Jul 2 , Jul 13}, and being sub cycles of Tonina's 18 haab TLZ equation solution, marker dates at 18 haab intervals define a companion structure in celebration of this astronomy. Tonina's 18 haab spans highlight a snapshot in time when 5 Saros lunar eclipses, progressed across 9y and 4½y solar transits of the TLZ equation construct, interlocked to the sequence of 18 haab spans aligned at ¼ and ¾ lunar cycle stations. A chinstrap glyph associated with the 18 haab span markers may well refer to the TLZ equation, in context of Tonina's latitude, where vertical sun transits are bound to Saros lunar eclipses as sub cycles of Tonina's TLZ equation construct.
This paper uses a revised 82½ GMT correlation preempting the '83 GMT variant, in adopting a 90ºW longitude correlation authority using day's ending date subtraction heuristics, which corrects a 1d Long Count aberration in the traditional '83 GMT correlation, and Tonina's astro-calendric structures are thus more precisely discernible as a result.