Friday, August 28, 2015

The Sothic Cycle, Corrected

The Sothic Cycle, Corrected


by Brendan Bombaci

Copyright 2015
All Rights Reserved
ISBN 978-1-329-51731-8


Abstract


Sothic Cycle” is the name given to the astrophysical discrepancy between the 365-day ancient Egyptian solar year and the heliacal rising of Sirius. An estimated duration of the cycle (1,461 years) has been used to more accurately date events in ancient Egyptian historical records, but fails to account for (1) the 400-year leap cycles which subtract extra leap days that accumulate as an artifact of leap years being useful only for a solar year of 365.25 days rather than the actual 365.2422 days, as well as (2) the precession of equinoxes, a cycle so-called because it desynchronizes any given constellation on the ecliptic from the spring equinox sunrise by one degree every 72 years (coming full circle in nearly 26,000 years). In this brief article I describe these complications and the mathematics that must be used to correct for the multi-decade error in the Sothic Cycle caused thereby.

Keywords: Sothic Cycle, Sirius, calendar, Egypt, Precession, relative dating, calibration, intercalation, leap year

Introduction


The Sothic Cycle is a name given to the no longer observable but once confusing desynchronization and resetting of the heliacal rising of the star Sirius (“Sothis” in Greek) with sunrise on the first day of the ancient Egyptian solar year. This was caused by a lack of leap year intercalation. It has been rightly asserted by historians and archaeologists that this cycle caused the numerous discrepancies seen in ancient Egyptian history regarding the start of the solar year, but it is causal only in part. It has been and still is an incomplete application of the cycle to simply multiply the 4 years it takes to acquire a Leap Year day by 365.25 days in order to derive its duration. As such, the cycle has been imprecisely determined to be 1,461 years.  There are two mechanisms that are unaccounted for, one unavoidably astrophysical and the other merely mathematical.

Background


The current school of thought on the Sothic Cycle originated in historian Eduard Meyer’s original 1904 realization about it when researching Egyptian historical records. His idea was soon professionally perpetuated, starting with its uncritically promotional inclusion in an annex of the influential Egyptian history textbook from 1924, “A History of Ancient Egypt, 2nd Ed.,” written by the Rockefeller-funded professor J.H. Breasted of the University of Chicago (Mackey 2003). This annex was titled “Chronological Table of Kings,” and in it Breasted boldly altered known ancient Egyptian historical dates via Meyer’s Sothic Cycle calculation, calling them “astronomically fixed.” His Sothic Cycle calibration method became granted, but criticism of it existed prior to my own. 

Perhaps the earliest criticism, published by Luby (1941), was of the incorrect application of leap year mechanics in this cycle. As such, he calculated the Sothic Cycle duration by dividing 365.2422 days per year by 0.2422 (to obviate both leap years and leap cycles), and was satisfied with the resulting solution of 1,508 years. Rose (1994) later called for a wider acceptance of the idea that Egyptians used a 3-year “triennium” from time to time when the 4-year quadrennium (after which one degree of sky would precess) desynchronized from the actual rising of Sirius. She offers an elaborate but oddly estimated accounting for the discrepancy between the Egyptian 365-day and actual solar year lengths, resulting in a declaration that the Sothic Cycle is actually 1452 years in duration. More recently, it has been suggested that the value used for the current cycle “is not totally exact: the Sothic cycle is not fixed because of the proper motion of the star and the length of [the] Sothic year evolves over time” (Quiles et al. 2013:424, emphasis added). The authors provide no explanation for this statement, however.

Methods


The Sothic Cycle Mechanism

The first of the two missing factors in the current value of the Sothic Cycle is the leap cycle (Seidelmann 2005) that Luby corrected for. With his simple math in mind, we don’t need to retroactively remove 3 leap years per every 400 years of the current value (a process that can easily lead to error). In as much, to reveal the actual duration of the cycle, we can begin by resetting it to a value of 1,508 years.  Starting there, we must account for the much more slowly slipped degrees of celestial/solar alignment, caused by the Precession of Equinoxes or “Platonic Great Year” cycle. That cycle, in total, was estimated by the Hebrews to resolve in 25,920 years (Hebra 2003) when it realigns the rise of the sun at the spring equinox with a particular sub-degree of the ecliptic. This number was either (1) approximated to the actual precession duration to be well-rounded for the Babylonian sexagesimal or “base 60” divisional system that our modern timekeeping and navigation systems are based on, or (2) actually quite representative of the precessional duration as it existed then, when the Earth’s axial tilt (the cause for precession) was at a different degree of obliquity.  In as much that 1,508 years divided by the 72 years in one degree of said precession is an extra 20.244 shifted degrees during that time, we must deduce that the cycle actually completes sooner than 1,508 years: 20.244 times the 4.058 years in one degree of properly intercalated Sothic Cycle shift equals 82.15 years. Subtracting this from 1,508 gives a corrected ancient Sothic Cycle duration of 1425.85 years. Recently, however, we have come to recognize with advanced technology that precession takes 25,772 years to complete, so each degree takes 71.6 years rather than 72, meaning that 21.06 extra degrees or 85.467 years would have to be subtracted from the 1,508 year basis, giving a Sothic Cycle duration of 1422.533 years.  Until it is proven that axial tilt changes affect the duration of precession, it may be best to use this latter calculation.  For purposes of dating events within dynasties, the variance is somewhat negligible.

Additional Factors

There has been another critique of the Sothic Cycle which calls into question the original historical dates offered by Censorinus (which the cycle became cross-referenced with), pointing out a lack of historical specificity in astronomical viewing locations, as well as differences in calendrical system nuances between geographically and temporally distanced population groups whose accounts we reference, and even differences in star-shrouding atmospheric haze over the millennia and periodically during extreme weather regimes (O’Mara 2003). It appears that there is a multitude of factors we must consider, outside of celestial mechanics, to derive a veritable astronomical referencing system. An example of some very recent and impressively thorough research, that can easily hit that mark with a future revision including the Sothic Cycle correction, is the Bayesian modeled period-matching of solar, lunar, and Sothic calendars, cross-referenced with radiocarbon dating, performed by Quiles et al. (2013) for the purposes of providing an absolute chronology for the 18th Dynasty. 

Conclusions


Much research continues to use or attempt usage of the currently valued Sothic cycle referencing system as either a result of it being presumed totally verified by the peer review process, and/or a result of there being no better tool for the task. By the data I provide, it becomes obvious that this following leads (1) researchers to depend upon and publish work based on officially granted but actually confounded data, and (2) therefore a vast readership of journals, textbooks, and magazines to a misguided trust in the results. It is now apparent that we must not only realign the historical dates that we do surely know of with this proposed Sothic Cycle correction, but also reevaluate a large number of dates by way of deeper textual research and correlation of it with absolute dating methods used on germane artifacts and features. There is hope yet for justifiably method-skeptical Egyptologists (and for all who aren’t but should be), and for those archaeologists and historians working with other cultures who derive their relative dating from Egyptological work.

References


Hebra, Alex, Measure for Measure: The Story of Imperial, Metric, and Other Units, The John Hopkins University Press (2003), 53.

Mackey, Damien F., ‘Fall of the Sothic Theory: Egyptian Chronology Revisited,’ Journal of Creation 17, issue 3 (2003), 70-73.

O’Mara, Patrick, ‘Censorinus, The Sothic Cycle, and Calendar Year One in Ancient Egypt: The Epistemological Problem,’ JNES 62, no. 1 (2003), 17-26.

Quiles, A., E. Aubourg, B. Berthier, E. Delque-Količ, G. Pierrat-Bennefois, M.W. Dee, G. Andreu-Lanoë, C. Bronk Ramsey, and C. Moreau, ‘Bayesian Modeling of an Absolute Chronology for Egypt’s 18th Dynasty by Astrophysical and Radiocarbon Methods,’ JoAS 40 (2003), 423-432.

Rose, Lynn E., ‘The Astronomical Evidence for Dating the End of the Middle Kingdom of Ancient Egypt to the Early Second Milennium: A Reassessment,’ JNES 53, no. 4 (1994), 237-261.

Seidelmann, P. Kenneth, ed., Explanatory Supplement to the Astronomical Almanac, University Science Books (U.S. Naval Observatory: Washington, D.C., 2005), 580-581.


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