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Adages and axioms
Early astrologers and astronomers can be recited to have tracked specific time cycles in association with the orbital returns (Sun and Moon).
Axioms and certain adages appear to have also been followed--in association with a scribing method--to measure and meter out the celestial circuits.
Perhaps the most ancient collection of once-used axioms and time formulas can be recognized from a manuscript attributed to Enoch (one of the Bible patriarchs). It is here significant an entire section of this early-written literature focuses upon "the revolutions of the heavenly luminaries". (The section detailing the "revolutions of the heavenly luminaries" is known as Enoch's astronomical book).
Among the most intriguing of the lunar-solar relationships detailed in Enoch's astronomical book is the description of a whole-number of days (a rate of lag) between 8 lunar years (or 96 synodic months) and 8 solar years.
To be more specific, the noted lag-rate relationship is unusual in the regard that a whole number of day units does appear to exist between the boundary of 96 synodic months and 8 solar years.
Note that the number of days in 8 solar years are 2921.93752 days; while the actual days in 8 lunar years (or 96 lunar months) are 2834.93664 days. The day difference in 8 solar years and the corresponding lag in lunar periods is then a whole-day difference of 87 days.
2921.93752 solar days minus 2834.93664 lunar days ----------------------------- equals 87.00088 days of lag
The description of this lag-relationship is entirely valid and indicates that even very early astronomers may have been effective in tracking various Earth-Moon cycles.
When describing this particular lag-relationship, the cited Enoch literature shows a whole-day difference of 80 days (not the correct whole-day difference of 87 days). The difference of 7 days--as is indicated in what has survived from the Enoch literature--is consequently somewhat of a mystery.
In the light of modern astronomy, the cited cycle of 8 solar years and lunar-lag relationship is of special interest in regard that a small amount of lag difference can currently be observed between the rate of the synodic month (of 29.53059 days) and a whole-day count of 29 days.
The lag difference between the two rates averages out to be a little over half a day--or 0.53059 days. (Note that 29.53059 days minus 29 days is equal to 0.53059 days).
Based upon this indicated half-day count difference, it follows that if the rate of the synodic month is always counted out in correspondence with a whole-day rate of 29 days, the cited difference of the half-day rate (0.53059 days per lunar month) would eventually accumulate or accrue to the sum of exactly 105 half days in every cycle of 8 solar years.
This inherent correspondence reveals that the rate of 105 half days in 8 years is all but perfectly equal to the rate of 0.53059 days per lunar month). Essentially, 0.53059 days per lunar month--if extended for the number of months in 8 years or for 98.94613 lunar months--is precisely equal to the length of 105 half days.
This ultimately means that if each synodic period is systematically scribed relative to always 29 days, and if 105 half days are additionally scribed relative to the passage of 8 years, the boundary of every 105th half day will inherently correspond with the boundary of 8 solar years--on the average.
Thus, the number of lag days in each synodic period of the Moon CAN be used to precisely scribe the limits of a cycle of 8 solar years (in average time). A scribe of 29 days per lunar month and the additional scribe of 105 half days has an 8-year average that equals 5843.87555 half days. (This 8-year average quite perfectly correspondends with the limits of 8 solar years--which is equivalent to 5843.87504 half days).
The cited scribe of lunar periods and half-day cycles (on the average) can be recognized as a very precise method of determining the limits of 8 solar years. In this modern era, the cited method of scribing half days averages out to be only 0.00051 more days than an actual cycle of 8 solar years. The average result of the cited scribe is almost perfect. (Due to the tiny rate by which the spin of the Earth appears to be slowing down, the cited scribe of 8 years can be predicted to have at one time been absolutely perfect. The time when a perfect scribe was possible can be predicted at about 20 centuries ago.)
Track of a 30-day cycle
The effectiveness of ancient astronomers in measuring and metering the orbital returns can further be recognized from those records that indicate the track of a 30-day cycle.
The primal count of a cycle of 30 days can especially be recited from portions of the previously cited astronomical book of Enoch.
For pertinent information of Enoch's endless count of 30 days, refer to the online document entitled: 'Time Portals or Annual Gates'.
The following quote illustrates that the count of a 30-day month may have been in use from a very early time in the ancient Middle East:
"The old Babylonian year consisted of 360 days--twelve months of thirty days each... The Assyrian year contained 360 days; a decade was made up of 3,600 days. Assyrian documents reveal a thirty-day month... Anciently, the Persian year also had 360 days of twelve months containing thirty days each. The Egyptian year was 360 days in length... The Mayan year originally consisted of 360 days... In South America, in ancient times, the year consisted of 360 days with twelve months. The same was true in China--360 days with twelve months... Plutarch wrote the Roman year was [originally] 360 days. Various Latin authors record the month as being thirty days in length... The Hindu year was made up of twelve months of thirty days each... All the historical computations found in Hindu history used a 360-day year with months of thirty days each... (Worlds in Collision, Velikovsky, 124, 331-341).
It seems clear that a 30-day cycle may have been reckoned throughout the ancient world.
"During the reign of Romulus... they only kept to one rule that the whole course of the year contained three hundred and sixty days". (Lives, The Life of Numa, by Plutarch, translated by John Dryden).
The reckoning of a 30-day month would, of course, have required periodic intercalation--where, amid a count of 30-day months, intercalation would specifically have been required at the rate of 5 days per solar year.
In some early-used, time-tracking systems it is of interest that intercalation appears to have been deferred beyond the limits of only a single year.
According to an early Assyrian method of time tracking, calendar intercalation was determined on the basis of a running '10 count':
"The year attested in Kultepe texts... every three years [required] the insertion of 15... days called shapattum... Throughout the [3 years] Assyrians counted ten-day periods ... For three years, these [counts] ran congruently with the months and the years. Then, after the insertion of a 15-day shapattum period, they overlapped from one month into the next, returning to congruency with the months after the next shapattum...." (From Britannica, 1972, Calendar, Babylonian And Assyrian Calendars).
In the Kultepe calendar, it is significant that a 3-year cycle was reckoned and also a half-month cycle appears to have then been intercalated. Furthermore, a repetitive count of '10' was used in correspondence with each calendar month of always 30 days. Of additional interest is that the cited half-month interval (shapattum) would inherently have renewed in association with the running count of the '10 days'.
The half month would have either been overlapped, or renewed in coincidence with the unbroken count of '10'. Prior to a shapattum, the count of 10 would hypothetically have progressed across each month of 30 days in correspondence with month-day 10... month-day 20... month-day 30... etc. After the first shapattum (or after the insertion of the half month) the count of 10 would then have progressed across each of the 30-day months in correspondence with month-day 5... month-day 15... month-day 25... etc. After reckoning the second shapattum, the count of 10 would have then progressed again in correspondence with month-day 10... month-day 20... month-day 30... (or the same as before the first shapattum).
A plausible interpretion of the cited count of 10 is that this unbroken count was performed to define "stations" of the Sun and Moon. Of significance here is that--by accounting for stations of the Sun and Moon--early priest-astronomers would inherently have been capable of performing an accurate (even perfect) measure of each passing tropical year.
For pertinent information about a time track of lunar and solar stations, refer to the following online publications:
Historic literature additionally indicates the ancients held knowledge of the tropical zodiac (12 annual divisions).
Of significance here is that a segment of early astronomers appear to have interpreted certain lunar days in association with the circle of the zodiac.
An intruiging interpretation of how counts of both lunar and solar days can be used to track 360 degrees of time in each annual circle can be derived from certain artifacts of early stick calendars.
For example, a pictorial calendar from prior to the time of Titus (A.D. 79-81) indicates a repetitious day-by-day count of certain time cycles. Furthermore, a charting of the 12 signs of the zodiac is indicated from the appearance of the cited pictorial calendar (Attilio Degrassi, Inscriptions Italiae, 1963, XIII, pp. 308-309, refer to plate 56).
Some historic artifacts are likewise clear in indicating that specific day cycles were once tracked to augment charting the circle of the zodiac as well as the 7 planetary domains.
In addition to the planetary domains, early zodiac calendars are found to have also sometimes contained two vertically positioned columns with 30 numbered holes.
The shown photograph is of a replica largely based upon a stick calendar from Saint Felicity oratory in Rome.
It is obvious from the cited artifacts that time cycles were sometimes tracked by the moving of a peg relative to a predetermined arrangement of markers or bored holes. (Updating of the location of a peg to another marker or hole would have been required on a daily basis).
In exploring more of how the ancients would have used the above shown calendar, a knob or a stick would have been moved in correspondence with the top row comprised of 7 holes. Another knob or stick would have been moved in correspondence with the two columns consisting of 30 numbered holes. Yet a third knob would have been periodically moved around the center circle of holes to track the circle of the zodiac.
From the 30 numbered holes shown on certain among the early used zodiac-calendars, it seems certain that a 30-day cycle was reckoned in association with 12 divisions in each annual cycle.
The cited row of 7 holes that appears on some historic artifacts does almost surely indicate that a planetary cycle of 7 days was simultaneously being time tracked--as is further shown below.
For a technical discussion concerning how the cited stick calendar could have been used in an effective track of the tropical year, refer to the online publications previously listed.
The week cycle
The cited artifact of a stick calendar indicates that a week cycle of 7 days may have been known among the Romans as early as the first century.
It is--however--not clear from the historical record that first-century Romans would have subdivided time in units of the 7-day cycle.
The Roman practice of counting the 7 planetary days probably began to grow popular about the beginning part of the second century.
The usage of the week among the Romans in the third century is attested to by Dio Cassius (c. 200-220 CE) who wrote: "The dedication of the days to the seven stars which are called planets was established by Egyptians, and it spread also to all men not so very long ago... [This dedication now] prevails everywhere..." (Dio Cassius, Historia 37,18).
The interpretation of a week cycle of 7 planetary days--as it would have been understood by Romans of the third century--appears to have originated among earlier Babylonian and Egyptian astronomers. (More primal Babylonian and Egyptian priests appear to have reckoned a running cycle of 7 hours in association with 7 planetary gods). The Romans came to ultimately believe that the 7 planetary gods were to be honored in a specific order or sequence--as follows: 1. Saturn; 2. Sun; 3. Moon; 4. Mars; 5. Mercury; 6. Jupiter; 7. Venus.
While the week cycle did not grow to become popular among the Romans until the second century, the use of a week cycle was already popular in regions of the Middle East from more ancient times. It is here of interest that astronomers in this respective region appear to have tracked a cycle of 7 running days all throughout the Second-Temple Era. Furthermore, a running count of the week--a king's cycle--can be recited to have been in use from prior to the sixth century.
For pertinent information concerning the early time track of "weeks of days" and "weeks of years", refer to the following online publications:
The indicated Egyptian track of the annual circle in time segments of 10 degrees (36 segments per year) points to the possibility that Egyptian astronomers may have been knowledgeable of a 70-day cycle--and from very ancient times. The Egyptian reverence for a cycle of 70 days can seemingly be recited from the Bible book of Genesis (refer to 50:3). It here becomes significant that--if the rate of one day is routinely scribed in association with a cycle of 70 days--the residual days inherently become equal to 360 days (360.0245 days) on an annual basis. This accurate annual scribe means that an ancient astronomer could have effectively measured and metered out each and every degree of the annual circle through the simple scribe of a 70-day cycle.
Lunar and solar cycles
In summary to the above, it is clear that--through the reckoning of cross-referenced lunar and solar cycles--it would have been possible for early astronomers to very effectively measure and meter each passing tropical year.
It here seems to be of significance that in addition to an accounting of solar days, the reckoning of special lunar days may have also been performed.
For additional information concerning the combinational time track of both lunar and solar cycles, refer to the following online publications:
Priest-astronomers in the ancient past appear to have been effective (even perfect) in measuring and metering out the apparent lunar and solar orbits.
Please feel free to download and distribute--but not sell--the articles and booklets listed above. (Note that the published material is subject to constant revision. Be advised that corrections, amendments, and new interpretations are frequently made.)