Revised: February 21, 2010 ++
Copyright © 2010-2016 James D. Dwyer
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The following paragraphs describe an easy to understand time-tracking system. The system that is subsequently documented only requires the day count of a primary cycle as well as the day count of a secondary cycle.
The currently described day-count system is significant in that the turn of each passing tropical year can very accurately be determined.
To be a bit more specific about a system that is effective for measuring and metering the cycle of the tropical year, the count of primarly and secondary time wheels are required. In association with counting the cited two cycles, an exclusive day count can then be equated to the revolution of the tropical year. In essence, an annual calendar can be derived from out of the revolution of two time cycles.
In terms of accuracy, a two-count system can achieve an annual calendar that paces the cycle of the tropical year to within an average difference of only 2 seconds. This means that the cited primary and secondary cycles can remain of fixed length, and no additional insertion or deletion of days is every required, even across a time run of many thousands of years. The accounting of only two short cycles can thus achieve what is probably the most accurate calendar that can be derived from out of the spin and orbital phenomenon.
The subsequently presented time-tracking system is predicated upon a solar day of 24 hours (or also 86400 seconds) and a tropical year of 365.24219 days (or also 365 days, 5 hours, 48 minutes, and 45 seconds).
Each passing tropical year can effectively be metered out by simply tracking 40 days (as an unbroken cycle). However, a calendar predicated upon this time track must add a day each 9 years (as is further shown below).
The cited measurement of the tropical year only requires that 39 days in each cycle of 40 days be exclusively counted. (Hint: This count can achieve a sum of 356 days per year).
The following diagram more clearly illustrates that -- as long as 40th days are never counted -- the revolution of each solar year can exactly be paced by an exclusive count of the other days:
_____________________________________ A PERFECT 9-YEAR CALENDAR * _____________________________________ Renewal = 1 day Year 1 = 356 days Year 2 = 356 days Year 3 = 356 days Year 4 = 356 days Year 5 = 356 days Year 6 = 356 days Year 7 = 356 days Year 8 = 356 days Year 9 = 356 days * - Each 40th day (a perpetual rate) must be leaped or intercalated apart from days comprising the the cited calendar count. ____________________________________ Calendar count = 3205.00000 days 40th rate uncounted = 82.17949 days Average 9-year rate = 3287.17949 days Average calendar rate = 365.24217 days Solar-year rate = 365.24219 days Average difference = 2 seconds (!)
The diagram shows that each passing solar year can very effectively be measured and metered out in correspondence with a numbered count of 356 days -- when 40th days throughout the time stream are never numbered among the other days.
An exclusive count of 3205 days in association with the passage of 9 solar circles requires the perpetual reckoning of 'unbroken cycles'. In essence, the track of a cycle of 40 days must never be preempted be the insertion/omission of any other day.
The cited calendar count of 9 years inherently aligns with each time segment of 9 tropical years (on the average). This equivalency is easy to recognize in that the rate of 1 day in 40 days is equal to 2.5 percent of time and the rate of 3205 days in 9 years is equal to 97.5 percent of time. Thus, in combination, these two rates of days can exactly account for all of time (100 percent).
In this modern era, the track of a 40-day cycle can be used to determine the epoch of each passing solar year to within the limits of 2 seconds (on average). However, because Earth's spin appears to be slowing down by a tiny amount with each passing century, it can be recognized that the track of a 40-day cycle could have been used to exactly (perfectly!) measure and meter the solar-year rate in some era of the past. The era when the solar year could have been perfectly measured and metered out using a track of 40 days was probably within very recent centuries.
The above cited count of 40 days is additionally significant in that each passing year can also be metered and measured by counting out a somewhat different primary cycle. The focus of the current section then provides detail of a diverse method by which the span of the tropical year can be tracked.
To be more specific about another method by which each passing year can be measured, a cycle of 9 years can effectively be time tracked within the context of counting a cycle of 360 days (as a primary cycle). In tandem with counting a primary cycle of 360 days, a calendar count of 360 days is also performed in parallel. The purpose of the secondary count of 360 days is to define/delimit a set of days that keeps pace with the traverse of each tropical year.
A double count of 360 days can achieve an accurate annual track as long the following rules are applied:
The above stated rules are required to properly intercalate an annual calendar of 360 days. The set of rules could also be stated in terms of counting a 90 day cycle. For example, a day could be added to the calendar at a frequency of each 90 days, while yet an additional day could be added to the calendar at a frequency of each 360 days.
The rules required to intercalate a 360-day calendar could, in the most simple form, be expressed in the context of a rate of 5 days for every complete revolution of the primary time cycle (360 days).
Obviously, more than a single set of rules would be apropos for intercalating a calendar of 360 days. In any case, a base rate of intercalation equal to 5 days for each time segment of 360 days would be required.
From the given detail of the current model it should be clear that no other adjustment is required other than the addition of 5 days upon the completion of each primary cycle of 360 days. Also, the addition of 1 more day is required in those occasional years that contain all 5 quarter nodes of the primary count.
Thus, a precise 360-day calendar can be derived from out of the time track of an endless cycle of 360 days. The cited double counts function perfectly together in that a primary cycle (360 days) is used to define/delimit an exclusive set of days each year. The additionally defined days each year, normally 5 days, are simply not counted like the other calendar days (360 days in each tropical year).
The following diagram shows that the time traverse of each tropical year can effectively be measured and metered out by tracking primary and secondary cycles of 360 days -- where the secondary cycle represents a calendar count that is preempted by the inclusion of additional days:
_____________________________________ A PERFECT 9-YEAR CALENDAR * _____________________________________ Renewal = 1 day Year 1 = 360 days Year 2 = 360 days Year 3 = 360 days Year 4 = 360 days Year 5 = 360 days Year 6 = 360 days Year 7 = 360 days Year 8 = 360 days Year 9 = 360 days * - 5 days are added every 360 days and 1 more day is added to years containing a 5th quarter node. ____________________________________ Average calendar rate = 365.24217 days Solar-year rate = 365.24219 days Average difference = 2 seconds (!)
Of course, the 360-day model as diagrammed, clocks to the very same high degree of accuracy as the above cited calendar that was predicated upon a cycle of 40 days. Again, it seems of some certain significance that the accounting of only two short cycles can achieve what is probably the very most accurate calendar that can be derived from out of the spin and orbital phenomenon.
Of significance here is that several of the old-world calendars appear to have been predicated upon the revolution of 360 days. In some of the systems that used a 360-day count, intercalation of 5 days was deferred beyond the limits of a single year. For example the Kultepe Calendar appears to have been predicated upon a count of 10 days. This count (ten) was repeated across a time grid of 30-day cycles. "For three years, the ten counts ran congruently with the months and the years. Then, after the insertion of a 15-day shapattum period, they [the '10 counts'] overlapped from one month into the next, returning to congruency with the months after the next shapattum... " (Britannica, 1972).
For additional information about a primary count of 360 days, refer to the following online publications:
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