Mapping the Year : Reconciliation of Weeks
The system by which a circle is neatly divided into 360 parts, may be regarded as an attempt to represent the cycle of 365 days in the year. 365 being a particularly difficult number for any practical use in simple calculation, it would make perfect sense to adopt 360 as a valid approximation. Indeed, there is precedence for this contained in the myths of Egypt: which regarded the year as 360 days, with 5 ‘unlucky’ days at the end.
By using this approximation, the year can be readily mapped onto a circle, with the added benefit that it is a number which allows even division by all the numbers 1 through 10 (except 7 [#1]) and the all important 12, which refers to the months of the year.
The subdivision of these basic units, the degree, are a little less easily rationalised: 1º(degree) = 60′ (minutes) which are further split such that 1′ = 60″ (seconds). However, by applying the sexagesimal system at the unit level, each unit is neatly subdivided into a decimal factorisation of the whole circle (i.e. 60×60=3,600 = 10×360).
The true purpose of such a subdivision, particularly given that such small increments were incapable of being realised until relatively recently in our history, is a bit of a mystery. I would like to propose, however, that the system is rather revealing regarding the potential knowledge of the priest class who designed it.
Indeed, it would appear that the system demonstrates a knowledge of the precession of the equinoxes and may even have been an attempt to resolve the apparent irrational relationship between the solar and lunar calendars.
Precession of the equinox is a phenomena resulting from the wobble of the earth on its axis of tilt. This causes the stellar background to slowly rotate around the poles, as evidenced by the circular motion of the pole stars and, most obviously, by the rotation of the position of the equinox around the zodiac. It is generally accepted that a complete cycle around the zodiac takes approximately 26,000 years [#5] and that a period of approximately 2,160 years is required for the equinox to move from one constellation to the next: equivalent to 360/12= 30º of the zodiac.
Thus, it takes:
- 2160 years to precess 30º
- 2160/6=360 years to process 5º [#2]
- 360/5 = 72 years [#3] to process 1º
- 72/60 = 1.2 years [#4] to process 1′ (1 minute arc)
- 1.2/60 = 0.02 years to process 1″ (1 second arc)
But, 0.02 years = 7.3 days.
Hence, 1″ (second) of precession, by virtue of the sexagesimal basis of the system of angular measurement, approximates to a period of time which we call a week.
The week is, however, commonly regarded as primarily defined by the lunar cycle; equating to approximately 1/4 of the cycle. The average period of time between consecutive full moons is 29.5 days.
- 29.5/4 = 7.37 days
The discrepancy between the two values obtained equates to a period of 1hour, 40 minutes, 28 seconds [#5] (or 0.95% of the period defined as quarter of the lunar cycle [#6]).
These simple calculations would appear to imply that the sexagesimal system of angular measurement, largely impractical until relatively recently, may have been an attempt to reconcile solar movement across the stellar background with the lunar changes evidenced nightly.
If this is the case, the solution is indeed elegant, simple, and ultimately provides evidence that precessional changes were regarded as significant by very early peoples of Sumeria and Babylon who were responsible for codifying the system.
#1 : See Great Pyramid Pages for development of this.
#2 : This should be interesting in itself. 360 years + 5º of precession = 365 days.
#3 : See Sacred Geometry Pages for discussion on significance of these numbers.
#4 : 1.2 years = 1 year + 73 days [#3]
#5 : Using the generally accepted value of 26,000 years for a complete precessional cycle yields closer parity with the lunar quarter value.
- 26,000 / 360 = 72.22222 years
- 72.22222/60 = 1.2037 years
- 1.2037 / 60 = 0.0201 years
- 0.0201 years = 7.34 days
This equates to an error of 0.03 days from the value obtained from the lunar quarter calculation; equal to a period of 43 minutes, 12 seconds (or 0.41% of the period defined as a quarter lunar cycle).
#6 : < 5% discrepancy generally regarded as significant by most statistical criteria.
Copyright: Esoteric Numbers Group 2004