Sacred Number

The Earth - Moon - Sun system is a numerical contruction based especially on the numbers 18 and 19. The first, eighteen, is a canonical or harmonic number because it only contains powers of 2 and 3, the first two primes. The second, 19, is a prime number divisible by no lower number. As a prime 19 has the cache of being associated with Creation and indeed the Moon manifests 19 very strongly in a number of ways.

Known to the (classical) Greeks as the Metonic period, in 19 solar years the Moon's phase and its location in the stars repeats to quite high accuracy. Since the Sun illuminates the Moon to generate its phase, then the Sun also must be in the same relative position to the Moon, nineteen years later.

Also known to the Greeks (but demonstrably known also in prehistory)  there is a period of just over 18 years in which an eclipse of a given sort will recur. Thus, after 18 years of an eclipse (solar or lunar) one can make an important prediction of another, similar one. This "just over 18 years" is in fact the time it takes for exactly 19 eclipse years - bringing 19 in again - a type of year (346.62 days long) mentioned in the previous article and associated with the movements of the lunar nodes - the crossing points at which all eclipses take place.

In the 1990's, probably 1993, an amazing "fact" arose for me. If one builds an 18:19 right angled triangle, the third side is almost 6 in length. Conversely, if 19 and 6 are used then the base becomes 18.027 solar years long and the Saros period is 18.030 years long. It seemed to me that this near-Pythagorean triangle of 18:19:6 had been incorporated in the relative lengths of the solar and eclipse year and hence in 19 times these.

The Near Pythagorean Triangle that occurs with 18:19 when the third side is whole,
to accurately approximate the Saros Period of 18.030 years or 19 eclipse years.

The simplest thing to realise about the Saros is that 223 (a prime) lunations occur within it and that in 19 years, 235 lunations complete the Metonic. The difference is 5 + 7 = 12 lunations, the length of the lunar year. This is true because such cycles exhaust their variety in a symmetrical fashion, so that there is, in a sense, a lunar year (of 12 lunar months) at both the beginning and the end of the Metonic. An eclipse one lunar year (12 lunations) into the 19 years will result in an eclipse at the end - and the whole thing is continuous whilst, for the sake of understanding, we must measure starting points. In reality, continuously, the Moon's position is a repetition of where it was 19 years ago as well as where it will be in 19 years.

The actual triangle has the Saros period as 223 lunations and the Metonic as 235 lunations long giving an 18.030 year Saros period. The "unit" becomes 12 lunations and the third side 6 times 12 = 72. 235 divided by 19 is, of course, 12 and 7/19ths of a lunation or 12.36842105 rather than the actual of 12.36826623 lunations per solar year, yet accurate to 99.998748% which is why the Metonic is an accurate 19 year synchronicity.

The Paradigm of Number Field as Cosmic Generative Principle

Something needs to change about how we view co-incidences between such a triangle and the reality found in time. The geometry represents a property found within the number field itself and this is the credible explanation for such a geometry "being used", that the number field can do very special things when these special relationships between numbers can be embodied within dynamical systems. Rather like the strange attractors of chaos theory, such arrangements allow far simpler time relationships to occur that seem mystical to us but are in fact artifices of number.

I am not saying that this is a physical explanation (yet) for how the Moon could have come to have such relationships based around 19. Rather, that these relationships do work in the same sense that a machine allows things to be achieved that are otherwise impossible. Were such work associated with the number field, just as harmony is, then such structures in time echo to the fundamental structure of the universe prior to any Big Bang. In this sense, they might function like natural laws based on number rather than on physics, as in gravitation and the like.

The Golden Mean is already a perfect example of such an edifice since, it is the only real number proportion to one where the reciprocal and the square have the same fractional part (0.6180 = the reciprocal and 2.6180... the square). This artifice is found broadly in life but astronomically in the orbit of Venus through the Fibonacci series (see Matrix of Creation and Sacred Number on this).  Venus manifests phi just as the Moon manifests the properties of the number field relating to 19. Jupiter and Saturn manifest 18:19 in their synodic periods to give us the seven day week.

Mystifying numerical relationships, that appear regressive to modern science, probably belong to the number field, a field that few study in depth or with practical application. If these relationships are found, as I and others have shown, in the practical dynamics of the Earth's environment; then the association with prehistorical knowledge and then later mysticism has given a false impression of superstitious thinking when the facts speak for themselves - of a valid numerical not physical knowledge.

How this works can be shown using the triangle of the previous entry involving 18.618 and 19.618:

 The third side is quite interesting, apparently physically meaningless*, being just over 10 times the reciprocal of phi. I would like to work out an intermediate hypotenuse that is 19 long - the Metonic in years whilst the Draconic is 18.618 years (year of the lunar nodes) which period is 19.618 eclipse years long.

*The actual length of the third side is 6.1835265 which was rounded up in the diagram to 6.184. However, the number of lunations in half a year is 6.18413, two numbers within 99.99% of each other. There are 6800.076 days in a Draconic period of 18.618 solar years and 19.618 eclipse years in the same period making the form of the triangle correspond to the same period and the division of it by different units, the solar and eclipse years.

19² - (18.618)² = 361 - 346.62 = 14.38 and the sqrt is 3.792. If we divide the third side above (6.1835) by this the result is 1.631. This is nearly 1.618 as if, with N:N+1 and N=N.618, the whole number hypotenuse is found near the golden mean point on the third side, as below:

 In nature, such a working fact could generate an integer relationship where it would otherwise be highly unlikely.