Month: June 2024

The Modularity of Seven

Sacred Geometry is metrical, it is based upon the interactive properties of “natural” (that is, whole) numbers and cosmic constants.

We live in a civilization where everything is thought to be functionally due to forces and laws, these all calculated using numbers and algebra. For this reason, it is hard to see the influence of numbers acting directly in situations to reveal that, geometrical forms are only possible due to numbers. One such form is the equal perimeter circle and square: this figuring heavily in my later books, as an ancient model, and in postings on this website (opens in new tab).

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The Martian Moon Resonance

As with the other outer planets, Mars has a resonant relationship with the Lunar Year. UPDATED.

When I wrote Matrix of Creation in 2001, many planetary resonances were revealed and most of these involved small whole-number relationships between both sidereal and synodic periods in the solar system. At that time, only the Jupiter and Saturn synods (of the two visible outer planets) had been identified, as 9/8 and 16/15 of the lunar year (see chapter 9). The implied units of these ratios were 1.5 and 0.8 lunar months (respectively).

Mars is closer to the Earth and Moon than these giant planets and, since all the giants have numerical ratios to the lunar year, what of Mars whose synodic period is effectively 780 days: This is over 2 solar years (2.14) and 2.2 lunar years, a fractional relationship of 11/5 lunar years. That the moon has such a simple fractional relationship with all of the outer planets implies a previously unknown (at least in recent times) principle, in which the moon is gravitationally affected by the “loops of proximity”, seen when such planets approach, at a frequency defined by their synodic period. In the case of Mars this is very long, proximity happening every 780 days.

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The Cellular World of Twelve

The foot has twelve inches just as the British shilling had twelve pence. A good case can be made for twelve as a base like 10, since there are 12 months within the year and many ancient monuments can be seen to have employed duodecimal alongside decimal number, to good effect.

Until 1971 the currency in the United Kingdom of Britain was duodecimal, called pounds, shillings and pence.

This old system of currency, known as pounds, shillings and pence or lsd, dated back to Roman times when a pound of silver was divided into 240 pence, or denarius, which is where the ‘d’ in ‘lsd’ comes from. (lsd: librum, solidus, denarius). see historic-uk.com

There were 12 pence in a shilling and 20 shillings in a pound, that is 240 pennies. The change to a decimal (100) pence in a pound caused a lot of inflation during the changeover due to price opportunism, then part lasting recession. In British heads the skill of giving and taking change in a duodecimal arithmetic was soon lost. In the late 70’s my mother, when visiting the US, was amusingly referencing “old money”, alongside the exchange rate between a decimal pound and the decimal dollar, just as Greeks had problems with the Euro.

History of Decimal Measures

Napoleon sought to “rationalize” all the ancient weights and measures of France culminating in the decimal units within modern science, firstly CGS (Centimeter-Gram-Seconds) and then MKS (Meters-Kilogram-Seconds).

The Meter exemplifies the situation: it contains 100 centimeters and 1000 millimeters whereas the root foot for the worldwide and only ancient metrology is that called English which has 12 inches (each a “thumb” in French) and each inch halves, quarters, eighths and sixteenths of an inch, but also 10ths etc., that is a duodecimal system and decimal notation as with 12 = 10 +2.

The metrology of the ancient world had no need for decimalization since it had been formed to employ all the integer numbers, using fractions of a foot – fractions being a combined multiplication (numerator) and division (denominator) operation. That is, there was no base-10 decimal notation when metrology was developed and one can suggest that decimalization was created in the wake of treasuries, mints and central banks.

However, decimal notation emerged much earlier with the alphabetic form of writing languages down. Cuneiform had used compound sounds (called syllables such as “no”) but the new Phoenician alphabets notated the consonants and vowels of specific languages, now called phonemes of sound (for exampple, the phonemes “n” and “o”). This reduces the number of symbols needed to notate speech, and in turn these symbols could then have a decimal function and words could also be numbers, in a code called Gematria:

Gematria is the practice of assigning a numerical value to a name, word or phrase by reading it as a number, or sometimes by using an alphanumerical cipher. Wikipedia on Gematria.

As the name implies, Alpha equals 1, Beta =2, D = 4, J = 10, etc.. Words could then encode a number, as in the Bible where Adam equals the three letters A.D.M whose numerical values in Hebrew/ Aramaic (1.4.40): when added up they “mean” 45. The later letters were values in tens and hundreds so that decimalization probably goes back to the 1st millennium BCE.

Figure 1 Numeric equivalence of Hebrew Alphabet

We are therefore needing to go earlier than the decimal base-10 system or indeed the use of any base at all, to see into the world of the megalithic astronomer and different relationships to numbers.

This previous world which gave birth to a type of math that is not arithmetical but instead used the factors within integers and rational fractions, initially through measured geometrical proportionality but then through sets of measures all rational fractions of the common foot.

Prehistory: Non-Decimal Measures

The earliest number encountered by early astronomers would have been (when they counted) the twelve lunar months within a year. The properties of the number twelve are generally taken to come from its factors (such as 4 x 3), it Platonic solid (the duodecahedron) – see next section. There were no twelve hours in half a day. We will the take a deeper approach, of visualizing the set of numbers within twelve, as {1,2,3,4,5,6,7,8,9,10,11,12}

Factors within Twelve

Twelve does not contain is the prime number 5 nor any higher prime factor. However, in counting to 12, there are two factors containing 5, namely 5 and 10. And there are, of course, the prime numbers and their ennumerated multiples, such as, for 7, {14, 21, 28, 35, 42, 49, 56, …}. This means the number field is made up of empty slots into which the number one greater than the preceding number must then be a prime number. And any prime number can then be doubled, tripled, etc., to become enumerated itself. That is, which we call prime numbers are those that happen to have no preceding number of which it is a multiple of any (previously arisen) number.

Numbers Within Twelve

Twelve does not contain is the prime number 5 nor any higher prime factor. However, in counting to 12, there are two factors containing 5, namely 5 and 10. And there are, of course, the prime numbers and their ennumerated multiples, such as, for 7, {14, 21, 28, 35, 42, 49, 56, …}. This means the number field is made up of empty slots into which the number one greater than the preceding number must then be a prime number. And any prime number can then be doubled, tripled, etc., to become enumerated itself. That is, which we call prime numbers are those that happen to have no preceding number of which it is a multiple of any (previously arisen) number.

Figure 2 The inner structure of Twelve

Figure of (top) the first twelve numbers, four of which divide by three, making the even numbers (orange) alternate with the odd numbers in serpentine fashion. Numbers dividing by 5 then alternate down then up, every two threes.  (bottom) the color keys used. (One could show primes with italics)

In a following post, the consequences of this inner structure reveal Twelve’s cellular structure within the number field.