## 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.

## Design of the Taj Mahal: its Façade

The Taj Mahal is one of the most recognizable buildings on earth. It was built by a Moghul king as a memorial for his dead queen and for love itself. The Mughals became famous for their architecture and the Persian notion of the sacred garden though their roots were in Central Asia just north of Persia.

I had been working on Angkor Wat, for my soon to be released book: Sacred Geometry in Ancient Goddess Cultures, where the dominant form of its three inner boundary walls (surrounding the inner sanctum) were in the rectangular ratio of outer walls of six to five. A little later I came across a BBC program about the Mughals and construction of the Taj by a late Moghul ruler, indicating how this style almost certainly arose due the Central Asian influences and amongst these the Samanids and the Kwajaghan (meaning “Masters of Wisdom”). I had also been working on the facades of two major Gothic Cathedrals (see post), and when the dimensions of the façade of the Taj Mahal was established, it too had dimensions six to five. An online pdf document decoding the Taj Mahal, established the likely unit of measure as the Gaz of 8/3 feet (a step of 2.5 feet of 16/15 English feet; the Persepolitan root foot *(see below: John Neal. 2017. 81-82 ). Here, the façade is 84 by 70 gaz.

## The Moon is Key to our Survival

With the advent of many orbital missions, the Moon is threatened with orbital and other changes due to space travel.

The modern theory of relativity has joined the worlds of space and time, now called spacetime. As beings we live in space while moving through time, and both these are assumed to be neutral dimensions having mere extension. However, spacetime is distorted by the massive gravitational objects found in solar systems, these exerting an attractive force on all objects including ourselves. As humans, we are therefore locked onto the surface of the earth by gravity, viewing a solar system of eight orbiting planets seen in the sky from the surface of the third planet from the sun. The earth has an unusually large moon which has fallen into resonance with the planets, a resonance then belonging to time.

The Moon was formed 4 to 5 billion years ago and this affected the Earth’s geology, stabilized its tilt (giving stability to the seasons) and providing tidal reaches on coasts. But apart from such direct physical changes to the earth, the moon has now developed resonances with the solar system, especially its outer giant planets, and this has given time on earth a highly specific resonant environment, based upon the lunar month and year of 12 lunar months. This resonant network appears to be numerical when counting days, months and years, in between significant events in the sky.

The structure of time is numerical because of these resonances between the moon, the sun and the planets. This resonance came to be known by previous civilizations and was thought meaningful in explaining how the world was created. Time was deemed spiritual because its organisation allowed human beings to understand the purpose of life and of the earth through the structure of time. In particular, the moon was a key to unlocking the time world as a link to a higher or spiritual world, a literal sky heaven organised according to numbers.

Continue reading “The Moon is Key to our Survival”

## The Stonehenge Crop Circle of 2002

One sees most clearly how a single concrete measure such as 58 feet can take the meaning of the design into the numbers required to create it. However, metrology of feet and types of feet can hide the elegance of a design.

photo by Steve Alexander of TemporaryTemples.co.uk

I received Michael Glickman’s Crop Circles: The Bones of God at the weekend and each chapter is a nicely written and paced introduction to a given years worth of crop circles generally in the noughties. The above is the second in proximity to Stonehenge reminding keen croppers of an earlier one. This cicle preceeded the late-season (August) circle at Crooked Soley that I have an analysis of soon to be posted, drawing on Allan Brown’s small book on it.

Glickman’s chapter 10 : Stonehenge Ribbons and Crooked Soley provided a tentative analysis of the Ribbons as having the ends of the ribbons measuring 58 feet. The design was observed as making use of a single half circle building block for most of the emergent six arms emerging from the center. Michael suggested that there were 13 equal units of 58 feet across the structure.

Figure 10.4 Showing thirteen divisions of one of the three diameters of ribbons. photo: Steve Alexander.

From this I was able to observe that clearly the divisions were not equal in size and the white ones were clearly smaller as was the central circle’s diameter. Scanning the picture and placing it in my Visio program, so that a rectangle of 58mm was equal to the diameter of the right hand ribbon end, it was possible to determine that the ratio between these lengths was 5 to 4, or 5/4, from which the shorter white length must be 46.4 feet and that the diameter can be seen as 9 units across, that is 104.4 feet. The unit is 104.4 feet divided by 9 which equals 11.6 feet, which is 10 feet of 1.16 feet, the root reciprocal of the Russian foot of 7/6 feet, that is 7/6 feet divided by 175/176 (= 1.16). Going down the “Russian” root led to the diagram below.

My analysis of Michael Glickman’s figure reveals a span of 580 Russian Feet.

There are parallax errors so I have had to show the ideal designed shortened across the left-hand of the design, but the design has many numerical aspects where each arm is 27 units so that two arms are 54 which, plus the center, gives 58 times 10 equaling 580 Russian feet. But then I noted that 58 feet, divided by 5, gave the unit as 11.6 English feet while 58 feet divides into the 58 unit diameter across the crop circle.

Now we see a set of multiples of 29 are there as numbers {29 58 87 116 145 174 203 232 261 … }. The reciprocal Russian at 1.16 feet and the unit of 11.6 feet are decimal echoes of the number 29. The formula of the Proto Megalithic yard is 87/32 feet and 261/8 inches.

To be continued

One sees most clearly how a single concrete measure such as 58 feet can take the meaning of the design into the numbers required to create it.

## Chartres 3: Design of West Façade

The design of the twin towers of Chartres point to an extraordinary understanding of its designers, quite unlike pre or modern understandings of the outer planets and their harmonic ratios. We have already seen a propensity for using the ordinary English foot to indicate days-as-feet within the structure. The Façade hosts what is perhaps the most famous “rose window”, though it was only in later centuries that it would be termed thus, as the cult of the Virgin Mary became more widespread. But this cathedral was strongly dedicated to the Virgin, when built.

The two towers are separated by the same distance as the rose window is above the footings, namely 100 feet, while the façade is 150 feet wide. This has led me to rationalize the façade as being six units across of 25 feet, while the façade appears to end (and the towers begin) 200 feet above the footings.

Interpretation of the western Facade as composed as towers 4 apart, width 6 apart and height 8 units, all of 25 feet. The Rose Window is held within two 3,4,5 triangles within a wall of 2 units square.

That is the façade was therefore designed as a three by four rectangle, the rose window centrally located within a square of side length 50 feet.

In simplest units of 50 feet, 8 by 6 becomes the proportion 4 by 3, with diagonals that are 10 units (that is, 250 feet) where the rose is at the crossings of those diagonals, held between two 3,4,5 triangles.

This first Pythagorean triangle holds all of the ratios of regular musical harmony, having 4/3 (fourth), 5/4 (major third), 6/5 (minor third) between its sides, which multiplied together equal 60 and summed equal 12.

NEXT: to come

##### Interpreting Chartres

Yet to come: the design of the Rose Window.

## Chartres 1: the cosmic coding of its towers in height

The lunar crescent atop the “moon” tower’s cross.

Chartres, in north-west France, is a very special version of the Gothic transcept cathedral design. Having burnt down more than once, due to wooden ceilings, its reconstruction over many building seasons and different masonic teams, as funds permitted, would have needed strong organizing ideas to inform the work (as per Master Masons of Chartres by John James).

Continue reading “Chartres 1: the cosmic coding of its towers in height”