Category: Geometry and Metrology

Sacred numbers within metrologically-quantified geometries.

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.

Continue reading “Design of the Taj Mahal: its Façade”

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
  1. the cosmic coding of its towers in height
  2. the harmony in its towers
  3. design of the west façade

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).

As shown below, Chartres main towers are unequal in height and the “western” facade itself does not align to east-west, as normal Christian churches do. The left tower is also higher than the right tower and, it has been said, the left represents the Sun and the right the Moon. The height of the left tower, to its globe below its cross, is indeed the solar year of 365 days in feet. But the height of the shorter right tower, to its own globe, is not the 354.367 days of the lunar year (of 12 months); rather, it is the top of its cross, sporting a crescent moon suggesting it is a moon tower, that is 354 and a third feet high.

The cosmic time coding of the two towers as solar year->lunar year between the globe’s height (on left in red) and the top of the cross (on right in blue). But the left tower also indicates the Saturn synod of 378 days to the top of its cross. The for-square rectangle, geometrically relating the solar (diagonal) and lunar years, is shown.

That is, the height of the lunar year in feet, from the same starting point as the solar tower’s height as the solar year, the lunar year would be to the top of the lunar cross, where the crescent is attached, and not to its globe. There is then a reasonable connection between the solar and lunar years and the two towers. However, it is also interesting to see the number of days, as feet, of the left tower to its own cross. It is exactly 378 feet, the synodic period of Saturn in days. Readers of my books and this site will remember that the ratio between the lunar year and Saturn synod is exactly 16/15: a musical semitone within the ancient tuning system called Just intonation.

This arrangement suggests Chartres was built to be a time-factored monument, which may be why the cathedral was aligned to midsummer sunrise (which was a megalithic norm) rather than being aligned east-west. Built on top of a solitary promontory, horizon events would have been clear across the flat fertile plains.

NEXT: the harmony in its towers

Interpreting Chartres
  1. the cosmic coding of its towers in height
  2. the harmony in its towers
  3. design of the west façade

Yet to come: the design of the Rose Window.

Dun Torcuill: The Broch that Modelled the World

image above courtesy Marc Calhoun


Script

This video introduces an article on a Scottish iron-age stone tower or brock which encoded the size of the Earth. 

You can view the full article on sacred dot number sciences dot org, searching for BROCK, spelt B R O C H.

In the picture above [1] the inner profile of the thick-walled Iron-Age broch of Dun Torceill is the only elliptical example, almost every other broch having a circular inner court.

Torceill’s essential data was reported by Euan MacKie in 1977 [2]: The inner chamber of the broch is an ellipse with axes nearly 23:25 (and not 14:15 as proposed by Mackie).

The actual ratio directly generates a metrological difference, between the major and minor axis lengths, of 63/20 feet. When multiplied by the broch’s 40-foot major axis, this π-like yard creates a length of 126 feet which, multiplied again by π as 22/7, the simplest accurate approximation to the π ratio, between a diameter and circumference of a circle, as used in the ancient and prehistoric periods., generates 396 feet. If each of these feet represented ten miles, this number is an accurate approximation to the mean radius of the Earth, were it a sphere.

If we take the size of the moon in that model, as being 3/11 of 396 feet this would give a circle radius 108 feet and one can see that, using the moon, the outer perimeter of the brock was probably elliptical too.

Thank you for watching.