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A Hint of Rational Unity Among Irrational Constants

The voice of our collective past is becoming louder and more defined. Our systems of weights and measures inherited from time immemorial are profoundly less arbitrary than contemporary thought tends to imagine. After all, with each new life born, the true depths and interconnectivity of this field may only hope to be understood anew. So quickly may the higher purpose and interrelationships of our dimensional quantifications escape our collective grasp... The degrees of a circle, the length of a meter or a foot, the base 10 decimal system, the second and so many others- their origins are all ancient, their purposes far more elaborate than most dare to comprehend.

Units of weight and measure are an effort to quantify our multidimensional reality to an interrelated scheme that is true to pure numerical relationships, so that we may navigate our lives by pure reason. The ancients understood our physical world to be divine mathematical plan, geometry was sacred, number was the fingerprint of life and knowledge of these things was the wisdom of the gods. Temples were built to encapsulate these treasures of knowledge, religions were devised to humanize this knowledge through anthropomorphization.

The Great Pyramid of Giza is the greatest of these temples, and here is where the true feats of understanding possessed by antiquity stand on display to this day. This was a temple of constants, built to the scales of the Earth and in ratio to the fundamental mechanics of reality itself.

Here we see a diagram listing several of the mathematical constants found in the Great Pyramid to date. I go into much more depth regarding the pyramid in my article here- The Great Pyramid of Giza- Temple of Constants

A mathematical constant is a "number" (a ratio really) that serves a special function in calculation. The discovery of a new mathematical constant represents a true achievement for a civilization. The ability to calculate and comprehend the innermost and outermost workings of reality.

Many notable efforts have been put forth in recent years in unveiling the mathematics of this structure, and to discern what it may have to tell us about the nature of the mathematical constants in the way that the structure ties them all together. What is truly profound here is that within the design of this temple, so many disparate constants are made to coexist in a most remarkable and absolutely ingenious display of unity. It is as if the Great Pyramid is the grand unifying equation expressed in stone, and at the scale harmonic with our physical realm!

The work of Alan Green in particular was able to demonstrate that within the basic dimensions of the Great Pyramid, the ratios of myriad mathematic constants may be found. Alongside the constants, he was able to show that the major units of measure, both "contemporary" and ancient, such as the foot, the meter and the cubit were also found in ratio, and that these units themselves correspond to the constants. What better way to measure the harmony of the world, than by basing our units of measure off of mathematical constants?

This work of Alan’s brought me briefly down a tangent that produced the interesting results I quickly present to you here.

A Hint of Rational Unity

As we see in some of Alan’s work with the Great Pyramid (and a plate from the work of William Shakespeare), the 3 points of any 2 “numbers” represented by a line the length of their magnitudes may be made to fit within a circle if they are set to a right angle and the hypotenuse that unites them is given as the circle’s diameter; this is Thales Theorem.

I realized this would be the ideal way to determine a sort of prime and essential geometric harmony between these otherwise irrational numbers, if there was one.

Part of this inspiration was from knowledge of the fact that the 3, 4, 5 triangle does just this.

I laid out all the constants found within the Great Pyramid in this fashion as well as added some other significant ones and began to work to determine if any order of number would give them a harmonic unity.

I suspected a popular ratio found within units of measure that was highly divisible and spiritually/ religiously significant could be at play. It was not long until I found the one that worked.


Circle Diameter 216

Let 216 define the diameter of the circle and expand its grid to 216 ^2. Let all constants share a hypotenuse set to 216 as the circle’s diameter and let the ratio of the constant to 1 touch at a right angle. Angle the hypotenuse to span 1 unit of the 216 grid. Every connection will fall upon a point or line within this grid, suggesting a unity between these irrational constant numbers that result from the infinite sums of myriad essential mathematical concepts.

The constants which I tried and found to work are:

-The Prime Reciprocal constant


-Feigenbaum b

-Brun's Constant

-The Tribonnaci Constant

-Phi and 1/Phi

-The 3-4-5 triangle mentioned above

-Feigenbaum a

-Euler's Constant

-Blackhouse's Constant

-The Square Root of 2.

Surely there are more... I have not had the time to comprehensively explore them all.

Yes, the image above is hard to see. The original image is 9000 pixels wide and 25 megabytes alone, and the working file was done in vectors so that I could employ a really high resolution zoom to check the integrity of the alignments.

Lets zoom in.

All constants originating/ converging to a point.

-Feigenbaum b

All constants originating/ converging to the adjacent point of the diameter at a pitch of 1 unit.

Pi, Feigenbaum a, Brun's constant.

Pi, Brun, Tribonacci, Phi

3-4-5 triangle and 1/Phi

Clearly the accuracy and consistency of these alignments among several of the most quintessential mathematical constants speaks of a beautiful and mind bendingly intricate cohesion amongst our universe's mathematical behaviors.

This curious geometry was a project I had worked on over a year ago in 2016 and it left me with a long list of calculations that I should endeavor to compute, in order to uncover more specific details of the message it teases, and with requisite mathematical precision. Unfortunately, other projects and responsibilities overwhelmed and it has been locked in the closet ever since. I present it here now in its current state in case it may spark a flame in another, or trouble me enough to continue along its path sooner rather than later ;)

On The Significance of 216

The number 216 is one that spans science, religion and units of measure. This is because it is highly divisible amongst several geometric orders of number.

I could wax on about how this works, and I may do that in a later update to this article, but perhaps the best resource to see the extent to how this number fits into the harmonics of scale would be the many videos of Alan L of SGD. I cannot recommend his works enough, his channel is a veritable compendium of information in the realm of weights and measures and he has hardly uttered a word I do not agree with completely.

You will note in the videos above that 216 is a number in use in calendars, in time keeping, in astronomical distances and proportions of the heavenly bodies, in navigation, in geometry, in arithmetic, in technology new and ancient, in architecture and music alike.

An important fact to consider is that repeating 0's after any harmonic number (such as 216,000) still retains the geometry and numerical relationships within it, but simply adds more resolution in orders of magnitude. The fact that that great cycles and vast astronomical distances of our macrocosm can be so great yet still lead with 216 is testament to the wisdom of the base 10 counting system and its ability to compute the mathematics of nature. A story for another time...

216 in the compass, in arithmatic, in planetary time cycles, in religious allegory, in fundamental geometry and as the circumference of the Earth and the Moon! Image credit- Alan L of SGD

Please take the time to review the great contributions of Alan Green in decoding the mathematical constants within the system of weights and measures and our ancient architecture, as well as the fantastic documentation of Alan L in compiling the details of how these weights and measures span and guide human history.


Clay Taylor

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