The Royal Cubit

The English word “cubit” comes from the Latin word “cubitum” or elbow.

Interpreting this, we might say that it hints at a sacred proportion within the human body. Measured from the fingertips, it’s the 1:√2 ratio of the forearm to the deltoid tuberosity:

In the artwork below, Seshat’s arm bands made of leopard claws hint at this:

In Seshat’s right hand, the marker signifies 1 unit from the bottom of the shen ring, with the vertical length of the sacred cord at √2. In her left hand, she holds the cord in the middle. These ratios are also found in nested squares and the 2D projections of stellated cuboctahedrons.

To the Egyptians the Stretching of the Cord ritual was born during the Old Kingdom. This was the archaic time of Djoser, Imhotep, Snefru, Amenhotep and Kanofer. The ceremony dealt with the dimensions of sacred temples and was governed by the lunar gods Seshat and Thoth.

The cuboctahedron (associated with the seventh chakra) was considered “perfect”. It held an almost mythical status in geometry because it represented the definition of structural and energetic equilibrium. While the five Platonic solids were praised for their surface symmetry, they all possessed an internal tension—their outer edges do not equal the radial distances from their centres to their vertices. The cuboctahedron eliminated this drama entirely. In the figure below, we can see the stellated cuboctahedron:

…whose orthographic projection looks like nested squares

…that can share the same master diagonal as the lunar diameter:

From the wireframe above comes the lotus pattern below. It shows a series of nested squares that are drawn from the midpoint of their parents. This is the same as dividing each side by √2. While we have only drawn a short sequence below, in reality these fractal squares regress far beyond our visual acuity:

Above: the Royal Cubit is really a yardstick of the stellated cuboctahedron

In the Book of the Dead, the deceased had to face 42 judges before the god Osiris. The soul would recite the 42 Negative Confessions denying specific sins. If the heart could be balanced with a feather then the soul passed on to paradise. But why 42?

Well, if we take the diameter of the Moon (3,474 km) and drop it through the 42 steps of the sequence above, we get a geometric output:

Now, let’s look at how that $165.65\text{ cm}$ chord naturally relates to the Royal Cubit without forcing anything:

That number is profound because it represents $\pi \; as\; \surd 10.\; Indeed$​, ancient cultures used $\surd 10$ as “harmonic $\pi$” because it effortlessly bridged the decimal system with circular geometry. ($\surd 10\; also$shows up in pentagons and decagons).

Why were the Egyptians precise about the lunar diameter but more wily with $\pi ?$$Because\; they\; chose\; the\; resonant\; approximation\; that\; fit\; the\; cosmology\; and\; avoided\; \pi ’s\; entropic\; value.\; In\; other\; words,\; they\; prioritised\; universal\; harmony.$

Why did they divide 165.65 cm by π to get the Royal Cubit in the first place? Well, because the cuboctahedron was perceived as being PERFECT and therefore having circular properties. When they divided by π, the Egyptians were effectively unwrapping the “periodic” geometry to get a more “spatial” quality.

Harmonic $\pi \; =$3.16227766…

Why do we care about the difference between harmonic $\pi \; and\; entropic\; \pi ?\; Well,\; like\; the\; variance\; between\; the\; Fibonacci\; spiral\; and\; the\; golden\; mean\; spiral,\; one\; is\; real\; and\; one\; is\; imaginary.\; The\; difference\; in\; \pi ’s\; case\; is\; about\; 0.66\; of\; one\; percent—the\; Devil\; really\; is\; in\; the\; detail.\; “Transcendental”\; \pi \; then,\; separates\; us\; from\; the\; natural\; world\; because\; it\; is\; purely\; theoretical.$

Indeed, think about what an irrational, transcendental number actually is. It cannot be captured as a clean fraction. Its decimal tail spirals out into infinity without ever settling into a repeating pattern, a predictable rhythm or a final resolution. It is a mathematical system that is constantly running away from wholeness. That is the very definition of entropy—infinite dispersion, non-containment and the breakdown of a unified centre.

Above: an implied Moon and Earth

So the Moon was the “Rosetta Stone” of the planets that anchored their entire measurement system. Here we are reminded that Thoth as Lord of the Cubit was a lunar deity. At their cultural zenith then, the Egyptians made their mathematics “fit” in a very specific way: they encoded ratios that linked human and cosmic scales.

By utilising a harmonic version of $\pi$ embedded within their standardised units of measure, the Egyptians didn’t just build temples—they built instruments of resonance designed to tune human consciousness to the exact frequency of the living universe. Harmonic $\pi \; then,\; was\; used\; in\; every\; major\; structure\; along\; the\; Nile\; including\; the\; pyramids.$

So the human body, the cuboctahedron and the Royal Cubit were all attempts to point at the same underlying principle: coherence across scale. In other words, civilisations only bloomed when their symbols, biology and cosmology were mutually sympathetic. Cultures flourished then, when meaning, myth and consciousness participated in a common order.

Today, our metric and imperial systems are mere abstractions. A metre is the distance light travels in a vacuum in 1/299,792,458 of a second—nobody feels that in their bones! This fall from universal relativity was one of the most enduring mathematical debaucheries in our history: our reductionistic science remains unaware of Ma’at’s influence to this day.

Our technological world is all about exactness and is therefore tone deaf.
Ancient Egypt was all about resonance and was therefore coherent.
They are far from the same thing!