Beyond the Pythagorean Theorem

For the Pythagoreans, the tetractys (from the ancient Greek τετρακτύς) represented the arithmetic sequence of the first four natural numbers (or more precisely, the positive integers), a quartet that geometrically could be presented in the form of an equilateral triangle of side four in measurement, to form a pyramid which summarizes the fundamental relationship between the first four digits and the decade: 1 + 2 + 3 + 4 = 10.

*
*      *
*      *      *
*      *      *      *

The school of Pythagoras not only was called Tetractys, but his followers also gave oaths on the tetractys.

In this context, the number 1 represents a point, and in the case of the United Micronations Multi-Oceanic Archipelago (UMMOA) it also represents the city of Cyberterra. The number 1 also represents the fundamental unity, the wholeness, the completeness, the Fire element.

The 2 represented for two points, a line segment, and in the case of the UMMOA it also represents your connection to Cesidian Root through your ISP. The number 2 also represents duality, complementary opposites, the feminine and the masculine (it’s the first true female number), the Air element.

The 3 represented three points, a triangle, and in the case of the UMMOA it also represents triangles of islands such as Navassa Island-Bajo Nuevo Bank-Serranilla Bank, or the Palmyra Atoll-Jarvis Island-Baker Island. The number 3 also represents a measure of space and time, the dynamics of life (this is the first true male number), the creation, the Water element.

The 4 represented four points, a tetrahedron (the simplest regular polyhedron with four faces), and in the case of the UMMOA it represents the State in three dimensions, its islands scattered all over the whole earth. The number 4 also represents the material element, the structural elements, the Earth element.

So far a kind of pyramid is formed which summarises the fundamental relationship between the first four digits and the decade: 1 + 2 + 3 + 4 = 10. The number 10 mathematically is a triangular number, and that was the essence of the simplest Pythagorean tetractys, one that represented the entire material universe.

When one complicates the simplest tetractys though, when you add up a fifth digit, an interesting thing happens: 1 + 2 + 3 + 4 + 5 = 15, and in fact there are 15 UMMOA members now!

*
*      *
*      *      *
*      *      *      *
*      *      *      *      *

The number 15 mathematically is a triangular number as well. Before the 15th component the UMMOA had 14 components, and the number 14 mathematically is a square pyramidal number.

The number 5 represents the five points, a hyperpyramid, which is also called 5-cell, 4-simplex, or pentachoron by mathematicians, and it is a simple regular polychoron, and a natural extension of the triangle (two-dimensional) and the tetrahedron (three-dimensional) in the fourth dimension. In the case of the UMMOA it indicates that the State, in fact, goes beyond three dimensions, and also includes a fourth dimension. Number 5 (2 + 3) according to the Pythagoreans represented the union of the female (2) and male (3), ie marriage, but it also represents the non-material, metaphysical dimension, the dynamics of spiritual life, ie the Idea (ίδέα), the quintessence, the Hieron (ίερόν) or “Divine Thing” element.

In short, the UMMOA is more than a mathematical point in the middle of the Adriatic Sea; is more than a special Internet connection; is more than many triangles of islands in the Pacific Ocean and Caribbean Sea; and it is even more than numerous islands scattered on the whole earth. The UMMOA also contains a non-material dimension, a spiritual dimension.

In short, the UMMOA goes beyond the Pythagorean theorem, but not necessarily beyond the thinking of Pythagoras himself, who made use of mathematics for spiritual development, something which in fact distinguishes the Pythagorean tradition from all the other great traditions.

Advertisements

Comments are closed.