The Square Root of Two

I. Математика

Sacred Geometry

The Sphere

Starting with what may be the simplest and most perfect of forms, the sphere is an ultimate expression of unity, completeness, and integrity. There is no point of view given greater or lesser importance, and all points on the surface are equally accessible and regarded by the center from which all originate. Atoms, cells, seeds, planets, and globular star systems all echo the spherical paradigm of total inclusion, acceptance, simultaneous potential and fruition, the macrocosm and microcosm.

The Circle

The circle is a two-dimensional shadow of the sphere. The ratio of the circumference of a circle to its diameter, Pi, is the original transcendental and irrational number. (Pi equals about 3.14159265358979323846264338327950288419716939937511…) It cannot be expressed in terms of the ratio of two integers, or in the language of sacred symbolism, the essence of the circle exists in a dimension that transcends the linear rationality that it contains.

The Point

At the center of a circle or a sphere is always an infinitesimal point. The point needs no dimension, yet embraces all dimension.

Life itself as we know it is inextricably interwoven with geometric forms, from the angles of atomic bonds in the molecules of the amino acids, to the helical spirals of DNA, to the spherical prototype of the cell, to the first few cells of an organism which assume vesical, tetrahedral, and star (double) tetrahedral forms prior to the diversification of tissues for different physiological functions. Our human bodies on this planet all developed with a common geometric progression from one to two to four to eight primal cells and beyond.

The Square Root of Two

The square root of 2 embodies a profound principle of the whole being more than the sum of its parts. (The square root of two equals about 1.414213562…) The orthogonal dimensions (axes at right angles) form the conjugal union of the horizontal and vertical which give birth to the greater offspring of the hypotenuse. The new generation possesses the capacity for synthesis, growth, integration and reconciliation of polarities by spanning both perspectives equally.

The fact that the root is irrational expresses the concept that our higher dimensional faculties can’t always necessarily be expressed in lower order dimensional terms – e.g. “And the light shineth in darkness; and the darkness comprehended it not.” (from the Gospel of St. John, Chapter 1, verse 5). By the same token, we have the capacity to surpass the genetically programmed limitations of our ancestors, if we can shift into a new frame of reference

II. Простые механизмы

Gears

A gear is just a toothed wheel, sometimes called a cog. To do any work with a gear, you need to have at least two cogs with their teeth fitting into each other. Because the teeth fit together, when you turn one gear, the other one turns too! Gears come in many different sizes, which help them do work. If you connect one big gear with a small one, you can turn the big gear slowly and it will make the little gear turn quickly. Since it takes less energy to turn the big gear slowly than it would to turn the little one quickly, you are saving energy and making work easier by using gears.

One gear can make another one turn faster, but it can also make it turn in a different direction. When you turn a big gear to the right, the little one will move to the left. This is good for many machines where the direction needs to change in order for the machine to work.

When two or more gears are connected, it's called a 'gear train.' The gear that you turn is called the 'driver' and the last gear that you are trying to move is called the 'driven' gear. Sometimes there will be several gears in between the driver and the driven—those are called 'idlers.'