Search our site
• • • • • • • • • •



"The union of the mathematician with the poet,
fervor with measure,
passion with correctness,
this surely is the ideal."

William James

We continue with a review of The Beginner's Guide to Constructing the Universe by Michael S. Schneider. This most excellent book will open your mind to the use of numbers throughout nature. For that matter, the numbers one through ten also permeate our technological, social, political and spiritual lives. In Part One we concentrated on a brief summary of the numbers one through five. Here we will examine the numbers six through ten.

Creative Mathematics



""Six days shalt though labor and do all thy work."

We encounter the Hexad, or six sided figure, in countless natural phenomena and human designs, from beehives to faucets handles, and floor tiles to snow flakes. All true insects have six legs. This arrangement of 120 degree joinery allows close-packing and true efficiency of material, time, energy and strength. Hexagonal tessellation (redundant patterning) occurs profusely in nature.

Most designs using a circle as a base will utilize hexagonal structure. Examples are the umbrella, bicycle wheels, parachutes and a camera lens, to name a few. These examples utilize different combinations of hexagonal designs for strength and efficiency. Most nuts and bolts also use hexagonal designs.



"He found the vast Thought with seven heads that is born of the Truth"
Maha Upanishad

According to Schneider, "The number seven occupies a critical place within the Dekad, [1 – 10] where it acts as both a link and a chasm. As a link between the first six and last three terms, 1 x 2 x 3 x 4 x 5 x 6 x 7 equals 7 x 8 x 9 x 10 (equals 5040). As a chasm, with seven absent, 1 x 2 x 3 x 4 x 5 x 6 equals 8 x 9 x 10 (equals 720). Whether the value of seven is present or absent, its location serves as a pivot balancing the ten. No other number or position within the Dekad does this."

Seven does not form a finite relationship with any other number. Any number divided by seven leaves an endless loop of repeating decimals. A seven-sided figure is impossible to draw with perfect mathematical precision. Seven also impinges on our lives in the diatonic musical scale. As Schneider points out, "The seven-note scale is meant to model the hidden side of the macrocosmic design, the universe ruled by mathematical harmonies of music. The scale structure implies that the universe emerges from absolute divinity, descends through a seven-state celestial hierarchy, and returns to absolute divinity."



"Change has an absolute limit: This produces two modes;
the two modes produce four forms, the four forms produce eight trigrams;
the eight trigrams determine fortune and misfortune."

The Octad weaves together the Monad's unity, expansion and cycles, as well as the Dyad's polarity and Tetrad's materialization. Eightfold geometry has long been an ancient symbol for the Mother Goddess. Depicted mythologically as an eight-legged spider or "spinner", she has created the world through her weaving of warp and woof. The Egyptian, Greek and Mayan traditions all perceived their great goddesses as spinstresses and embroiderers.

Modern physics has modeled the Periodic Table of Elements on an eightfold structure. There are eight main groups of elements. Atomic properties recur in cycles of eight. Elements in the same columns have the same number of electrons, between one and eight in the outer most peripheries of their orbits. Cell mitosis also takes place in eight stages.

Other familiar elements in our lives based on the Octad are DNA molecules, the geometry of chess (see chess article) and anything relying on the use of octaves; the musical scale; the I Ching and the eight phases of the moon, to name a few.



The Ennead "flows around the other numbers
within the Dekad like an ocean."
Nichomachus of Gerasa

Multiplying by nine reveals a mirror symmetry among numbers. If any number is multiplied by nine the resulting digits always add to nine. For example 2 x 9 = 18; 3 x 9 = 27, 4 x 9 = 36 and so on. Thus, the Hebrews referred to nine as the symbol of immutable Truth.

Creative Mathematics

The Ennead, or nine pointed star, is an ancient and sacred symbol. It comprises three trinities. The Egyptian, Celtic, Greek and Christian myths all have an ennead of nine gods and goddesses, representing the entire archetypal range of principles.

The magic square is also considered sacred and full of power in the Islamic, Tibetan, Buddhist, Celtic, Indian and Jewish traditions. A magic square is when each number is used only once, but the horizontal, vertical and diagonal sums are all equal. The Chinese have patterned their architectural temples along the harmonious principles of the magic square.



Creative Mathematics
According to Schneider, "Ten represents a recapitulation of the whole. It holds within itself the two parents of numbers (one and two) and their seven children (three through nine). Ten is a portrait of the whole family of archetypes gathered together, simultaneously displaying each of their principles.

According to Pythagoras ten is the "perfect number" symbolizing fulfillment and new beginnings. The Babylonian, Egyptian, Mayan, Roman, Hebrew, Greek and Arabic numerical systems all utilize a ten as a base. The study of the Tetraktys, pictured at the left, was the core teaching in Pythagorean schools of natural science of philosophy. The Tetraktys comprises the point, line, surface and volume.

The modern physics T.O.E. (Theory of Everything) or String Theory, postulates a ten dimensional universe in which the three dimensions of space (length, width and height) are a trinity, plus the dimension of time.


For a true appreciation of how the numbers one through ten impinge upon your everyday life you need to read this fascinating book. Creative mind depends upon a flexible understanding of nature and man, and how they relate. Creative problem solving also relies upon an understanding of numbers and their relationships. There is a wealth of knowledge and wisdom here that will enrich your understanding of mathematics as a basis for the arts and sciences. Thus, your relationship to these arts will be inspired and elevated as you venture to express yourself through them.

The following link is a brief synopsis of Seminars given by Michael. To contact Michael for more information on when and where his next workshop is you can email him at Michael Schneider.

© J.L. Read, 1997. All Rights Reserved.
Back to Top
Back to Science page
Back to Techniques page






This site is dedicated in loving memory
to its creator, Janet L. Read
1949 — 2000


  | Puzzles | Creativity | Science | Books |
Home | Site Map | Links

© Enchanted Mind, 2002. All rights reserved.
"Magic Happens™" is a Service Mark of World IT Professionals, Inc.
Unicorn symbol courtesy of MJV Spring