A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art, and Science

A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art, and Science

by Michael S. Schneider
HarperCollins. New York, 1994; xxxii +352pages; hardcover.

Number symbolism and mysticism are pervasive in the world's cultural traditions. In the West, the Pythagoreans and the Kabbalists have provided two major approaches to the meaning of numbers; while the East has its own numerological traditions. The symbolism of numbers is also a major concern of Freemasonry and of modern Theosophy. From H. P. Blavatsky's Secret Doctrine, with its preoccupation with number symbols in the Stanzas of Dzyan and explications of them, to the writings of later Theosophists like Claude Bragdon, who integrated art, architecture, and mathematics, Theosophical literature has treated numbers as emblems of the timeless wisdom.

A Beginner's Guide is an eclectic survey of the symbolism of numbers one through ten as (according to the blurb on the dust jacket) "a wisdom neither ancient nor New Age but timeless." Its author, Michael Schneider, is a mathematics teacher who "designed the geometry harmonizing the statues at the entrance to the Cathedral of St. John the Divine in New York City." He writes in the grand tradition of mathematicians who have perceived their calling as all art of order and a yoga of understanding.

In his introduction to the book, the author distinguishes between secular mathematics (which is what is taught in schools and used in ordinary applications), symbolic or philosophical mathematics (which is the main subject of this book-a view of numbers as an expression of the order of creation), and sacred mathematics (the use of numbers to raise consciousness from mayavic to the Real, from the phenomenal to the noumenal, from the typical to the archetypal). It is the possibility of the last that is the real fascination of the study of numbers.

The body of this well-illustrated and clearly written book is divided into ten chapters, one for each of the first ten numbers, 1 to 10. One misses a chapter on zero, mystically or sacredly speaking the most important of the numbers and one of considerable value even in secular mathematics (try multiplying or dividing LClX by XXXlI to see how important 0 is). However, the chapter on I includes the circle, which overlaps the symbolism of zero.

The book includes a wealth of topics related more or less closely to numbers: mandalas, the ouraboros, the geometer's tools, Mobius strips, checkerboards, the vesica piscis, the principle of the arch, primary colors of pigments and light, labyrinths, the Orphic Egg, the Platonic solids, the Golden Mean (also rectangle, triangle, and spiral), the Fibonacci Series, Escher illusions, the Zodiac, Stonehenge, the musical scale, the electromagnetic spectrum, chakras, the Rainbow Bridge to Valhalla, ziggurats, the caduceus, mitosis, the I Ching, the DNA molecule, lunar phases, the enneagram, the Otz Chiim, the tetraktys, and the Cathedral of St. John the Divine. Here indeed is God the Geometer's plenty.

It is said that the gods created the universe by numbers. And if each of us is a creator in training, then the title of this attractive, entertaining, and informative volume suggests it is a handbook for future Dhyan Chohans, or universe-creators. Studying the book mayor may not prepare readers to construct a universe. It will, however, tell them much about the inner side of numbers and open their eyes to the rich symbolism of mathematics and geometry.


Summer 1996