A Beginner's Guide to Constructing the Universe
The Mathematical Archetypes of Nature, Art, and Science
A Voyage From 1 to 10
by Michael S. Schneider
(352 pages, pb, $17.50)
HarperPerennial, 1995
ISBN 0-06-092671-6
A multifaceted confabulation of information, quotes, images, drawings, and just about
everything else you can possibly imagine for an introduction to Pythagorean "number
thinking". Michael's forte is his background as a teacher. The text is remarkably
clear, even elegant, full of a tangible goodness and enthusiasm that makes for the best of
"good reads". Perfect for beginners, and thought-provoking for advanced
explorers.
Chapter Titles
GEOMETRY AND THE QUEST FOR
REALITY BY JOHN MICHELL
INTRODUCTION
1 MONAD WHOLLY ONE
2 DYAD IT TAKES TWO TO TANGO
3 TRIAD THREE-PART HARMONY
4 TETRAD MOTHER SUBSTANCE
5 PENTAD REGENERATION
6 HEXAD STRUCTURE-FUNCTION-ORDER
7 HEPTAD ENCHANTING VIRGIN
8 OCTAD PERIODIC RENEWAL
9 ENNEAD THE HORIZON
10 DECAD BEYOND NUMBER
EPILOGUE NOW THAT
YOU'VE CONSTRUCTED THE UNIVERSE ...
.
From the Introduction, pp. xxii-xxiv
Sacred Mathematics
.
The terms "sacred sites," "sacred geography," "sacred
architecture," "sacred arithmetic," and "sacred geometry" seem
overused today. To the ancients the "sacred" had a particular significance
involving consciousness and the profound mystery of awareness. How are you and I aware of
these very words and their significance? Now that you've read them, these words are no
longer just on the page. They're within your awareness. Sacred space is within us. Not in
our body or brain cells but in the volume of our consciousness. Wherever we go we bring
the sacred within us to the sacred around us. We consecrate locations and studies by the
presence of this awareness, not just the other way around. Why should the sites of stone
temples and wonderful cathedrals be more sacred than a rocky desert or concrete city
street if we bring holy consciousness to each of them? Geographic locations are no more or
less sacred than any other, although they may be powerful telluric sites. Awareness is the
ultimate sacred wonder. Why endow objects outside ourselves as sacred and ignore the same
source within us? A surprising amount of the world's religious art and architecture has
been designed using the timeless symbolic patterns of nature and number, but these
patterns remain symbolic of our own sacred inner realm, symbolic of the
subtle structure of awareness whose source is the same as archetypal number. All this was
understood in ancient times and deemed so important that it was built into the culture on
every level.
.
Modern science tells us that what we commonly call "reality" is a compilation of
pictures based on a narrow sense-band view of surface features. The world we perceive is a
small slice of a vast, mostly invisible energy-event. Mathematics can take us beyond our
ordinary limits to the cosmic depths. Plato at his Academy required the study of
mathematics as a prerequisite for philosophia, a term signifying "the love of
wisdom" and "to lift the soul to truth." just over a century earlier
Pythagoras had invented the word "philosophy" as a result of a question posed to
him. When asked "Are you wise?" he is said to have answered "No, but I'm a lover
of wisdom." Both Pythagoras and Plato suggested that all citizens learn the
properties of the first ten numbers as a form of moral instruction. The study and
contemplation of number and geometry can show us, if we look with the eyes of ancient
mathematical philosophers, that neither outer nature nor human nature is the hodgepodge it
may seem. Symbolic mathematics provides a map of our own inner psychological and sacred
spiritual structure. But studying number properties and intellectually knowing the road
map, the symbolism, is not the same as actually taking the journey. We take that journey
by finding within ourselves the universal principles these properties represent and by
applying the knowledge to our own growth. We pay attention to paying attention, in
imageless awareness, directing sustained attention to that which the symbols refer to
within us. When the lessons of symbolic or philosophical mathematics seen in nature, which
were designed into religious architecture or art, are applied functionally (not
just intellectually) to facilitate the growth and transformation of consciousness,
then mathematics may rightly be called "sacred." To me, the terms "sacred
arithmetic" and "sacred geometry" only have significance when grounded in
the experience of self-awareness. Religious art is sacred not only due to its subject
matter but also because it was designed using the subtle symbolic language of number,
shape, and proportion to teach self-understanding and functional self-development. Ancient
Egyptian arts, crafts, and architecture perhaps provide the best accessible examples of
design that used the symbolism of number, geometry, and nature to teach an accelerated
form of self-development to trained initiates who knew how to translate the symbolism into
meditative exercises.
.
Thus, true sacred geometry cannot be taught through books, but must remain as part of the
ancient oral tradition passed from teacher to pupil, mouth to ear. Because over centuries
this knowledge was passed along secretly so as not to conflict with the prevailing
intolerant religious authorities or be disposed to those considered profane, there is
still an aura of mysticism about it. But nature's patterns and those of our inner life are
familiar to everyone and always available to us. The power which we seek is the power with
which we seek. When we feel separate from the archetypes of nature, number, and shape
we make them mystical, but this only keeps our selves in a mist, There is no need for
secrecy and "occultism" any longer. These are everyone's life-facts. We can
apply them to better appreciate the world, and we'll need them once we realize the urgency
of cooperating with the way the world works. This book is concerned with dispelling the
mysticism surrounding sacred mathematics by reintegrating the timeless knowledge of number
and shape with its familiar expressions in nature, art, and its practical significance for
self-development.
.
Studying, contemplating, and living in agreement with universal principles is a social
responsibility and can be a spiritual path. It is becoming clear that when we cooperate
with nature's ways we succeed; when we resist, we struggle. Implications for our
environmental crises are obvious. Rather than an antagonist, nature can be our teacher to
learn from and cooperate with to mutual benefit. To understand nature better, we first
need to recognize the roles of its basic patterns.