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.
