Return to Pythagoras
Sacred Geometry
by Robert Lawlor
(112 pages, pb, $15.95)
New York, Thames and Hudson, 1982
ISBN 0-500-81030-3
If you have always wondered what Pythagoras meant by "All is number", why
Pythagoras and Plato held up mathematics and music (in their original sense) as the
foundation for creation, this book will help you gain some practical insight. Everything
Robert Lawlor writes is brilliant (see reviews of his other books). And the book is filled
with illustrations and examples.
Chapter II, Sacred Geometry: Metaphor of Universal Order, is a tour de force essay on how
influential is the center of the number line...whether it is zero or one. The book is
worth that chapter alone.
Chapter Titles
I The Practice of Geometry
II Sacred Geometry: Metaphor of Universal Order
III The Primal Act: The Division of Unity
IV Alternation
V Proportion and the Golden Section
VI Gnomonic Expansion and the Creation of Spirals
VII The Squaring of the Circle
VIII Meditation: Geometry becomes Music
IX Anthropos
X The Genesis of Cosmic Volumes
Selected quotes:
p. 4
In science today we are witnessing a general shift away from the assumption that the
fundamental nature of matter can be considered from the point of view of substance
(particles, quanta) to the concept that the fundamental nature of the material world is
knowable only through its underlying patterns of wave forms.
Both our organs of perception and the phenomenal world we perceive seem to be best
understood as systems of pure pattern, or as geometric structures of form and proportion.
Therefore, when many ancient cultures chose to examine reality through the metaphors of
geometry and music (music being the study of the proportional laws of sound frequency),
they were already very close to the position of our most contemporary science.
Professor Amstutz of the Mineralogical Institute at the University of Heidelberg recently
said: 'Matter's latticed waves are spaced at intervals corresponding to the frets on a
harp or guitar with analogous sequences of overtones arising from each fundamental. The
science of musical harmony is in these terms practically identical with the science of
symmetry in crystals.'
The point of view of modern force-field theory and wave mechanics corresponds to the
ancient geometric-harmonic vision of universal order as being an interwoven configuration
of wave patterns. Bertrand Russell, who began to see the profound value of the musical and
geometric base to what we now call Pythagorean mathematics and number theory, also
supported this view in The Analysis of Matter: 'What we perceive as various
qualities of matter,' he said, 'are actually differences in periodicity.'
p. 5
Within the human consciousness is the unique ability to perceive the transparency
between absolute, permanent relationships, contained in the insubstantial forms of
geometric order, and the transitory, changing forms of our actual world. The content of
our experience results from an immaterial, abstract, geometric architecture which is
composed of harmonic waves of energy, nodes of rationality, melodic forms springing forth
from the eternal realm of geometric proportion.
p. 16
Ancient geometry rests on no a priori axioms or assumptions. Unlike Euclidean and the more
recent geometries, the starting point of ancient geometric thought is not a network of
intellectual definitions or abstractions, but instead a meditation upon a metaphysical
Unity, followed by an attempt to symbolize visually and to contemplate the pure, formal
order which springs forth from this incomprehensible Oneness. It is the approach to the
starting point of the geometric activity which radically separates what we may call the
sacred from the mundane or secular geometries. Ancient geometry begins with One,
while modern mathematics and geometry begin with Zero.
p. 21
Unity is a philosophic concept and a mystic experience expressible mathematically. The
Western mentality, however, withdrew its discipline of acknowledging a supra-rational,
unknowable mystery as its first principle. But in rejecting this reverence to a single
unknowable unity, our mathematics and science developed into a system requiring complex,
interconnected hypotheses, imaginary entities such as those mentioned above [negative
numbers, infinite decimal numbers, algebraic and transcendental irrational numbers,
imaginary and complex numbers] and unknown x quantities which must be manipulated,
quantified or equalized as in the algebraic form of thought. So the unknown appears not
just once but at every turn, and can be dealt with only by seeking quantitative solutions.
Our present thought is based on the following numerical and logical sequence:
-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5
With zero in the centre, there is a quantitative expansion 1, 2, 3 ... and our sense of
balance requires having -1, -2, -3 ... on the other side, giving a series of non-existent
abstractions (negative quantities) which demand an absurd logic. The system has a
break-point, zero, disconnecting the continuum and dissociating the positive numbers from
the negative balancing series.
In the ancient Egyptian numerical progression, beginning with one rather than zero, all
the elements are natural and real:
1/5, 1/4, 1/3, 1/2, 1, 2, 3, 4, 5
All the elements flow out from the central unity in accordance with the law of inversion
or reciprocity. The Egyptians based their mathematics on this simple, natural series of
numbers, performing sophisticated operations with it for which we now need complex algebra
and trigonometry. We have already seen the natural demonstration of this series in the
physical laws of sound. The plucked string, when divided in half, produced double the
frequency of vibrations. Thus this series expresses the essential law of Harmony.
