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The value of this ubiquitous
phenomenon was deeply understood and profoundly appreciated by
the greatest intellects of the ages. History abounds with
examples of exceptionally learned men who held a special
fascination for this mathematical formulation. Pythagoras chose
the five-pointed star, in which every segment is in golden ratio
to the next smaller segment, as the symbol of his Order;
celebrated 17th century mathematician Jacob Bernoulli had the
Golden Spiral etched into his headstone; Isaac Newton had the
same spiral carved on the headboard of his bed (owned today by
the Gravity Foundation, New Boston, NH). The earliest known
aficionados were the architects of the Gizeh pyramid in Egypt,
who recorded the knowledge of phi in its construction
nearly 5000 years ago. Egyptian engineers consciously
incorporated the Golden Ratio in the Great Pyramid by giving its
faces a slope height equal to 1.618 times half its base, so that
the vertical height of the pyramid is at the same time the
square root of 1.618 times half its base. According to Peter
Tompkins, author of Secrets of the Great Pyramid (Harper
& Row, 1971), "This relation shows Herodotus' report to
be indeed correct, in that the square of the height of the
pyramid is Öf
x Öf
= f,
and the areas of the face 1 x f
= f."
Furthermore, using these proportions, the Egyptian scientists
(apparently in order to build a scale model of the Northern
Hemisphere) used pi and phi in an approach so
mathematically sophisticated that it accomplished the feat of
squaring the circle and cubing the sphere (i.e., making them of
equal area and volume), a feat which was not duplicated for well
over four thousand years.
While the mere mention of the
Great Pyramid may serve as an engraved invitation to skepticism
(perhaps for good reason), keep in mind that its form reflects
the same fascination held by pillars of Western scientific,
mathematical, artistic and philosophic thought, including Plato,
Pythagoras, Bernoulli, Kepler, DaVinci and Newton. Those who
designed and built the pyramid were likewise demonstrably
brilliant scientists, astronomers, mathematicians and engineers.
Clearly they wanted to enshrine for millennia the Golden Ratio
as something of transcendent importance. That such a
caliber of people, who were later joined by some of the greatest
minds of Greece and the Enlightenment in their fascination for
this ratio, undertook this task is itself important. As for why,
all we have is conjecture from a few authors. Yet that
conjecture, however obtuse, curiously pertains to our own
observations. It has been surmised that the Great Pyramid, for
centuries after it was built, was used as a temple of initiation
for those who proved themselves worthy of understanding the
great universal secrets. Only those who could rise above the
crude acceptance of things as they seemed to discover what, in
actuality, they were, could be instructed in "the
mysteries," i.e., the complex truths of eternal order and
growth. Did such "mysteries" include phi?
Tompkins explains, "The pharaonic Egyptians, says Schwaller
de Lubicz, considered phi not as a number, but as a
symbol of the creative function, or of reproduction in an
endless series. To them it represented `the fire of life, the
male action of sperm, the logos [referenced in] the
gospel of St. John.'" Logos, a Greek word, was
defined variously by Heraclitus and subsequent pagan, Jewish and
Christian philosophers as meaning the rational order of the
universe, an immanent natural law, a life-giving force hidden
within things, the universal structural force governing and
permeating the world.
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