Lesson 18: The Meaning Of Phi
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.
Consider when reading such deep yet vague descriptions that
these people could not clearly see what they sensed. They did not have graphs and
the Wave Principle to make nature's growth pattern manifest and were doing the best they
could to describe an organizational principle that they discerned as shaping the natural
world. If these ancient philosophers were right that a universal structural force governs
and permeates the world, should it not govern and permeate the world of man? If forms
throughout the universe, including man's body, brain and DNA, reflect the form of phi,
might man's activities reflect it as well? If phi is the life-force in the
universe, might it be the impulse behind the progress in man's productive capacity? If phi
is a symbol of the creative function, might it govern the creative activity of man? If
man's progress is based upon production and reproduction "in an endless series,"
is it not reasonable that such progress has the spiraling form of phi, and that
this form is discernible in the movement of the valuation of his productive capacity,
i.e., the stock market? Just as the initiated Egyptians learned the hidden truths of order
and growth in the universe behind the apparent randomness and chaos (something that modern
"chaos theory" has finally rediscovered in the 1980s), so the stock market, in
our opinion, can be understood properly if it is taken for what it is rather than
for what it crudely appears to be upon cursory consideration. The stock market is not a
random, formless mess reacting to current news events but a remarkably precise recording
of the formal structure of the progress of man.
Compare this concept with astronomer William Kingsland's
words in The Great Pyramid in Fact and in Theory that Egyptian astronomy/astrology
was a "profoundly esoteric science connected with the great cycles of man's
evolution." The Wave Principle explains the great cycles of man's evolution and
reveals how and why they unfold as they do. Moreover, it encompasses micro as well as
macro scales, all of which are based upon a paradoxical principle of dynamism and
variation within an unaltered form.
It is this form that gives structure and unity to the
universe. Nothing in nature suggests that life is disorderly or formless. The word
"universe" means "one order." If life has form, then we must not
reject the probability that human progress, which is part of the reality of life, also has
order and form. By extension, the stock market, which values man's productive enterprise,
will have order and form as well. All technical approaches to understanding the stock
market depend on the basic principle of order and form. Elliott's theory, however, goes
beyond all others. It postulates that no matter how minute or how large the form, the
basic design remains constant.
Elliott, in his second monograph, used the title Nature's
Law — The Secret of the Universe in preference to "The Wave Principle"
and applied it to all sorts of human activity. Elliott may have gone too far in saying
that the Wave Principle was the secret of the universe, as nature appears to have
created numerous forms and processes, not just one simple design. Nevertheless, some of
history's greatest scientists, mentioned earlier, would probably have agreed with
Elliott's formulation. At minimum, it is credible to say that the Wave Principle is one of
the most important secrets of the universe. Even this grandiose claim at first may appear
to be only so much tall talk to practically-minded investors, and quite understandably so.
The grand nature of the concept stretches the imagination and confounds the intellect,
while its applicability is as yet unclear. First we must ask, can we both theorize and
observe that there is indeed a principle that operates on the same mathematical basis in
the heavens and earth as it does in the stock market?
The answer is yes. The stock market has the very same
mathematical base as do these natural phenomena. The idealized Elliott concept of the
progression of the stock market is an excellent base from which to construct the Golden
Spiral, as Figure 3-10 illustrates with a rough approximation. In this construction, the
top of each successive wave of higher degree is the touch point of the logarithmic
expansion.
Figure 3-10
This result is possible because at every degree of stock
market activity, a bull market subdivides into five waves and a bear market subdivides
into three waves, giving us the 5-3 relationship that is the mathematical basis of the
Elliott Wave Principle. We can generate the complete Fibonacci sequence, as we first did
in Figure 1-4, by using Elliott's concept of the progression of the market. If we start
with the simplest expression of the concept of a bear swing, we get one straight line
decline. A bull swing, in its simplest form, is one straight line advance. A complete
cycle is two lines. In the next degree of complexity, the corresponding numbers are 3, 5
and 8. As illustrated in Figure 3-11, this sequence can be taken to infinity.
Figure 3-11
Next Lesson: Phi and the Stock Market |
