In the 1930s, Ralph Nelson Elliott discovered that stock prices trend and
reverse in recognizable patterns, which he called waves. The patterns he
discerned combine to form larger versions of the same patterns, making the
entire process a fractal. The basic design is five waves in one direction
followed by three in the other, as Figure 1 illustrates.
The sequence both
expands and subdivides in the same manner, as illustrated in Figure 2.
Figure 3 shows the same phenomenon at one greater degree of complexity. In this
illustration, waves I and II are the first two subdivisions of yet a larger
five wave sequence, so the process never ends.
The number of waves at the various degrees, or relative sizes, of trend,
reproduce the Fibonacci sequence, as this Figure 4 illustrates. At the highest
degree, a decline is one wave, an advance is one wave, and a full cycle is two
waves. At the next lower degree, the subdivisions are three waves, five waves
and eight waves. At the next lower degree, the subdivisions are 13, 21 and 34.
This progression continues along the Fibonacci sequence as each lower degree
is discerned.
The periodical Nature in 1995 published a study that concluded that the stock market's fractal dimension is .65. This is close to the Fibonacci ratio but not exact. More recently, the October 1997 New Scientist reports an auction-market simulation study conducted by Guido Caldarelli of Manchester University, which found that the price changes that resulted mimic the stock market. The resulting form had a fractal dimension of .62, which is essentially the Fibonacci ratio. I suggest that the fractal dimension of human herding behavior may ultimately prove to be .618034.
The stock market averages are not a frivolous measure. They are important. They
record man's valuation of his own aggregate productive enterprise. That this
valuation fluctuates in a fractal manner with a Fibonacci base suggests a link
to other growth phenomena of life. The idealized wave form also suggests a
spiraling progress for mankind through history, as Figure 5 illustrates. The
peak of each first wave of successively higher degree can serve as a touch
point for a logarithmic spiral, which is also a form found in natural patterns
of growth and expansion.
My conclusion, then, is that mankind's productive progress through history is a growth pattern that reflects other natural processes of growth and expansion throughout the universe.
My upcoming book will address questions of how and why.
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