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PREDICTIONS – 10 Years Later - Santa Fe Institute

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6. A HARD FACT OF LIFE<br />

place in a natural way will depend on how closely the market share<br />

evolution resembles an S-shaped pattern. This pattern can be made to<br />

appear as a straight line when viewed through the appropriate “eyepiece.”<br />

STRAIGHT LINES IN NATURE<br />

A popular belief claims that there are no straight lines in nature. Precise<br />

mathematical shapes such as circles, flat surfaces, right angles, and ellipses,<br />

are not encountered during a stroll through the woods. These<br />

shapes are thought of as human inventions; therefore, they are stamped<br />

“unnatural.” Rudolf Steiner, a twentieth-century Western guru with a<br />

significant following in Central Europe, built his philosophy around<br />

“The Natural.” Among other things he did, he made sure that an enormous<br />

concrete building was erected—itself a monument to his<br />

theories—featuring practically no right angles. 3<br />

Could a natural phenomenon produce a straight line? Undoubtedly<br />

yes; I can think of many examples, but I want to concentrate on natural<br />

growth in competition, which so far has been described as following an<br />

S-shape. The logistic function used in the one-to-one natural substitutions<br />

is such that if one divides the number of the “new” by the number<br />

of the “old” at any given time and plots this ratio on a logarithmic vertical<br />

scale, one gets a straight line. It is a mathematical transformation.<br />

The interest in doing this is to eliminate the need for computers and sophisticated<br />

fitting procedures when searching for “naturalness” in<br />

substitution processes.<br />

Consider the following hypothetical case. You are concerned about<br />

the new hamburger stand that opened recently across the street from<br />

yours. You worry that its guarantee of home delivery in less than ten<br />

minutes may not only cut into your business but put you out of it altogether.<br />

People may just decide to save the gas and order their<br />

sandwiches from wherever they happen to be. To make it easy, let us<br />

also suppose that the stand across the street has set up a public counting<br />

device, which advertises the number of hamburgers it has sold so<br />

far.<br />

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