PREDICTIONS – 10 Years Later - Santa Fe Institute

3. INANIMATE PRODUCTION LIKE ANIMATE REPRODUCTION
Since that time I have tried to fit S-curves to many products. Often I
have been disappointed, particularly when computer models began appearing
in rapid succession with little differentiation. The VAX 11/750
was a long-lived, well-positioned product, which had its own market
niche. Today’s models overlap and often share market niches with other
products. Life cycles are too short and behave too irregularly to be fitted
to the theoretical curve. What is emerging as a better candidate for a
growth-curve description is a whole family of models, a generation of
technology.
But this was also considered by Lotka. He linked the growth of a
population to the growth of an individual. A colony of unicellular organisms,
regarded as a whole, is analogous to the body of a multicellular
organism. Imagine a cup of soup left on the table for several days. Bacteria
will grow in it subject to food limitations. The transformation
changes a “grain” of the substances in the soup into a “body” for the
bacteria. H. G. Thornton has studied the example and has shown that
bacterial growth (measured by the surface area occupied) follows the
same familiar growth curve pattern. (Appendix C, Figure 3.2).
Whether it is bacteria in a bowl of soup, rabbits in a fenced-off grass
field, or automobiles in society, there is a progressive transformation of
a limited resource into a resident population. If the multiplication is exponential—situations
in which one unit brings forth another—the overall
pattern of growth is symmetric. It is this symmetry that endows S-curves
with predictive power; when you are halfway through the process, you
know how the other half will be. The symmetry of the logistic function
can be mathematically demonstrated, but it can also become evident intuitively.
• • •
There is road construction going on next to a 13th-century
church in central Paris. In front of a magnificent stained-glass
window, red steel barrels filled with small stones line the work
site. A teenage vandal passing by at night looks at the glass
mosaic, which contains over a hundred small stained-glass
pieces. The bright street light reveals a black hole; one piece is
missing. The contents of the barrel give him an idea, and he
throws a stone at the hole. He misses, but his projectile knocks
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