PREDICTIONS – 10 Years Later - Santa Fe Institute

1. SCIENCE AND FORETELLING
gue that Bach may have disapproved of this!) Thus transposing became
possible, musical ensembles flexible, and life generally easier for all
musicians.
As it happens, equal-temper tuning is very close to the natural octave
so that the differences are almost imperceptible. The natural octave,
however, may have more profound reasons for existence. Purist musicians
claim that piano and violin can no longer play together and
sometimes demand an old-fashioned tuning for a favorite recital. Furthermore,
studying the natural octave may provide insights and
understanding on a cosmological level. In his book In Search of the Miraculous,
Peter Ouspensky, the Russian mathematicians and
philosopher, recounts ideas that relate the natural octave to the creation
of the universe! 12 The seeker of pure and esoteric truth should be wary
of elegant formulations such as those of Bach and Gauss.
Independently of arguments of elegance, the logistic function is intimately
associated with the law of natural growth. One can visualize this
law either with the bell-shaped or with the S-shaped curve. Both are
seeded with a parameter describing the ceiling, the capacity of the niche
in process of being filled. The important difference between them, from
the statistical analysis point of view, is that the S-curve, which usually
depicts a cumulative rate of growth, is much less sensitive to fluctuations
because one year’s low is compensated for by another year’s high.
Therefore, the S-curve representation of a natural growth process provides
a more reliable way to forecast the level of the ceiling. From an
intuitive point of view, an S-curve promises the amount of growth that
can be accomplished while a bell-curve heralds the coming end of the
process as a whole.
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