“The
spider has constructed a web of statistical probability, honed to near
perfection by millions of years of evolution.” (Robert J. Hustwit)
Photo by Alfonso Diaz.
The design of a complex regulator often includes the making of a model
of the system to be regulated. The making of such a model has hitherto
been regarded as optional, as merely one of many possible ways.
In this paper a theorem is presented which shows, under
very broad conditions, that any regulator that is maximally both successful
and simple must be isomorphic with the system
being regulated. (The exact assumptions are given.) Making a model
is thus necessary.
The theorem has the interesting corollary that the
living brain, so far as it is to be successful and efficient as a regulator
for survival, must proceed, in learning by the
formation of a model (or models) of its environment.
