Each net corresponds to a matrix. The result of connecting them
corresponds to the result of multiplying the matrices. This is itself a
matrix, and is linear.
For a different computational system based on magnetism, see A
non-deterministic approach to analogy, involving the Ising model of
ferromagnetism by Hofstadter, AI box copy H114. This treats the
solution of analogy problems as a ``phase change'', like the change from
solid to liquid or liquid to gas.
Continuing the above, we can use similar arguments to show that there
are some physical phenomena that we can't describe by any theory. In
essence, we can view a theory as a set of rules (i.e. a program) that
predicts (i.e. outputs) the observations it explains. But this theory
(program) will be stored in a brain or a computer (a finite machine).
But a finite machine can hold only a finite number of programs. So it
can predict only a finite number of different observations. If the
observations we're trying to predict don't fall in that set, no program
(theory) our machine can hold will be capable of explaining them. See
page 357 of Casti. Is psychology too complex to be described by any
theory we can store?
Wed Feb 14 23:47:23 GMT 1996