Mind, Body, World- Foundations of Cognitive Science, 2013a

In Lovecraft’s (1933) story, the witch Keziah “might have had excellent reasons
for living in a room with peculiar angles; for was it not through certain angles that
she claimed to have gone outside the boundaries of the world of space we know?”
Shannon’s (1938) scholarly paper led to astonishing conclusions for similar reasons:
it detailed equivalence between the formal and the physical. It proved that electric
circuits could be described in two very different vocabularies: one the physical
vocabulary of current, contacts, switches and wires; the other the abstract vocabulary
of logical symbols and operations.
2.4 Multiple Procedures and Architectures
According to a Chinese proverb, we all like lamb, but each has a different way to cook
it. This proverb can be aptly applied to the circuits of switches for which Shannon
(1938) developed a logical interpretation. Any of these circuits can be described as
defining a logical function that maps inputs onto an output: the circuit outputs a
current (or not) depending on the pattern of currents controlled by one or more
switches that flow into it. However, just like lamb, there are many different ways to
“cook” the input signals to produce the desired output. In short, many different circuits
can be constructed to compute the same input-output function.
To illustrate this point, let us begin by considering Shannon’s (1938) selective
circuit, which would be off when 0 or 2 of its 4 relays were closed, but which would
be on when any other number of its relays was closed. In Shannon’s original formulation,
20 components—an arrangement of 20 different switches—defined a circuit
that would behave in the desired fashion. After applying logical operations to simplify
the design, Shannon reduced the number of required components from 20
to 14. That is, a smaller circuit that involved an arrangement of only 14 different
switches delivered the same input-output behaviour as did the 20-switch circuit.
Reflecting on these two different versions of the selective circuit, it’s clear that
if one is interested in comparing them, the result of the comparison depends on the
perspective taken. On the one hand, they are quite different: they involve different
numbers of components, related to one another by completely different patterns of
wiring. On the other hand, in spite of these obvious differences in details, at a more
abstract level the two designs are identical, in the sense that both designs produce
the same input-output mapping. That is, if one built a truth table for either circuit
that listed the circuit’s conductivity (output) as a function of all possible combinations
of its 4 relays (inputs), the two truth tables would be identical. One might
say that the two circuits use markedly different procedures (i.e., arrangements of
internal components) to compute the same input-output function. They generate
the same behaviour, but for different reasons.
32 Chapter 2