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

given in Table 2-2 (Hillis, 1998). “This idea of a universal set of blocks is important: it
means that the set is general enough to build anything” (p. 22).
To consider the implications of the universal set of logic gates to comparing circuits,
let us return to our imaginary circuit x. We could have two different versions
of this circuit, based on different architectures. In one, the behaviour of the circuit
would depend upon wiring up some arrangement of all the various logical operations
given in Table 2-2, where each operation is a primitive—that is, carried out by
its own special relay. In the other, the arrangement of the logical operations would
be identical, but the logical operations in Table 2-2 would not be primitive. Instead,
we would replace each special relay from the first circuit with a circuit involving
NOT, AND, and OR that would produce the desired behaviour.
Let us compare these two different versions of circuit x. At the most abstract
level, they are identical, because they are generating the same input-output behaviour.
At a more detailed level—one that describes how this behaviour is generated in
terms of how the logical operations of Table 2-2 are combined together—the two are
also identical. That is, the two circuits are based on the same combinations of the
Table 2-2 operations. However, at a more detailed level, the level of the architecture,
the two circuits are different. For the first circuit, each logical operation from Table
2-2 would map onto a physical device, a special relay. This would not be true for the
second circuit. For it, each logical operation from Table 2-2 could be decomposed
into a combination of simpler logical operations—NOT, AND, OR—which in turn
could be implemented by simple switches. The two circuits are different in the sense
that they use different architectures, but these different architectures are used to
create the same logical structure to compute the same input-output behaviour.
We now can see that Shannon’s (1938) discoveries have led us to a position
where we can compare two different electrical circuits by asking three different
questions. First, do the two circuits compute the same input-output function?
Second, do the two circuits use the same arrangement of logical operations used to
compute this function? Third, do the two circuits use the same architecture to bring
these logical operations to life? Importantly, the comparison between two circuits
can lead to affirmative answers to some of these questions, and negative answers to
others. For instance, Shannon’s two selective circuits use different arrangements of
logical operations, but are based on the same architecture, and compute the same
input-output function. The two versions of our imaginary circuit x compute the
same input-output function, and use the same arrangement of logical operations,
but are based on different architectures.
Ultimately, all of the circuits we have considered to this point are governed by the
same physical laws: the laws of electricity. However, we will shortly see that it is possible
to have two systems that have affirmative answers to the three questions listed
in the previous paragraph, but are governed by completely different physical laws.
34 Chapter 2