Disorder/Order: Discovery or Invention? - Understanding Understanding: Essays on Cybernetics and Cognition - page 278

namics is upheld, even with the demon working. Because in order for the
demon to judge whether these molecules are fast or slow, he must of course
have a flashlight to see these molecules; but a flashlight has a battery, and
batteries run out, and there of course goes the hope of having defeated the
Second Law of Thermodynamics!)
But there is another point that I would like to make regarding this
demon, and that is that he is the incorporation par excellence not only of
any principle that generates distinctions and order, but also of a general
notion of computation. One of the most fundamental concepts of compu-
tation, I submit, was developed in the thirties by the English mathemati-
cian Alan Turing. He exemplified his notion with the aid of a fictitious
machine, a conceptual device, the internal states of which are controlled by
one, and are controlling the other one of the machine's two external parts.
The first one is a (theoretically infinite) long tape that is subdivided into
equal-sized squares on which from a given alphabet (one may say “lan-
guage”), erasable symbols can be written. The other part is a reading/writing
head which scans the symbol on the square below it and, depending upon
the machine's internal state, will either change this symbol or else leave it
unchanged. After this it will move to the next square, either to the left or
to the right, and finally will change its internal state. When these operations
are completed, a new cycle can begin, with the head now reading the symbol
on the new square. In a famous publication, Turing proved that this machine
can indeed compute all computable numbers or, as I would say in reference
to our topic, all “conceivable arrangements.” 1
What I would like now to demonstrate is that this machine—whose name
is, of course, the “Turing Machine”—and Maxwell's demon are functional
isomorphs or, to put it differently, that the machine's computational com-
petence and the demon's ordering talents are equivalent. The purpose of
my bringing up this equivalence is, as you may remember from my intro-
ductory comments, to associate with the notions of disorder, order, and
complexity, measures that permit us to talk about different degrees of order,
say: “More order here!” or “Less order there!”, and to watch the processes
that are changing these degrees.
Let us now quickly go through the exercise of this demonstration by com-
paring the machine's M and the demon's D actions during the five steps of
one complete cycle. Step (i): M reads symbol, D watches molecule; (ii): M
compares symbol with internal state, D compares molecule's speed with
internal standard; (iii): M operates on symbol and tape, D on aperture,
opening or closing it; (iv): M changes its internal states, D its internal stan-
dard; (v): M and D go back to (i). Q.E.D.
Knowing about this equivalence puts us in the position of transforming
any ordering problem into a computational one. Consider, for instance, an
1 “On Computable Numbers with an Application to the Entscheidungsproblem,”
in Proceedings of the London Mathematical Society 2, no. 42 (1936), 230-65.