Responsibilities of Competence - Understanding Understanding: Essays on Cybernetics and Cognition - page 194

tional isomorph of a Universal Turing Machine. Thus, the three concepts of
regulation, entropy retardation, and computation constitute an interlaced
conceptual network which, for me, is indeed the essence of Cybernetics.
I shall now briefly justify my claim that Maxwell's Demon is not only the
paradigm for regulation but also for computation.
When I use the term “computation” I am not restricting my self to
specific operations as, for instance, addition, multiplication, etc. I wish to
interpret “computation” in the most general sense as a mechanism, or “algo-
rithm”, for ordering . The ideal, or should I say the most general, represen-
tation of such mechanism is, of course, a Turing Machine, and I shall use
this machine to illuminate some of the points I wish to make.
There are two levels on which we can think of “ordering”. The one is
when we wish to make a description of a given arrangement of things. The
other one when we wish to re-arrange things according to certain descrip-
tions. It will be obvious at once that these two operations constitute indeed
the foundations for all that which we call “computation”.
Let A be a particular arrangement. Then this arrangement can be
computed by a universal Turing machine with a suitable initial tape expres-
sion which we whall call a “description” of A: D(A). The length L(A)
of this description will depend on the alphabet (language) used. Hence,
we may say that a language a 1 reveals more order in the arrangement A
than another language a 2 , if and only if the length L 1 (A) of the suitable
initial tape description for computing A is shorter than L 2 (A), or mutatis
mutandis .
This covers the first level of above, and leads us immediately to the
second level.
Among all suitable initial tape descriptions for an arrangement A 1 there
is a shortest one: L*(A 1 ). If A 1 is re-arranged to give A 2 , call A 2 to be of a
higher order than A 1 if and only if the shortest initial tape description
L*(A 2 ) is shorter than L*(A 1 ), or mutatis mutandis .
This covers the second level of above, and leads us to a final statement
of perfect ordering (computation).
Among all arrangements A i there is one, A*, for which the suitable initial
tape description is the shortest L*(A*).
I hope that with these examples it has become clear that living organisms
(replacing now the Turing machine) interacting with their environment
(arrangements) have several options at their disposal: (i) they may develop
“languages” (sensors, neural codes, motor organs, etc.) which “fit” their
given environment better (reveal more order); (ii) they may change their
surroundings until it “fits” their constitution; and (iii), they may do both.
However, it should be noted that whatever option they take, it will be done
by computation. That these computations are indeed functional isomorphs
of our demon's activity is now for me to show.
The essential function of a Turing machine can be specified by five
operations: