Cf: Cybernetics : Regulation In Biological Systems : Selection 2
(Please see the above-linked blog post for a much better formatted copy.)
Regulation In Biological Systems
10/4. What has just been said is well enough known. It enables us, however, to join these facts on to the ideas
developed in this book and to show the connexion exactly.
For consider what is meant, in general, by "survival". Suppose a mouse is trying to escape from a cat, so that the
survival of the mouse is in question. As a dynamic system, the mouse can be in a variety of states; thus it can be in
various postures, its head can be turned this way or that, its temperature can have various values, it may have two ears
or one. These different states may occur during its attempt to escape and it may still be said to have survived. On
the other hand if the mouse changes to the state in which it is in four separated pieces, or has lost its head, or has
become a solution of amino-acids circulating in the cat's blood then we do not consider its arrival at one of these
states as corresponding to "survival".
The concept of "survival" can thus be translated into perfectly rigorous terms, similar to those used throughout the
book. The various states (M for Mouse) that the mouse may be in initially and that it may pass into after the affair
with the cat is a set M_1, M_2, ..., M_k, ..., M_n. We decide that, for various reasons of what is practical and
convenient, we shall restrict the words "living mouse" to mean the mouse in one of the states in some subset of these
possibilities, in M_1 to M_k say. If now some operation C (for cat) acts on the mouse in state M_i, and C(M_i) gives,
say, M_2, then we may say that M has "survived" the operation of C, for M_2 is in the set M_1, ..., M_k.
If now a particular mouse is very skilled and always survives the operation C, then all the states C(M_1), C(M_2), ...,
C(M_k), are contained in the set M_1, ..., M_k. We now see that this representation of survival is identical with that
of the "stability" of a set (S.5/5). Thus the concepts of "survival" and "stability" can be brought into an exact
relationship; and facts and theorems about either can be used with the other, provided the exactness is sustained.
The states M are often defined in terms of variables. The states M_1, ..., M_k, that correspond to the living organism
are then those states in which certain *essential variables* are kept within assigned ("physiological") limits.