Regulation In Biological Systems

Survival

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 ( for Mouse) that the mouse may be in initially and that it may pass into after the affair with the cat is a set   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 to say.  If now some operation (for cat) acts on the mouse in state and gives, say, then we may say that has “survived” the operation of for is in the set

If now a particular mouse is very skilled and always survives the operation then all the states are contained in the set   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 are often defined in terms of variables.  The states that correspond to the living organism are then those states in which certain essential variables are kept within assigned (“physiological”) limits.