REGULATION IN BIOLOGICAL SYSTEMS 10/4 



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 (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^, M2, ■ . ., 

 M;., . . ., M„. 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^ to My^ say. If now some operation C (for cat) 

 acts on the mouse in state M,-, and C{Mi) gives, say, M2, then we 

 may say that M has "survived" the operation of C, for Mz is in 

 the set Ml, . . ., A/'y^. 



If now a particular mouse is very skilled and always survives the 

 operation C, then all the states C(A/i), CiMj), . . ., C{M,^, are 

 contained in the set Mi, . . ., M,^. We now see that this repre- 

 sentation of survival is identical with that of the "stability" of a 

 set (S.5/5). Thus the concepts of "survival" and "stabihty" 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 

 Ml, . . ., M,^, that correspond to the living organism are then those 

 states in which certain essential variables are kept within assigned 

 ("physiological") limits. 



Ex. 1 : If « is 10 and k is 5, what would the operation C{M-i) = M9 correspond 



to? 

 Ex. 2: (Continued.) What would the operation CCMg) = M4 correspond to? 

 Ex. 3: What would be an appropriate definition of "lethal", if C's attack were 



invariably fatal to M? 



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