Book, and that can be made as rigorous, objective, and unambig-
Uous as one pleases.
The foundation. Let us start at the beginning. The most basic
Facts in biology are that this earth is now two thousand million
Years old, and that the biologist studies mostly that which exists
Today. From these two facts follow a well-known deduction,
Which I would like to restate in our terms.
We saw in S.4/23 that if a dynamic system is large and com-
Posed of parts with much repetition, and if it contains any prop-
Erty that is autocatalytic, i.e. whose occurrence at one point
Increases the probability that it will occur again at another point,
Then such a system is, so far as that property is concerned, essen-
Tially unstable in its absence. This earth contained carbon and
Other necessary elements, and it is a fact that many combinations
Of carbon, nitrogen, and a few others are self-reproducing. It fol-
Lows that though the state of “being lifeless” is almost a state of
Equilibrium, yet this equilibrium is unstable (S.5/6), a single devi-
Ation from it being sufficient to start a trajectory that deviates
More and more from the “lifeless” state. What we see today in the
Biological world are these “autocatalytic” processes showing all
The peculiarities that have been imposed on them by two thousand
Million years of elimination of those forms that cannot survive.
The organisms we see today are deeply marked by the selective
Action of two thousand million years’ attrition. Any form in any
Way defective in its power of survival has been eliminated; and
Today the features of almost every form bear the marks of being
Adapted to ensure survival rather than any other possible outcome.
Eyes, roots, cilia, shells and claws are so fashioned as to maximise
The chance of survival. And when we study the brain we are again
Studying a means to survival.
196
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
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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 val-
Ues, 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 sur-
Vived. 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 corre-
Sponding 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 M1,
M2, …, Mk, …, Mn. 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 M1 to Mk say. If now some operation C (for
Cat) acts on the mouse in state Mi, and C(Mi) gives, say, M2, then
We may say that M has “survived” the operation of C, for M2 is in
the set M1, … Mk.
If now a particular mouse is very skilled and always survives
the operation C, then all the states C(M1), C(M2), …, C(Mk), are
contained in the set M1, …, Mk. We now see that this representa-
Tion of survival is identical with that of the “stability” of a set (S.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
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M1, …, Mk, that correspond to the living organism are then those
States in which certain essential variables are kept within
Assigned (“physiological”) limits.
Ex. 1: If n is 10 and k is 5, what would the operation C(M7) = M9 correspond
To?
Ex. 2: (Continued.) What would the operation C(M8) = M4 correspond to?
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