A car has an attractive appearance, its being sold to one house is
Likely to increase its chance of being sold to adjacent houses. And
If a species is short of food, the existence of one member
Decreases the chance of the continued, later existence of another
Member.
Sometimes these effects are of great complexity; sometimes
However the change of the variable “number having the property”
Can be expressed sufficiently well by the simple transformation
n' = kn, where k is positive and independent of n.
When this is so, the history of the system is often acutely depen-
dent on the value of k, particularly in its relation to + 1. The equa-
Tion has as solution, if t measures the number of time- intervals
that have elapsed since t = 0, and if n0 was the initial value:
n = n0 e (k - 1)t
Three cases are distinguishable.
(1) k < 1. In this case the number showing the property falls
Steadily, and the density of parts having the property decreases. It
70
Is shown, for instance, in a piece of pitchblende, by the number of
Atoms that are of radium. It is also shown by the number in a spe-
Cies when the species is tending to extinction.
(2) k = 1. In this case the number tends to stay constant. An
Example is given by the number of molecules dissociated when
The percentage dissociated is at the equilibrial value for the condi-
Tions obtaining. (Since the slightest deviation of k from 1 will take
The system into one of the other two cases it is of little interest.)
(3) k > 1. This case is of great interest and profound importance.
The property is one whose presence increases the chance of its
Further occurrence elsewhere. The property “breeds”, and the sys-
Tem is, in this respect, potentially explosive, either dramatically,
As in an atom bomb, or insidiously, as in a growing epidemic. A
Well known example is autocatalysis. Thus if ethyl acetate has
Been mixed with water, the chance that a particular molecule of
Ethyl acetate will turn, in the next interval, to water and acetic acid
Depends on how many acetate molecules already have the prop-
Erty of being in the acid form. Other examples are commonly
Given by combustion, by the spread of a fashion, the growth of an
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Avalanche, and the breeding of rabbits.
It is at this point that the majestic development of life by Dar-
Winian evolution shows its relation to the theory developed here
Of dynamic systems. The biological world, as noticed in S.4/21, is
A system with something like the homogeneity and the fewness of
Immediate effects considered in this chapter. In the early days of
The world there were various properties with various k’s. Some
Had k less than 1— they disappeared steadily. Some had k equal to
They would have remained. And there were some with k
Greater than I— they developed like an avalanche, came into con-
Flict with one another, commenced the interaction we call “com-
Petition”, and generated a process that dominated all other events
In the world and that still goes on.
Whether such properties, with k greater than I, exist or can exist
In the cerebral cortex is unknown. We can be sure, however, that
~f such do exist they will be of importance, imposing outstanding
Characteristics on the cortex’s behaviour. It is important to notice
That this prediction can be made without any reference to the par-
Ticular details of what happens in the mammalian brain, for it is
True of all systems of the type described.
The remarks made in the last few sections can only illus-
Trate, in the briefest way, the main properties of the very large sys-
Tem. Enough has been said, however, to show that the very large
71
A N I N T R O D UC T I O N T O C Y B E R NE T I C S
System is not wholly different from the systems considered in the
Earlier chapters, and to show that the construction of a really ade-
Quate theory of systems in general is more a question of time and
Labour than of any profound or peculiar difficulty.
The subject of the very large system is taken up again in S.6/14.
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72
Chapter
5
ST ABI LI TY
The word “stability” is apt to occur frequently in discussions
Of machines, but is not always used with precision. Bellman refers
To it as “. . . stability, that much overburdened word with an unsta-
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