Ticular definition; rather we shall refer to a relation between the
System and some definite, given, observer who is going to try to
Study or control it. In this book I use the words “very large” to
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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
TH E MA C HI N E WI TH I N PUT
Imply that some definite observer en, with definite resources and
Techniques, and that the system some practical way, too large for
Him; so that he cannot observe completely, or control it com-
Pletely, or carry out the calculations for prediction completely. In
Other words, he says the system “very large” if in some way it
Beats him by its richness and complexity.
Such systems are common enough. A classic case occurred
When the theoretical physicist of the nineteenth century tried to
Use Newtonian mechanics to calculate how a gas would behave.
The number of particles in an ordinary volume of gas is so vast
That no practical observation could record the system’s state, and
No practical relation could predict its future. Such a system was
“very ” in relation to the nineteenth century physicist.
The stock-breeder faces a “very large” system in the genes he is
G to mould to a new pattern. Their number and the complexities
Of their interactions makes a detailed control of them by impossi-
Ble in practice.
Such systems, in relation to our present resources for observa-
Tion control, are very common in the biological world, and in its
Social and economic relatives. They are certainly common in the
Brain, though for many years the essential complexity was given
Only grudging recognition. It is now coming to be recognised,
However, that this complexity is something that can be ignored no
Longer. “Even the simplest bit of behavior”, says Lashley,
“requires the integrated action of millions of neurons.... I have
Come to believe almost every nerve cell in the cerebral cortex may
Be excited in every activity.... The same neurons which maintain
The memory traces and participate in the revival of a memory are
Also involved, in different combinations, in thousands of other
Memories acts.” And von Neumann: “The number of neurons in
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The central nervous system is somewhere of the order of 1010. We
Have absolutely no past experience with systems of this degree of
Complexity. All artificial automata made by man have numbers of
Parts which by any comparably schematic count are of the order
To 106.” (Cerebral Mechanisms in Behavior.)
It should be noticed that largeness per se in no way invalidates
The principles, arguments, and theorems of the previous chapters.
Though the examples have been confined to systems with only a
States or a few variables, this restriction was solely for the author’s
And reader’s convenience: the arguments remain valid without any
Restriction on the number of states or variables in the system. It is a
Peculiar advantage of the method of arguing about states, rather
62
Than the more usual variables, that it requires no explicit mention of
The system’s number of parts; and theorems once proved true are
True for systems of all sizes (provided, of course, that the systems
Conform to the suppositions made in the argument).
What remains valid is, of course, the truth of the mathematical
Deductions about the mathematically defined things. What may
Change, as the system becomes very large, is the applicability of
These theorems to some real material system. The applicability,
However, can be discussed only in relation to particular cases. For
The moment, therefore, we can notice that size by itself does not
Invalidate the reasonings that have been used so far.
Random coupling. Suppose now that the observer faces a
System that, for him, is very large. How is he to proceed ? Many
Questions arise, too many to be treated here in detail, so I shall
Select only a few topics, letting them serve as pattern for the rest.
(See S.6/19 and Chapter 13.) First, how is the system to be speci-
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Fied ?
By definition, the observer can specify it only incompletely.
This is synonymous with saying that he must specify it “statisti-
Cally”, for statistics is the art of saying things that refer only to
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