Some aspect or portion of the whole, the whole truth being too
Bulky for direct use. If it has too many parts for their specification
Individually they must be specified by a manageable number of
Rules, each of which applies to many parts. The parts specified by
One rule need not be identical; generality can be retained by
Assuming that each rule specifies a set statistically. This means
That the rule specifies a distribution of parts and a way in which it
Shall be sampled. The particular details of the individual outcome
Are thus determined not by the observer but by the process of sam-
Pling (as two people might leave a decision to the spin of a coin).
The same method must be used for specification of the cou-
Pling. If the specification for coupling is not complete it must in
Some way be supplemented, for ultimately some individual and
Single coupling must actually occur between the parts. Thus the
Coupling must contain a “random” element. What does this mean?
To make the discussion definite, suppose an experimenter has
Before him a large number of identical boxes, electrical in nature,
Each with three input and three output terminals. He wishes to form
An extensive network, coupled “at random”, to see what its proper-
Ties will be. He takes up some connecting wires and then realises
That to say “couple them at random” is quite insufficient as a defi-
Nition of the way of coupling; all sorts of “couplings at random”
63
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
Are possible. Thus he might, if there are n boxes, label 6n cards
With numbers from 1 to 6n, label the terminals similarly, shuffle
The cards and then draw two cards to nominate the two terminals
That shall be joined with the first wire. A second pair of cards will
Name the terminals joined by the second wire; and so on. A deci-
Sion would have to be made whether the first two drawn cards were
To be replaced or not before the next shuffling and drawing. The
Decision is important, for replacement allows some terminals to
Have no wire and others to have several, while non-replacement
Forces every terminal to have one wire and one only. This distinc-
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Tion would probably be significant in the characteristics of the net-
Work and would therefore require specification. Again, the method
Just mentioned has the property of allowing output to be joined to
Output. If this were undesirable a new method would have to be
Defined; such might be: “Label the inputs 1 to 3n and also outputs
To 3n; label 3n cards with numbers 1 to 3n; join a wire to input 1
And draw a card to find which output to connect it to; go on simi-
Larly through inputs 2, . . ., 3n”. Here again replacement of the card
Means that one output may go to several inputs, or to none; non-
Replacement would give one output to each input.
Enough has probably been said to show how essential an accu-
Rate definition of the mode of sampling can be. Sometimes, as
When the experimenter takes a sample of oxygen to study the gas
Laws in it, he need not specify how he obtained the sample, for
Almost all samples will have similar properties (though even here
The possibility of exact definition may be important, as Rayleigh
And Ramsay found when some specimens of nitrogen gave persis-
Tently different atomic weights from others).
This “statistical” method of specifying a system— by specifica-
Tion of distributions with sampling methods— should not be
Thought of as essentially different from other methods. It includes
The case of the system that is exactly specified, for the exact spec-
Ification is simply one in which each distribution has shrunk till
Its scatter is zero, and in which, therefore, “sampling” leads to one
Inevitable result. What is new about the statistical system is that
The specification allows a number of machines, not identical, to
Qualify for inclusion. The statistical “machine” should therefore
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Be thought of as a set of machines rather than as one machine. For
This chapter, however, this aspect will be ignored (it is taken up
Fully in Chapter 7).
It will now be seen, therefore, that it is, in a sense, possible for
an observer to specify a system that is too large for him to specify!
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