About how long a given act of selection may take, for when actual
Cases are examined, the time taken may, at first estimate, seem too
Long for any practical achievement. The question becomes specially
Important when the regulator is to be developed for regulation of a
Very large system. Approximate calculation of the amount of selec-
Tion likely to be necessary may suggest that it will take a time far
Surpassing the cosmological; and one may jump to the conclusion
That the time taken in actually achieving the selection would have to
Be equally long. This is far from being the case, however.
The basic principles have been made clear by Shannon, espe-
Cially in his Communication theory of secrecy systems. He has
Shown that if a particular selection is wanted, of 1 from N, and if
The selector can indicate (or otherwise act appropriately) only as
To whether the required element is or is not in a given set, then the
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Method that achieves the whole selection in the fewest steps is
Selection by successive dichotomies, so that the early selections
Are between group and group, not between elements. This method
Is much faster than the method of examining the N one by one,
Seriatim. And if N becomes very large, the method of selecting
Among groups becomes almost incomparably faster. Lack of
Space prohibits an adequate treatment of this important subject,
But it should not be left until I have given an example to show
Something of how enormously faster the dichotomising method is.
Let us consider a really big selection. Suppose that, somewhere in
The universe (as visible to the astronomer) there is a unique atom; the
Selector wants to find it. The visible universe contains about
Galaxies, each of which contains about 100000,000000
Suns and their systems; each solar system contains about 300000
Bodies like the earth, and the earth contains about 1,000000,000000
Cubic miles. A cubic mile contains about 1000,000000,000000,000000
Dust particles, each of which contains about 10000,000000,000000
atoms. He wants to find a particular one!
Let us take this as a unit of very large-scale selection, and call
It 1 mega-pick; it is about 1 from 1073. How long will the finding
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Of the particular atom take?
Two methods are worth comparing. By the first, the atoms are
Examined one at a time, and a high-speed electronic tester is used to
Examine a million in each second. Simple calculation shows that the
Number of centuries it would take to find the atom would require
More than the width of this page to write down. Thus, following this
Method dooms the selection to failure (for all practical purposes).
In the second method he uses (assuming it possible) the method
Of dichotomy, asking first: is the atom in this half or that? Then,
Taking what is indicated, is it in this half or that?. And so on. Sup-
Pose this could be done only at one step in each second. How long
would this method take ? The answer is: just over four minutes!
With this method, success has become possible.
This illustration may help to give conviction to the statement
That the method of selection by groups is very much faster than the
Method of searching item by item. Further, it is precisely when the
Time of searching item by item becomes excessively long that the
Method of searching by groups really shows its power of keeping
The time short.
Selection and reducibility. What does this mean when a
Particular machine is to be selected ? Suppose, for definiteness
That it has 50 inputs, that each input can take any one of 25 values,
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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
RE GU LA TI N G TH E V ER Y LA R GE SY STE M
And that a particular one of the possible forms is sought. This
Selection is just about 1 megapick, and we know that the attempt
To select seriatim is hopeless. Can the selection be made by
Groups? We can if there can be found some practical way of
Grouping the input-states.
A particular case, of great practical importance, occurs when
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The whole machine is reducible (S.4/14) and when the inputs go
Separately to the various sub-systems. Then the sequence: select
The right value for part 1, on part 1’s input; select the right value
For part 2, on part 2’s input; and so on— corresponds to the selec-
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