Occurs when the many initial possibilities are reduced to the final
Few or one— can easily be measured. We can use the same scales
255
A b
B a
And
↓
P q r
?
R q r
Can such a selection be represented by the fixing of an input
Value? Such a choice might occur in the early stages of design, as
When the first decision is made whether the components shall be
Electronic or hydraulic.
In fact this case is contained in the former, and can be repre-
Sented in it by a mere change of notation. Thus the choice just
mentioned can equally be represented as that between µ and v in
The (reducible) machine, whose states are couples:
↓
µ
ν
(a,p) (a,q) (a,r) (b,p) (b,q) (b,r)
(b .) (b .) (b .) (a .) (a .) (a .)
R) (. q) (. r) (. r) (. q) (. r)
254
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
As are used for measuring variety and information (S.7/7 and 9/11)
And they can be measured either directly or logarithmically.
The measure, besides being convenient, has the natural prop-
Erty that it specifies the capacity that the channel C must have
Designer → Machine
C
If the transmission of the necessary variety or information from
Designer to Machine is to be possible.
It will be noticed that this method does nothing to answer the
Question “how much design is there in this machine (without ref-
Erence to what it might have been)?” for the measure exists only
Over the set of possibilities. It applies, not to the thing that results,
But to the act of communication (S.13/11).
The exercises will help to give reality to the somewhat abstract
Arguments, and will show that they agree satisfactorily with what
Is evident intuitively.
Ex. 1: At one stage in the design of a certain electrical machine, three distinct
Ohmic resistances must have their values decided on. Each may have any
One of the values 10, 15, 22, 33, 47, 67 or loo ohms independently. How
Much variety must the designer supply (by the law of Requisite Variety) if
The possibilities are to be reduced to one?
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Ex. 2: (Continued. A similar three is to have its resistances selected to the near-
est ohm, i.e. from the set 10, 11, 12, …, 99, 100. How much variety must
The designer now supply ?
Ex. 3: Three resistances can each have the value of 10, 20 or 30 ohms. If they
Are connected in parallel, how much variety must the designer supply if the
Possible electrical properties are to be reduced to one ?
Ex. 4: How much design is needed if the decision lies between the two
Machines, both with states a, b, c, d:
Exactly the same measure may be applied to the design of
A Markovian machine. Thus the variety between the two Marko-
Vian machines
↓
↓
1/3 1/2 1/4
1/3 . 1/2
1/3 1/2 1/4
And
1/3 1/3 1/3
1/3 1/3 1/3
1/3 1/3 1/3
Is just 1 bit, for we are choosing between two objects, whose inner
Contents— the various fractions— are here irrelevant. (This quantity
Of 1 bit is, of course, different from the 1.58 bits that would be asso-
Ciated with the right-hand matrix regarded as an information source
That produces 1 58 bits on the average, at each step (S.9/12).)
Selection in stages. The process of selection may be either
More or less spread out in time. In particular, it may take place in
Discrete stages.
The driver about to choose a new car often proceeds in this way.
He first says, perhaps, “It must cost less than £1000”. This crite-
Rion effects some reduction in the number of possibilities. Then
Perhaps he adds that it must also be able to take five people. So he
Goes on. Each new criterion makes the surviving possibilities
Fewer. If he can buy only one car then the criteria must eventually
Reduce the possibilities to one. Somehow this reduction must be
Made, even if the spin of a coin has to be used as final selector.
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The abstract selection (or design) of a machine can similarly
Take place in stages. Thus suppose the machine has the four states
A, b, c, d. The transformation T
A b c d
T: ↓ * * * *
— in which the asterisks are not yet decided on— leaves all possi-
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