On whether it was hot, tepid, or cold. This method would work sat-
Isfactorily if the time between despatch and receipt was short, but
Not if it were long; for whichever of the three states were selected
Originally, the states after a short time would be either “tepid” or
“cold”, and after a long time, “cold” only. Thus the longer the
Time between despatch and receipt, the less is the system’s capac-
Ity for carrying information, so far as this depends on its being at
A particular state.
Ex. 1: If a ball will rest in any one of three differently coloured basins, how much
Variety can be stored ?
Ex. 2: (Continued.) If in addition another ball of another colour can be placed,
By how much is the variety increased ?
Ex. 3: That a one-one transformation causes no loss of variety is sometimes used
As a parlour trick. A member of the audience is asked to think of two digits.
He is then asked to multiply one of them by 5, add 7, double the result, and
Add the other number. The result is told to the conjurer who then names the
Original digits. Show that this transformation retains the original amount of
Variety. (Hint: Subtract 14 from the final quantity.)
Ex. 4 (Continued.) What is the set for the first measure of variety?
Ex. 5: (Another trick.) A member of the audience writes down a two-digit
Number, whose digits differ by at least 2. He finds the difference between
This number and the number formed by the same digits in reverse order. To
The difference he adds the number formed by reversing the digits of the dif-
Ference. How much variety survives this transformation?
Ex. 6: If a circuit of neurons can carry memory by either reverberating or not,
How much variety can the circuit carry ? What is the set having the variety ?
Ex. 7: Ten machines, identical in structure, have run past their transients and now
Have variety constant at zero. Are they necessarily at a state of equilibrium ?
Law of Experience. The previous section showed that the
Variety in a machine (a set being given and understood) can never
Increase and usually decreases. It was assumed there that the
Machine was isolated, so that the changes in state were due only
To the inner activities of the machine; we will now consider what
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Happens to the variety when the system is a machine with input.
Consider first the simplest case, that of a machine with one
Parameter P that changes only at long intervals. Suppose, for clar-
Ity, that the machine has many replicates, identical in their trans-
Formations but differing in which state each is at; and that we are
Observing the set of states provided at each moment by the set of
Machines. Let P be kept at the same value for all and held at that
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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
Q UA N TI TY O F V AR IE TY
Value while the machines change step by step. The conditions are
Now as in the previous section, and if we measure the variety in
State over the set of replicates, and observe how the variety
Changes with time, we shall see it fall to some minimum. When the
variety has reached its minimum under this input-value (P~), let P
Be changed to some new value (P2), the change being made uni-
Formly and simultaneously over the whole set of replicates. The
Change in value will change the machine’s graph from one form to
another, as for example (if the machine has states A, B,…, F,)
From
A
↓
D
C
↓
E ← F
(P1)
B
To
A → B
↑
D → E
P2)
C
↑
F
Under P1, all those members that started at A, B or D would go to
D, and those that started at C, E, or F would go to E. The variety,
After some time at P1, would fall to 2 states. When P is changed to
P2, all those systems at D would go, in the first step, to E (for the
Transformation is single-valued), and all those at E would go to B.
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