Pound target, then that sequence will be produced, regardless of
D’s values during the sequence. (It is assumed for convenience
That the components move in step.) Thus the fact that R is a perfect
213
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
REQ U ISI TE V A RI ETY
Regulator gives C complete control over the output, in spite of the
Entrance of disturbing effects by way of D. Thus, perfect regula-
Tion of the outcome by R makes possible a complete control over
The outcome by C.
We can see the same facts from yet another point of view. If an
Attempt at control, by C over E:
C → E
Is disturbed or made noisy by another, independent, input D, so
That the connexions are
D
E
C
Or
C
D
T → E
Then a suitable regulator R, taking information from both C and D,
And interposed between C and T:
D → T → E
↑
C → R
May be able to form, with T, a compound channel to E that trans-
Mits fully from C while transmitting nothing from D.
The achievement of control may thus depend necessarily on the
Achievement of regulation. The two are thus intimately related.
Ex. 1: From Table 31/3/l form the set of transformations, with c as parameter,
That must be used by R if C is to have complete control over the outcome.
Hint: What are the operands?)
Ex. 2: If, in the last diagram of this section, C wants to transmit to E at 20 bits/
Second, and a source D is providing noise at 5 bits/second, and T is such
That if R is constant, E will vary at 2 bits/second, how much capacity must
The channel from D to R have (at least) if C s control over E is to be
Complete?
Ex. 3: (Continued.) How much capacity (at least) is necessary along the channel
From C to R ?
Ex. 4: (Continued.) How much along that from R to T?
In our treatment of regulation the emphasis has fallen on its
Property of reducing the variety in the outcome; without regula-
Tion the variety is large— with regulation it is small. The limit of
This reduction is the regulation that holds the outcome rigorously
Constant. This point of view is undoubtedly valid, but at first it
May seem to contrast sharply with the naive view that living
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Organisms are, in general, anything but immobile. A few words,
In addition to what was said in S.11/13, may be useful.
It should be appreciated that the distinction between “constant”
And “varying” often depends on the exact definition of what is
Being referred to. Thus if a searchlight follows an aircraft accu-
Rately we may notice either that the searchlight moved through a
Great range of angles (angles in relation to the earth) or that the
Angle it made with the aircraft remained constant at zero. Obvi-
Ously both points of view are valid; there is no real contradiction
In this example between “great range” and “constant”, for they
Refer to different variables.
Again, the driver who steers a car accurately from one town to
Another along a winding lane can be regarded either as one who
Has caused the steering wheel to show much activity and change
Or as one who, throughout the trip, has kept the distance between
Car and verge almost constant.
Many of the activities of living organisms permit this double
Aspect. On the one hand the observer can notice the great deal of
Actual movement and change that occurs, and on the other hand he
Can observe that throughout these activities, so far as they are co-
Ordinated or homeostatic, there are invariants and constancies that
Show the degree of regulation that is being achieved.
Many variations are possible on the same theme. Thus if varia-
Ble x is always doing just the same as variable y, then the quantity
X – y is constant at zero. So if y’s values are given by some outside
Factor, any regulator that acts on x so as to keep x – y constant at
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