Essentially independent of the discrete steps that we have consid-
Ered to be taken by D, R, and T in this chapter. Thus, T gives the
Outcome, and any particular outcome may be compared with
Another, as unit with unit. Each individual outcome may, how-
Ever, in another context, be analysed more finely. Thus a thirsty
Organism may follow trajectory 1 and get relief, or trajectory 2
And die of thirst. For some purposes the two outcomes can be
Treated as units, particularly if they are to be contrasted. If how-
Ever we want to investigate the behaviour in more detail, we can
Regard trajectory 1 as composed of a sequence of states, separated
By steps in time that are of quite a different order of size from
Those between successive regulatory acts to successive distur-
Bances.)
We can now interpret the general phenomenon of regulation in
Terms of communication. If R does nothing, i.e. keeps to one
Value, then the variety in D threatens to go through T to E, con-
Trary to what is wanted. It may happen that T, without change by
R, will block some of the variety (S.11/9), and occasionally this
Blocking may give sufficient constancy at E for survival. More
Commonly, a further suppression at E is necessary; it can be
Achieved, as we saw in S.11/6, only by further variety at R.
We can now select a portion of the diagram, and focus attention
On R as a transmitter:
D → R → T
210
E
The law of Requisite Variety says that R’s capacity as a regulator
Cannot exceed R’s capacity as a channel of communication.
In the form just given, the law of Requisite Variety can be
Shown in exact relation to Shannon’s Theorem 10, which says that
If noise appears in a message, the amount of noise that can be
Removed by a correction channel is limited to the amount of infor-
Mation that can be carried by that channel.
Thus, his “noise” corresponds to our “disturbance”, his “correc-
Tion channel” to our “regulator R”, and his “message of entropy
H” becomes, in our case, a message of entropy zero, for it is con-
Stancy that is to be “transmitted”. Thus the use of a regulator to
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Achieve homeostasis and the use of a correction channel to sup-
Press noise are homologous.
Ex. 1: A certain insect has an optic nerve of a hundred fibres, each of which can
Carry twenty bits per second; is this sufficient to enable it to defend itself
Against ten distinct dangers, each of which may, or may not, independently,
Be present in each second?
Ex. 2: A ship’s telegraph from bridge to engine-room can determine one of nine
Speeds not oftener than one signal in five seconds, and the wheel can deter-
Mine one of fifty rudder-positions in each second. Since experience has
Shown that this means of control is normally sufficient for full regulation,
Estimate a normal upper limit for the disturbances (gusts, traffic, shoals, etc.)
That threaten the ship’s safety.
Ex. 3: A general is opposed by an army of ten divisions, each of which may
Manoeuvre with a variety of 106 bits in each day. His intelligence comes
Through 10 signallers, each of whom can transmit 60 letters per minute for 8
Hours in each day, in a code that transmits 2 bits per letter. Is his intelli-
Gence-channel sufficient for him to be able to achieve complete regulation?
Ex. 4: (Continued.) The general can dictate orders at 500 bits/minute for 12
Hours/day. If his Intelligence were complete, would this verbal channel be
Sufficient for complete regulation ?
The diagram of immediate effects given in the previous
Section is clearly related to the formulation for “directive correla-
Tion” given by Sommerhoff, who, in his Analytical Biology, uses
The diagram
Rt1
CVo
Et1
T0
T1
211
T2
Gt2
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
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