And this is so; for the next two steps can be any one of HH, HT,
TH or TT, with probabilities 1/4, 1/4, 1/4 and 14, which gives H
= 2 bits. Briefly it can be said that the entropy of a length of
Markov chain is proportional to its length (provided always that
It has settled down to equilibrium).
Quite another way of making the measurement on the chain is
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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
I N CESSA N T TR AN SMI SSIO N
Introduced when one considers how fast in time the chain is being
Produced by some real physical process. So far this aspect has
Been ignored, the sole graduation being in terms of the chain’s
Own steps. The new scale requires only a simple rule of proportion
For its introduction. Thus if (as in S.9/12) the insects’ “unit time”
For one step is twenty seconds, then as each 20 seconds produces
Bits, 60 seconds will produce (60/20)0 84 bits; so each insect
Is producing variety of location at the rate of 2 53 bits per minute.
Such a rate is the most natural way of measuring the capacity of
A channel, which is simply anything that can be driven by its input
To take, at each moment, one of a variety of states, and which can
Transmit that state to some receiver. The rate at which it can trans-
Mit depends both on how fast the steps can succeed one another
And on the variety available at each step.
It should be noticed that a “channel” is defined in cybernetics
Purely in terms of certain behavioural relations between two
Points; if two points are so related then a “channel” exists between
Them, quite independently of whether any material connexion can
Be seen between them. (Consider, for instance, Exs. 4/15/2, 6/7/
Because of this fact the channels that the cyberneticist sees
May be very different from those seen by one trained in another
Science. In elementary cases this is obvious enough. No one
Denies the reality of some functional connexion from magnet to
Magnet, though no experiment has yet demonstrated any interme-
Diate structure.
Sometimes the channel may follow an unusual path. Thus the
Brain requires information about what happens after it has emitted
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“commands” to an organ, and usually there is a sensory nerve
From organ to brain that carries the “monitoring” information.
Monitoring the vocal cords, therefore, may be done by a sensory
Nerve from cords to brain. An effective monitoring, however, can
Also be achieved without any nerve in the neck by use of the sound
Waves, which travel through the air, linking vocal cords and brain,
Via the ear. To the anatomist this is not a channel, to the commu-
Nication engineer it is. Here we need simply appreciate that each
Is right within his own branch of science.
More complex applications of this principle exist. Suppose we
Ask someone whether 287 times 419 is 118213; he is likely to reply
“I can’t do it in my head— give me pencil and paper”. Holding the
Numbers 287 and 419, together with the operation “multiply”, as
Parameters he will then generate a process (a transient in the termi-
Nology of S.4/5) which will set up a series of impulses passing
Down the nerves of his arm, generating a series of pencil marks on
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The paper, then the marks will affect his retina and so on to his brain
Where an interaction will occur with the trace (whatever that may
Be) of “118213”; he will then give a final answer. What we must
Notice here is that this process, from brain, through motor cortex,
Arm, pencil, marks, light rays, retina, and visual cortex back to
Brain, is, to the communication engineer, a typical “channel”, link-
Ing “transmitter” to “receiver”. To the cyberneticist, therefore, the
White matter, and similar fibres, are not the only channels of com-
Munication available to the brain: some of the communication
Between part and part may take place through the environment.
Redundancy. In S.7/14 it was stated that when a constraint
Exists, advantage can usually be taken of it. An illustration of this
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Thesis occurs when the transmission is incessant.
For simplicity, reconsider the traffic lights — Red, Yellow, and
Green— that show only the combinations
Red
Red and Yellow
Green
Yellow.
Each component (each lamp or colour) can be either lit or unlit, so
The total variety possible, if the components were independent
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