Phabet is applied first to the message, then to the first coded form to
Give a second (doubly-) coded form, then to the second coded form,
And so on for many codings. The final form might be thought to be
Extremely mixed, and to need for its decoding as many operations
Backwards as were used forwards; in fact, as can easily be verified,
It differs from the original message only by as much as is caused by
A single application of some one-one coding. The final message can
Thus be turned back to the original by a single operation.
Ex.: Arrange the cards of a pack in order, and place it on the table face down-
Wards. Cut. Cut again. Cut again and again until you are satisfied that the
Original order is lost totally. Now pick the pack up and examine its order;
How much order has been lost?
TR A NS MIS S I O N O F V A R I E T Y
The previous chapter has introduced the concept of “variety”,
A concept inseparable from that of “information”, and we have
Seen how important it is, in some problems, to recognise that we
Are dealing with a set of possibilities.
In the present chapter we shall study how such possibilities are
Transmitted through a machine, in the sense of studying the rela-
Tion that exists between the set that occurs at the input and the con-
Sequent set that occurs, usually in somewhat coded form, at the
Output. We shall see that the transmission is, if the machine is
Determinate, perfectly orderly and capable of rigorous treatment.
Our aim will be to work towards an understanding good enough
To serve as a basis for considering the extremely complex codings
Used by the brain.
Ubiquity of coding. To get a picture of the amount of coding
That goes on during the ordinary interaction between organism and
Environment, let us consider, in some detail, the comparatively sim-
Ple sequence of events that occurs when a “Gale warning” is broad-
Cast. It starts as some patterned process in the nerve cells of the
Meteorologist, and then becomes a pattern of muscle-movements as
He writes or types it, thereby making it a pattern of ink marks on
Paper. From here it becomes a pattern of light and dark on the
Announcer’s retina, then a pattern of retinal excitation, then a pat-
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Tern of nerve impulses in the optic nerve, and so on through his
Nervous system. It emerges, while he is reading the warning, as a
Pattern of lip and tongue movements, and then travels as a pattern
Of waves in the air. Reaching the microphone it becomes a pattern
Of variations of electrical potential, and then goes through further
Changes as it is amplified, modulated, and broadcast. Now it is a
Pattern of waves in the ether, and next a pattern in the receiving set.
Back again to the pattern of waves in the air, it then becomes a pat-
Tern of vibrations traversing the listener’s ear-drums, ossicles, coch-
Lea, and then becomes a pattern of nerve-impulses moving up the
Auditory nerve. Here we can leave it, merely noticing that this very
140
De-coding. The general study of codings is best introduced
By noticing some of the features of military codings.
We must be careful from the beginning not to interpret “code”
Too narrowly. At first we tend to think only of those methods that
Turn each letter of the message to some other letter, but this class
Is too restricted, for there are many other methods. Thus the
“Playfair” code operates on the letters in pairs, turning each pair
(a vector with two components ) to some other pair. Other codes
Put the letters into some new arrangement, while others are
Wholly arbitrary, turning, for instance, “two divisions will arrive”
To “Arthur”. These considerations make it clear that if the coding
Is a transformation, the operand is the whole message rather than
A letter (though the latter possibility is not excluded). The trans-
Formation is therefore essentially of the form
M1 M2 M3 …
C1 C2 C3 …
where M1, M2, . . . are the various messages and C1, C2, … are
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Their coded forms. A coding, then, is specified by a transforma-
U: ↓
141
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
T RA N SMISSI O N O F VA R IE TY
Tion.
Often the method uses a “key-word” or some other factor that
Is capable of changing the code from one form to another. Such a
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