Two messages meet, even though each affects the same physical
Set of variables. Through all the changes, provided that no variety
Is lost and that the mechanism is determinate in its details, the two
Messages can continue to exist, passing merely from one coding
To another. All that is necessary for their recovery is a suitable
Inverter; and, as S.8/7 showed, its construction is always possible.
159
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
Ex. 1: (See Ex. 2/14/11.) If A"' is at the point (0,0) and B"' at (0,1), reconstruct
The position of A.
Ex. 2: A transducer has two parameters: α (which can take the values a or A) and
β (which can take the values b or B). Its states— W, X, Y, Z— are trans-
Formed according to:
↓ W XYZ
A,b) WYYY
A,B) XX W W
A,b) ZW XX
A,B) YZZZ
Two messages, one a series of α − values and the other a series of β − values,
Are transmitted simultaneously, commencing together. If the recipient is
interested only in the α − message, can he always re-construct it, regardless
of what is sent by β? (Hint: S.8/6.)
Ex. 3: Join rods by hinge-pins, as shown in Fig. 8/17/1:
Fig 8/17/1
The pinned and hinged joints have been separated to show the construc-
Tion.) P is a pivot, fixed to a base, on which the rod R can rotate; similarly
For Q and S. The rod M passes over P without connexion; similarly for N and
Q. A tubular constraint C ensures that all movements, for small arcs, shall be
To right or left (as represented in the Figure) only.
Movements at A and B will cause movements at L and N and so to Y and
Z and the whole can be regarded as a device for sending the messages “posi-
Tion of A” and “position of B”, via L and N, to the outputs Y and Z. It will
Be found that, with B held fixed, movements at A cause movements of both
L and N; similarly, with A held fixed, movements at B also affect both L and
N. Simultaneous messages from A and B thus pass through both L and N
Simultaneously, and evidently meet there. Do the messages interact destruc-
Tively? (Hint: How does Y move if A alone moves?)
Ex. 4: (Continued.) Find the algebraic relation between the positions at A, B, Y
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And Z. What does “decoding” mean in this algebraic form?
160
Chapter
9
I NC E SSANT T R ANSM ISS ION
The present chapter will continue the theme of the previous,
And will study variety and its transmission, but will be concerned
Rather with the special case of the transmission that is sustained
For an indefinitely long time. This is the case of the sciatic nerve,
Or the telephone cable, that goes on incessantly carrying mes-
Sages, unlike the transmissions of the previous chapter, which
Were studied for only a few steps in time.
Incessant transmission has been specially studied by Shannon,
And this chapter will, in fact, be devoted chiefly to introducing his
Mathematical Theory of Communication, with special emphasis
On how it is related to the other topics in this Introduction.
What is given in this chapter is, however, a series of notes,
Intended to supplement Shannon’s masterly work, rather than a
Description that is complete in itself. Shannon’s book must be
Regarded as the primary source, and should be consulted first. I
Assume that the reader has it available.
The non-determinate transformation. If the transmission is to
Go on for an indefinitely long time, the variety must be sustained,
And therefore not like the case studied in S.8/11, in which T’s
Transmission of variety stopped after the first step. Now any deter-
Minate system of finite size cannot have a trajectory that is infi-
Nitely long (S.4/5). We must therefore now consider a more
Comprehensive form of machine and transformation— the non-
Determinate.
So far all our transformations have been single-valued, and
Have thus represented the machine that is determinate. An exten-
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