Of a message being decoded and in whether the decoding could be
Done or not— by whom did not matter. We are now turning to the
Question of how a mechanism can be built, by us, so that the
Mechanism shall do the decoding automatically. We seek, not a
Restored message but a machine. How shall it be built? What we
Require for its specification, of course, is the usual set of transfor-
Mations (S.4/1).
A possible method, the one to be used here, is simply to convert
The process we followed in the preceding section into mechanistic
Form, using the fact that each transition gives information about
The parameter-value under which it occurred. We want a
Machine, therefore, that will accept a transition as input and give
The original parameter value as output. Now to know which tran-
sition has occurred, i.e. what are the values of i and j in “Xi -> Xj”,
Is clearly equivalent to knowing what is the value of the vector
(i,j); for a transition can also be thought of as a vector having two
Components. We can therefore feed the transitions into an inverter
If the inverter has an input of two parameters, one to take the value
Of the earlier state and the other to take the value of the later.
Only one difficulty remains: the transition involves two states
That do not exist at the same moment of time, so one of the
Inverter’s inputs must behave now according to what the trans-
Ducer’s output was. A simple device, however, will get over this
Difficulty. Consider the transducer
↓
q
r
s
Q q q
R r r
S s s s
Suppose it is started at state r and is given the input Q S S R Q S R
R Q; its output will be r q s s r q s r r q, i.e. after the first letter it
Just repeats the input, but one step later. Two such transducers in
147
Q
R
146
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
Series will repeat the message two steps later, and so on. Clearly
There is no difficulty in principle in getting delay.
Suppose that the first transducer, the coder, is:
↓
A
B
C D
Q D A D B
R B B B C
S A C A D
What we require is a machine that, e.g.
|
|
|
Given input A, A will emit S
A, B ,,,, R
A, D ,,,, Q
B, A ,,,, Q
Etc.
(The input A,C will never actually come to it, for the transition
Cannot be emitted from the coder.)
The three machines are coupled thus:
→ Coder → Delayer
↓
Inverter →
The delayer has the simple form:
↓
The inverter will now emit the same sequence as was put into
The coder. Thus suppose Q was put in and caused the transition
A → D in the coder. This implies that the inverter will be receiv-
Ing at this step, D directly from the coder (for the coder is at D),
And a from the delayer (for the coder was at A the step before).
With input (a, D), the inverter goes to state Q, which is the state
We supposed. And similarly for the other possible states put in.
Thus, given a transducer that does not lose distinctions, an
Automatic inverter can always be built. The importance of the
Demonstration is that it makes no reference to the transducer’s
Actual material— it does not matter whether it is mechanical, or
Electronic, or neuronic, or hydraulic— the possibility of inversion
Exists. What is necessary is the determinateness of the coder’s
Actions, and its maintenance of all distinctions.
Ex. 1: Why cannot the Coder of S.8/5 be used as example?
Ex. 2: Complete the specification of the inverter just given.
Ex. 3: Specify a two-step delayer in tabular form.
a
a
b
c
d
Q
b
a
b
c
d
c
a
b
c
d
R
d
a
b
c
d
S
A
B
C
D
And the inverter the form:
↓
This section may be omitted at first reading.) Now that the
Construction of the inverter has been identified in the most general
Form, we can examine its construction when the transducer is less
|
|
|
General and more like the machines of every-day life. The next
Step is to examine the construction of the inverter when the trans-
Дата добавления: 2019-11-16; просмотров: 211; Мы поможем в написании вашей работы! |
Мы поможем в написании ваших работ!