Labelled I and II, and their canonical representations were found to be
I: x' = x + 1— α
II: x' = (1 + α)x — 2 + α.
Unfortunately the labels “I” and “II” have since become detached and it is
Now not known which is which. Suggest a simple test that will re- identify
Them.
Inaccessible states. Examination of the transformations
↓
f
g
h
j
F j j f
H f h f
Shows that the state g, once past in the protocol, cannot be made
To re-appear by any manipulations of the input. The transitions
From g thus cannot be explored further or tested repeatedly. This
Fact, that certain states of the Box cannot be returned to at will, is
Very common in practice. Such states will be called inaccessible.
In its most dramatic form it occurs when the investigation of a
New type of enemy mine leads to an explosion— which can be
Described more abstractly by saying that the system has passed
From a state to which no manipulation at the input can make the
System return. Essentially the same phenomenon occurs when
Experiments are conducted on an organism that learns; for as time
Goes on it leaves its “unsophisticated” initial state, and no simple
Manipulation can get it back to this state. In such experiments,
However, the psychologist is usually investigating not the partic-
Ular individual but the particular species, so he can restore the ini-
Tial state by the simple operation of taking a new individual.
Thus the experimenter, if the system is determinate, must either
Restrict himself to the investigation of a set of states that is both
Closed and freely accessible, such as f, h, j in the example, or he
Must add more states to his input so that more transformations
Become available and thus, perhaps, give a transition to g.
Deducing connexions. It is now clear that something of the
Connexions within a Black Box can be obtained by deduction. For
Direct manipulation and observation gives the protocol, this (if the
System is determinate) gives the canonical representation, and this
Gives the diagram of immediate effects (one for each input state)
|
|
|
(S.4/13). But we must go cautiously.
It must be noticed that in a real system the “diagram of internal
92
α
β
Connexions” is not unique. The radio set, for instance, has one dia-
Gram of connexions if considered electrically and another if con-
Sidered mechanically. An insulator, in fact, is just such a
Component as will give firm mechanical connexion while giving
No electrical connexion. Which pattern of connexions will be
Found depends on which set of inputs and outputs is used.
Even if the diagram of immediate effects is unique, it does not
Indicate a unique pattern of connexions within the Box. Thus sup-
Pose a Black Box has an output of two dials, x and y; and suppose
It has been found that x dominates y. The diagram of immediate
Effects is thus
x → y
(in which the two boxes are parts of the whole Box). This relation-
Ship can be given by an infinity of possible internal mechanisms.
A particular example occurs in the case in which relays open or
Close switches in order to give a particular network of connexions.
It has been shown by Shannon that any given behaviour can be
Produced by an indefinitely large number of possible networks.
Thus let x represent a contact that will be closed when the relay X
Is energised, and let x represent one that will be opened. Suppose
Similarly that another relay Y has similar contacts y and y. Sup-
Pose that the network is to conduct from p to q when and only
When both X and Y are energised.
Fig. 6/7/1
The network A of Fig. 6/7/1, in which x and y are connected in
Series, will show the required behaviour. So also will B, and C,
And an indefinitely large number of other networks.
The behaviour does not specify the connexions uniquely.
|
|
|
Ex.: (Ex. 6/5/4 continued.) Deduce the diagram of immediate effects when the
input is fixed at α. (Hint: S.4/13.)
93
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
TH E BL AC K B O X
Дата добавления: 2019-11-16; просмотров: 274; Мы поможем в написании вашей работы! |
Мы поможем в написании ваших работ!