Method— by regarding the balance as a transducer carrying information from
The coins to the observer— give a number below which the number of bal-
Ancings cannot fall. (Hint: What is the variety at a single balancing if the
Results can be only: equality, left pan heavier, right pan heavier?)
Has no immediate effect on the cortex) the action has to take place
Through a chain of systems: the sense organs, the sensory nerves,
The sensory nuclei, and so on; and some delay is thereby imposed.
Even within one such part some transfer has to take place from
Point to point thereby delaying its transfer to the next part.
Conversely, if a system such as T is found on testing to transmit
Its variety to another system only over a number of steps, then it
May be predicted that T, if examined in detail, will be found to
Consist of sub- systems coupled so that not all of T’s variables
Have an immediate effect on S.
Ex. 1: If T consists of the sub-systems A, . . ., F joined to each other and to S as
Shown in the diagram of immediate effects:
A ← B → C ←
↓↑
D → E → F
S
Delay. The arrangement of the system of S.8/13:
Q → R → S
Can also be viewed as
T → S
In which Q and R have been regarded as forming a single system
T which is, of course, absolute. If now an observer studies the
Transfer of variety from T to S, with exactly the same events as
Those of S.8/13 actually occurring, he will find that the variety is
Moving across in small quantities, step by step, unlike the transfer
Of S.8/11, which was complete in one step.
The reason for the distinction is simply that in S.8/11 the whole
Of the dominating system (T) had an immediate effect on the dom-
Inated (U), while in S.8/13 T contained a part Q which had no
Immediate effect on the receiver S. Q’s effect had to be exerted
Through R, and was thereby delayed.
This more time-consuming transfer is common in real systems
Simply because many of them are built of parts not all of which
Have an immediate effect on the receiving system. Thus if the cer-
Ebral cortex, as receiver, is affected by the environment (which
156
How many steps are necessary for all the variety in T to be transferred to S?
|
|
|
Ex. 2: (Continued.) How long does it take to get a “message”, telling of T’s state,
Uniquely from T to S?
Ex. 3: If J, with the variables w, x, y, z, dominates K, with the variable k, by the
transformation w' = w— y, x' = w + xz, y' = 2wy— z, z, = yz2, k'= x— 3k, how
Many steps are necessary for all the variety in J to be transferred to K?
Ex. 4: (Continued.) In the same system, how long would it take to get a message
From w to z?
To improve our grasp of these matters, let us next consider
The case of two systems joined so that there is feedback:
T ← U →
S.8/11 showed that T will pass variety to U; will U, now having
This variety, pass it back to T and thereby increase T’s variety still
Further ?
Again the answer is given straightforwardly when we consider
A set of replicates. Suppose that initially the variety existed only
Between the T’s, the U’s being all at the same state. Divide the
Whole set into sub- sets, each sub-set consisting of those with T at
A particular state, so that set i, say, consists of the systems with T
At state Ti. Within such a subset there is now no variety in state,
And no variety can develop, for the whole (T,U)-system is abso-
Lute. The initial variety of the T’s, therefore, will not increase,
Either at the first step or subsequently. In a determinate system,
Feedback does not lead to a regenerative increase in variety.
157
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
What was important in the argument about U’s feedback to T is
That what U feeds back to T is highly correlated with what is in T,
For each U feeds back into the particular T that acted on it a step
Earlier, and no other. The argument thus demands an accurate
|
|
|
Treatment of the correspondences between the various T’s and U’s.
The arguments of the previous few sections have shown that
Though the matter can be treated in words in the simple cases
(those just considered), the attempt to handle complex cases in the
Verbal form is likely to lead to intolerable complexities. What is
Wanted is a symbolic machinery, an algebra, which will enable the
Relations to be handled more or less mechanically, with the rules
Дата добавления: 2019-11-16; просмотров: 232; Мы поможем в написании вашей работы! |
Мы поможем в написании ваших работ!