Single-valued. This more subtle aim is referred to in S.7/4 and 9/
It is not incompatible with what has just been said: it merely
Means that it is the probability that is the important variable, not
The variable that is giving the probability. Thus, if I study a rou-
Lette-wheel scientifically I may be interested in the variable
“probability of the next throw being Red”, which is a variable
That has numerical values in the range between 0 and 1, rather than
40
In the variable “colour of the next throw”, which is a variable that
Has only two values: Red and Black. A system that includes the
Latter variable is almost certainly not predictable, whereas one that
Includes the former (the probability) may well be predictable, for
The probability has a constant value, of about a half.)
The “absolute” system described and used in Design for a Brain
Is just such a set of variables.
It is now clear why it can be said that every determinate
Dynamic system corresponds to a single-valued transformation (in
Spite of the fact that we dare not dogmatise about what the real
World contains, for it is full of surprises). We can make the state-
Ment simply because science refuses to study the other types, such
As the one-variable pendulum above, dismissing them as “cha-
Otic” or “non-sensical”. It is we who decide, ultimately, what we
Will accept as “machine-like” and what we will reject. (The sub-
Ject is resumed in S.6/3.)
41
TH E MA C HI N E WI TH I N PUT
Chapter
4
The special case in which the several transformations act on the
Same set of operands. Thus, if the four common operands are a, b,
C, and d, there might be three transformations, R1, R2, and R3:
a b c da b c dR2: ↓ b a d cR1: ↓ c d d b
These can be written more compactly as
↓
a b c dR3: ↓ d c d b
d
T H E M A CH IN E W I T H I N PU T
In the previous chapter we studied the relation between trans-
Formation and machine, regarding the latter simply as a unit. We
Now proceed to find, in the world of transformations, what corre-
Sponds to the fact that every ordinary machine can be acted on by
Various conditions, and thereby made to change its behaviour, as
|
|
|
A crane can be controlled by a driver or a muscle controlled by a
Nerve. For this study to be made, a proper understanding must be
Had of what is meant by a “parameter”.
So far, each transformation has been considered by itself; we
Must now extend our view so as to consider the relation between
One transformation and another. Experience has shown that just the
Same methods (as S.2/3) applied again will suffice; for the change
From transformation A to transformation B is nothing but the transi-
tion A → B. (In S.2/3 it was implied that the elements of a transfor-
Mation may be anything that can be clearly defined: there is
Therefore no reason why the elements should not themselves be
Transformations.) Thus, if T1, T2, and T3 are three transformations,
There is no reason why we should not define the transformation U:
T T TU: ↓ T1 T2 T3221
All that is necessary for the avoidance of confusion is that the
Changes induced by the transformation T1 should not be allowed
To become confused with those induced by U; by whatever
Method is appropriate in the particular case the two sets of
Changes must be kept conceptually distinct.
An actual example of a transformation such as U occurs when
Boy has a toy-machine T1 built of interchangeable parts, and the
Dismantles it to form a new toy-machine T2 . (In this case the
Changes that occur when T1 goes from one of its states to the next
(i.e. when T1 “works”) are clearly distinguishable from the change
That occurs when T1 changes to T2.)
Changes from transformation to transformation may, in general
Be wholly arbitrary. We shall, however, be more concerned with
42
a
b
c
C d d b
B a d c
|
|
|
D c d b
Дата добавления: 2019-11-16; просмотров: 247; Мы поможем в написании вашей работы! |
Мы поможем в написании ваших работ!