Plexity” as a subject in its own right.
Prominent among the methods for dealing with complexity is
Cybernetics. It rejects the vaguely intuitive ideas that we pick up
From handling such simple machines as the alarm clock and the
Bicycle, and sets to work to build up a rigorous discipline of the sub-
Ject. For a time (as the first few chapters of this book will show) it
Seems rather to deal with truisms and platitudes, but this is merely
Because the foundations are built to be broad and strong. They are
Built so that cybernetics can be developed vigorously, without t e
Primary vagueness that has infected most past attempts to grapple
With, in particular, the complexities of the brain in action.
Cybernetics offers the hope of providing effective methods for
5
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
The study, and control, of systems that are intrinsically extremely
Complex. It will do this by first marking out what is achievable
(for probably many of the investigations of the past attempted the
Impossible), and then providing generalised strategies, of demon-
Strable value, that can be used uniformly in a variety of special
Cases. In this way it offers the hope of providing the essential
Methods by which to attack the ills— psychological, social, eco-
Nomic— which at present are defeating us by their intrinsic com-
Plexity. Part III of this book does not pretend to offer such
Methods perfected, but it attempts to offer a foundation on which
Such methods can be constructed, and a start in the right direction.
PART ONE
M EC HANI S M
The properties commonly ascribed to any object
Are, in last analysis, names for its behavior.
(Herrick)
6
Chapter
2
C HANGE
The most fundamental concept in cybernetics is that of “dif-
Ference”, either that two things are recognisably different or that
One thing has changed with time. Its range of application need not
Be described now, for the subsequent chapters will illustrate the
Range abundantly. All the changes that may occur with time are
Naturally included, for when plants grow and planets age and
Machines move some change from one state to another is implicit.
|
|
|
So our first task will be to develop this concept of “change”, not
Only making it more precise but making it richer, converting it to
A form that experience has shown to be necessary if significant
Developments are to be made.
Often a change occurs continuously, that is, by infinitesimal
Steps, as when the earth moves through space, or a sunbather’s
Skin darkens under exposure. The consideration of steps that are
Infinitesimal, however, raises a number of purely mathematical
Difficulties, so we shall avoid their consideration entirely. Instead,
We shall assume in all cases that the changes occur by finite steps
In time and that any difference is also finite. We shall assume that
The change occurs by a measurable jump, as the money in a bank
Account changes by at least a penny. Though this supposition may
Seem artificial in a world in which continuity is common, it has
Great advantages in an Introduction and is not as artificial as it
Seems. When the differences are finite, all the important ques-
Tions, as we shall see later, can be decided by simple counting, so
That it is easy to be quite sure whether we are right or not. Were
We to consider continuous changes we would often have to com-
Pare infinitesimal against infinitesimal, or to consider what we
Would have after adding together an infinite number of infinitesi-
Mals— questions by no means easy to answer.
As a simple trick, the discrete can often be carried over into the
Continuous, in a way suitable for practical purposes, by making a
Graph of the discrete, with the values shown as separate points. It
9
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
C H A NG E
Is then easy to see the form that the changes will take if the points
Were to become infinitely numerous and close together.
|
|
|
In fact, however, by keeping the discussion to the case of the
Finite difference we lose nothing. For having established with cer-
Tainty what happens when the differences have a particular size
Дата добавления: 2019-11-16; просмотров: 253; Мы поможем в написании вашей работы! |
Мы поможем в написании ваших работ!