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CYBERNETICS
or control and communication
in the animal and the machine
NORBERT WIENER
second edition
THEM. PRESS
Cambridge, Massachusetts
Fourth Printing, 1985
To ARTURO ROSENBLUETH
for many years my companion in science
Preface
to the Second Edition
Cybeeti
Cyberneti,
vii
PREFACE
PREFACE
T
t.
=
A wt+ Bsinwt
<wt
<wt
<wt
X
y
Nonlinear Proble in Random Theory.
1
1
2
IX
X
2
yy
PREFACE
Cae, Massache,
Marci�, 1961
CONTENTS
PART I
19
4
8
Introduction
V
V
PART II
1961
PART I
ORIGINAL EDITION
1948
Introduction
I
CYBERNETI
INTRODUCTION
3
4
CYBERNECS
the
means of realizing them, were sent in to Dr. Vannevar Bush r
TRODUCTION
5
not
not
6
CYBERNETICS
y
TRODUCTION
7
1
CYBERNECS
axia.
tabes dorsalis,
1
INTRODUON
9
CYBERNETICS
ry.
2
3
CYBERNETICS
n n = n
14
CYBERNECS
it
of Pennsylvania were already constructing machines, and the
INTRODUCTION
16
CYBERNETICS
1
3
N.,
Lee, Y. W.,
3
17
18
CYBERNETICS
Gestalt,
INTRODUCTION
cn
20
CYBERNETICS
1
INTRODUCTION
22
CYBERNECS
Gestalt,
INTRODUCTION 23
24
CYBERNETICS
importance of the notion and the technique of communication in
INTRODUCTION
25
26
CYBERNETICS
27
1
comtition.
28
CYBERNETICS
survive the second.
However
,
taking the second revolution as
29
Nmr, 1947
I
Newtonian and Bergsonian Time
W. Hey
y
NEWTONIAN AND BESONIAN TIME
31
32
CYBERNECS
NEWTONIAN AND BESONIAN TIME
33
If
If
34
CYBERNETICS
will
35
36
37
1
c
38
li
li
engineers of ancient days were land surveyors, astronomers, and
NEWTONIAN AND BERGSONIAN TIME
39
40
CYBERNECS
41
42
CYBERNETICS
In
In
43
44 CYBERNECS
II
Groups and Statistical Mechanics
45
46 CYBERNECS
se
47
2N N
N
2N
48 CYBERNETICS
will
ti
I
J
o
(2.01)
I
T
f(t)
7'
0
49
(2.02)
It
1
It
2
It
l
50
CYBERNETICS
1
A B
prt retant BA.
A B. A
x
BA
AB
GROUPS AND STATISTICAL MECHANICS
51
A
1
1
1
,
J
1
1
•
If
x
,
f(x)
T, f(x)
T,
g(x)
1
•
If
1
CYBERNECS
1
character grp
If
T + T,
+ =
<>T
T,
In
T
+
=
If = e'"
If,
T
In
1
'"
n
2
0
:
f:
2
CYBERNETICS
T
f(x)
x E. In f(x)
T
'x) x
In
f(x)
2
;
IE
2
N
/N
(x)
2
f(
T
•x)
+ n-o
A
A
N
.!�
2
A Je
f(x)
L:
IE
GROUPS AND STATISTICAL MECHANICS
55
1
I
N
'
l.i.m.
L
I
N
'
lim
L
+
E
n
L
E
™ �
56
entropy.
m n m
m n
57
A
B,
A
B,
B A.
58
In
In
69
III
Time Series, Information,
and Communication
60
decision. If
A
B,
a priori
A B
n
I I I
n
+
n
+
If
n
a priori
a posteriori
a posteriori
b)
ii
x
62
CYBERNETICS
+
a
posteo
3
=
1
L:
f
-
I I
1
=
I I
=
L:
J
s:
r:
J
L:
2
J
+
J
(-x
2
bb
+
w
b
w
+
b)]
J
[-½
2
(
a
�
2
2
(
a
f
!
b
64
+
y
+
J
+
+
2 0
g
2 X
:
I
(3.11)
+
(a
,
:
n
n
m
+
+
m
n
n
=
R
-
r:
r:
J
-
n
J
n
-
-
y
,•
y
J
m
Xn
)
Xn-
m
+I,
Xn
• • •,
T
+ )
< <
(-<<)
t)
f
+
+
O
68 CYBERNECS
y
=
oft
n
1
Xn Xn
tn,
S.
J:
X
f
-f
1
n
,1
n.
L
I
[
§' ]
�
If
(§')
A
,
k
i
X
J
1
2 n
L
L
n
q,
0
'
L
0
1
L
a)
t
a,
CYBERNETICS
=
.
=
oft
K
=
-
r:
K
(t)
y
)
y
)
=
=
f
f
'
if s
[
- � -
2
du
(
:
s:
]
]
2
= -
=
s:
=
J:
CYBERNETICS
Moreover,
f
l
•
J
o
_ +
=
L
ds
Tl,
Tn
r
:
+ =
represents a very important ensemble of time seri in the variable t,
y
.
=
ds
K(s
ds
T.
+
+
[f:
u:
[:
n
!�
{
f
f{
il
T
0
0
If"
T,
K(t) ds(t,
1
�,
[
J
o
n=O
n.
2
m
m
2
2
2
0
1
1
2
s: [i
2
1
'
2
2
1)
/2],
2
-
1
t
2
2
1
1
1
TIME SERIES, INFORMATION, AND COMMUNICATION
77
T,
K(t
1
,a)
-
2
1
, a)
T,
f: T,
i
: {H[G(A),
[H(u,
R(u)
R(G)
R(G)
=
G(a)
a
G,
y
2
}
1
J
:
n
n
n
n
t.
1
,
2
,
v
x
T
t;s
t,
CYBERNETICS
I
f
f
1
0
'
O
-t
n
L:
L
:
dW,
L:-A
J:
+ +
2
f/
A,
A
.C
l
f
f
f
w) A
T,
and the mean square error of prediction is
CYBERNETICS
f
+
f
+
0
s: s:
+
J
.'
r:
r:
2
I
0
I
2 -
I
f
2 -
2
will
Hence
f
error, is
y)
f
Jo
_
f
wave
lter. a l
a lea
d
.
CYBERNECS
f�
=
f
f
=
-
f
2
]
I
I
I
=
�
-
=
= =
l
=
f.
r:
f
A
(
A
(
A (
:
L
:
2
au
88
CYBERNETICS
n
in statistical equilibrium
0
N
,
+
0
N
N
N-
o
1
s·
n
w
lnw
d
w
2 -
n
-
1
n
-
G(w)
1
n
n
2
l
w
CYBERNETICS
(w)
n
n
J
'
L
µ
e(
µ
w
I etw(µ
-
�)
du
0
Is•
2
-
·
(
,-1
)
i
L
0
i
2
0
i
w
f
'
-
: N(n
dT
,
2
dTI'
f_.
If' I'
92
Ir
:
a,j'
1
In
In
TIME SERIES, INFORMATION, AND COMMUNICATION
93
0
94
CYBERNETICS
IV
Feedback and Oscillation
ataxia.
tabes dsalis.
95
96
CYBERNETICS
FEEDBACK AND OSCILLATION 97
98
CYBERNETICS
t,
t
t.
n
•
2
(4.01)
(4.02)
99
= f
+
= f
+
+
f
= f
+ f
a(x) = {-i
X
zt
ezt
=
0
+
+
=
+
+
+
+
iv
y
■
X
Y=X-AY
AY
�AY
Y,
X
A Y
Y = X -MY
A
AY
X
l + M
+
= -
+
iv
=
+
In
A
+
+ kiy
-ky
v=
+
2
2
u
z
+
v
2
u
(
1
:
u
+iv=
2
+
kiy
+
2
2
2
2
u
+
2
22
V
+
2
22
-
u + v
+ k'y')'
+
2
+
+
+
+
p p
2
p
+
t,
p½
=
cos
2
kzr
p
p
p
3 3
I
+
f
p
f
t•
A
T
A(z)
u
+ iv e-Tt T
y
T
y
+
+
+
+
3
2
2
2
+
3
,
3
2
dt
2
dt
3
2
y
u iide
1
z'
+
+
2
=
v,
y
to y
CYBERNETICS
A dA.
dA/A.
A
B=-
O+A
+ �)
0
I
+
A
dA
0
A
O
O
y
can
+
Dt
In
In
In
In
In
1
t
L
1
•"
+
L
+
-
l
1
-
w
-
&a.
+
hoostasis.
The Wisdom of Body,
The Fitness of te Environment,
V
Computing Machines
and the Nervous System
I
(2
1
-
N
I
=
I
=
x
N N
2
1I
N
2
1
/
N
=
+
+
+
n
CYBERNETICS
It
It
It
I
O I
O J
negation,
I
O O I; l
ical addition,
O I
0 0 I
I I I
l
ical multiplication,
0,
CYBERNETICS
neurons
s
y
napses.
mem,
1
22
tel
ph
type repeaters.
124
Peau de Cn,
1
machina ratiocinatrix calculus
ratiocinator
All logic is limited by the
limitations
of the human mind when it is engaged in that activity known
as l
ical thinking.
seems
n
n.
P n n
=
P P
P
1
265 (1936).
1
26
P
n for
aective tone.
128
FIG. 7
could
a po
132
VI
Gestalt and Universals
133
134
CYBERNETICS
GESTALT AND UNIVERSALS
135
136
CYBERNETICS
w
1
e
137
138
If
If A
A 0.
A
S
S Q(S), TS
S T Q(TS)
TS.
If
T,
f Q(TS) dT
S
139
S
Q(TS)
CYBERNETICS
Fto. 8
GESTALT AND UNIVERSALS
Gestalt.
1
1
43
VII
C
y
bernetics and Ps
y
chopatholog
y
fortiori
a
priori
9
145
In
If
146
As
148
deeper memories, nor indeed is a suciently malignant state of
The more violent of these involve a surgical intervention into the
conscienc e.
>
1
CYBERNETICS AND PSYCHOPATHOLOGY
151
152
CYBERNETICS
A
2
•
CYBERNETICS AND PSYCHOPATHOLOGY
153
a
154
CYBERNETICS
VIII
Information, Language,
and Society
156
CYBERNETICS
a priori
INFORMATION, LANGUAGE, ANn SOCIETY
157
158 CYBERNECS
ff
f f
f
This
CYBERNECS
that
INFORMATION, LANGUAGE, AND SOCIETY
161
162
CYBERNECS
163
specie
164
CYBERNETICS
aeternitatis.
Note
NOTE
165
PART II
SUPPLEMENTARY CHAPTERS
I 9 6 I
IX
On Learning
and Self-Reproducing Machines
169
170
1
will
1
72
3
174
CYBERNETICS
t
176
1
hine
self-propting
1
78
CYBERNETICS
1
Nlinear Problems in Random The
.
CYBERNETICS
X
Brain Waves
and Self-Organizing S
y
stems
y
182 CYBERNETICS
in
uo,
183
It
I.
f(t)
f(t f(t It
f(t
f(t
f(t)
l
184
1
A
j(t) j(t
=
(10.01)
1
A).
0.5
I
I
I
I
186
/(t) /(t +
f(t ) +
f(t +
Photometer
-
urce
y
f(t
2
,
CYBERNETICS
:
+
i
+
G(t) K
G(t) K
G(t)
+
K
1
K
2
,
K
1
K
2
,
w.
K
1
K
2
+
(2n
(2n
N;
T
28 ----------
24
20
16
! 12
< 8
=
SPECTRUM
CYBERNETICS
1
1
t
n
1
da f
f
1
n
0
-
Tk
T
T
a
TT
Ta T
a =
a
2
a
A
'
A
a = a
A-�
0
0
Acta Matmatica
=
2
+ T
I
J
T
-
Jim
a)
T
-T
+
T)
K(t
2
)
I
A
-
A
f
B
B
2
2
+
I
:
B
+
=
=
will
I
-
B
B
2
1
�
1
T
2
2
u)K(t
u)]
[
J
2
+
2
2
2
2
2
2
2
2
2
2
+
2
2
2
+
2
2
2
2
2
m
f
f
u)
u)
u)
u)
du
-
f
u)
u)
1/A
1/A,
J
!
f
u)
A
u)
f
J
!
f
!
f
2
j
20 _JI-�
CYBERNETICS
BRAIN WAVES AND SE-ORGANIZING SYSTEMS
199
I
1
2
201
CYBERNETICS
b je,
Index
ao
INDEX
8
148
INDEX
7
8
1
INDEX
182
210
444
211
212
