Cybernetics
or Control and Communication
in the Animal and the Machine

III. Time Series, Information, and Communication

III. Time Series, Information, and Communication

III. Time Series, Information, and Communication

Chapter III

(3.01)

Time Series, Information, and Communication

(3.02)

measure of ( a, b )
measure of ( 0, 1)

(3.03)

∫ f ( x) dx = 1
−∞

(3.04)

Chapter III

measure1 of the amount of information associated with the
curve f1(x) is
∞

∫ [log f ( x)] f ( x) dx
2

−∞

(3.05)

∞

∫ [log f ( x)] f ( x) dx = b − a log b − a = log b − a
2

−∞

(3.06)

(3.07)

∞

−∞

−∞

∫ dx ∫ dyf ( x, y ) = 1

(3.08)

and the amount of information is
∞

∞

−∞

−∞

∫ dx ∫ dyf ( x, y ) log f ( x, y )
1

(3.081)

Time Series, Information, and Communication

Note that f1(x, y) is of the form ϕ(x)ψ(y) and
∞

∞

−∞

−∞

∫ φ ( x) dx = ∫ ψ ( y ) dy = 1

(3.082)

then
∞

∞

−∞

−∞

∫ dx ∫ dyφ ( x) ψ ( y ) = 1

(3.083

and
∞

∞

−∞

−∞

∫ dx ∫ dyf ( x, y ) log f ( x, y )
1

∞

∞

−∞

−∞

(3.084)

= ∫ dxφ ( x ) log 2 φ ( x ) + ∫ dyψ ( y ) log 2 ψ ( y )

2π a , while a

variable v lies between the same two limits with a probability

exp ( − x2 2b ) dx

2π b . How much information do we gain con-

(3.09)

Chapter III

∫
2π [ab ( a + b )]

∞
−∞

{

}

(3.091)

∫

∞

−∞

This follows from the fact that

(3.10)

Time Series, Information, and Communication

(3.11)

∫ φ ( x) log φ ( x) dx
−∞

(3.12)

Chapter III

n

R

n

n

n

n

R

(3.13)

∫ dx
−∞

n − m +1

∞

∫ dxn f ( x1 ,  , xn )
−∞

(3.14)

∑ J  x

−1

f ( x1 ,  , xn )

(3.141)

Time Series, Information, and Communication

Chapter III

Time Series, Information, and Communication

( −∞ < λ < ∞ )

( −∞ < µ < ∞ )

(3.15)

(3.16)

Chapter III

an = ∫ e t t n f (t ) dt
−∞

(n = 0, 1, 2,)

(3.17)

Time Series, Information, and Communication

Chapter III

(2π )n t1 (t 2 − t1 ) (t n − t n−1 )

n

(3.18)

Time Series, Information, and Communication

∫ dα x (t , α ) x (t , α ) x (t , α )
1

= (2π )

−n

n

[t1 (t 2 − t1 ) (t n − t n−1 )]− 2
1

(3.19)

under the assumption that 0  t1    t n , Let us put

ξ1  ξn = ∑ Ak ξ1λk ,1 (ξ2 − ξ1 )λk ,2  (ξn − ξn −1 )λk ,n

(3.20)

where λk,1 + λk,2 + ··· + λk,n = n. The value of the expression in Eq.
3.19 will become

∑ A (2π )
k

−n2

t1λk ,1 (t 2 − t1 )λk ,2  (t n − t n −1 )λk ,n 

− 12

(3.21)

Chapter III

if every λk,j is even,
= ∑ Ak ∏ ( number of ways of dividing λk , j terms into pairs)
k

j

× (t j − t j −1 ) 2
1

= ∑ Ak ( numbers of ways of dividing n terms into pairs
k

whose elements both belong in the same group of

λk , j terms into which λ is separated ) × (t j − t j −1 ) 2
1

= ∑ Aj ∑ ∏ ∫ dα [ x (t k , α ) − x (t k −1 , α )][ x (t q , α ) − x (t q −1 , α )]
0

j

∫ dα x (t , α ) x (t , α ) x (t , α ) = ∑ ∏ ∫ dα x (t , α ) x (t , α )
0

n

j

k

ξ (t , α , β ) = x (t , α ) (t  0 )
ξ (t , α , β ) = x ( −t , β ) (t < 0 )

(3.23)

Time Series, Information, and Communication

α = .α1α 2  α n 

β = .β1β2  βn  

(3.24)

and to put

ξ (t , γ ) = ξ (t , α , β )

(3.25)

We now wish to define
∞

∫ K (t ) dξ (t , γ )

(3.26)

−∞

∞

−∞

−∞

∫ K (t ) dξ (t , γ ) = − ∫ K ′ (t ) ξ (t , γ ) dt

(3.27)

Under these circumstances, we have formally
1

∞

−∞

∞

∫ dγ ∫ K (t ) dξ (t , γ )∫ K (t ) dξ (t , γ )
1

−∞

∞

∞

−∞

−∞

= ∫ dγ ∫ K1 ′ (t ) ξ (t , γ ) dt ∫ K2 ′ (t ) ξ (t , γ ) dt
∞

∞

−∞

−∞

= ∫ K1 ′ ( s) ds ∫ K2 ′ (t ) dt ∫ ξ ( s, γ ) ξ (t , γ ) dγ
Now, if s and t are of opposite signs,

(3.28)

Chapter III

∫ ξ ( s, γ ) ξ (t , γ ) dγ = 0

(3.29)

while if they are of the same sign, and |s| < |t|,
1

∫ ξ ( s, γ ) ξ (t , γ ) dγ = ∫ x ( s , α ) x ( t , α ) dα
=

=

= s

(3.30)

Thus:
1

∞

−∞

∞

∫ dγ ∫ K (t ) dξ (t , γ )∫ K (t ) dξ (t , γ )
1

−∞

∞

s

∞

s

= − ∫ K1 ′ ( s) ds ∫ tK2 ′ (t ) dt − ∫ K2 ′ ( s) ds ∫ tK1 ′ (t ) dt
0

−∞

s

−∞

s

(3.31)

∞

−∞

−∞

= − ∫ sd [ K1 ( s) K2 ( s)] = ∫ K1 ( s) K2 ( s) ds
In particular,
1

∞

−∞

∞

∫ dγ ∫ K (t + τ ) dξ (t , γ )∫ K (t + τ ) dξ (t , γ )
∞

−∞

= ∫ K ( s) K ( s + τ 2 − τ1 ) ds
−∞

Moreover,

(3.32)

Time Series, Information, and Communication

n

∞

∫ dγ ∏ ∫ K (t + τ ) dξ (t , γ )
0

k

−∞

k =1

(3.33)

∞

= ∑ ∏ ∫ K ( s) K ( s + τ j − τ k ) ds
−∞

∫ K (t + τ ) dξ (τ , γ ) = f (t , γ )

(3.34)

−∞

Φ (τ ) = ∫ K ( s) K ( s + τ ) ds
−∞

(3.35)

∞

= ∫ K ( s + t ) K ( s + t + τ ) ds
−∞

(3.36)

n

(3.37)

it will consist of precisely the terms in
1

∞

−∞

m

∞

−∞

∫ dγ  ∫ K (t − τ ) dξ (t , γ ) ∫ dγ  ∫ K (t + σ − τ ) dξ (t , γ )

n

(3.38)

Chapter III

together with a finite number of terms involving as factors
powers of
∞

∫ K (σ + τ ) K (τ ) dτ

(3.39)

−∞

{∫  [f (t , γ )] dγ }

lim ∫  [ f (t , γ )]  [ f (t + σ , γ )] dγ =
σ →∞

(3.40)

∫  [ f (t , γ )] dγ = ∫ { [ f (t , γ )] dγ }

(3.41)

T

∫  [ f (t , γ )] dγ = lim T ∫  [ f (t , γ )] dt
0

T →∞

1 0
 [ f (t , γ )] dt
T →∞ T ∫− T

(3.42)

= lim

Time Series, Information, and Communication

1 0
f (t , γ ) f (t − τ , γ ) dt
T ∫− T

(3.43)

exp i ∫ K (t ) dξ (t , γ )
 −∞


(3.44)

Formally, this may be written
1

∞

in

∞

∫ dγ ∑ n !  ∫ K (t ) dξ (t , γ )
0

n=0

n

−∞

{
2 m! {

}
}

=∑

m

{ ∫ [ ( )] }

= exp −

1 ∞
K t
2 −∞

(3.45)

dt

Chapter III

b

∞

a

−∞

∫ dλ exp i ∫ K (t + τ , λ ) dξ (τ , γ )

(3.46)

∫ dγ exp {is [ξ (t , γ ) − ξ (t , γ )]}
1

∞

b

{

b

∞

}

∫ dλ exp − 2 ∫ [ K (t + τ , λ )] dt − iσ K (t , λ )
a

−∞

(3.48)

Let us take K(t1, λ) and a new independent variable µ and
solve for λ, obtaining

λ = Q (t1 , µ )

(3.49)

Then Expression 3.48 becomes
K (t1 ,b )

∫ ( ) e µσ d µ
i

K t1 ,a

(3.50)

(3.51)

{

∞

∫ dλ exp − 2 ∫ [ K (t + τ , λ )] dt
a

−∞

}

(3.52)

Time Series, Information, and Communication

as a function of K(t1, λ) and t1. That is, there is a known function
F(u, v), such that

{

λ

∞

}

∫ dλ exp − 2 ∫ [ K (t + τ , λ )] dt = F [ K (t , λ ) , t ]
a

−∞

(3.53)

(3.54)

(3.55)

(3.56)

Then the function

{ ∫ [ ( )] } ( )

exp −

1 ∞
H u, t
2 −∞i

dt = R u

(3.57)

(3.58)

(3.59)

or

λ=∫

dG
+ const = S (G ) + const
R (G )

(3.60)

Chapter III

This constant will be given by
G (a ) = 0

(3.61)

or
a = S ( 0 ) + const

(3.62)

{

b

∞

∫ dλ exp − 2 ∫ [ K (t , λ )] dt
a

−∞

}

(3.63)

with
1

b

∞

a

−∞

∫ dγ ∫ dλ exp i ∫ K (t , λ ) dξ (t , γ )

(3.64)

Time Series, Information, and Communication

∫ K (t + τ ) dξ (τ , γ )

(3.65)

−∞

sequence of zeros of ∫ K D (t + τ ) dξ (τ , γ ) from −∞ to ∞ will be
−∞

Chapter III

(3.66)

∫ K ( s) K ( s + t ) ds
−∞

(3.67)

Time Series, Information, and Communication

Here of course K is real.
Let us put
∞

K ( s) = ∫ k (ω ) e iω s dω
−∞

(3.68)

(3.69)

Thus a knowledge of Φ(τ) is tantamount to a knowledge of
k(ω)k(−ω). Since, however, K(s) is real,
∞

K ( s) = ∫ k (ω )e − iω s dω
−∞

(3.70)

(3.71)

1 ∞ F (u )
du
π ∫−∞ u − ω

(3.72)

Chapter III

∫ e λω d [ M (λ )]
i

(3.73)

(3.74)

f (t , γ ) = ∫ K (t + τ ) dξ (τ , γ )
−t

(3.75)

On the other hand, it can be shown that we may write 1/k(ω) in
the form
∞

lim ∫ e iλω dN n ( λ )
n→∞

(3.76)

where the Nn’s are properly determined; and that this can be
done in such a way that
τ

∞

−t

ξ (τ , γ ) = lim ∫ dt ∫ Q n (t + σ ) f (σ , γ ) dσ
n→∞

(3.77)

Here the Qn’s must have the formal property that
∞

∞

−t

−t

f (t , γ ) = lim ∫ K (t + τ ) dτ ∫ Q n (τ + σ ) f (σ , γ ) dσ
n→∞

(3.78)

In general, we shall have
∞

∞

−t

−t

ψ (t ) = lim ∫ K (t + τ ) dτ ∫ Q n (τ + σ ) ψ (σ ) dσ
n→∞

or if we write (as in Eq. 3.68)

(3.79)

Time Series, Information, and Communication

∞

K ( s) = ∫ k (ω ) e iω s dω
−∞
∞

Q n ( s) = ∫ qn (ω ) e iω s dω

(3.80)

−∞
∞

ψ ( s) = ∫ Ψ (ω ) e iω s dω
−∞

then

Ψ (ω ) = lim (2π ) 2 Ψ (ω ) qn ( −ω ) k (ω )
3

n→∞

(3.81)

Thus
lim qn ( −ω ) =
n→∞

(3.82)

(2π ) 2 k (ω )
3

K (t + A + τ ) dξ (τ , γ )
K (t + A + τ ) dξ (τ , γ )

(3.83)

∞

+ ∫ K (t + A + τ ) dξ (τ , γ )
−t

∫

t
−t − A

A

[ K (t + A + τ )]2 dτ = ∫0 [ K (τ )]2 dτ

(3.84)

Chapter III

∫ k (t + A + τ ) dξ (τ , γ )
−t

∞

∞

−t

−τ

= lim ∫ k (t + A + τ ) dτ ∫ Q n (τ + σ ) f (σ , γ ) dσ
n→∞

(3.85)

If we now put
kA (ω ) =

1 ∞
K (t + A) e − iωt dt
2π ∫0

(3.86)

and if we apply the operator of Eq. 3.85 to etωt, obtaining
∞

∞

−t

−τ

lim ∫ K (t + A + τ ) dτ ∫ Q n (τ + σ ) e iωσ dσ = A (ω ) e iγ wt
n→∞

(3.87)

we shall find out (somewhat as in Eq. 3.81) that
A (ω ) = lim (2π ) 2 qn ( −ω ) kA (ω )
3

n→∞

(3.88)

m (t ) + n(t ) = ∫ K (τ ) dξ (t − τ , γ )
0

(3.89)

and let the message be of the form
∞

∞

−∞

−∞

m (t ) = ∫ Q (τ ) dξ (t − τ , γ ) + ∫ R (τ ) dξ (t − τ , δ )

(3.90)

Time Series, Information, and Communication

∫ Q (τ + a ) dξ (t − τ , γ )

(3.901)

and the mean square error of prediction is
a

∞

∫ [ Q ( τ ) ] dτ + ∫ [ R ( τ ) ] dτ
2

−∞

(3.902)

−∞

Furthermore, let us suppose that we know the following
quantities:
1

φ22 (t ) = ∫ dγ ∫ dδ n (t + τ ) n (τ )
∞

= ∫ [ K ( t + τ ) − Q ( t + τ ) ] [ K ( τ ) − Q ( τ ) ] dτ
−∞
∞

= ∫ [ K ( t + τ ) − Q ( t + τ ) ] [ K ( τ ) − Q ( τ ) ] dτ
0

+ ∫ [ K ( t + τ ) − Q ( t + τ ) ] [ − Q ( τ ) ] dτ
−t

+∫

−t
−∞

(3.903)

∞

Q ( t + τ ) Q ( τ ) dτ + ∫ R ( t + τ ) R ( τ ) dτ
−∞

∞

∞

−t

= ∫ K ( t + τ ) K ( τ ) d τ − ∫ K ( t + τ ) Q ( τ ) dτ
∞

∞

−∞

−∞

+ ∫ Q ( t + τ ) Q ( τ ) dτ + ∫ R ( t + τ ) R ( τ ) dτ
1

φ11 (τ ) = ∫ dγ ∫ dδ m ( t + τ ) m (τ )
∞

∞

−∞

−∞

= ∫ Q ( t + τ ) Q ( τ ) dτ + ∫ R ( t + τ ) R ( τ ) d τ
1

(3.904)

φ12 (τ ) = ∫ dγ ∫ dδ m (t + τ ) n (τ )
1

= ∫ dγ ∫ dδ m (t + τ ) [ m (τ ) + n (τ )] − φ11 (τ )
1

∞

∞

−t

−t

= ∫ dγ ∫ K (σ + t ) dξ (τ − σ , γ )∫ Q (τ ) dξ (τ − σ , γ ) − φ11 (τ )
∞

= ∫ K (t + τ ) Q (τ ) dτ − φ11 (τ )
−t

(3.905)

Chapter III

The Fourier transforms of these three quantities are, respectively,

(3.907)

That is,

Φ11 (ω ) + Φ12 (ω ) + Φ12 (ω ) + Φ22 (ω ) = k (ω ) 2

(3.908)

and
q (ω ) k (ω ) = Φ11 (ω ) + Φ21 (ω )

(3.909)

Φ11 (ω ) + Φ21 (ω )
k (ω )

(3.910)

Hence
Q (t ) = ∫

∞
−∞

Φ11 (ω ) + Φ21 (ω ) iωt
e dω
k (ω )

(3.911)

and thus the best determination of m(t), with the least mean
square error, is

Time Series, Information, and Communication

(3.912)

∞

∞

−∞

∫ dξ (t − τ , γ ) ∫

(3.913)

∞

∫ [ R ( τ ) ] d τ = Φ ( 0 ) − ∫ [ Q ( τ ) ] dτ
2

−∞

−∞

=

=

(3.914)
and a part dependent on the lag:

a

Chapter III

a

∞

2
∫−∞ [Q (τ )] dt = ∫−∞ dt ∫−∞

Φ11 (ω ) + Φ21 (ω ) iωt
e dω
k (ω )

(3.915)

Φ12 (ω ) ≡ Φ21 (ω ) ≡ 0

(3.916)

(3.917)

∫ M (τ ) dξ (t − τ , γ )

(3.918)

−A

which we have when we know all values of
A

A

−A

−A

∫ M (τ ) dξ (t − τ , γ ) + ∫ N (τ ) dξ (t − τ , δ )

(3.919)

Time Series, Information, and Communication

 π nτ 
∫− A M (τ ) exp  i A  dτ
A

(3.920)

Thus, by Eq. 3.09, the total amount of information available
concerning M is
2

∞

∑ 2 log

 π nτ 
∫− A N (τ ) exp  i A  dτ
A

n =−∞

(3.921)

∞

∞

(3.922)

−∞

Chapter III

Time Series, Information, and Communication

φm = ∫ f m (α ) f 0 (α ) dα
0

(3.923)

φm = lim

1 N
∑0 f − k +m (α ) f − k (α )
N →∞ N + 1

= lim

for almost all α. Let us put

(3.924)

Chapter III

φn =

1 π
Φ (ω ) e inω dω
2π ∫−π

(3.925)

or
∞

Φ (ω ) = ∑ φn e − inω

(3.926)

−∞

(3.927)

and let
G (ω ) =

(3.928)

Let
e G(ω ) = k (ω )

(3.929)

(3.930)

If now we put for the best linear prediction of fn(α) with a lead
of ν
∞

∑ f ν (α ) Wν

(3.931)

n−

we shall find that
∞

∞

π

∑ Wµ e µω = 2π k (ω ) µ∑ν e ω (µ ν ) ∫ π k (u) e µ du
0

i

=

i

−

−

−i u

(3.932)

This is the analogue of Eq. 3.88. Let us note that if we put

Time Series, Information, and Communication

kµ =

1 π
k (u ) e − iµu du
2π ∫−π

(3.933)

then
∞

∞

∑ Wµ e

iµω

=e

∑ν kµ e µω

− iνω

i

∞

∑ kµ e µω

i

(3.934)

(3.935)

Then Eq. 3.934 becomes
∞



ν −1

∞



∑ Wµ e µω = e νω 1 − ∑ kµ e µω ∑ qλ e λω 
i

−i

i

i

(3.936)

In particular, if ν = 1,
∞



∞



∑ Wµ e µω = e ω 1 − k ∑ qλ e λω 
i

−i

i

(3.937)

or
Wµ = − qλ +1k0

(3.938)

Thus for a prediction one step ahead, the best value for fn+1(α) is
∞

− k0 ∑ qλ +1 f n − λ (α )
0

(3.939)

Chapter III

f n (α ) = ∫ K ( n − τ ) dξ (τ , α )
−∞

(3.940)

(3.941)

∫ M (n − τ ) dξ (t , γ )
−∞

(3.942)

in the presence of a noise
∞

∫ N (n − τ ) dξ (t , δ )
−∞

(3.943)

when γ and δ are independent, will be the precise analogue of
Expression 3.922, namely,

Time Series, Information, and Communication

∞

∞

(3.944)

−∞

where over (−π, π),
∞

∫ M ( τ ) e τ dτ
iu

−∞

(3.945)

represents the power distribution of the message in frequency,
and
∞

∫ N ( τ ) e τ dτ
iu

−∞

(3.946)

Chapter III

Time Series, Information, and Communication

Chapter III

IV Feedback and Oscillation

V. Computing Machines and the Nervous System

V. Computing Machines and the Nervous System

V. Computing Machines and the Nervous System

▶

1 1 1 ν1 + 2 ν 2 + + ν n + 2 2 2n

(1/2)ν₁ + (1/2²)ν₂ + ... + (1/2ⁿ)νₙ + ...

(5.07)

ν = ν0 +

▶

where every νn is either 1 or 0. There exist at present two great types of computing machines: those like the Bush differential analyzer,1 which are known as analogy machines, where the data are represented by measurements on some continuous scale, so that the accuracy of the machine is determined by the accuracy of construction of the scale; and those, like the ordinary desk adding and multiplying machine, which we call numerical machines, where the data are represented by a set of choices among a number of contingencies, and the accuracy is determined by the sharpness with which the contingencies are distinguished, the number of alternative contingencies presented at every choice, and the number of choices given. We see that for highly accurate work, at any rate, the numerical machines are preferable, and above all, those numerical machines constructed on the binary scale, in which the number of alternatives presented at each choice is two.

其中每个νₙ是1或0。目前存在两种主要类型的计算机：那些

▶

Our use of machines on the decimal scale is conditioned merely by the historical accident that the scale of ten, based on our fingers and thumbs, was already in use when the Hindus made the great discovery of the importance of the zero and the advantage of a positional system of notation. It is worth retaining when a large part of the work done with the aid of the machine consists in transcribing onto the machine numbers in the conventional decimal form, and in taking off the machine numbers which must be written in the same conventional form. This is, in fact, the use of the ordinary desk computing machine, as employed in banks, in business offices, and in many statistical laboratories.

我们在十进制刻度上使用机器仅仅是出于历史偶然，即人类

▶

It is not the way that the larger and

这不是较大和

Chapter V

▶

more automatic machines are best to be employed; in general, any computing machine is used because machine methods are faster than hand methods. In any combined use of means of computation, as in any combination of chemical reactions, it is the slowest which gives the order of magnitude of the time constants of the entire system. It is thus advantageous, as far as possible, to remove the human element from any elaborate chain of computation and to introduce it only where it is absolutely unavoidable, at the very beginning and the very end.

更自动化的机器的最佳使用方式；一般来说，使用任何计算机是因为

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Under these conditions, it pays to have an instrument for the change of the scale of notation, to be used initially and finally in the chain of computations, and to perform all intermediate processes on the binary scale. The ideal computing machine must then have all its data inserted at the beginning, and must be as free as possible from human interference to the very end. This means that not only must the numerical data be inserted at the beginning, but also all the rules for combining them, in the form of instructions covering every situation which may arise in the course of the computation.

在这些条件下，值得拥有一个用于改变数制刻度的仪器，

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Thus the computing machine must be a logical machine as well as an arithmetic machine and must combine contingencies in accordance with a systematic algorithm. While there are many algorithms which might be used for combining contingencies, the simplest of these is known as the algebra of logic par excellence, or the Boolean algebra. This algorithm, like the binary arithmetic, is based on the dichotomy, the choice between yes and no, the choice between being in a class and outside.

因此计算机必须是逻辑机器也是算术机器，并且必须结合

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The reasons for its superiority to other systems are of the same nature as the reasons for the superiority of the binary arithmetic over other arithmetics.

它优于其他系统的原因与二进制优于其他系统的原因性质相同。

Computing Machines and the Nervous System

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Thus all the data, numerical or logical, put into the machine are in the form of a set of choices between two alternatives, and all the operations on the data take the form of making a set of new choices depend on a set of old choices. When I add two one-­digit numbers, A and B, I obtain a two-­digit number commencing with 1, if A and B are both 1, and otherwise with 0. The second digit is 1 if A ≠ B, and is otherwise 0.

因此，所有输入机器的数据，无论是数字的还是逻辑的，都采取在几个可能性之间进行选择的形式。

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The addition of numbers of more than one digit follows similar but more complicated rules. Multiplication in the binary system, as in the decimal, may be reduced to the multiplication table and the addition of numbers, and the rules for multiplication for binary numbers take on the peculiarly simple form given by the table × 0 1 0 0 0 1 0 1

多位数字的加法遵循类似但更复杂的规则。乘法

(5.08)

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Thus multiplication is simply a method to determine a set of new digits when old digits are given. On the logical side, if O is a negative and I a positive decision, every operator can be derived from three: negation, which transforms I into O and O into I; logical addition, with the table ⊕ O I O O I I I I

因此乘法只是一种在给定旧数字时确定一组新数字的方法。

(5.09)

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and logical multiplication, with the same table as the numerical multiplication of the (1, 0) system, namely,  O I O O O I O I

以及逻辑乘法，使用与(1, 0)系统的数值乘法相同的真值表。

(5.10)

Chapter V

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That is, every contingency which may arise in the operation of the machine simply demands a new set of choices of contingencies I and O, depending according to a fixed set of rules on the decisions already made. In other words, the structure of the machine is that of a bank of relays, capable each of two conditions, say "on" and "off"; while at each stage the relays assume each a position dictated by the positions of some or all the relays of the bank at a previous stage of operation. These stages of operation may be definitely "clocked" from some central clock or clocks, or the action of each relay may be held up until all the relays which should have acted earlier in the process have gone through all the steps called for.

也就是说，机器运行中可能出现的每一种情况只需要一组新的

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The relays used in a computing machine may be of very varied character. They may be purely mechanical, or they may be electro-­mechanical, as in the case of a solenoidal relay, in which the armature will remain in one of two possible positions of equilibrium until an appropriate impulse pulls it to the other side. They may be purely electrical systems with two alternative positions of equilibrium, either in the form of gas-­filled tubes, or, what is much more rapid, in the form of high-­vacuum tubes.

计算机中使用的继电器可以是各种类型的。它们可以是纯机械的。

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The two possible states of a relay system may both be stable in the absence of outside interference, or only one may be stable, while the other is transitory. Always in the second case and generally in the first case, it will be desirable to have special apparatus to retain an impulse which is to act at some future time, and to avoid the clogging up of the system which will ensue if one of the relays does nothing but repeat itself indefinitely. However, we shall have more to say concerning this question of memory later.

继电器系统的两种可能状态在没有外部干扰时都可以是稳定的。

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It is a noteworthy fact that the human and animal nervous systems, which are known to be capable of the work of a

值得注意的是，已知能够进行

Computing Machines and the Nervous System

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computation system, contain elements which are ideally suited to act as relays. These elements are the so-­called neurons or nerve cells. While they show rather complicated properties under the influence of electrical currents, in their ordinary physiological action they conform very nearly to the "all-­or-­none" principle; that is, they are either at rest, or when they "fire" they go through a series of changes almost independent of the nature and intensity of the stimulus.

计算的人体和动物神经系统包含理想地适合用作继电器的元素。这些元素就是

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There is first an active phase, transmitted from one end to the other of the neuron with a definite velocity, to which there succeeds a refractory period during which the neuron is either incapable of being stimulated, or at any rate is not capable of being stimulated by any normal, physiological process. At the end of this effective refractory period, the nerve remains inactive, but may be stimulated again into activity. Thus the nerve may be taken to be a relay with essentially two states of activity: firing and repose.

首先有一个活动阶段，以确定的速度从神经元的一端传递到另一端。

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Leaving aside those neurons which accept their messages from free endings or sensory end organs, each neuron has its message fed into it by other neurons at points of contact known as synapses. For a given outgoing neuron, these vary in number from a very few to many hundred. It is the state of the incoming impulses at the various synapses, combined with the antecedent state of the outgoing neuron itself, which determines whether it will fire or not.

除了那些从游离末梢或感觉末梢器官接收信息的神经元外，每个

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If it is neither firing nor refractory, and the number of incoming synapses which "fire" within a certain very short fusion interval of time exceeds a certain threshold, then the neuron will fire after a known, fairly constant synaptic delay. This is perhaps an oversimplification of the picture: the "threshold" may not depend simply on the number of synapses but on their "weight" and their geometrical relations to one another with respect to the neuron into which they feed; and

如果它既不在发放中也不在不应期中，并且在某个短时间内接收到的"发放"的传入突触数量超过

Chapter V

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there is very convincing evidence that there exist synapses of a different nature, the so-­called "inhibitory synapses," which either completely prevent the firing of the outgoing neuron or at any rate raise its threshold with respect to stimulation at the ordinary synapses. What is pretty clear, however, is that some definite combinations of impulses on the incoming neurons having synaptic connections with a given neuron will cause it to fire, while others will not cause it to fire. This is not to say that there may not be other, non-­neuronic influences, perhaps of a humoral nature, which produce slow, secular changes tending to vary that pattern of incoming impulses which is adequate for firing.

有非常令人信服的证据表明存在性质不同的突触，即所谓的"抑制性"

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A very important function of the nervous system, and, as we have said, a function equally in demand for computing machines, is that of memory, the ability to preserve the results of past operations for use in the future. It will be seen that the uses of the memory are highly various, and it is improbable that any single mechanism can satisfy the demands of all of them. There is first the memory which is necessary for the carrying out of a current process, such as a multiplication, in which the intermediate results are of no value once the process is completed, and in which the operating apparatus should then be released for further use.

神经系统的一个非常重要的功能，也是——正如我们所说——同样需要的功能

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Such a memory should record quickly, be read quickly, and be erased quickly. On the other hand, there is the memory which is intended to be part of the files, the permanent record, of the machine or the brain, and to contribute to the basis of all its future behavior, at least during a single run of the machine. Let it be remarked parenthetically that an important difference between the way in which we use the brain and the machine is that the machine is intended for many successive runs, either with no reference to each other, or with a

这样的记忆应该能快速记录、快速读取和快速擦除。另一方面，

Computing Machines and the Nervous System

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minimal, limited reference, and that it can be cleared between such runs; while the brain, in the course of nature, never even approximately clears out its past records. Thus the brain, under normal circumstances, is not the complete analogue of the computing machine but rather the analogue of a single run on such a machine. We shall see later that this remark has a deep significance in psychopathology and in psychiatry.

记忆最小，引用有限，并且可以在两次运行之间清除；而人脑在

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To return to the problem of memory, a very satisfactory method for constructing a short-time memory is to keep a sequence of impulses traveling around a closed circuit until this circuit is cleared by intervention from outside. There is much reason to believe that this happens in our brains during the retention of impulses, which occurs over what is known as the specious present. This method has been imitated in several devices which have been used in computing machines, or at least suggested for such a use.

回到记忆问题，构建短期记忆的一个非常令人满意的方法是

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There are two conditions which are desirable in such a retentive apparatus: the impulse should be transmitted in a medium in which it is not too difficult to achieve a considerable time lag; and before the errors inherent in the instrument have blurred it too much, the impulse should be reconstructed in a form as sharp as possible. The first condition tends to rule out delays produced by the transmission of light, or even, in many cases, by electric circuits, while it favors the use of one form or another of elastic vibrations; and such vibrations have actually been employed for this purpose in computing machines. If electric circuits are used for delay purposes, the delay produced at every stage is relatively short; or, as in all pieces of linear apparatus, the deformation of the message is cumulative and very soon becomes intolerable.

这种保持装置有两个理想条件：脉冲应该被传递

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To avoid this, a second consideration comes into play; we must insert somewhere in the cycle a relay which does not serve to repeat the form

为了避免这一点，我们需要考虑第二个因素；我们必须在中某处插入一个继电器

Chapter V

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of the incoming message but rather to trigger off a new message of prescribed form. This is done very easily in the nervous system, where indeed all transmission is more or less of a trigger phenomenon. In the electrical industry, pieces of apparatus for this purpose have long been known and have been used in connection with telegraph circuits.

不是触发新的传入消息，而是触发一个规定形式的新消息。这是通过

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They are known as telegraph-­type repeaters. The great difficulty of using them for memories of long duration is that they have to function without a flaw over an enormous number of consecutive cycles of operation. Their success is all the more remarkable: in a piece of apparatus designed by Mr.

它们被称为电报式转发器。将它们用于长时间记忆的主要困难是

▶

Williams of the University of Manchester, a device of this sort with a unit delay of the order of a hundredth of a second has continued in successful operation for several hours. What makes this more remarkable is that this apparatus was not used merely to preserve a single decision, a single "yes" or "no," but a matter of thousands of decisions. Like other forms of apparatus intended to retain a large number of decisions, this works on the scanning principle.

曼彻斯特大学的威廉姆斯，这种装置的单元延迟约为

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One of the simplest modes of storing information for a relatively short time is as the charge on a condenser; and when this is supplemented by a telegraph-­type repeater, it becomes an adequate method of storage. To use to the best advantage the circuit facilities attached to such a storage system, it is desirable to be able to switch successively and very rapidly from one condenser to another. The ordinary means of doing this involve mechanical inertia, and this is never consistent with very high speeds.

最简单的一种相对短时间的信息存储方式是电容器上的电荷。

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A much better way is the use of a large number of condensers, in which one plate is either a small piece of metal sputtered into a dielectric, or the imperfectly insulating surface of the dielectric itself, while one of the connectors to these condensers is a pencil of cathode rays moved by the condensers and magnets of a

更好的方法是使用大量电容器，其中一块极板要么是一个小点

Computing Machines and the Nervous System

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sweep circuit over a course like that of a plough in a ploughed field. There are various elaborations of this method, which indeed was employed in a somewhat different way by the Radio Corporation of America before it was used by Mr. Williams.

扫描电路沿着类似于犁过的田地的路径行进。有多种精化方法。

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These last-­named methods for storing information can hold a message for quite an appreciable time, if not for a period comparable with a human lifetime. For more permanent records, there is a wide variety of alternatives among which we can choose. Leaving out such bulky, slow, and unerasable methods as the use of punched cards and punched tape, we have magnetic tape, together with its modern refinements, which have largely eliminated the tendency of messages on this material to spread; phosphorescent substances; and above all, photography.

这些最后提到的信息存储方法可以在相当长的时间内保持信息，

▶

Photography is indeed ideal for the permanence and detail of its records, ideal again from the point of view of the shortness of exposure needed to record an observation. It suffers from two grave disadvantages: the time needed for development, which has been reduced to a few seconds, but is still not small enough to make photography available for a short-­time memory; and (at present [1947]) the fact that a photographic record is not subject to rapid erasure and the rapid implanting of a new record. The Eastman people have been working on just these problems, which do not seem to be necessarily insoluble, and it is possible that by this time they have found the answer.

摄影对于其记录的持久性和细节来说确实是理想的，从角度来看也是理想的

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Very many of the methods of storage of information already considered have an important physical element in common. They seem to depend on systems with a high degree of quantum degeneracy, or, in other words, with a large number of modes of vibration of the same frequency. This is certainly true in the case of ferromagnetism, and is also true in the case of materials with an exceptionally high dielectric constant, which are thus

已经讨论的许多信息存储方法具有一个重要的物理元素

Chapter V

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especially valuable for use in condensers for the storage of information. Phosphorescence as well is a phenomenon associated with a high quantum degeneracy, and the same sort of effect makes its appearance in the photographic process, where many of the substances which act as developers seem to have a great deal of internal resonance. Quantum degeneracy appears to be associated with the ability to make small causes produce appreciable and stable effects.

对于用于信息存储的电容器尤其有价值。磷光同样也是

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We have already seen in Chapter II that substances with high quantum degeneracy appear to be associated with many of the problems of metabolism and reproduction. It is probably not an accident that here, in a non-­living environment, we find them associated with a third fundamental property of living matter: the ability to receive and organize impulses and to make them effective in the outer world. We have seen in the case of photography and similar processes that it is possible to store a message in the form of a permanent alteration of certain storage elements.

我们在第二章中已经看到，具有高量子简并度的物质似乎与新陈代谢和生殖的许多问题有关。

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In reinserting this information into the system, it is necessary to cause these changes to affect the messages going through the system. One of the simplest ways to do this is to have, as the storage elements which are changed, parts which normally assist in the transmission of messages, and of such a nature that the change in their character due to storage affects the manner in which they will transport messages for the entire future. In the nervous system, the neurons and the synapses are elements of this sort, and it is quite plausible that information is stored over long periods by changes in the thresholds of neurons, or, what may be regarded as another way of saying the same thing, by changes in the permeability of each synapse to messages.

在将这个信息重新插入系统时，需要使这些改变影响通过系统的消息。

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Many of us think, in the absence of a better explanation of the phenomenon, that the storage of information in the brain can actually occur in this

我们中的许多人认为，在没有更好的现象解释的情况下，大脑中的信息存储实际上可以以这种方式发生。

Computing Machines and the Nervous System

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It is conceivable for such a storage to take place either by the opening of new paths or by the closure of old ones. Apparently it is adequately established that no neurons are formed in the brain after birth. It is possible, though not certain, that no new synapses are formed, and it is a plausible conjecture that the chief changes of thresholds in the memory process are increased.

可以设想这种存储可以通过打开新通路或关闭旧通路来实现。显然已经充分确定，出生后大脑中没有新的神经元形成。

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If this is the case, our whole life is on the pattern of Balzac's Peau de Chagrin, and the very process of learning and remembering exhausts our powers of learning and remembering until life itself squanders our capital stock of power to live. It may well be that this phenomenon does occur. This is a possible explanation for a sort of senescence.

如果是这样的话，我们的整个生命就是巴尔扎克《驴皮记》的模式，学习和记忆的过程本身就耗尽了我们的学习和记忆能力，直到生命本身耗尽了我们生活的资本储备。这种情况很可能确实存在。这是对某种衰老的一种可能解释。

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The real phenomenon of senescence, however, is much too complicated to be explained in this way alone. We have already spoken of the computing machine, and consequently the brain, as a logical machine. It is by no means trivial to consider the light cast on logic by such machines, both natural and artificial.

然而，真正的衰老现象过于复杂，不能仅用这种方式解释。我们已经谈到计算机——以及因此大脑——作为逻辑机器。

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Here the chief work is that of Turing.2 We have said before that the machina ratiocinatrix is nothing but the calculus ratiocinator of Leibniz with an engine in it; and just as modern mathematical logic begins with this calculus, so it is inevitable that its present engineering development should cast a new light on logic. The science of today is operational; that is, it considers every statement as essentially concerned with possible experiments or observable processes. According to this, the study of logic must reduce to the study of the logical machine, whether nervous or mechanical, with all its non-­removable limitations and imperfections.

这里的主要工作是图灵的。² 我们之前说过，推理机器无非是莱布尼茨的推理演算加上了一个引擎；正如现代数理逻辑始于这个演算，它当前的工程发展必然给逻辑带来新的启示。今天的科学是操作性的；也就是说，它将每个陈述视为本质上涉及可能的实验或可观察的过程。

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It may be said by some readers that this reduces logic to psychology, and that the two sciences are observably and demonstrably different. This is true in the sense that many psychological states and sequences of thought do not conform to the canons

有些读者可能会说，这将逻辑还原为心理学，而这两门科学显然是不同的。这在某种意义上是正确的，因为许多心理状态和思维序列并不符合

Chapter V

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of logic. Psychology contains much that is foreign to logic, but--and this is the important fact--­any logic which means anything to us can contain nothing which the human mind--­and hence the human nervous system--­is unable to encompass. All logic is limited by the limitations of the human mind when it is engaged in that activity known as logical thinking.

逻辑的规范。心理学包含许多与逻辑无关的东西，但——重要的是——任何对我们有意义的逻辑都不能包含人类心智——从而人类神经系统——无法容纳的东西。所有逻辑都受到人类心智在进行所谓逻辑思维活动时的局限性的限制。

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For example, we devote much of mathematics to discussions involving the infinite, but these discussions and their accompanying proofs are not infinite in fact. No admissible proof involves more than a finite number of stages. It is true, a proof by mathematical induction seems to involve an infinity of stages, but this is only apparent.

例如，我们将数学的大部分用于涉及无穷的讨论，但这些讨论及其伴随的证明实际上并不是无穷的。没有可接受的证明涉及无限多个步骤。诚然，数学归纳法的证明似乎涉及无穷多个步骤，但这只是表面现象。

▶

In fact, it involves just the following stages: 1. Pn is a proposition involving the number n. 2. Pn has been proved for n = 1. 3.

事实上，它只包括以下步骤：1. Pₙ是涉及数n的命题。2. Pₙ已对n=1得证。3.

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If Pn is true, Pn+1 is true. 4. Therefore, Pn is true for every positive integer n. It is true that somewhere in our logical assumptions there must be one which validates this argument.

如果Pₙ为真，则P_{n+1}为真。4. 因此，Pₙ对每个正整数n都为真。诚然，在我们的逻辑假设中，必须有一个能够验证这个论证。

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However, this mathematical induction is a far different thing from complete induction over an infinite set. The same thing is true of the more refined forms of mathematical induction, such as transfinite induction, which occur in certain mathematical disciplines. Thus some very interesting situations arise, in which we may be able--­with enough time and enough computational aids--­to prove every single case of a theorem Pn; but if there is no systematic way of subsuming these proofs under a single argument independent of n, such as we find in mathematical induction, it may be impossible to prove Pn for all n.

然而，这种数学归纳法与对无穷集合的完全归纳法截然不同。同样的道理也适用于更精细的数学归纳形式，如出现在某些数学学科中的超限归纳。因此出现了一些非常有趣的情况，在这种情况下，我们也许能够——

▶

This contingency is

这种偶然情况是

Computing Machines and the Nervous System

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recognized in what is known as metamathematics, the discipline so brilliantly developed by Gödel and his school. A proof represents a logical process which has come to a definitive conclusion in a finite number of stages. However, a logical machine following definite rules need never come to a conclusion.

在所谓的元数学中得到了认识，这门学科由哥德尔及其学派卓越地发展起来。一个证明代表了一个在有限步数内达到确定结论的逻辑过程。然而，遵循确定规则的逻辑机器可能永远达不到结论。

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It may go on grinding through different stages without ever coming to a stop, either by describing a pattern of activity of continually increasing complexity, or by going into a repetitive process like the end of a chess game in which there is a continuing cycle of perpetual check. This occurs in the case of some of the paradoxes of Cantor and Russell. Let us consider the class of all classes which are not members of themselves.

它可能在不同的阶段中持续运行而永不停止，要么描述一个不断增加复杂性的活动模式，要么进入一个重复过程，就像棋局中循环照将的局面永不结束。这在康托尔和罗素的一些悖论中有所体现。让我们考虑所有那些不是自身成员的类的类。

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Is this class a member of itself? If it is, it is certainly not a member of itself; and if it is not, it is equally certainly a member of itself. A machine to answer this question would give the successive temporary answers: "yes," "no," "yes," "no," and so on, and would never come to equilibrium.

这个类是不是自身的成员？如果是，它当然不是自身的成员；如果不是，它同样当然是自身的成员。回答这个问题的机器会给出连续的临时答案："是"、"否"、"是"、"否"，永达不到平衡。

▶

Bertrand Russell's solution of his own paradoxes was to affix to every statement a quantity, the so-­called type, which serves to distinguish between what seems to be formally the same statement, according to the character of the objects with which it concerns itself--­whether these are "things," in the simplest sense, classes of "things," classes of classes of "things," etc. The method by which we resolve the paradoxes is also to attach a parameter to each statement, this parameter being the time at which it is asserted. In both cases, we introduce what we may call a parameter of uniformization, to resolve an ambiguity which is simply due to its neglect.

伯特兰·罗素解决他自己悖论的方法是为每个陈述附加一个量——所谓的类型——它根据陈述所涉及的对象的特征来区分形式上相同的陈述——无论这些对象是"事物"、事物的类、事物的类的类等等。我们解决悖论的方法也是为每个陈述附加一个参数，这个参数就是它被断言的时间。

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We thus see that the logic of the machine resembles human logic, and, following Turing, we may employ it to throw light on human logic. Has the machine a more eminently human

因此我们看到机器的逻辑类似于人类的逻辑，并且遵循图灵，我们可以用它来阐明人类逻辑。机器是否有更突出的人类

Chapter V

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characteristic as well--­the ability to learn? To see that it may well have even this property, let us consider two closely related notions: that of the association of ideas and that of the conditioned reflex. In the British empirical school of philosophy, from Locke to Hume, the content of the mind was considered to be made up of certain entities known to Locke as ideas, and to the later authors as ideas and impressions.

特征——学习的能力？为了说明它甚至可能具有这一性质，让我们考虑两个密切相关的概念：联想和条件反射。在英国经验主义哲学流派中，从洛克到休谟，心灵的内容被认为是由某些实体构成的，洛克称之为观念，后来的作者则称之为观念和印象。

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The simple ideas or impressions were supposed to exist in a purely passive mind, as free from influence on the ideas it contained as a clean blackboard is on the symbols which may be written on it. By some sort of inner activity, hardly worthy to be called a force, these ideas were supposed to unite themselves into bundles, according to the principles of similarity, contiguity, and cause and effect. Of these principles, perhaps the most significant was contiguity: ideas or impressions which had often occurred together in time or in space were supposed to have acquired the ability of evoking one another, so that the presence of any one of them would produce the entire bundle.

简单的观念或印象被认为存在于纯粹被动的心灵中，就像干净的黑板对可能写在它上面的符号一样不受影响。通过某种内在的活动——几乎不能称之为力——这些观念据称按照相似性、接近性和因果性的原则将自己组合成束。在这些原则中，也许最重要的是接近性：

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In all this there is a dynamics implied, but the idea of a dynamics had not yet filtered through from physics to the biological and psychological sciences. The typical biologist of the eighteenth century was Linnaeus, the collector and classifier, with a point of view quite opposed to that of the evolutionists, the physiologists, the geneticists, the experimental embryologists of the present day. Indeed, with so much of the world to explore, the state of mind of the biologists could hardly have been different.

在这一切中隐含着一个动力学概念，但动力学的概念尚未从物理学渗透到生物和心理学科学中。十八世纪的典型生物学家是林奈——收集者和分类者——其观点与今天的进化论者、生理学家、遗传学家、实验胚胎学家截然相反。

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Similarly, in psychology, the notion of mental content dominated that of mental process. This may well have been a survival of the scholastic emphasis on substances, in a world in which the noun was hypostasized and the verb carried

同样，在心理学中，心理内容的概念主导了心理过程的概念。这很可能是在一个名词被实体化而动词几乎毫无重量的世界中，经院哲学强调实体的残余。

Computing Machines and the Nervous System

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little or no weight. Nevertheless, the step from these static ideas to the more dynamic point of view of the present day, as exemplified in the work of Pavlov, is perfectly clear. Pavlov worked much more with animals than with men, and he reported visible actions rather than introspective states of mind.

几乎没有分量。然而，从这些静态观念到今天以巴甫洛夫的工作为代表的更动态的视角，这一步是清晰可见的。巴甫洛夫更多地研究动物而不是人类，他报告的是可见的行为而不是内省的心理状态。

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He found in dogs that the presence of food causes the increased secretion of saliva and of gastric juice. If then a certain visual object is shown to dogs in the presence of food and only in the presence of food, the sight of this object in the absence of food will acquire the property of being by itself able to stimulate the flow of saliva or of gastric juice. The union by continguity which Locke had observed introspectively in the case of ideas now becomes a similar union of patterns of behavior.

他在狗身上发现，食物的存在会引起唾液和胃液分泌的增加。如果某种视觉对象在食物存在时——且仅在食物存在时——呈现给狗，那么即使没有食物，这个对象的视觉本身也会获得刺激唾液或胃液流动的能力。洛克在内省中观察到的观念的接近性联合，现在变成了行为模式的类似联合。

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There is one important difference, however, between the point of view of Pavlov and that of Locke, and it is precisely due to this fact that Locke considers ideas and Pavlov patterns of action. The responses observed by Pavlov tend to carry a process to a successful conclusion or to avoid a catastrophe. Salivation is important for deglutition and for digestion, while the avoidance of what we should consider a painful stimulus tends to protect the animal from bodily injury.

然而，巴甫洛夫和洛克的观点有一个重要的区别，而这恰恰是因为洛克考虑的是观念而巴甫洛夫考虑的是行动模式。巴甫洛夫观察到的反应倾向于将过程引向成功的完成或避免灾难。唾液分泌对于吞咽和消化很重要，而避免我们认为是痛苦刺激的事物则保护动物免受身体伤害。

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Thus there enters into the conditioned reflex something that we may call affective tone. We need not associate this with our own sensations of pleasure and pain, nor need we in the abstract associate it with the advantage of the animal. The essential thing is this: that affective tone is arranged on some sort of scale from negative "pain" to positive "pleasure"; that for a considerable time, or permanently, an increase in affective tone favors all processes in the nervous system that are under way at the time and gives them a secondary power to increase affective tone; and that a decrease in affective tone

因此，条件反射中引入了一种我们可以称为情感色调的东西。我们不必将此与我们自己的快乐和痛苦的感觉联系起来，也不必在抽象的意义上将其与动物的利益联系起来。关键之处在于：情感色调是在从消极的"痛苦"到积极的"快乐"的某种尺度上安排的；

Chapter V

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tends to inhibit all processes under way at the time and gives them a secondary ability to decrease affective tone. Biologically speaking, of course, a greater affective tone must occur predominantly in situations favorable for the perpetuation of the race, if not the individual, and a smaller affective tone in situations which are unfavorable for this perpetuation, if not disastrous. Any race not conforming to this requirement will go the way of Lewis Carroll's Bread-­and-­Butter Fly, and always die.

倾向于抑制当时正在进行的所有过程，并赋予它们降低情感色调的次级能力。从生物学上讲，当然，更高的情感色调必须主要出现在有利于种族延续——即使不是个体延续——的情境中，而更低的情感色调则出现在不利于这种延续的情境中。任何不符合这一要求的种族都将走上刘易斯·卡罗尔的黄油面包蝇的道路，最终灭绝。

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Nevertheless, even a doomed race may show a mechanism valid so long as the race lasts. In other words, even the most suicidal apportioning of affective tone will produce a definite pattern of conduct. Note that the mechanism of affective tone is itself a feedback mechanism.

然而，即使是一个注定灭绝的种族，也可能显示出在其存续期间有效的机制。换句话说，即使是最自杀式的情感色调分配方式也会产生确定的行动模式。注意，情感色调的机制本身就是一个反馈机制。

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It may even be given a diagram such as shown in Fig. 7. Here the totalizer for affective tone combines the affective tones given by the separate affective-­tone mechanisms over a short interval in the past, according to some rule which we need not specify now. The leads back to the individual affective-­tone

它甚至可以有如图7所示的图示。这里情感色调总加器根据某个我们无需详细说明的规则，将过去一个短时间间隔内各个情感色调机制给出的情感色调结合起来。

Fig. 7

Computing Machines and the Nervous System

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mechanisms serve to modify the intrinsic affective tone of each process in the direction of the output of the totalizer, and this modification stands until it is modified by later messages from the totalizer. The leads back from the totalizer to the process mechanisms serve to lower thresholds if the total affective tone is increasing, and to raise them if the total affective tone is decreasing. They likewise have a longtime effect, which endures until it is modified by another impulse from the totalizer.

反馈线用于将每个过程的固有情感色调朝着总加器输出的方向修改，这种修改一直保持到被总加器后来的消息再次修改。从总加器到过程机制的反馈线用于在总情感色调增加时降低阈值，在总情感色调减少时提高阈值。它们同样具有长期效应，持续到被来自总加器的另一个脉冲再次修改。

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This lasting effect, however, is confined to those processes actually in being at the time the return message arrives, and a similar limitation also applies to the effects on the individual affective-­tone mechanisms. I wish to emphasize that I do not say that the process of the conditioned reflex operates according to the mechanism I have given; I merely say that it could so operate. If, however, we assume this or any simular mechanism, there are a good many things we can say concerning it.

然而，这种持久效应仅限于在返回消息到达时实际存在的那些过程，类似的限制也适用于对各个情感色调机制的影响。我想强调，我并不是说条件反射的过程按照我给出的机制运作；我只是说它可以这样运作。

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One is that this mechanism is capable of learning. It has already been recognized that the conditioned reflex is a learning mechanism, and this idea has been used in the behaviorist studies of the learning of rats in a maze. All that is needed is that the inducements or punishments used have, respectively, a positive and a negative affective tone.

其中之一是，这种机制能够学习。人们已经认识到条件反射是一种学习机制，这一概念已用于行为主义对迷宫中的老鼠学习的研究。所需要的只是所用的奖励或惩罚分别具有积极和消极的情感色调。

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This is certainly the case, and the experimenter learns the nature of this affective tone by experience, not simply by a priori considerations. Another point of considerable interest is that such a mechanism involves a certain set of messages which go out generally into the nervous system, to all elements which are in a state to receive them. These are the return messages from the affective-tone totalizer, and to a certain extent the messages from the affective-­tone mechanisms to the totalizers.

这当然是事实，实验者通过经验而不是仅仅通过先验推理来了解这种情感色调的性质。另一个相当有趣的要点是，这种机制涉及一组特定的消息，这些消息通常进入神经系统，到达所有处于接收状态的目标。

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Indeed, the totalizer

实际上，总加器

Chapter V

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need not be a separate element but may merely represent some natural combinatory effect of messages arriving from the individual affective-tone mechanisms. Now, such messages ''to whom it may concern" may well be sent out most efficiently, with a smallest cost in apparatus, by channels other than nervous. In a similar manner, the ordinary communication system of a mine may consist of a telephone central with the attached wiring and pieces of apparatus.

不必是一个独立的元件，而可以仅仅代表来自各个情感色调机制的消息的某种自然组合效应。现在，这种"致相关人员"的消息可能通过神经系统以外的通道以最小的设备和成本最有效地发送出去。类似地，矿井的普通通信系统可以由一个电话交换总机和附属的线路及设备组成。

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When we want to empty a mine in a hurry, we do not trust to this, but break a tube of a mercaptan in the air intake. Chemical messengers like this, or like the hormones, are the simplest and most effective for a message not addressed to a specific recipient. For the moment, let me break into what I know to be pure fancy.

当我们想要紧急疏散矿井时，我们不依赖这个系统，而是在进气口打破一个硫醇管。像这样的化学信使——或荷尔蒙——是最简单、最有效的发送不针对特定接收者的消息的方式。暂且让我进入我所知道的纯粹幻想领域。

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The high emotional and consequently affective content of hormonal activity is most suggestive. This does not mean that a purely nervous mechanism is not capable of affective tone and of learning, but it does mean that in the study of this aspect of our mental activity, we cannot afford to be blind to the possibilities of hormonal transmission. It may be excessively fanciful to attach this notion to the fact that in the theories of Freud the memory--­the storage function of the nervous system--­and the activities of sex are both involved.

激素活动的高情感——从而高情感——含量是最具暗示性的。这并不意味着纯粹的神经机制不具备情感色调和学习能力，但它确实意味着，在研究我们精神活动的这一方面时，我们不能忽视激素传递的可能性。

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Sex, on the one hand, and all affective content, on the other, contain a very strong hormonal element. This suggestion of the importance of sex and hormones has been made to me by Dr. Lettvin and Mr.

一方面，性和所有情感内容都含有非常强的激素成分。关于性和激素重要性的这一建议是由莱特文博士和

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Oliver Selfridge, While at present there is no adequate evidence to prove its validity, it is not manifestly absurd in principle. There is nothing in the nature of the computing machine which forbids it to show conditioned reflexes. Let us remember that a computing machine in action is more than the concatenation of relays and storage mechanisms which the designer has

奥利弗·塞尔弗里奇提出的。虽然目前没有足够的证据证明其有效性，但它在原则上并非明显荒谬。计算机构造中没有任何东西禁止它表现出条件反射。让我们记住，运行中的计算机不仅仅是一系列设计师已经

Computing Machines and the Nervous System

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built into it. It also contains the content of its storage mechanisms, and this content is never completely cleared in the course of a single run. We have already seen that it is the run rather than the entire existence of the mechanical structure of the computing machine which corresponds to the life of the individual.

构建在其中的继电器和存储机制。它还包含其存储机制的内容，而这个内容在单次运行过程中从未被完全清除。我们已经看到，与个体生命相对应的是计算机的运行而非其机械结构的整体存在。

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We have also seen that in the nervous computing machine it is highly probable that information is stored largely as changes in the permeability of the synapses, and it is perfectly possible to construct artificial machines where information is stored in that way. It is perfectly possible, for example, to cause any message going into storage to change in a permanent or semi-­permanent way the grid bias of one or of a number of vacuum tubes, and thus to alter the numerical value of the summation of impulses which will make the tube or tubes fire. A more detailed account of learning apparatus in computing and control machines, and the uses to which it may be put, may well be left to the engineer rather than to a preliminary book like this one.

我们也已经看到，在神经计算机中，信息很可能主要以突触通透性的变化来存储，并且完全可以构建以这种方式存储信息的人工机器。例如，完全可以使任何进入存储的消息以永久或半永久的方式改变一个或多个真空管的栅偏压，从而改变使该管或多管发放的脉冲求和的数值。

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It is perhaps better to devote the rest of this chapter to the more developed, normal uses of modern computing machines. One of the chief of these is in the solution of partial differential equations. Even linear partial differential equations require the recording of an enormous mass of data to set them up, as the data involve the accurate description of functions of two or more variables.

也许最好将本章剩余部分用于讨论现代计算机更发达、更正常的用途。其中主要的一个是求解偏微分方程。即使线性偏微分方程也需要记录大量数据来建立它们，因为这些数据涉及两个或多个变量的函数的精确描述。

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With equations of the hyperbolic type, like the wave equation, the typical problem is that of solving the equation when the initial data are given, and this can be done in a progressive manner from the initial data to the results at any given later time. This is largely true of equations of the parabolic type as well. When it comes to equations of the elliptic type, where the natural data are boundary values rather than initial values, the natural methods of solution involve an

对于双曲型方程（如波动方程），典型的问题是给定初始数据求解方程，这可以从初始数据逐步推进到任何给定后期时刻的结果。这对于抛物型方程也大致成立。当涉及椭圆型方程时，其自然数据是边界值而非初始值，其自然的求解方法涉及

Chapter V

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iterative process of successive approximation. This process is repeated a very large number of times, so that very fast methods, such as those of the modern computing machine, are almost indispensable. In non-­linear partial differential equations, we miss what we have in the case of the linear equations--­a reasonably adequate, purely mathematical theory.

迭代的逐次逼近过程。这个过程需要重复非常多的次数，因此像现代计算机那样的极快方法几乎是不可或缺的。在非线性偏微分方程中，我们缺少线性方程所具有的东西——一个相当充分的纯数学理论。

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Here computational methods are not only important for the handling of particular numerical cases, but, as von Neumann has pointed out, we need them in order to form that acquaintance with a large number of particular cases without which we can scarcely formulate a general theory. To some extent this has been done with the aid of very expensive experimental apparatus, such as wind tunnels. It is in this way that we have become acquainted with the more complicated properties of shock waves, slip surfaces, turbulence, and the like, for which we are scarcely in a position to give an adequate mathematical theory.

在这里，计算方法不仅对于处理特定数值情况至关重要，而且——正如冯·诺依曼所指出的——我们需要它们来熟悉大量具体案例，没有这些案例我们几乎无法形成一般理论。在某种程度上，这是借助非常昂贵的实验设备（如风洞）来完成的。

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How many undiscovered phenomena of similar nature there may be, we do not know. The analogue machines are so much less accurate, and in many cases so much slower, than the digital machines that the latter give us much more promise for the future. It is already becoming clear in the use of these new machines that they demand purely mathematical techniques of their own, quite different from those in use in manual computation or in the use of machines of smaller capacity.

还有多少类似性质的未发现现象，我们不得而知。模拟机的精度低得多，而且在许多情况下速度也慢得多，因此数字机为我们提供了更大的未来前景。在这些新机器的使用中已经越来越清楚地表明，它们需要自己独特的纯数学技术，完全不同于手工计算或使用较小容量机器时所使用的技术。

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For example, even the use of machines for computing determinants of moderately high order or for the simultaneous solution of twenty or thirty simultaneous linear equations shows difficulties which do not arise when we study analogous problems of small order. Unless care is exercised in setting up a problem, these may completely deprive the solution of any significant figures whatever.

例如，即使使用机器计算中等阶数的行列式或同时求解二十或三十个联立线性方程，也会出现在研究类似的小阶数问题时不会出现的困难。除非在设置问题时仔细小心，否则这些困难可能完全使解失去任何有效数字。

Computing Machines and the Nervous System

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a commonplace to say that fine, effective tools like the ultra-rapid computing machine are out of place in the hands of those not possessing a sufficient degree of technical skill to take full advantage of them. The ultra-rapid computing machine will certainly not decrease the need for mathematicians with a high level of understanding and technical training. In the mechanical or electrical construction of computing machines, there are a few maxims which deserve consideration.

一个常识是，像超高速计算机这样精细有效的工具，放在那些不具备足够技术技能来充分利用它们的人手中是不合适的。超高速计算机肯定不会减少对具有高理解水平和技术训练的数学家的需求。在计算机的机械或电气构造中，有一些准则值得考虑。

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One is that mechanisms which are relatively frequently used, such as multiplying or adding mechanisms, should be in the form of relatively standardized assemblages adapted for one particular use and no other, while those of more occasional use should be assembled for the moment of use out of elements also available for other purposes. Closely related to this consideration is the one that in these more general mechanisms the component parts should be available in accordance with their general properties, and should not be allotted permanently to a specific association with other pieces of apparatus. There should be some part of the apparatus, like an automatic telephone-­switching exchange, which will search for free components and connectors of the various sorts and allot them as they are needed.

其一，相对频繁使用的机构，如乘法器或加法器，应该采用适合于特定用途而非其他用途的相对标准化的组件形式，而那些偶尔使用的机构应该在使用时从也可用于其他目的的元件中临时组装。与此密切相关的是，在这些更通用的机构中，组件应根据其一般属性可用，而不应永久分配给与其他设备的特定关联。

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This will eliminate much of the very large expense which is due to having a great number of unused elements which cannot be used unless their entire large assembly is used. We shall find this principle is very important when we come to consider traffic problems and overloading in the nervous system. As a final remark, let me point out that a large computing machine, whether in the form of mechanical or electric apparatus or in the form of the brain itself, uses up a considerable amount of power, all of which is wasted and dissipated in heat.

这将消除由于拥有大量未使用元件而导致的巨额费用——这些元件除非整个大型组件一起使用，否则无法使用。当我们考虑神经系统中的流量问题和过载问题时，会发现这个原则非常重要。作为最后的评论，让我指出，

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The blood leaving the brain is a fraction of a degree warmer

流出的血液比流入的血液温度高几分之一度。

Chapter V

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than that entering it. No other computing machine approaches the economy of energy of the brain. In a large apparatus like the Eniac or Edvac, the filaments of the tubes consume a quantity of energy which may well be measured in kilowatts, and unless adequate ventilating and cooling apparatus is provided, the system will suffer from what is the mechanical equivalent of pyrexia, until the constants of the machine are radically changed by the heat, and its performance breaks down.

没有一个计算机能像大脑那样节能。在像埃尼亚克或埃德瓦克这样的大型装置中，电子管的灯丝消耗的能量可以用千瓦来计量，除非提供足够的通风和冷却装置，否则系统会遭受机械意义上的高热，直到机器常数被热量彻底改变，其性能就会崩溃。

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Nevertheless, the energy spent per individual operation is almost vanishingly small, and does not even begin to form an adequate measure of the performance of the apparatus. The mechanical brain does not secrete thought "as the liver does bile," as the earlier materialists claimed, nor does it put it out in the form of energy, as the muscle puts out its activity. Information is information, not matter or energy.

尽管如此，每次单个操作所消耗的能量几乎小到可以忽略不计，根本无法形成衡量装置性能的适当标准。机械大脑并不像早期唯物主义者所声称的那样"像肝脏分泌胆汁一样"分泌思想，也不像肌肉输出活动那样以能量的形式输出思想。信息就是信息，不是物质也不是能量。

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No materialism which does not admit this can survive at the present day.

任何不承认这一点的唯物论在今天都无法生存。

VI Gestalt and Universals

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VI. Gestalt and Universals

VI. Gestalt and Universals

VI. Gestalt and Universals

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Among other things which we have discussed in the previous chapter is the possibility of assigning a neural mechanism to Locke's theory of the association of ideas. According to Locke, this occurs according to three principles: the principle of contiguity, the principle of similarity, and the principle of cause and effect. The third of these is reduced by Locke, and even more definitively by Hume, to nothing more than constant concomitance, and so is subsumed under the first, that of contiguity.

我们在前一章讨论的内容之一，是为洛克关于观念联想的理论赋予神经机制的可能性。根据洛克的观点，联想按照三个原则发生：接近原则、相似原则和因果原则。第三个原则——因果——被洛克、甚至更决定性地被休谟还原为仅仅是恒常共现，因此被归入第一个原则即接近原则。

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The second, that of similarity, deserves a more detailed discussion. How do we recognize the identity of the features of a man, whether we see him in profile, in three-­quarters face, or in full face? How do we recognize a circle as a circle, whether it is large or small, near or far; whether, in fact, it is in a plane perpendicular to a line from the eye meeting it in the middle, and is seen as a circle, or has some other orientation, and is seen as an ellipse?

第二个原则，即相似原则，值得更详细的讨论。我们如何识别一个人的面部特征，无论我们是从侧面、四分之三正面还是全正面看到他？我们如何识别一个圆是圆，不管它是大是小、是远是近；事实上，不管它是在垂直于从眼睛中间相交的视线的平面上而被视为一个圆，还是有其他取向而被视为一个椭圆？

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How do we see faces and animals and maps in clouds, or in the blots of a Rorschach test? All these examples refer to the eye, but similar problems extend to the other senses, and some of them have to do with intersensory relations. How do we put into words the call of a bird or the stridulations of an insect?

我们如何在云中，或在罗夏墨迹测试的墨迹中看到面孔、动物和地图？所有这些例子都涉及视觉，但类似的问题延伸到其他感觉，其中一些涉及感觉间关系。我们如何用语言描述鸟鸣或昆虫的摩擦声？

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How do we identify the roundness of a coin by touch?

我们如何通过触觉识别一枚硬币的圆形？

Chapter VI

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For the present, let us confine ourselves to the sense of vision. One important factor in the comparison of form of different objects is certainly the interaction of the eye and the muscles, whether they are the muscles within the eyeball, the muscles moving the eyeball, the muscles moving the head, or the muscles moving the body as a whole. Indeed, some form of this visual-­muscular feedback system is important as low in the animal kingdom as the flatworms.

目前，让我们局限于视觉。在比较不同物体的形状时，一个重要的因素无疑是眼睛和肌肉的相互作用，无论是眼球内的肌肉、移动眼球的肌肉、移动头部的肌肉，还是移动整个身体的肌肉。事实上，某种形式的这种视觉-肌肉反馈系统在低至扁形虫的动物界中就已经很重要了。

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There the negative phototropism, the tendency to avoid the light, seems to be controlled by the balance of the impulses from the two eyespots. This balance is fed back to the muscles of the trunk, turning the body away from the light, and, in combination with the general impulse to move forward, carries the animal into the darkest region accessible. It is interesting to note that a combination of a pair of photocells with appropriate amplifiers, a Wheatstone bridge for balancing their outputs, and further amplifiers controlling the input into the two motors of a twinscrew mechanism would give us a very adequate negatively phototropic control for a little boat.

在那里，负趋光性——即避开光线的倾向——似乎由来自两个眼点的脉冲平衡所控制。这种平衡被反馈到躯干的肌肉，使身体转向远离光线，并结合前进的一般冲动，将动物带入可达到的最黑暗区域。有趣的是，一对光电管配以适当的放大器、用于平衡其输出的惠斯通电桥，以及进一步控制双螺旋机构两个电机输入的放大器，就可以为我们的小船提供非常有效的负趋光控制。

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It would be difficult or impossible for us to compress this mechanism into the dimensions that a flatworm can carry; but here we merely have another exemplification of the fact that must by now be familiar to the reader, that living mechanisms tend to have a much smaller space scale than the mechanisms best suited to the techniques of human artificers, although, on the other hand, the use of electrical techniques gives the artificial mechanism an enormous advantage in speed over the living organism. Without going through all the intermediate stages, let us come at once to the eye-­muscle feedbacks in man. Some of these are of purely homeostatic nature, as when the pupil opens in the dark and closes in the light, thus tending to confine the

我们很难——甚至不可能——将这个机制压缩到扁形虫所能携带的尺寸；但这只是另一个事实的例证——读者现在应该已经熟悉了——即生命机制往往比最适合人类工匠技术的机制具有小得多的空间尺度，尽管另一方面，电气技术的使用赋予了人造机制相对于生命有机体在速度上的巨大优势。无需经过所有中间阶段，让我们直接来看人类的眼-肌反馈系统。其中一些纯粹是稳态性质的，例如瞳孔在黑暗中张开、在光线中闭合，从而倾向于将进入眼睛的光线限制在比原本可能更窄的范围内。

Gestalt and Universals

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flow of light into the eye between narrower bounds than would otherwise be possible. Others concern the fact that the human eye has economically confined its best form and color vision to a relatively small fovea, while its perception of motion is better on the periphery. When the peripheral vision has picked up some object conspicuous by brilliancy or light contrast or color or above all by motion, there is a reflex feedback to bring it into the fovea.

另一些则涉及这样一个事实：人类的眼睛经济地将最佳的形貌和色彩视觉限制在相对较小的中央凹，而其对运动的感知则在边缘更好。当周边视觉捕捉到某个因亮度、光对比度、颜色或——最重要的是——运动而引人注目的物体时，会有一个反射性反馈将其带入中央凹。

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This feedback is accompanied by a complicated system of interlinked subordinate feedbacks, which tend to converge the two eyes so that the object attracting attention is in the same part of the visual field of each, and to focus the lens so that its outlines are as sharp as possible. These actions are supplemented by motions of the head and body, by which we bring the object into the center of vision if this cannot be done readily by a motion of the eyes alone, or by which we bring an object outside the visual field picked up by some other sense into that field. In the case of objects with which we are more familiar in one angular orientation than another--writing, human faces, landscapes, and the like--there is also a mechanism by which we tend to pull them into the proper orientation.

这种反馈伴随着一个相互连接的次级反馈的复杂系统，这些反馈倾向于使双眼会聚，使吸引注意力的物体落在每只眼睛视野的同一部分，并使晶状体聚焦，使物体的轮廓尽可能清晰。这些动作由头部和身体的运动补充——当我们无法仅通过眼睛的运动轻易完成时，通过这些运动将物体带入视野中心；或者通过它们将其他感觉所捕捉到的视野外的物体带入视野。对于那些我们更熟悉某一种角度取向的物体——文字、人脸、风景等——还存在一种机制，使我们倾向于将它们拉到适当的方向。

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All these processes can be summed up in one sentence: we tend to bring any object that attracts our attention into a standard position and orientation, so that the visual image which we form of it varies within as small a range as possible. This does not exhaust the processes which are involved in perceiving the form and meaning of the object, but it certainly facilitates all later processes tending to this end. These later processes occur in the eye and in the visual cortex.

所有这些过程可以总结为一句话：我们倾向于将任何引起我们注意的物体带入一个标准位置和方向，使我们形成的视觉图像尽可能在最小范围内变化。这并没有穷尽感知物体形状和意义所涉及的过程，但它确实促进了所有后续旨在实现这一目标的过程。这些后续过程发生在眼睛和视觉皮层中。

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There is considerable evidence that for a considerable number of stages each step in this process diminishes the number of neuron channels involved in the

有相当多的证据表明，在相当多的阶段中，这一过程的每一步都减少了参与传递视觉信息的神经通道数量，并将这些信息逐步带入其被使用和保存在记忆中的形式。

Chapter VI

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transmission of visual information, and brings this information one step nearer to the form in which it is used and is preserved in the memory. The first step in this concentration of visual information occurs in the transition between the retina and the optic nerve. It will be noted that while in the fovea there is almost a one-­one correspondence between the rods and cones and the fibers of the optic nerve, the correspondence on the periphery is such that one optic nerve fiber corresponds to ten or more end organs.

视觉信息集中的第一步发生在视网膜和视神经之间的过渡中。值得注意的是，虽然在中央凹中，视杆细胞和视锥细胞与视神经纤维几乎是一一对应的，但在周边，一根视神经纤维对应着十个或更多的末端器官。

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This is quite understandable, in view of the fact that the chief function of the peripheral fibers is not so much vision itself as a pickup for the centering and focusing-­directing mechanism of the eye. One of the most remarkable phenomena of vision is our ability to recognize an outline drawing. Clearly, an outline drawing of, say, the face of a man, has very little resemblance to the face itself in color, or in the massing of light and shade, yet it may be a most recognizable portrait of its subject.

这一点相当容易理解，因为周边纤维的主要功能与其说是视觉本身，不如说是为眼睛的对中和聚焦-定向机制提供拾取。视觉中最引人注目的现象之一是我们识别轮廓图的能力。显然，一幅人脸的轮廓图在颜色或光影层次上与脸本身几乎没有相似之处，但它却可能成为该对象最具可辨识性的肖像。

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The most plausible explanation of this is that, somewhere in the visual process, outlines are emphasized and some other aspects of an image are minimized in importance. The beginning of these processes is in the eye itself. Like all senses, the retina is subject to accommodation; that is, the constant maintenance of a stimulus reduces its ability to receive and to transmit that stimulus.

对此最合理的解释是，在视觉过程的某个阶段，轮廓被强调，而图像的某些其他方面被最小化。这些过程始于眼睛本身。像所有感觉一样，视网膜会发生适应；也就是说，刺激的持续维持会降低其接收和传递该刺激的能力。

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This is most markedly so for the receptors which record the interior of a large block of images with constant color and illumination, for even the slight fluctuations of focus and point of fixation which are inevitable in vision do not change the character of the image received. It is quite different on the boundary of two contrasting regions. Here these fluctuations produce an alternation between one stimulus and another, and this alternation, as we see in the

对于记录具有恒定颜色和照明的大块图像内部的感受器来说，这一点最为明显，因为即使在视觉中不可避免的焦点和注视点的微小波动，也不会改变所接收图像的特征。在两个对比区域的边界上则完全不同。在这里，这些波动产生了一种刺激之间的交替，而这种交替，正如我们在后像现象中看到的，不仅不会通过适应使视觉机制疲劳，反而会增强其敏感性。

Gestalt and Universals

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phenomenon of after-­images, not only does not tend to exhaust the visual mechanism by accommodation but even tends to enhance its sensitivity. This is true whether the contrast between the two adjacent regions is one of light intensity or of color. As a comment on these facts, let us note that three-­quarters of the fibers in the optic nerve respond only to the flashing "on" of illumination.

无论两个相邻区域之间的对比是光强度方面的还是颜色方面的，都是如此。作为对这些事实的评论，让我们注意，视神经中四分之三的纤维只对照明的"开启"闪烁做出响应。

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We thus find that the eye receives its most intense impression at boundaries, and that every visual image in fact has something of the nature of a line drawing. Probably not all of this action is peripheral. In photography, it is known that certain treatments of a plate increase its contrasts, and such phenomena, which are of non-­linearity, are certainly not beyond what the nervous system can do.

因此我们发现，眼睛在边界处接收到最强烈的印象，并且事实上每个视觉图像都具有某种线条画的性质。可能并非所有这些活动都是外围的。在摄影术中，已知某些处理会增加底片的对比度，而这些属于非线性的现象，当然并非超出神经系统的能力范围。

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They are allied to the phenomena of the telegraph-­type repeater, which we have already mentioned. Like this, they use an impression which has not been blurred beyond a certain point to trigger a new impression of a standard sharpness. At any rate, they decrease the total unusable information carried by an image, and are probably correlated with a part of the reduction of the number of transmission fibers found at various stages of the visual cortex.

它们与我们之前提到的电报型中继器现象类似。像这样，它们利用一个尚未模糊到一定程度以上的印象来触发具有标准清晰度的新印象。无论如何，它们减少了图像所携带的不可用信息总量，并且可能与视觉皮层各个阶段发现的传输纤维数量减少的部分相关。

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We have thus designated several actual or possible stages of the diagrammatization of our visual impressions. We center our images around the focus of attention and reduce them more or less to outlines. We have now to compare them with one another, or at any rate with a standard impression stored in memory, such as "circle" or "square." This may be done in several ways.

因此，我们已经指出了视觉印象图解化过程的几个实际或可能的阶段。我们将图像围绕注意焦点对中，并将其或多或少地简化为轮廓。现在我们必须将它们相互比较，或者至少与记忆中存储的标准印象——如"圆"或"方形"——进行比较。这可以通过几种方式完成。

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We have given a rough sketch which indicates how the Lockean principle of contiguity in association may be mechanized. Let us notice that the principle of contiguity also covers much of the other Lockean principle of similarity. The different

我们已经给出了一个粗略的草图，说明了洛克联想中的接近原则如何可能被机械化。让我们注意，接近原则也涵盖了洛克另一个原则——相似原则——的大部分内容。同一物体的不同方面，通常可以在那些将其带入注意焦点的过程中，以及在其他使我们从不同距离、不同角度观察它的运动中被看到。

Chapter VI

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aspects of the same object are often to be seen in those processes which bring it to the focus of attention, and of other motions which lead us to see it, now at one distance and now at another, now from one angle and now from a distinct one. This is a general principle, not confined in its application to any particular sense and doubtless of much importance in the comparison of our more complicated experiences. It is nevertheless probably not the only process which leads to the formation of our specifically visual general ideas, or, as Locke would call them, "complex ideas." The structure of our visual cortex is too highly organized, too specific, to lead us to suppose that it operates by what is after all a highly generalized mechanism.

这是一个一般原则，并不局限于任何特定感觉的应用，并且无疑在我们比较更复杂的经验时具有相当的重要性。然而，它很可能不是导致我们特有的视觉一般概念——或者洛克所称的"复杂观念"——形成的唯一过程。我们的视觉皮层的结构过于高度组织化、过于特化，以至于不能让我们认为它是通过一个归根结底高度一般化的机制来运作的。

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It leaves us the impression that we are here dealing with a special mechanism which is not merely a temporary assemblage of general-­purpose elements with interchangeable parts, but a permanent sub-­assembly like the adding and multiplying assemblies of a computing machine. Under the circumstances, it is worth considering how such a sub-­assembly might possibly work and how we should go about designing it. The possible perspective transformations of an object form what is known as a group, in the sense in which we have already defined one in Chapter II.

它给我们留下的印象是，我们在这里处理的是一个特殊机制，它不仅仅是通用元素与可互换部件的临时组合，而是一个永久性的子组件，就像计算机的加法和乘法组件一样。在这种情况下，值得考虑这样的子组件可能如何运作，以及我们应该如何设计它。一个物体可能的透视变换构成一个所谓群，其意义我们已经在第二章中定义过。

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This group defines several sub-­groups of transformations: the affine group, in which we consider only those transformations which leave the region at infinity untouched; the homogeneous dilations about a given point, in which one point, the directions of the axes, and the equality of scale in all directions are preserved; the transformations preserving length; the rotations in two or three dimensions about a point; the set of all translations; and so on. Among these groups, the ones we have just mentioned are continuous; that is, the operations belonging to them are determined by the values of

这个群定义了几个变换子群：仿射群——其中我们只考虑那些使无穷远区域保持不变的变换；关于给定点的均匀膨胀——其中一点、轴的方向和所有方向上尺度的相等性得以保持；保持长度的变换；关于一点在二维或三维中的旋转；所有平移的集合；等等。在这些群中，我们刚才提到的是连续的；也就是说，属于它们的运算由适当空间中许多连续变化参数的值决定。

Gestalt and Universals

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a number of continuously varying parameters in an appropriate space. They thus form multidimensional configurations in n-­space, and contain sub-­sets of transformations which constitute regions in such a space. Now, just as a region in the ordinary two-­dimensional plane is covered by the process of scanning known to the television engineer, by which a nearly uniformly distributed set of sample positions in that region is taken to represent the whole, so every region in a group-­space, including the whole of such a space, can be represented by a process of group scanning.

因此，它们在n维空间中形成多维构型，并包含构成此类空间中区域的变换子集。正如普通二维平面上的区域通过电视工程师所知的扫描过程被覆盖——通过该过程，该区域中一组近乎均匀分布的样本位置被用来代表整体——群空间中的每个区域，包括整个这样的空间，都可以通过群扫描过程来表征。

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In such a process, which is by no means confined to a space of three dimensions, a net of positions in the space is traversed in a one-­dimensional sequence, and this net of positions is so distributed that it comes near to every position in the region, in some appropriately defined sense. It will thus contain positions as near to any we wish as may be desired. If these "positions," or sets of parameters, are actually used to generate the appropriate transformations, it means that the results of transforming a given figure by these transformations will come as near as we wish to any given transformation of the figure by a transformation operator lying in the region desired.

在这样的过程中——绝不限于三维空间——该空间中的一个位置网络以一维序列被遍历，并且这个位置网络的分布方式使得它在某种适当定义的意义上接近区域中的每个位置。因此，它将包含尽可能接近我们所需的任何位置。如果这些"位置"或参数集被实际用于生成适当的变换，这意味着通过这些变换变换给定图形所得的结果，将尽可能接近该图形由位于所需区域中的变换算子进行的任何给定变换。

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If our scanning is fine enough, and the region transformed has the maximum dimensionality of the regions transformed by the group considered, this means that the transformations actually traversed will give a resulting region overlapping any transform of the original region by an amount which is as large a fraction of its area as we wish. Let us then start with a fixed comparison region and a region to be compared with it. If at any stage of the scanning of the group of transformations the image of the region to be compared under some one of the transformations scanned coincides

如果我们的扫描足够精细，并且被变换的区域具有所考虑群变换区域的最大维度，这意味着实际遍历的变换将给出一个结果区域，其与原始区域的任何变换的重叠部分，在其面积中所占的比例可以大到我们想要的任何程度。让我们从一个固定的比较区域和一个待比较的区域开始。如果在群变换扫描的任何阶段，待比较区域在某个扫描变换下的图像与固定模式的吻合程度超过给定的容差，则记录为匹配，并称这两个区域相似。

Chapter VI

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more perfectly with the fixed pattern than a given tolerance allows, this is recorded, and the two regions are said to be alike. If this happens at no stage of the scanning process, they are said to be unlike. This process is perfectly adapted to mechanization, and serves as a method to identify the shape of a figure independently of its size or its orientation or of whatever transformations may be included in the group-region to be scanned.

如果在扫描过程的任何阶段都没有发生这种情况，则称它们不相似。这个过程完全适合机械化，并且可作为独立于物体大小、方向或待扫描群区域中包含的任何变换来识别图形形状的方法。

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If this region is not the entire group, it may well be that region A seems like region B, and that region B seems like region C, while region A does not seem like region C. This certainly happens in reality. A figure may not show any particular resemblance to the same figure inverted, at least in so far as the immediate impression--one not involving any of the higher processes--­is concerned.

如果这个区域不是整个群，那么很可能区域A看起来像区域B，区域B看起来像区域C，而区域A看起来却不像区域C。这在实际中确实会发生。一个图形可能与同一个图形的倒置版本没有特别的相似之处——至少就即时印象（不涉及任何高级过程）而言是如此。

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Nevertheless, at each stage of its inversion, there may be a considerable range of neighboring positions which appear similar. The universal "ideas" thus formed are not perfectly distinct but shade into one another. There are other more sophisticated means of using group scanning to abstract from the transformations of a group.

然而，在其反转的每个阶段，可能存在一个相当大的邻近位置范围，这些位置看起来是相似的。这样形成的"普遍"观念并非完全分明，而是互相渗透的。还有其他更复杂的方法可以利用群扫描来从群的变换中进行抽象。

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The groups which we here consider have a "group measure," a probability density which depends on the transformation group itself and does not change when all the transformations of the group are altered by being preceded or followed by any specific transformation of the group. It is possible to scan the group in such a way that the density of scanning of any region of a considerable class--­that is, the amount of time which the variable scanning element passes within the region in any complete scanning of the group--­is closely proportional to its group measure. In the case of such a uniform scanning, if we have any quantity depending on a set S of elements transformed by the group, and

我们在这里考虑的群具有一个"群测度"，一个依赖于变换群本身的概率密度，并且当群的所有变换被群中任何特定变换前置或后置而改变时，该概率密度不变。可以以一种方式扫描该群，使得任何相当大类的区域的扫描密度——即在任何完整的群扫描中，可变扫描元素在该区域内通过的时间量——与其群测度紧密成正比。

Gestalt and Universals

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if this set of elements is transformed by all the transformations of the group, let us designate the quantity depending on S by Q(S), and let us use TS to express the transform of the set S by the transformation T of the group. Then Q(TS) will be the value of the quantity replacing Q(S) when S is replaced by TS. If we average or integrate this with respect to the group measure for the group of transformations T, we shall obtain a quantity which we may write in some such form as

并且如果这个元素集被群的所有变换所变换，让我们将由S决定的量记为Q(S)，并用TS表示S被群的变换T变换后的结果。那么Q(TS)将是当S被替换为TS时替代Q(S)的量值。如果我们对变换T的群关于群测度取平均或积分，我们将得到一个可以写成某种形式的量，其中积分是在群测度上进行的。

∫ Q (TS ) dT

(6.01)

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where the integration is over the group measure. Quantity 6.01 will be identical for all sets S interchangeable with one another under the transformations of the group, that is, for all sets S which have in some sense the same form or Gestalt. It is possible to obtain an approximate comparability of form where the integration in Quantity 6.01 is over less than the whole group, if the integrand Q(TS) is small over the region omitted.

量6.01对于所有在群变换下可相互交换的集合S将是相同的，也就是说，对于所有在某种意义下具有相同形式或格式塔的集合S。如果在量6.01中的积分是在小于整个群的范围内进行，且被积函数Q(TS)在省略区域上很小，则可以得到形式的近似可比性。

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So much for group measure. In recent years, there has been a good deal of attention to the problem of the prosthesis of one lost sense by another. The most dramatic of the attempts to accomplish this has been the design of reading devices for the blind, to work by the use of photoelectric cells.

关于群测度的讨论到此为止。近年来，人们对用一种感觉替代另一种丧失的感觉的问题给予了大量关注。实现这一目标的最引人注目的尝试之一，是为盲人设计利用光电管工作的阅读设备。

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We shall suppose that these efforts are confined to printed matter, and even to a single type face or to a small number of type faces. We shall also suppose that the alignment of the page, the centering of the lines, the traverse from line to line are taken care of either manually or, as they may well be, automatically. These processes correspond, as we may see, to the part of our visual Gestalt determination which depends on muscular feedbacks and the use of our normal centering, orienting, focusing, and converging apparatus.

我们假设这些努力限于印刷品，甚至限于单一字体或少数几种字体。我们还假设页面的对齐、行对中、行间遍历由手工处理——或者也可能自动处理。正如我们所见，这些过程对应于我们的视觉格式塔确定中依赖于肌肉反馈以及我们正常的对中、定向、聚焦和会聚装置的那一部分。

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There now ensues the problem

现在出现的问题是，当扫描装置依次经过单个字母时确定其形状。

Chapter VI

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of determining the shapes of the individual letters as the scanning apparatus passes over them in sequence. It has been suggested that this be done by the use of several photoelectric cells placed in a vertical sequence, each attached to a sound-­making apparatus of a different pitch. This can be done with the black of the letters registering either as silence or as sound.

有人建议使用多个垂直排列的光电管来实现这一目的，每个光电管连接到一个不同音高的发声装置。这可以通过使字母的黑色部分要么记录为静音要么记录为声音来实现。

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Let us assume the latter case, and let us assume three photocell receptors above one another. Let them record as the three notes of a chord, let us say, with the highest note on top and the lowest note below. Then the letter capital F, let us say, will record ------------

让我们假设是后一种情况，并假设三个光电管接收器上下排列。让它们记录为一个和弦的三个音符——比如说，最高的音符在上，最低的在下。那么字母F，比如说，将记录为——

Duration of upper note

————­ Duration of middle note
—­

Duration of lower note

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The letter capital Z will record ------------ -------------- the letter capital O ----­

字母Z将记录为——字母O将记录为——

—­

▶

--and so on. With the ordinary help given by our ability to interpret, it should not be too difficult to read such an auditory code, not more difficult than to read Braille, for instance. However, all this depends on one thing: the proper relation of the photocells to the vertical height of the letters.

——等等。借助我们解释能力的普通帮助，阅读这种听觉代码应该不会太困难——例如，不会比阅读盲文更困难。然而，这一切都取决于一件事：光电管与字母垂直高度之间的适当关系。

▶

Even with standardized type faces, there still are great variations in the size

即使使用标准化字体，字体的大小仍然存在很大的变化。

Gestalt and Universals

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of the type. Thus it is desirable for us to be able to pull the vertical scale of the scanning up or down, in order to reduce the impression of a given letter to a standard. We must at least have at our disposal, manually or automatically, some of the transformations of the vertical dilation group.

因此，我们需要能够上下调整扫描的垂直尺度，以便将给定字母的印象还原为标准格式。我们至少必须能够手动或自动地利用垂直膨胀群的某些变换。

▶

There are several ways we might do this. We might allow for a mechanical vertical adjustment of our photocells. On the other hand, we might use a rather large vertical array of photocells and change the pitch assignment with the size of type, leaving those above and below the type silent.

有几种方法可以做到这一点。我们可以允许光电管进行机械垂直调整。另一方面，我们可以使用一个相当大的垂直光电管阵列，并根据字体大小改变音高分配，使字体上方和下方的光电管保持静音。

▶

This may be done, for example, with the aid of a schema of two sets of connectors, the inputs coming up from the photocells, and leading to a series of switches of wider and wider divergence, and the outputs a series of vertical lines, as in Fig. 8. Here the single lines represent the leads from the photocells, the double lines the leads to the oscillators, the circles on the dotted lines the points of connections between incoming and outgoing leads, and the dotted lines themselves the leads whereby one or another of a bank of oscillators is put into action. This was the device, to which we have referred in the introduction, designed by McCulloch for the purpose of adjusting to the height of the type face.

例如，这可以通过一个两套连接器的方案来实现——输入来自光电管，通向一系列发散程度越来越大的开关，而输出则是一系列垂直线，如图8所示。这里单线表示来自光电管的引线，双线表示通向振荡器的引线，虚线圆表示输入和输出引线之间的连接点，虚线本身则是用于启动某个振荡器组的引线。这就是我们在引言中提到的、由麦卡洛克设计的用于适应字体高度的装置。

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In the first design, the selection between dotted line and dotted line was manual.

在最初的设计中，虚线之间的选择是手动的。

Fig. 8

Chapter VI

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This was the figure which, when shown to Dr. von Bonin, suggested the fourth layer of the visual cortex. It was the connecting circles which suggested the neuron cell bodies of this layer, arranged in sub-­layers of uniformly changing horizontal density, and size changing in the opposite direction to the density. The horizontal leads are probably fired in some cyclical order.

正是这个图形，当展示给冯·博宁博士时，暗示了视觉皮层的第四层。正是这些连接圆暗示了这一层的神经元细胞体，它们排列成水平密度均匀变化的亚层，大小与密度呈相反方向变化。水平引线可能以某种循环顺序被激发。

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The whole apparatus seems quite suited to the process of group scanning. There must of course be some process of recombination in time of the upper outputs. This then was the device suggested by McCulloch as that actually used in the brain in the detection of visual Gestalt.

整个装置似乎非常适合群扫描过程。当然，必须存在某种在时间上重组上端输出的过程。这就是麦卡洛克提出的、在脑中实际用于检测视觉格式塔的装置。

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It represents a type of device usable for any sort of group scanning. Something similar occurs in other senses as well. In the ear, the transposition of music from one fundamental pitch to another is nothing but a translation of the logarithm of the frequency, and may consequently be performed by a group-scanning apparatus.

它代表了一种可用于任何类型的群扫描的装置类型。在其他感觉中也存在类似的情况。在耳朵中，音乐从一个基音到另一个基音的转调不过是频率对数的平移，因此可以通过群扫描装置来执行。

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A group-­scanning assembly thus has well-­defined, appropriate anatomical structure. The necessary switching may be performed by independent horizontal leads which furnish enough stimulation to shift the thresholds in each level to just the proper amount to make them fire when the lead comes on. While we do not know all the details of the performance of the machinery, it is not at all difficult to conjecture a possible machine conforming to the anatomy.

因此，群扫描组件具有明确的、适当的解剖结构。必要的开关操作可以由独立的水平引线执行——这些引线提供足够的刺激，将每个水平的阈值恰好调整到当引线激活时使其放电的程度。虽然我们不了解该机械装置性能的所有细节，但要猜想一个符合解剖结构的可能机器并不困难。

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In short, the group-­scanning assembly is well adapted to form the sort of permanent sub-­assembly of the brain corresponding to the adders or multipliers of the numerical computing machine. Lastly, the scanning apparatus should have a certain intrinsic period of operation which should be identifiable in the performance of the brain. The order of magnitude of this period

简而言之，群扫描组件非常适合形成大脑中对应于数值计算机加法器或乘法器的那种永久性子组件。最后，扫描装置应该具有某种内在的操作周期，这应该可以在大脑的性能中识别出来。这个周期的数量级应该体现在比较不同大小的物体形状所需的最短时间上。

Gestalt and Universals

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should show in the minimum time required for making direct comparison of the shapes of objects different in size. This can be done only when the comparison is between two objects not too different in size; otherwise, it is a long-­time process, suggestive of the action of a non-­specific assembly. When direct comparison seems to be possible, it appears to take a time of the order of magnitude of a tenth of a second.

这只能在两个物体的尺寸相差不太大时进行；否则，它是一个长时间的过程，暗示着非特定性组件的运作。当直接比较似乎可能时，它似乎需要大约十分之一秒的时间。

▶

This also seems to accord with the order of magnitude of the time needed by excitation to stimulate all the layers of transverse connectors in cyclical sequence. While this cyclical process then might be a locally determined one, there is evidence that there is a widespread synchronism in different parts of the cortex, suggesting that it is driven from some clocking center. In fact, it has the order of frequency appropriate for the alpha rhythm of the brain, as shown in electroencephalograms.

这也似乎与兴奋以循环顺序刺激所有横向连接层所需时间的数量级一致。虽然这个循环过程可能是一个局部决定的过程，但有证据表明，在大脑皮层的不同部位存在广泛的同步性，暗示它是由某个时钟中心驱动的。事实上，它的频率量级适合于脑电图中显示的α节律。

▶

We may suspect that this alpha rhythm is associated with form perception, and that it partakes of the nature of a sweep rhythm, like the rhythm shown in the scanning process of a television apparatus. It disappears in deep sleep, and seems to be obscured and overlaid with other rhythms, precisely as we might expect, when we are actually looking at something and the sweep rhythm is acting as something like a carrier for other rhythms and activities. It is most marked when the eyes are closed in waking, or when we are staring into space at nothing in particular, as in the condition of abstraction of a yogi,1 when it shows an almost perfect periodicity.

我们可以推测，这种α节律与形状感知有关，并且它具有扫描节律的性质，类似于电视装置扫描过程中显示的节律。它在深度睡眠中消失，并且当我们实际看东西时——扫描节律充当其他节律和活动的某种载波时——它似乎被其他节律掩盖和覆盖，正如我们可能预期的那样。当我们在清醒状态下闭上眼睛，或者当我们凝视虚空、什么都不看时——例如瑜伽修行者的入定状态——它最为明显，此时它表现出近乎完美的周期性。

▶

We have just seen that the problem of sensory prosthesis--the problem of replacing the information normally conveyed through a lost sense by information through another sense still available--is important and not necessarily insoluble. What makes it more hopeful is the fact that the memory and

我们刚刚看到，感觉代偿的问题——即用另一种仍可使用的感觉通道传来的信息替代通常通过丧失的感觉通道传来的信息——是重要的，并且并非必然不可解决。使这个问题更有希望的是，记忆和联想区域通常通过一种感觉来接近，但它们并非只有一把钥匙的锁，而是能够存储来自不属于其正常所属感觉的其他感觉所收集的印象。

Chapter VI

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association areas, normally approached through one sense, are not locks with a single key but are available to store impressions gathered from other senses than the one to which they normally belong. A blinded man, as distinguished perhaps from one congenitally blind, not only retains visual memories earlier in date than his accident but is even able to store tactile and auditory impressions in a visual form. He may feel his way around a room, and yet have an image of how it ought to look.

一个失明的人——或许与先天性盲人不同——不仅保留着事故发生前更早的视觉记忆，甚至能够将触觉和听觉印象以视觉形式存储。他可以在房间里摸索着走，却仍然拥有房间应该是什么样子的图像。

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Thus, part of his normal visual mechanism is accessible to him. On the other hand, he has lost more than his eyes: he has also lost the use of that part of his visual cortex which may be regarded as a fixed assembly for organizing the impressions of sight. It is necessary to equip him not only with artificial visual receptors but with an artificial visual cortex, which will translate the light impressions on his new receptors into a form so related to the normal output of his visual cortex that objects which ordinarily look alike will now sound alike.

因此，他的部分正常视觉机制是可以利用的。另一方面，他失去的不仅仅是眼睛：他还失去了他的部分视觉皮层的功能——这部分视觉皮层可以被视为用于组织视觉印象的固定组件。有必要不仅为他配备人工视觉感受器，还要配备一个人工视觉皮层，将他的新感受器上的光印象转换成与其视觉皮层正常输出相关的形式，使得通常看起来相似的物体听起来也相似。

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Thus the criterion of the possibility of such a replacement of sight by hearing is at least in part a comparison between the number of recognizably different visual patterns and recognizably different auditory patterns at the cortical level. This is a comparison of amounts of information. In view of the somewhat similar organization of the different parts of the sensory cortex, it will probably not differ very much from a comparison between the areas of the two parts of the cortex.

因此，这种用听觉替代视觉的可能性的标准，至少部分是在皮层水平上可识别地不同的视觉模式与可识别地不同的听觉模式数量的比较。这是信息量的比较。鉴于感觉皮层不同部分的组织有些相似，这种比较很可能与皮层两个部分的面积比较相差不大。

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This is about 100:1 as between sight and sound. If all the auditory cortex were used for vision, we might expect to get a quantity of reception of information about 1 per cent of that coming in through the eye. On the other hand, our usual scale for the estimation of vision is in terms of the relative distance at which a certain degree of resolution of pattern is obtained, and thus a 10/100 vision means

视觉和听觉之间的比例约为100:1。如果所有听觉皮层都用于视觉，我们可以预期接收到的信息量约为通过眼睛进入的信息量的1%。另一方面，我们评估视觉的通常尺度是以获得一定图案分辨率的相对距离来衡量的，因此10/100的视力意味着信息流量约为正常的1%。

Gestalt and Universals

▶

an amount of flow of information about 1 per cent of normal. This is very poor vision; it is, however, definitely not blindness, nor do people with this amount of vision necessarily consider themselves as blind. In the other direction, the picture is even more favorable.

这是非常差的视力；然而，这绝不是失明，拥有这种视力水平的人也不一定认为自己失明。另一方面，情况甚至更为乐观。

▶

The eye can detect all of the nuances of the ear with the use of only 1 per cent of its facilities, and still leave a vision of about 95/100, which is substantially perfect. Thus the problem of sensory prosthesis is an extremely hopeful field of work.

眼睛仅使用其1%的设施就能检测到耳朵的所有细微差别，同时仍保留约95/100的视力，这基本上是完美的。因此，感觉代偿问题是一个极有希望的研究领域。

VII Cybernetics and Psychopathology

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VII. Cybernetics and Psychopathology

VII. Cybernetics and Psychopathology

VII. Cybernetics and Psychopathology

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It is necessary that I commence this chapter with a disavowal. On the one hand, I am not a psychopathologist nor a psychiatrist, and lack any experience in a field where the guidance of experience is the only trustworthy one. On the other hand, our knowledge of the normal performance of the brain and the nervous system, and a fortiori our knowledge of their abnormal performance, is far from having reached that state of perfection where an a priori theory can command any confidence.

在开始本章之前，我必须先做一个声明。一方面，我不是精神病理学家或精神病学家，在这个唯有经验引导才值得信赖的领域中缺乏任何经验。另一方面，我们对大脑和神经系统正常运作的认识——更遑论对其异常运作的认识——远未达到先验理论能够令人信服的完善状态。

▶

I therefore wish to disclaim in advance any assertion that any particular entity in psychopathology, as for example any of the morbid conditions described by Kraepelin and his disciples, is due to a specific type of defect in the organization of the brain as a computing machine. Those who may draw such specific conclusions from the considerations of this book do so at their own risk. Nevertheless, the realization that the brain and the computing machine have much in common may suggest new and valid approaches to psychopathology and even to psychiatries.

因此，我事先声明，我不主张精神病理学中的任何特定实体——例如克雷佩林及其弟子描述的任何疾病状态——是由于大脑作为计算机的组织方式中的某一特定类型的缺陷所致。任何从本书的考量中得出此类具体结论的人，风险自负。尽管如此，认识到大脑和计算机有很多共同之处，可能为精神病理学乃至精神病学提供新的、有效的方法。

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These begin with perhaps the simplest question of all: how the brain avoids gross blunders, gross miscarriages of activity, due to the malfunction of individual components. Similar questions

这些方法首先从也许是最简单的问题开始：大脑如何避免由于个别组件故障而导致的严重错误、严重的活动失败？类似的问题涉及计算机，具有巨大的实际重要性，因为在这里，一个操作链——每个操作只需几分之一毫秒——可能持续数小时或数天。

Chapter VII

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referring to the computing machine are of great practical importance, for here a chain of operations, each covering a fraction of a millisecond, may last a matter of hours or days. It is quite possible for a chain of computational operations to involve 109 separate steps. Under these circumstances, the chance that at least one operation will go amiss is very far from negligible, even though, it is true, the reliability of modern electronic apparatus has far exceeded the most sanguine expectations.

一连串计算操作完全可能涉及10⁹个独立步骤。在这种情况下，至少有一个操作出错的可能性远非可以忽略不计——尽管现代电子设备的可靠性确实已经远远超出了最乐观的预期。

▶

In ordinary computational practice by hand or by desk machines, it is the custom to check every step of the computation and, when an error is found, to localize it by a backward process starting from the first point where the error is noted. To do this with a high-­speed machine, the check must proceed with the speed of the original machine, or the whole effective order of speed of the machine will conform to that of the slower process of checking. Furthermore, if the machine is made to keep all intermediate records of its performance, its complication and bulk will be increased to an intolerable point, by a factor which is likely to be enormously greater than 2 or 3.

在手工或台式计算机的常规计算实践中，习惯是检查每一步计算，当发现错误时，从最初注意到错误的位置开始通过反向过程定位错误。在高速计算机上执行此操作时，检查必须以原机的速度进行，否则机器的整体有效速度将服从于较慢的检查过程。此外，如果要求机器保留所有中间操作记录，其复杂性和体积将增加到无法容忍的程度——增加系数可能远远大于2或3。

▶

A much better method of checking, and in fact the one generally used in practice, is to refer every operation simultaneously to two or three separate mechanisms. In the case of the use of two such mechanisms, their answers are automatically collated against each other; and if there is a discrepancy, all data are transferred to permanent storage, the machine stops, and a signal is sent to the operator that something is wrong. The operator then compares the results, and is guided by them in his search for the malfunctioning part, perhaps a tube which has burnt out and needs replacement.

一种更好的检查方法——实际上也是实践中通常使用的方法——是让每一操作同时由两到三个独立的机制执行。在使用两个机制的情况下，它们的答案会自动相互核对；如果存在差异，所有数据传输到永久存储器，机器停止，并向操作员发送故障信号。操作员随后比较结果，并根据结果寻找故障部件——可能是一个已烧坏需要更换的电子管。

▶

If three separate mechanisms are used for each stage and single misfunctions are as rare as they are in fact, there will practically always be an agreement between two of

如果每个阶段使用三个独立机制，并且单次故障实际上像现实情况中那样罕见，那么几乎总会有两个机制的结果一致，而这种一致性将给出所需的结果。

Cybernetics and Psychopathology

▶

the three mechanisms, and this agreement will give the required result. In this case, the collation mechanism accepts the majority report, and the machine need not stop; but there is a signal indicating where and how the minority report differs from the majority report. If this occurs at the first moment of discrepancy, the indication of the position of the error may be very precise.

在这种情况下，核对机制接受多数报告，机器无需停止；但会有一个信号指示少数报告与多数报告在何处以及如何不同。如果在不一致发生的第一时刻就给出指示，则错误位置的指示可能非常精确。

▶

In a well-­designed machine, no particular element is assigned to a particular stage in the sequence of operations, but at each stage there is a searching process, quite similar to that used in automatic telephone exchanges, which finds the first available element of a given sort and switches it into the sequence of operations. In this case, the removal and replacement of defective elements need not be the source of any appreciable delay. It is conceivable and not implausible that at least two of the elements of this process are also represented in the nervous system.

在精心设计的机器中，没有特定的元件被分配给操作序列中的特定步骤，而是每一步都有一个搜索过程——与自动电话交换中使用的过程非常相似——找到给定类型的第一个可用元件并将其接入操作序列。在这种情况下，缺陷元件的移除和更换不会造成任何显著的延迟。可以想象——并非不合理——这一过程的至少两个要素在神经系统中也有所体现。

▶

We can hardly expect that any important message is entrusted for transmission to a single neuron, nor that any important operation is entrusted to a single neuronal mechanism. Like the computing machine, the brain probably works on a variant of the famous principle expounded by Lewis Carroll in The Hunting of the Snark: "What I tell you three times is true." It is also improbable that the various channels available for the transfer of information generally go from one end of their course to the other without anastomosing. It is much more probable that when a message comes in to a certain level of the nervous system, it may leave that point and proceed to the next by one or more alternative members of what is known as an "internuncial pool." There may be parts of the nervous system, indeed, where this interchangeability is much limited or abolished, and these are likely to be such highly specialized parts of the cortex as those which serve as the inward extensions of the organs of

我们很难预期任何重要信息会委托给单个神经元传输，也很难预期任何重要操作会委托给单个神经元机制。像计算机一样，大脑很可能基于刘易斯·卡罗尔在《猎鲨记》中阐述的著名原则的一个变体运作："我告诉你三遍的就是真理。"同样不太可能的是，可用于信息传输的各种通道会从一端到另一端全程不进行吻合。更可能的情况是，当一条消息到达神经系统的某一层次时，它可能离开该点，并通过一个或多个被称为"中间神经元池"的替代成员继续传递到下一层次。确实，神经系统的某些部分可能这种互换性非常有限或完全不存在，它们很可能是那些高度特化的大脑皮层区域——如服务于特殊感觉器官向内延伸的那些区域。

Chapter VII

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special sense. Still, the principle holds, and probably holds most clearly for the relatively unspecialized cortical areas which serve the purpose of association and of what we call the higher mental functions. So far we have been considering errors in performance which are normal, and pathological only in an extended sense.

然而，这个原则成立，并且很可能在那些服务于联想和我们所谓的高级心理功能的相对非特化的皮层区域最为清晰。到目前为止，我们一直在考虑正常范围内的表现错误，这些错误仅在广义上是病理性的。

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Let us now turn to those which are much more clearly pathological. Psychopathology has been rather a disappointment to the instinctive materialism of the doctors, who have taken the point of view that every disorder must be accompanied by material lesions of some specific tissue involved. It is true that specific brain lesions, such as injuries, tumors, clots, and the like, may be accompanied by psychic symptoms, and that certain mental diseases, such as paresis, are the sequellae of general bodily disease and show a pathological condition of the brain tissue; but there is no way of identifying the brain of a schizophrenic of one of the strict Kraepelin types, nor of a manic-­depressive patient, nor of a paranoiac.

现在让我们转向那些明显更具病理性的错误。精神病理学对医生们本能性的唯物主义来说颇为令人失望——他们秉持着每一种障碍都必须伴随有关组织的某种特定物质损伤的观点。确实，特定的脑损伤——如创伤、肿瘤、血块等——可能伴有精神症状，某些精神疾病如麻痹性痴呆是全身性疾病的后果，并表现出脑组织的病理状态；但目前无法识别严格克雷佩林类型的精神分裂症、躁狂抑郁患者或偏执狂患者的大脑有何特征。

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These disorders we call functional, and this distinction seems to contravene the dogma of modern materialism that every disorder in function has some physiological or anatomical basis in the tissues concerned. This distinction between functional and organic disorders receives a great deal of light from the consideration of the computing machine. As we have already seen, it is not the empty physical structure of the computing machine that corresponds to the brain--­to the adult brain, at least--­but the combination of this structure with the instructions given it at the beginning of a chain of operations and with all the additional information stored and gained from outside in the course of this chain.

这些障碍被称为功能性的，这种区分似乎与近代唯物主义的教条相悖——即每一种功能紊乱在有关组织中都有某种生理或解剖基础。这种功能性与器质性障碍的区别，从对计算机的考察中获得了大量启示。正如我们已经看到的，对应于大脑的——至少是成人大脑——并非计算机的空虚物理结构，而是这种结构与在操作链开始时给予它的指令，以及在此过程中存储和从外部获得的所有附加信息的结合。

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This information is stored in some physical form--­in the form of memory--­but part of it is in the form of circulating memories,

这些信息以某种物理形式存储——以记忆的形式——但其中一部分以循环记忆的形式存在，其物理基础在机器关闭或大脑死亡时消失；

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with a physical basis which vanishes when the machine is shut down or the brain dies, and part in the form of long-­time memories, which are stored in a way at which we can only guess, but probably also in a form with a physical basis which vanishes at death. There is no way yet known for us to recognize in the cadaver what the threshold of a given synapse has been in life; and even if we knew this, there is no way we can trace out the chain of neurons and synapses communicating with this, and determine the significance of this chain for the ideational content which it records. There is therefore nothing surprising in considering the functional mental disorders as fundamentally diseases of memory, of the circulating information kept by the brain in the active state, and of the long-­time permeability of synapses.

另一部分以长期记忆的形式存在，其存储方式我们只能猜测，但可能也以某种在死亡时消失的物理基础形式存在。目前还没有已知的方法可以在尸体中识别某个突触在生命中的阈值；即使我们知道这一点，也无法追踪与这一突触通信的神经元和突触链，并确定这一链条对于其所记录的思想内容的意义。因此，将功能性精神障碍从根本上视为记忆疾病——大脑在活跃状态下保持的循环信息疾病，以及突触长期通透性的疾病——并不令人惊讶。

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Even the grosser disorders such as paresis may produce a large part of their effects not so much by the destruction of tissue which they involve and the alteration of synaptic thresholds as by the secondary disturbances of traffic--­the overload of what remains of the nervous system and the re-­routing of messages--­which must follow such primary injuries. In a system containing a large number of neurons, circular processes can hardly be stable for long periods of time. Either, as in the case of memories belonging to the specious present, they run their course, dissipate themselves, and die out, or they comprehend more and more neurons in their system, until they occupy an inordinate part of the neuron pool.

即使是像麻痹性痴呆这样更严重的障碍，其大部分效果可能并非直接来自所涉及的组织破坏和突触阈值改变，而是来自次级的交通紊乱——即神经系统剩余部分的超负荷和消息的重新路由——这些必然继发于此类初级损伤。在包含大量神经元的系统中，循环过程很难长时间保持稳定。要么像属于当下感觉的记忆那样，它们走完自己的过程、消散并消失；要么它们将越来越多的神经元纳入自己的系统，直到占据神经元池中不成比例的部分。

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This is what we should expect to be the case in the malignant worry which accompanies anxiety neuroses. In such a case, it is possible that the patient simply does not have the room, the sufficient number of neurons, to carry out his normal processes of thought. Under such conditions, there may be less going on in the brain

这应该就是伴随焦虑性神经症的恶性忧虑所发生的情况。在这种情况下，患者可能根本没有足够的空间——足够数量的神经元——来进行正常的思维过程。在这种条件下，大脑中可能发生更少的事情来加载尚未受影响的神经元，

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to load up the neurons not yet affected, so that they are all the more readily involved in the expanding process. Furthermore, the permanent memory becomes more and more deeply involved, and the pathological process which occurred at first at the level of the circulating memories may repeat itself in a more intractable form at the level of the permanent memories. Thus what started as a relatively trivial and accidental reversal of stability may build itself up into a process totally destructive to the ordinary mental life.

使它们更容易被卷入扩展中的过程。此外，永久记忆变得越来越深地卷入，最初发生在循环记忆水平的病理过程，可能在永久记忆水平上以更顽固的形式重复。因此，最初相对微不足道和偶然的稳定性逆转，可能自我构建成一个对正常精神生活完全具有破坏性的过程。

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Pathological processes of a somewhat similar nature are not unknown in the case of mechanical or electrical computing machines. A tooth of a wheel may slip under just such conditions that no tooth with which it engages can pull it back into its normal relations, or a high-­speed electrical computing machine may go into a circular process which there seems to be no way to stop. These contingencies may depend on a highly improbable instantaneous configuration of the system, and, when remedied, may never--­or very rarely--­repeat themselves.

类似性质的病理过程在机械或电子计算机中并非没有先例。齿轮的齿可能在某种条件下滑脱，使得与之啮合的齿无法将其拉回正常关系；或者高速电子计算机可能进入一个似乎无法停止的循环过程。这些偶然情况可能取决于系统的一个极不可能的即时配置，一旦被修正，可能永远不会——或极少——重复出现。

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However, when they occur, they temporarily put the machine out of action. How do we deal with these accidents in the use of the machine? The first thing which we try is to clear the machine of all information, in the hope that when it starts again with different data the difficulty may not recur.

然而，当它们发生时，它们会暂时使机器无法工作。我们如何处理使用机器时的这些事故？我们首先尝试的是清除机器中的所有信息，希望当它用不同的数据重新启动时，困难不会重现。

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Failing this, if the difficulty is in some point permanently or temporarily inaccessible to the clearing mechanism, we shake the machine or, if it is electrical, subject it to an abnormally large electrical impulse, in the hope that we may reach the inaccessible part and throw it into a position where the false cycle of its activities will be interrupted. If even this fails, we may disconnect an erring part of the apparatus, for it is possible that what yet remains may be adequate for our purpose.

如果这失败了，如果困难在于永久或暂时无法被清除机制触及的某一点，我们就摇晃机器——或者如果是电子的，给它施加一个异常大的电脉冲——希望我们可以触及无法接近的部分，将其抛入一个使其错误循环被中断的位置。如果连这也失败了，我们可以断开装置中有问题的部分，因为剩下的部分可能仍然足以满足我们的目的。

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Now there is no normal process except death which completely clears the brain from all past impressions; and after death, it is impossible to set it going again. Of all normal processes, sleep comes the nearest to a non-pathological clearing. How often we find that the best way to handle a complicated worry or an intellectual muddle is to sleep over it!

现在，除了死亡之外，没有正常过程能够完全清除大脑中所有过去的印象；而死亡之后，我们无法让它重新运作。在所有正常过程中，睡眠最接近非病理性的清除。我们常常发现，处理复杂的忧虑或智力混乱的最好方法就是睡一觉！

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However, sleep does not clear away the deeper memories, nor indeed is a sufficiently malignant state of worry compatible with an adequate sleep. We are thus often forced to resort to more violent types of intervention in the memory cycle. The more violent of these involve a surgical intervention into the brain, leaving behind it permanent damage, mutilation, and the abridgment of the powers of the victim, as the mammalian central nervous system seems to possess no powers whatever of regeneration.

然而，睡眠并不能清除更深的记忆，也无法与足够恶性的忧虑状态相兼容以获得充足的睡眠。因此，我们常常被迫诉诸更暴力的干预手段来干预记忆循环。其中更暴力的手段涉及对大脑的外科干预，会留下永久性损伤、残缺和受害者能力的削减——因为哺乳动物的中枢神经系统似乎完全没有再生的能力。

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The principal type of surgical intervention which has been practiced is known as prefrontal lobotomy, and consists in the removal or isolation of a portion of the prefrontal lobe of the cortex. It has recently been having a certain vogue, probably not unconnected with the fact that it makes the custodial care of many patients easier. Let me remark in passing that killing them makes their custodial care still easier.

已经实践的主要外科干预类型被称为前额叶白质切断术，包括切除或隔离前额叶皮层的一部分。最近它颇为流行，这很可能与它使许多患者的监护变得更容易这一事实不无关系——请允许我顺便指出，杀死他们会使监护更加容易。

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However, prefrontal lobotomy does seem to have a genuine effect on malignant worry, not by bringing the patient nearer to a solution of his problems but by damaging or destroying the capacity for maintained worry, known in the terminology of another profession as the conscience. More genei:ally, it appears to limit all aspects of the circulating memory, the ability to keep in mind a situation not actually presented. The various forms of shock treatment--electric, insulin, metrazol--­are less drastic methods of doing a very similar thing.

然而，前额叶白质切断术似乎确实对恶性忧虑有真正的效果——不是通过使患者更接近问题的解决，而是通过破坏或损害维持忧虑的能力——用另一种职业的术语来说，这被称为良知。更一般地说，它似乎限制了循环记忆的所有方面，即保持对未实际呈现的情境进行思考的能力。各种形式的休克治疗——电休克、胰岛素、戊四氮——是执行非常类似事情的较温和方法。

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They do not destroy brain tissue or at least are not intended to destroy it, but they do have a decidedly damaging effect on the

它们不破坏脑组织——或至少不旨在破坏它——但它们确实对记忆有明显的破坏性影响。就这涉及循环记忆而言，并且就这种记忆主要是在近期的精神障碍期间受损、可能已不值得保留而言，休克治疗相对于白质切断术确实有某些可取之处；

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memory. In so far as this concerns the circulating memory, and in so far as this memory is chiefly damaged for the recent period of mental disorder, and is probably scarcely worth preserving anyhow, shock treatment has something definite to recommend it as against lobotomy; but it is not always free from deleterious effects on the permanent memory and the personality. As it stands at present, it is another violent, imperfectly understood, imperfectly controlled method to interrupt a mental vicious circle.

但它并非总是没有对永久记忆和人格的有害影响。就目前而言，它是另一种暴力的、不完全理解的、不完全控制的方法，用以打断精神上的恶性循环。这并不排除它在许多情况下是目前我们能做的最佳选择。白质切断术和休克治疗是本质上更适合处理恶性循环记忆和恶性忧虑的方法，而非更深层的永久记忆——尽管它们在此也可能产生某些效果并非不可能。正如我们所说，在长期确立的精神障碍病例中，永久记忆与循环记忆同样严重紊乱。

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This does not prevent its being in many cases the best thing we can do at present. Lobotomy and shock treatment are methods which by their very nature are more suited to handle vicious circulating memories and malignant worries than the deeper-­seated permanent memories, though it is not impossible that they may have some effect here too. As we have said, in long-­established cases of mental disorder, the permanent memory is as badly deranged as the circulating memory.

我们似乎没有任何纯粹的药物或外科武器来差别化地干预永久记忆。这就是精神分析和其他类似的心理治疗措施发挥作用的地方。无论精神分析是取正统弗洛伊德意义上的，还是荣格和阿德勒的修正版本，或者我们的心理治疗根本不是严格的精神分析，我们的治疗显然基于这样一个概念：心灵中存储的信息存在于许多可及性水平上，比通过直接、无辅助的内省所能接触到的信息要丰富和多样得多；这些信息受到情感经验的关键性制约，而我们不能总是通过这种内省揭示这些经验——要么因为它们从未在我们的成人语言中被明确表达过，要么因为它们已被确定的机制所掩埋——情感性的，尽管通常是非自愿的；

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We do not seem to possess any purely pharmaceutical or surgical weapon for intervening differentially in the permanent memory. This is where psychoanalysis and other similar psychotherapeutic measures come in. Whether psychoanalysis is taken in the orthodox Freudian sense or in the modified senses of Jung and of Adler, or whether our psychotherapy is not strictly psychoanalytic at all, our treatment is clearly based on the concept that the stored information of the mind lies on many levels of accessibility and is much richer and more varied than that which is accessible by direct unaided introspection; that it is vitally conditioned by affective experiences which we cannot always uncover by such introspection, either because they never were made explicit in our adult language, or because they have been buried by a definite mechanism, affective though generally involuntary; and that the content of these stored

而且这些存储经验的内容及其情感色调，以可能是病理性的方式，在很大程度上制约了我们后来的活动。精神分析技术包括一系列发现和解释这些隐藏记忆的方法，使患者接受它们的本来面目，并通过接受来修改——如果不是它们的内容，至少是它们所携带的情感色调——从而使它们变得不那么有害。所有这些都与本书的观点完全一致。

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experiences, as well as their affective tone, conditions much of our later activity in ways which may well be pathological. The technique of the psychoanalyst consists in a series of means to discover and interpret these hidden memories, to make the patient accept them for what they are and by their acceptance modify, if not their content, at least the affective tone they carry, and thus make them less harmful. All this is perfectly consistent with the point of view of this book.

这也解释了为什么在某些情况下，休克治疗和心理治疗的联合使用是合理的——将身体或药物治疗用于神经系统的回响现象，将心理治疗用于长期记忆——这些记忆如果没有干扰，可能从内部重新建立被休克治疗打断的恶性循环。我们已经提到过神经系统的交通问题。许多作者——如达西·汤普森——已经评论过，每种组织形式都有一个上限尺寸，超过该尺寸就无法运作。

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It perhaps explains, too, why there are circumstances where a joint use of shock treatment and psychotherapy is indicated, combining a physical or pharmacological therapy for the phenomena of reverberation in the nervous system, and a psychological therapy for the long-­time memories which, without interference, might re-establish from within the vicious circle broken up by the shock treatment. We have already mentioned the traffic problem of the nervous system. It has been commented on by many writers, such as D'Arcy Thompson,1 that each form of organization has an upper limit of size, beyond which it will not function.

因此，昆虫的组织受限于管道长度——超过该长度，通过气孔将空气直接扩散到呼吸组织的方法将失效；陆生动物不能太大，否则腿或其他与地面接触的部分将被其重量压碎；树木受限于将水和矿物质从根部输送到叶子、将光合作用产物从叶子输送到根部的机制；等等。同样的情况也出现在工程结构上。摩天大楼的尺寸受限于这样一个事实：当它们超过一定高度时，上层所需的电梯空间将消耗下层横截面的过度部分。

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Thus the insect organization is limited by the length of tubing over which the spiracle method of bringing air by diffusion directly to the breathing tissues will function; a land animal cannot be so big that the legs or ether portions in contact with the ground will be crushed by its weight; a tree is limited by the mechanism for transferring water and minerals from the roots to the leaves, and the products of photosynthesis from the leaves to the roots; and so on. The same sort of thing is observed in engineering constructions. Skyscrapers are limited in size by the fact that when they exceed a certain height, the elevator space needed for the upper stories consumes an excessive part of the cross section of the lower floors.

超过一定跨度，用具有给定弹性特性的材料能够建造的最好的悬索桥将在自身重量下坍塌；而超过更大的跨度，任何用给定材料建造的结构都将在自身重量下坍塌。类似地，按照恒定、非扩展计划建造的单个电话交换局的规模是有限的，这种限制已被电话工程师非常彻底地研究过。在电话系统中，重要的限制因素是用户无法接通电话的时间比例。

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Beyond a certain span, the best-­possible

99%的成功率即使对于最苛刻的用户来说也肯定足够满意；90%的成功呼叫可能足以保证业务以合理的便利进行。75%的成功率已经令人烦恼，但仍能勉强维持业务；而如果一半的呼叫都以失败告终，用户将开始要求拆除他们的电话。现在，这些都是总体数据。

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suspension bridge which can be built out of materials with given elastic properties will collapse under its own weight; and beyond a certain greater span, any structure built of a given material or materials will collapse under its own weight. Similarly, the size of a single telephone central, built according to a constant, non-expanding plan, is limited, and this limitation has been very thoroughly studied by telephone engineers. In a telephone system, the important limiting factor is the fraction of the time during which a subscriber will find it impossible to put a call through.

如果呼叫经过n个不同的交换阶段，并且失败概率在每个阶段是独立且相等的，那么要获得总成功概率p，每个阶段的成功概率必须是p^(1/n)。因此，要在五个阶段后获得75%的呼叫完成概率，每个阶段必须有约95%的成功概率。要获得90%的成功率，每个阶段必须有98%的成功概率。

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A 99 per cent chance of success will certainly be satisfactory for even the most exacting; 90 per cent of successful calls is probably good enough to permit business to be carried on with reasonable facility. A success of 75 per cent is already annoying but will permit business to be carried on after a fashion; while if half the calls end in failures, subscribers will begin to ask to have their telephones taken out. Now, these represent over-­all figures.

要获得50%的成功率，每个阶段必须有87%的成功概率。可以看出，涉及的阶段越多，当单个呼叫的失败超过临界水平时，服务变得极其糟糕的速度就越快；而当未完全达到这一临界失败水平时，服务变得极其良好的速度也越快。因此，涉及许多阶段并为一定失败水平设计的交换服务，在流量达到临界点之前不会表现出明显的失败迹象，

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If the calls go through n distinct stages of switching, and probability of failure is independent and equal for each stage, in order to get a probability of total success equal to p, the probability of success at each stage must be p1/n. Thus to obtain a 75 per cent chance of the completion of the call after five stages, we must have about 95 per cent chance of success per stage. To obtain a 90 per cent performance, we must have 98 per cent chance of success at each stage.

这时它会完全崩溃，我们就有了灾难性的交通阻塞。在动物中拥有最发达神经系统的人类——其行为可能依赖于最长链的有效操作神经元——很可能在过载边缘非常近的地方高效地执行复杂类型的行为，届时他将以严重和灾难性的方式崩溃。这种过载可能以几种方式发生：要么是待承载的流量过多，要么是承载流量的通道被物理移除，要么是这些通道被不良的交通系统过度占用——如已增长到成为病理性忧虑程度的循环记忆。

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To obtain a 50 per cent performance, we must have 87 per cent chance of success at each stage. It will be seen that the more stages which are involved, the more rapidly the service becomes extremely bad when a critical level of failure for the individual call is exceeded, and extremely good when this critical level of failure is not quite reached. Thus a switching service involving many stages and designed for a certain level of failure shows no obvious signs of failure until the

在所有这些情况下，都会有一个时刻——相当突然地——正常流量不再有足够的分配空间，我们将面临一种精神崩溃的形式，很可能达到精神错乱的程度。这将首先影响涉及最长神经元链的官能或操作。有可观证据表明，这些正是我们通常评价尺度中被认为"最高"的过程。

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traffic comes up to the edge of the critical point, when it goes completely to pieces, and we have a catastrophic traffic jam. Man, with the best-developed nervous system of all the animals, with behavior that probably depends on the longest chains of effectively operated neuronic chains, is then likely to perform a complicated type of behavior efficiently very close to the edge of an overload, when he will give way in a serious and catastrophic way. This overload may take place in several ways: either by an excess in the amount of traffic to be carried, by a physical removal of channels for the carrying of traffic, or by the excessive occupation of such channels by undesirable systems of traffic, like circulating memories which have increased to the extent of becoming pathological worries.

证据如下：在接近生理极限内的温度升高，已知能提高大多数——如果不是全部——神经元过程的执行容易度。这对较高过程的影响更大，大致按照我们通常对其"高级"程度的估计顺序。现在，对单个神经元-突触系统中任何过程的促进，当该神经元与其他神经元串联组合时，应该是累积的。因此，一个过程通过温度升高获得的促进程度，是其涉及神经元链长度的粗略度量。

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In all these cases, a point will come--­quite suddenly--­when the normal traffic will not have space enough allotted to it, and we shall have a form of mental breakdown, very possibly amounting to insanity. This will first affect the faculties or operations involving the longest chains of neurons. There is appreciable evidence that these are precisely the processes which are recognized to be the highest in our ordinary scale of valuation.

因此我们看到，人脑相对于其他大脑在使用更长神经元链方面的优势，是精神障碍在人类中最为显著、也可能最为常见的一个原因。还有另一种更特定的方式来考虑一个非常类似的问题。让我们首先考虑两个几何相似的大脑，灰质和白质的质量通过相同的比例因子相关，但线性尺寸之比为A:B。

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The evidence is this: a rise in temperature within nearly physiological limits is known to produce an increase in the ease of performance of most if not of all neuronic processes. This is greater for the higher processes, roughly in the order of our usual estimate of their degree of "highness." Now, any facilitation of a process in a single neuron-synapse system should be cumulative as the neuron is combined in series with other neurons. Thus the amount of assistance a process receives through a rise in temperature is a rough measure of the length of the neuron chain it involves.

设灰质中细胞体的体积和白质中纤维的横截面积在两个大脑中相同。那么两种情况下细胞体的数量之比为A³:B³，长距离连接器的数量之比为A²:B²。这意味着对于相同的细胞活动密度，大脑中纤维的活动密度是小脑的A:B倍。

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We thus see that the superiority of the human brain to others in the length of the neuron chains it employs is a reason why

如果我们将人脑与较低等哺乳动物的大脑进行比较，会发现它更加褶皱。灰质的相对厚度大致相同，但它分布在一个远更复杂的沟回系统上。这样做的效果是以白质为代价增加了灰质的量。

Chapter VII

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mental disorders are certainly most conspicuous and probably most common in man. There is another more specific way of considering a very similar matter. Let us first consider two brains geometrically similar, with the weights of gray and of white matter related by the same factor of proportionality, but with different linear dimensions in the ratio A:B.

在一个脑回内，白质的减少主要是纤维长度的减少而非数量的减少，因为脑回的对侧褶皱比同尺寸的光滑脑更靠近。另一方面，就不同脑回之间的连接器而言，它们需要行进的距离实际上由于大脑的褶皱而增加。因此，人脑在短距离连接器方面似乎相当高效，但在长距离干线方面则相当有缺陷。

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Let the volume of the cell bodies in the gray matter and the cross sections of the fibers in the white matter be of the same size in both brains. Then the number of cell bodies in the two cases bears the ratio A3:B3, and the number of long-­distance connectors the ratio A2:B2. This means that for the same density of activity in the cells, the density of activity in the fibers is A:B times as great in the case of the large brain as in that of the small brain.

这意味着在交通阻塞的情况下，涉及大脑彼此相距甚远的部分的过程应该首先受到影响。也就是说，涉及多个中枢、多个不同运动过程以及相当数量的联想区域的过程，在精神错乱情况下应该是最不稳定的。

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If we compare the human brain with that of a lower mammal, we shall find that it is much more convoluted. The relative thickness of the gray matter is much the same, but it is spread over a far more involved system of gyri and sulci. The effect of this is to increase the amount of gray matter at the expense of the amount of white matter.

这些正是我们通常归类为高级的过程，我们获得了另一种对我们预期的确认——似乎被经验所证实——即高级过程在精神错乱中最先退化。有些证据表明，大脑中的长距离路径倾向于完全离开大脑而穿过较低级的中枢。

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Within a gyrus, this decrease of the white matter is largely a decrease in length rather than in number of fibers, as the opposing folds of a gyrus are nearer together than they would be on a smooth-­surfaced brain of the same size. On the other hand, when it comes to the connectors between different gyri, the distance they have to run is increased if anything by the convolution of the brain. Thus the human brain would seem to be fairly efficient in the matter of the short-­distance connectors, but quite defective in the matter of long-­distance trunk lines.

切断一些长距离大脑白质回路所造成的异常小的损伤表明了这一点。似乎这些表面连接是如此不充分，以至于它们只提供了真正需要的一小部分连接。关于这一点，利手性和半球优势的现象很有趣。

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This means that in case of a traffic jam the processes involving parts of the brain quite remote from one another should suffer first. That is, processes involving several centers, a number of different motor processes, and a considerable number of

利手性似乎在低等哺乳动物中也存在，尽管不如人类显著——部分原因可能是它们所执行的任务所需的组织和技能程度较低。然而，即使在较低级的灵长类动物中，左右侧在肌肉技能方面的选择似乎也比人类少。众所周知，正常人的右利手通常与左脑优势相关，少数人的左利手与右脑优势相关。

Cybernetics and Psychopathology

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association areas should be among the least stable in cases of insanity. These are precisely the processes which we should normally class as higher, and we obtain another confirmation of our expectation, which seems to be verified by experience, that the higher processes deteriorate first in insanity. There is some evidence that the long-­distance paths in the brain have a tendency to run outside of the cerebrum altogether and to traverse the lower centers.

也就是说，大脑功能并非均匀分布在两个半球上，其中一个半球——优势半球——承担了高级功能的绝大部分。诚然，许多本质上双侧的功能——例如涉及视野的功能——各自在相应半球中都有代表，尽管并非所有双侧功能都是如此。然而，大多数"高级"区域仅限于优势半球。

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This is indicated by the remarkably small damage done by cutting some of the long-­distance cerebral loops of white matter. It almost seems as if these superficial connections were so inadequate that they furnish only a small part of the connections really needed. With reference to this, the phenomena of handedness and of hemispheric dominance are interesting.

例如，在成人中，次半球的大面积损伤造成的后果远不如优势半球中类似损伤严重。巴斯德在职业生涯相对早期时右侧遭受过脑出血，导致中等程度的单侧瘫痪——偏瘫。当他去世时，他的大脑被检查，发现他患有右侧损伤，范围之大以至于据说受伤后"他只有半个大脑"。顶叶和颞叶确实有大面积病变。

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Handedness seems to occur in the lower mammals, though it is less conspicuous than in man, probably in part because of the lower degree of organization and skill demanded by the tasks which they perform. Nevertheless, the choice between the right and the left side in muscular skill does actually seem to be less than in man even in the lower primates. The right-­handedness of the normal man, as is well known, is generally associated with a left-brainedness, and the left-handedness of a minority of humans with a right-­brainedness.

尽管如此，在此次损伤之后他完成了一些最出色的工作。右利手成人左侧的类似损伤几乎肯定是致命的，并且肯定会将患者降低到精神和神经残疾的动物状态。

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That is, the cerebral functions are not distributed evenly over the two hemispheres, and one of these, the dominant hemisphere, has the lion's share of the higher functions. It is true that many essentially bilateral functions--­those involving the fields of vision, for example--­are represented each in its appropriate hemisphere, though this is not true for all bilateral functions. However, most of the "higher" areas are confined to the dominant hemisphere.

据说在婴儿早期情况要好得多；在生命的头六个月中，对优势半球的大范围损伤可能迫使通常的次半球接替其位置；因此患者看起来比损伤发生在更晚阶段时正常得多。这与神经系统在生命最初几周表现出的巨大可塑性，以及后来迅速发展的巨大僵硬性相当一致。可能在没有这种严重损伤的情况下，利手性在非常年幼的儿童中是相当灵活的。然而，早在学龄之前，自然的利手性和大脑优势就终身确定了。

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For example, in the adult, the effect of an

过去人们认为左利手是一种严重的社会劣势。由于大多数工具、课桌和体育器材主要是为右利手设计的，这确实在一定程度上是如此。此外，在过去，左利手还受到某种迷信式的反对——就像胎记或红发等许多偏离人类常态的次要变异一样。

Chapter VII

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extensive injury in the secondary hemisphere is far less serious than the effect of a similar injury in the dominant hemisphere. At a relatively early age in his career, Pasteur suffered a cerebral hemorrhage on his right side which left him with a moderate degree of one-­sided paralysis, a hemiplegia. When he died, his brain was examined, and he was found to be suffering from a right-­sided injury, so extensive that it has been said that after his injury "he had only half a brain." There certainly were extensive lesions of the parietal and temporal regions.

出于各种动机的混合，许多人曾试图甚至成功地通过教育改变他们孩子外部的利手性——尽管当然他们无法改变其在半球优势上的生理基础。结果发现，在许多情况下，这些半球转换者患有口吃及其他语言、阅读和书写方面的缺陷，严重到损害了他们的生活前景和正常职业生涯的希望。我们现在至少看到了这种现象的一种可能解释。

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Nevertheless, after this injury he did some of his best work. A similar injury of the left side in a right-­handed adult would almost certainly have been fatal and would certainly reduce the patient into an animal condition of mental and nervous crippledness. It is said that the situation is considerably better in early infancy, and that in the first six months of life an extensive injury to the dominant hemisphere may compel the normally secondary hemisphere to take its place; so that the patient appears far more nearly normal than he would be had the injury occurred at a later stage.

随着次手的教育，次半球中处理熟练运动——如书写——的那部分也得到了部分教育。然而，由于这些运动与阅读、言语及其他与优势半球密不可分联系的活动以尽可能紧密的关联进行，涉及此类过程的神经元链必须从一个半球穿到另一个半球再返回；在任何复杂的过程中，它们必须反复这样做。现在，像人脑这样大的大脑中，半球之间的直接连接器——大脑连合——数量如此之少，以至于它们几乎没有什么用处，半球间的交通必须通过脑干的迂回路径进行——我们对这些路径的了解非常不完善，但它们肯定很长、稀少且容易中断。

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This is quite in accordance with the general great flexibility shown by the nervous system in the early weeks of life, and the great rigidity which it rapidly develops later. It is possible that, short of such serious injuries, handedness is reasonably flexible in the very young child. However, long before the child is of school age, the natural handedness and cerebral dominance are established for life.

结果，与言语和书写相关的过程非常容易卷入交通阻塞，口吃就成为世界上最自然的事情。也就是说，人脑可能已经太大了，无法有效利用所有解剖学上似乎存在的能力。在猫中，优势半球的破坏似乎比人类造成的损伤相对较小，而次半球的破坏可能造成更大的损伤。

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It used to be thought that left-­handedness was a serious social disadvantage. With most tools, school desks, and sports equipment primarily made for the right-­handed, it certainly is to some extent. In the past, moreover, it was viewed with some of the superstitious disapproval that has attached to so many minor variations from the human norm, such as birthmarks or red hair.

无论如何，两个半球的功能分配更为均等。在人类中，通过大脑体积和复杂性的增加所获得的收益，被这样一个事实部分抵消——即更少的器官部分可以同时被有效使用。

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From a combination of

有趣的是，我们可能正面临自然界的某种局限——在这种局限中，高度特化的器官达到效率递减的水平，并最终导致物种的灭绝。人脑在其通往这种破坏性特化的道路上，可能已经像最后一批雷兽的巨大鼻角一样走得那么远了。

Cybernetics and Psychopathology

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motives, many people have attempted and even succeeded, in changing the external handedness of their children by education, though of course they could not change its physiological basis in hemispheric dominance. It was then found that in very many cases these hemispheric changelings suffered from stuttering and other defects of speech, reading, and writing, to the extent of seriously wounding their prospects in life and their hopes for a normal career. We now see at least one possible explanation for the phenomenon.

一个组织——其元素本身也是小组织——的概念既非陌生亦非新颖。古希腊的松散联盟、神圣罗马帝国及其类似构成的封建同时代者、瑞士誓约同盟、尼德兰联合共和国、美利坚合众国及其南部的众多联合州、苏维埃社会主义共和国联盟——都是政治领域中组织层次结构的例子。霍布斯的"利维坦"——由较小的人组成的国家人——是同一思想在低一层尺度上的例证，而莱布尼茨将生命有机体视为一个充满其他生命有机体（如血细胞）的充实体的处理，则只是同一方向的又一步。

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With the education of the secondary hand, there has been a partial education of that part of the secondary hemisphere which deals with skilled motions, such as writing. Since, however, these motions are carried out in the closest possible association with reading, speech, and other activities which are inseparably connected with the dominant hemisphere, the neuron chains involved in processes of the sort must cross over from hemisphere to hemisphere and back; and in a process of any complication, they must do this again and again. Now, the direct connectors between the hemispheres--­the cerebral commissures--­in a brain as large as that of man are so few in number that they are of very little use, and the interhemispheric traffic must go by roundabout routes through the brain stem, which we know very imperfectly but which are certainly long, scanty, and subject to interruption.

事实上，这几乎不过是细胞理论的哲学前奏——根据该理论，大多数中等大小的动植物和所有大型动植物都由细胞构成，这些细胞具有独立生命有机体的许多——如果不是全部——属性。多细胞生物本身可能成为更高层次生物的构建砖石，例如葡萄牙僧帽水母——它是一种由分化的腔肠动物水螅体组成的复杂结构，其中各个个体以不同方式被改变以服务于整个群落的营养、支撑、运动、排泄、繁殖和支持。

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As a consequence, the processes associated with speech and writing are very likely to be involved in a traffic jam, and stuttering is the most natural thing in the world. That is, the human brain is probably too large already to use in an efficient manner all the facilities which seem to be anatomically present. In a cat, the destruction of the dominant hemisphere seems to produce relatively less damage than in man, and the destruction of the secondary hemisphere probably more

严格来说，这种物理上联合的群体在组织方面提出的哲学问题，并不比在较低个体性水平上出现的问题更深奥。对于人类和其他社会性动物——狒狒或牛的群体、海狸群落、蜂群、黄蜂或蚂蚁的巢穴——情况则大不相同。

Chapter VII

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damage. At any rate, the apportionment of function in the two hemispheres is more nearly equal. In man, the gain achieved by the increase in size and complication of the brain is partly nullified by the fact that less of the organ can be used effectively at one time.

群落生活的整合程度很可能接近单个个体行为所显示的水平，但个体可能拥有固定的神经系统，各元素之间具有永久的拓扑关系和永久连接，而群落则由在空间和时间上具有变动关系、没有永久、不可打破的物理连接的个体组成。蜂巢的所有神经组织都是某只蜜蜂的神经组织。那么，蜂巢如何一致行动——而且是高度可变、适应性强、有组织的一致性行动？

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It is interesting to reflect that we may be facing one of those limitations of nature in which highly specialized organs reach a level of declining efficiency and ultimately lead to the extinction of the species. The human brain may be as far along on its road to this destructive specialization as the great nose horns of the last of the titanotheres.

显然，秘密在于其成员之间的相互通信。这种相互通信在复杂性和内容上可以有很大差异。对于人类，它涵盖了语言和文学的全部复杂性，以及更多。

VIII Information, Language, and Society

IX. On Learning and Self-Reproducing Machines

IX On Learning and Self-­Reproducing Machines

IX. On Learning and Self-Reproducing Machines

IX On Learning and Self-­Reproducing Machines

IX. On Learning and Self-Reproducing Machines

IX On Learning and Self-­Reproducing Machines

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Two of the phenomena which we consider to be characteristic of living systems are the power to learn and the power to reproduce themselves. These properties, different as they appear, are intimately related to one another. An animal that learns is one which is capable of being transformed by its past environment into a different being and is therefore adjustable to its environment within its individual lifetime.

他的对手在前一阶段，努力走出能够阻止对方做出致胜或求和走法的一步。如果他自己能在该阶段走出致胜的一步，他就会这样做——而这就不是倒数第二步而是棋局的最后阶段了。在此之前一步的另一个棋手会试图以这样的方式行动，使得对手最好的资源也无法阻止他以致胜走法结束，如此回溯下去。

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An animal that multiplies is able to create other animals in its own likeness at least approximately, although not so completely in its own likeness that they cannot vary in the course of time. If this variation is itself inheritable, we have the raw material on which natural selection can work. If the hereditary invariability concerns manners of behavior, then among the varied patterns of behavior which are propagated some will be found advantageous to the continuing existence of the race and will establish themselves, while others which are detrimental to this continuing existence will be eliminated.

有些游戏如井字棋——整个策略已知——可以从一开始就启动这种策略。当这可行时，它显然是玩该游戏的最佳方式。然而，在像国际象棋和西洋跳棋这样的许多游戏中，我们的知识不足以允许这种完整的策略，因此我们只能近似。

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The result is a certain sort of racial or phylogenetic learning, as contrasted with the ontogenetic learning of the individual. Both ontogenetic and phylogenetic learning are modes by which the animal can adjust itself to its environment.

冯·诺依曼式的近似理论倾向于引导棋手以最大的谨慎行动，假设对手是完全聪明的棋手大师。然而，这种态度并不总是合理的。在战争中——这是一种游戏——这通常会导致不具决定性的行动，往往不比失败好多少。

Chapter IX

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Both ontogenetic and phylogenetic learning, and certainly the latter, extend themselves not only to all animals but to plants and, indeed, to all organisms which in any sense may be considered to be living. However, the degree to which these two forms of learning are found to be important in different sorts of living beings varies widely. In man, and to a lesser extent in the other mammals, ontogenetic learning and individual adaptability are raised to the highest point.

让我举两个历史例子。当拿破仑在意大利与奥地利人作战时，他的部分优势在于他知道奥地利人的军事思维方式僵化守旧，因此他完全有理由假设他们无法利用法国大革命士兵发展出的新的、决定性的作战方法。

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Indeed, it may be said that a large part of the phylogenetic learning of man has been devoted to establishing the possibility of good ontogenetic learning. It has been pointed out by Julian Huxley in his fundamental paper on the mind of birds1 that birds have a small capacity for ontogenetic learning. Something similar is true in the case of insects, and in both instances it may be associated with the terrific demands made on the individual by flight and the consequential pre-­emption of the capabilities of the nervous system which might otherwise be applied to ontogenetic learning.

当纳尔逊与欧洲大陆联合舰队作战时，他的优势在于他与一支多年来掌控海洋的海军作战，这支部队发展出了他深知敌人无法企及的思维方法。如果他没有充分利用这一优势——相反，如果他假设面对的是拥有同等海军经验的敌人而不得不谨慎行事——他可能在长期内仍会获胜，但不可能如此迅速和决定性地获胜，从而建立起最终导致拿破仑垮台的严密海上封锁。

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Complicated as the behavior patterns of birds are--­in flying, in courtship, in the care of the young, and in nest building--­they are carried out correctly the very first time without the need of any large amount of instruction from the mother. It is altogether appropriate to devote a chapter of this book to these two related subjects. Can man-­made machines learn and can they reproduce themselves?

因此，在这两种情况下，指导因素都是指挥官及其对手已知的历史记录——如同他们过去行动的统计表现——而不是试图针对完美对手下出完美棋局。在这些情况下直接使用冯·诺依曼博弈论方法将是徒劳的。类似地，关于国际象棋理论的书籍不是从冯·诺依曼的角度写的。

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We shall try to show in this chapter that in fact they can learn and can reproduce themselves, and we shall give an account of the technique needed for both these activities. The simpler of these two processes is that of learning, and it is there that the technical development has gone furthest. I shall talk here particularly of the learning of game-­playing machines

它们是棋手在与高水平、知识渊博的其他棋手对弈的实践经验中得出的原则汇编；它们确立了赋予丢子、机动性、控制、发展以及其他可能随游戏阶段变化的因素以一定的数值或权重。制造会下某种象棋的机器并不太难。仅仅是遵守游戏规则、只走出合法着法，这对于相当简单的计算机来说很容易实现。

On Learning and Self-­Reproducing Machines

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which enables them to improve the strategy and tactics of their performance by experience. There is an established theory of the playing of games--­the von Neumann theory.2 It concerns a policy which is best considered by working from the end of the game rather than from the beginning. In the last move of the game, a player strives to make a winning move if possible, and if not, then at least a drawing move.

事实上，使普通的数字计算机适应这些目的并不困难。现在面临的问题是游戏规则内的策略。对于棋子、控制、机动性等的每一种评估，本质上都可以还原为数值形式；当这样做时，国际象棋书籍的格言可以用于确定每个阶段的最佳走法。这样的机器已经制造出来；它们能下出相当不错的业余象棋，尽管目前还不能达到大师级别。

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His opponent, at the previous stage, strives to make a move which will prevent the other player from making a winning or a drawing move. If he can himself make a winning move at that stage, he will do so, and this will not be the next to the last but the last stage of the game. The other player at the move before this will try to act in such a way that the very best resources of his opponent will not prevent him from ending with a winning move, and so on backward.

想象一下，你正与这样的机器对弈。为了使情况公平，假设你是在通讯象棋，不知道你在与这样的机器对弈，也没有这种知识可能引起的偏见。自然，如象棋中一贯的情况，你会对你的对手的棋风人格形成判断。

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There are games such as ticktacktoe where the entire strategy is known, and it is possible to start this policy from the very beginning. When this is feasible, it is manifestly the best way of playing the game. However, in many games like chess and checkers our knowledge is not sufficient to permit a complete strategy of this sort, and then we can only approximate to it.

你会发现，当同一局面在棋盘上出现两次时，你的对手每次的反应都是一样的，你会发现他的棋风人格非常僵硬。如果你的任何技巧有效，那么在相同的条件下它总是有效。因此，对于一个专家来说，摸清机器对手的套路并每次都击败它并不太难。

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The von Neumann type of approximate theory tends to lead a player to act with the utmost caution, assuming that his opponent is the perfectly wise sort of a master. This attitude, however, is not always justified. In war, which is a sort of game, this will in general lead to an indecisive action which will often be not much better than a defeat.

然而，有些机器不能这样轻易地被击败。假设每隔几局，机器会暂停一下，将其设施用于另一个目的。这一次，它不对阵对手，而是检查之前记录在存储器中的所有对局，以确定棋子价值、控制、机动性等不同评估指标的什么权重分配最有利于获胜。

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Let me give two historical examples. When Napoleon fought the Austrians in Italy, it was part of his effectiveness that he knew the Austrian mode of military thought to be hidebound and traditional, so that he was quite justified in assuming that they were incapable

通过这种方式，它不仅从自己的失败中学习，也从对手的成功中学习。它现在用新的估值取代旧有的估值，作为一个新的、更好的机器继续下棋。这样的机器不再具有那么僵硬的棋风人格，

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of taking advantage of the new decision-­compelling methods of war which had been developed by the soldiers of the French Revolution. When Nelson fought the combined fleets of continental Europe, he had the advantage of fighting with a naval machine which had kept the seas for years and which had developed methods of thought of which, as he was well aware, his enemies were incapable. If he had not made the fullest possible use of this advantage, instead of acting as cautiously as he would have had to act under the supposition that he was facing an enemy of equal naval experience, he might have won in the long run but could not have won so quickly and decisively as to establish the tight naval blockade which was the ultimate downfall of Napoleon.

曾经对它有效的技巧最终将失败。不仅如此，随着时间推移，它可能会吸收对手的一些策略。所有这些在国际象棋中都很难做到，事实上，这种技术的充分发展——使得机器能够下出大师级象棋——尚未完成。

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Thus, in both cases, the guiding factor was the known record of the commander and of his opponents, as exhibited statistically in the past of their actions, rather than an attempt to play the perfect game against the perfect opponent. Any direct use of the von Neumann method of game theory in these cases would have proved futile. In a similar way, books on chess theory are not written from the von Neumann point of view.

西洋跳棋提供了一个更简单的问题。棋子价值的同质性大大减少了需要考虑的组合数量。此外，部分由于这种同质性的结果，跳棋游戏比国际象棋少了很多明确的阶段划分。

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They are compendia of principles drawn from the practical experience of chess players playing against other chess players of high quality and wide knowledge; and they establish certain values or weightings to be given to the loss of each piece, to mobility, to command, to development, and to other factors which may vary with the stage of the game. It is not very difficult to make machines which will play chess of a sort. The mere obedience to the laws of the game, so that only legal moves are made, is easily within the power of quite simple computing machines.

即使在西洋跳棋中，残局的主要问题也不再是吃子，而是与敌方建立接触以便能够吃子。类似地，象棋中走法的估值必须针对不同阶段独立进行。不仅残局与中局在首要考虑因素上不同，而且开局比中局更致力于将棋子调动到攻击和防御的自由机动位置。

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Indeed, it is not hard to adapt an ordinary digital machine to these purposes.

结果是，我们不能仅仅满足于对整个游戏的各个加权因素进行统一评估，而必须将学习过程分成若干独立的阶段。只有这样，我们才能有望构建一台能下出大师级象棋的学习机器。

On Learning and Self-­Reproducing Machines

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Now comes the question of policy within the rules of the game. Every evaluation of pieces, command, mobility, and so forth, is intrinsically capable of being reduced to numerical terms; and when this is done, the maxims of a chess book may be used for the determination of the best moves of each stage. Such machines have been made; and they will play a very fair amateur chess, although at present not a game of master caliber.

一级编程的思想——在某些情况下可能是线性的——与二级编程相结合——后者使用更广泛的过去记录来确定一级编程中要执行的策略——已经在本章前面结合预测问题提到过。预测器利用飞机飞行的近期过去作为工具，

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Imagine yourself in the position of playing chess against such a machine. To make the situation fair, let us suppose you are playing correspondence chess without the knowledge that it is such a machine you are playing and without the prejudices that this knowledge may excite. Naturally, as always is the case with chess, you will come to a judgment of your opponent's chess personality.

通过线性运算预测未来；但确定正确的线性运算是一个统计问题，其中飞行的长期过去以及许多类似飞行的过去被用来提供统计基础。使用长期过去来确定基于短期过去要执行的策略所需的统计研究是高度非线性的。事实上，在利用维纳-霍普夫方程进行预测时，该方程系数的确定是以非线性方式进行的。

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You will find that when the same situation comes up twice on the chessboard, your opponent's reaction will be the same each time, and you will find that he has a very rigid personality. If any trick of yours will work, then it will always work under the same conditions. It is thus not too hard for an expert to get a line on his machine opponent and to defeat him every time.

一般来说，学习机器通过非线性反馈运作。由塞缪尔和渡边描述的西洋跳棋机器，在10到20小时的编程操作基础上，可以相当一贯地击败为其编程的人。渡边关于使用编程机器的哲学思想非常令人兴奋。

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However, there are machines that cannot be defeated so trivially. Let us suppose that every few games the machine takes time off and uses its facilities for another purpose. This time, it does not play against an opponent, but examines all the previous games which it has recorded on its memory to determine what weighting of the different evaluations of the worth of pieces, command, mobility, and the like, will conduce most to winning.

一方面，他正在处理一种证明初等几何定理的方法——该方法按照优雅性和简单性的某些标准以最优方式符合——作为不是针对单个对手而是针对我们所谓的"标准对手"的学习游戏。渡边正在研究的类似游戏也在逻辑归纳中进行，当我们希望建立一种在类似的准美学意义上最优的理论时——基于对经济性、直接性等的评估——通过确定留待自由的有限数量参数的评估值。诚然，这只是有限的逻辑归纳，但非常值得研究。许多我们不常视为游戏的斗争活动形式，从博弈机理论中获得了大量启示。

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In this way, it learns not only from its own failures but its opponent's successes. It now replaces its earlier valuations by the new ones and goes on playing as a new and better machine. Such a machine would no longer have as rigid a personality, and the

一个有趣的例子是猫鼬与蛇的搏斗。正如吉卜林在《里基-蒂基-塔维》中所指出的，猫鼬对眼镜蛇的毒液并非免疫，尽管其坚硬毛发的皮毛在一定程度上保护了它，使蛇难以咬穿。正如吉卜林所说，搏斗是一场与死亡的舞蹈，是肌肉技巧和敏捷性的较量。没有理由认为猫鼬的个别动作比眼镜蛇更快或更准。

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tricks which were once successful against it will ultimately fail. More than that, it may absorb in the course of time something of the policy of its opponents. All this is very difficult to do in chess, and as a matter of fact the full development of this technique, so as to give rise to a machine that can play master chess, has not been accomplished.

然而，猫鼬几乎总是杀死眼镜蛇而毫发无损地胜出。它是如何做到的呢？我在这里根据看过这样的搏斗以及此类搏斗的电影，给出一个在我看来似乎有效的描述。我不保证我的观察作为解释的正确性。

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Checkers offers an easier problem. The homogeneity of the values of the pieces greatly reduces the number of combinations to be considered. Moreover, partly as a consequence of this homogeneity, the checker game is much less divided into distinct stages than the chess game.

猫鼬从佯攻开始，这激使蛇出击。猫鼬闪避并做出另一个这样的佯攻，因此我们有了两只动物活动的一种有节奏的模式。然而，这种舞蹈并非静止的，而是逐步发展的。随着它继续，猫鼬的佯攻相对于眼镜蛇的出击的相位越来越提前，直到最终猫鼬在蛇伸展身体、无法快速移动时发起攻击。这一次猫鼬的攻击不是佯攻，而是精准致命的咬穿蛇脑。

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Even in checkers, the main problem of the end game is no longer to take pieces but to establish contact with the enemy so that one is in a position to take pieces. Similarly, the valuation of moves in the chess game must be made independently for the different stages. Not only is the end game different from the middle game in the considerations which are paramount, but the openings are much more devoted to getting the pieces into a position of free mobility for attack and defense than is the middle game.

换句话说，蛇的行为模式局限于单个出击，每次只考虑一次，而猫鼬的行为模式则涉及搏斗整个过去历史的可观（即使不是很长）片段。在这个意义上，猫鼬的行为就像一台学习机器，其攻击的真正致命性依赖于更高度组织的神经系统。正如几年前一部沃尔特·迪士尼电影所展示的，我们西部的一种鸟——走鹃——攻击响尾蛇时也会发生非常类似的情况。

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The result is that we cannot be even approximately content with a uniform evaluation of the various weighting factors for the game as a whole, but must divide the learning process into a number of separate stages. Only then can we hope to construct a learning machine which can play master chess. The idea of a first-­order programming, which may be linear in certain cases, combined with a second-­order programming, which uses a much more extensive segment of the past for the determination of the policy to be carried out in the first-­order programming, has been mentioned earlier in this book in connection with the problem of prediction.

虽然这种鸟用喙和爪战斗，而猫鼬用牙齿，但活动模式非常相似。斗牛也是同样事物的一个很好例证。因为必须记住，斗牛不是一项运动，而是一场与死亡的舞蹈，展示公牛和人的优美和交织协调的动作。

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The predictor uses the immediate past of the flight of the airplane as a tool for the

公平对待公牛并不在其中，从我们的观点来看，我们可以忽略公牛被预先刺激和削弱的阶段——这些阶段的目的是将比赛带到一个水平，使两个参与者模式之间的互动发展得最为高度。熟练的斗牛士有一个大的可能动作库——如挥动披肩、各种闪避和旋转等——旨在将公牛带入一个它完成冲锋并伸展着身体的姿势，而斗牛士正好准备将剑刺入公牛的心脏。

On Learning and Self-­Reproducing Machines

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prediction of the future by means of a linear operation; but the determination of the correct linear operation is a statistical problem in which the long past of the flight and the past of many similar flights are used to give the basis of the statistics. The statistical studies necessary to use a long past for a determination of the policy to be adopted in view of the short past are highly non-­linear. As a matter of fact, in the use of the Wiener-Hopf equation for prediction,3 the determination of the coefficients of this equation is carried out in a non-­linear manner.

我关于猫鼬与眼镜蛇搏斗或斗牛士与公牛搏斗所说的，也适用于人与人之间的体力竞赛。考虑小剑决斗。它包含一系列佯攻、格挡和刺击，每位参与者都意图使对手的剑偏离路线到足以让他能够刺中而不至于陷入双重遭遇。同样，在冠军网球赛中，就每个单独击球而言，仅仅完美地发球或回球是不够的；策略应该是迫使对手进入一系列回球，使他逐步处于更不利的位置，直到他无法安全回球。

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In general, a learning machine operates by non-­linear feedback. The checker-­playing machine described by Samuel4 and Watanabe5 can learn to defeat the man that programmed it in a fairly consistent way on the basis of from 10 to 20 operating hours of programming. Watanabe's philosophical ideas on the use of programming machines are very exciting.

这些体力竞赛和我们假设博弈机所玩的那类游戏，都具有相同的学习元素——即根据对手和自身习惯的经验来学习。对于身体对抗的游戏如此，对于智力因素更强的竞赛——如战争和模拟战争的兵棋推演——也是如此，我们的参谋军官通过这些游戏获得其军事经验的要素。

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On the one hand, he is treating a method of proving an elementary geometrical theorem which shall conform in an optimal way according to certain criteria of elegance and simplicity, as a learning game to be played not against an individual opponent but against what we may call "Colonel Bogey." A similar game which Watanabe is studying is played in logical induction, when we wish to build up a theory which is optimal in a similar quasi-­aesthetic way, on the basis of an evaluation of economy, directness, and the like, by the determination of the evaluation of a finite number of parameters which are left free. This, it is true, is only a limited logical induction, but it is well worth studying. Many forms of the activity of struggle, which we do not ordinarily consider as games, have a great deal of light thrown on them by the theory of game-­playing machines.

这对于经典陆战和海战都是如此，对于新的、尚未尝试的原子武器战争也同样成立。一定程度的机械化——类似于通过机器学习的西洋跳棋机械化——在所有这些方面都是可能的。没有什么比设想第三次世界大战更危险的了。值得考虑的是，部分危险是否可能内在于对学习机器的无防御使用。

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One interesting example is the fight between a mongoose and a snake. As Kipling

我曾一次又一次地听到这样的说法：学习机器不能让我们面临任何新的危险，因为我们可以随时关掉它们。但真的可以吗？要有效关掉一台机器，我们必须拥有关于危险点是否已经到来的信息。仅仅我们已经制造了机器这个事实并不能保证我们拥有这样做的适当信息。

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points out in "Rikki-­Tikki-­Tavi," the mongoose is not immune to the poison of the cobra, although it is to some extent protected by its coat of stiff hairs which makes it difficult for the snake to bite home. As Kipling states, the fight is a dance with death, a struggle of muscular skill and agility. There is no reason to suppose that the individual motions of the mongoose are faster or more accurate than those of the cobra.

这一点已经隐含在这样一个事实中：西洋跳棋机器可以在非常有限的运行时间后击败为其编程的人。此外，现代数字机器的极高运行速度妨碍了我们感知和思考危险指示的能力。关于具有巨大能力和执行策略能力的非人装置及其危险的想法，并不新鲜。新鲜的是我们现在拥有了这种有效的装置。

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Yet the mongoose almost invariably kills the cobra and comes out of the contest unscathed. How is it able to do this? I am here giving an account which appears valid to me, from having seen such a fight, as well as motion pictures of other such fights.

在过去，类似的可能性被归于魔法技术——这正是如此多传说和民间故事的主题。这些故事深入探索了魔法师的道德处境。我已经在一本名为《人有人的用处》的早期著作中讨论了魔法传说伦理学的某些方面。

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I do not guarantee the correctness of my observations as interpretations. The mongoose begins with a feint, which provokes the snake to strike. The mongoose dodges and makes another such feint, so that we have a rhythmical pattern of activity on the part of the two animals.

我在此重复我在那里讨论过的一些材料，以便在新的学习机器的背景下更精确地呈现它们。最著名的魔法故事之一是歌德的《魔法师的学徒》。在这个故事中，魔法师留下他的学徒和杂役独自做打水的杂务。因为男孩懒惰而机灵，他把工作转给了一把扫帚——他对扫帚念了从主人那里听到的魔法咒语。

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However, this dance is not static but develops progressively. As it goes on, the feints of the mongoose come earlier and earlier in phase with respect to the darts of the cobra, until finally the mongoose attacks when the cobra is extended and not in a position to move rapidly. This time the mongoose's attack is not a feint but a deadly accurate bite through the cobra's brain.

扫帚顺从地为他做了工作，却不肯停下。男孩快要被淹死了。他发现自己没有学会——或忘记了——停止扫帚的第二句咒语。绝望中，他拿起扫帚柄，在膝盖上折断，却惊恐地发现扫帚的每一半都继续打水。幸运的是，在他完全被毁灭之前，主人回来了，念出停止扫帚的权力之言，并狠狠责骂了学徒一番。

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In other words, the snake's pattern of action is confined to single darts, each one for itself, while the pattern of the mongoose's action involves an appreciable, if not very long, segment of the whole past of the fight. To this extent the mongoose acts like a learning machine, and the real deadliness of its attack is dependent on a much more highly organized nervous system. As a Walt Disney movie of several years ago showed, something very similar happens when one of our western birds, the road runner, attacks a rattlesnake.

另一个故事是《天方夜谭》中渔夫和精灵的故事。渔夫在网中捞起了一个用所罗门封印封口的罐子。这是所罗门囚禁叛逆精灵的容器之一。精灵以一团烟雾出现，巨大的身影告诉渔夫，在监禁的头几年他曾决心用权力和财富奖赏他的拯救者，但如今他已决定立即杀死他。幸运的是，渔夫找到了将精灵骗回瓶中的方法，然后他把罐子扔到了海底。

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While the bird fights with

比这两个故事更可怕的是世纪初英国作家W·雅各布斯所写的《猴掌》寓言。一位退休的英国工人在桌边与妻子和一位朋友——一位刚从印度回来的英国军士长——坐在一起。军士长向主人展示了一个干燥、皱缩的猴掌形式的护身符。

On Learning and Self-­Reproducing Machines

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beak and claws, and a mongoose with its teeth, the pattern of activity is very similar. A bullfight is a very fine example of the same thing. For it must be remembered that the bullfight is not a sport but a dance with death, to exhibit the beauty and the interlaced coordinating actions of the bull and the man.

一位印度圣人——他希望通过它来展示违抗命运的愚蠢——赋予了它向三人各实现三个愿望的力量。士兵说他不知道第一个主人的前两个愿望是什么，但最后一个愿望是死亡。他本人——正如他告诉朋友的——是第二个主人，但不愿谈论他自己经历的恐怖。他将猴掌扔进火中，但他的朋友将其捡回并希望测试其力量。

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Fairness to the bull has no part in it, and we can leave out from our point of view the preliminary goading and weakening of the bull, which have the purpose of bringing the contest to a level where the interaction of the patterns of the two participants is most highly developed. The skilled bullfighter has a large repertory of possible actions, such as the flaunting of the cape, various dodges and pirouettes, and the like, which are intended to bring the bull into a position in which it has completed its rush and is extended at the precise moment that the bullfighter is ready to plunge the estoque into the bull's heart. What I have said concerning the fight between the mongoose and the cobra, or the toreador and the bull, will also apply to physical contests between man and man.

他的第一个愿望是200英镑。不久后传来敲门声，他儿子受雇公司的官员进入房间。父亲得知他的儿子已在机器中丧生，但公司——在不承认任何责任或法律义务的情况下——愿意支付给父亲200英镑作为慰问金。

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Consider a duel with the small-­sword. It consists of a sequence of feints, parries, and thrusts, with the intention on the part of each participant to bring his opponent's sword out of line to such an extent that he can thrust home without laying himself open to a double encounter. Again, in a championship game of tennis, it is not enough to serve or return the ball perfectly as far as each individual stroke is considered; the strategy is rather to force the opponent into a series of returns which put him progressively in a worse position until there is no way in which he can return the ball safely.

悲痛欲绝的父亲做出了第二个愿望——希望儿子回来——当又传来敲门声并打开门时，出现了一个东西——虽然没有明说——是他儿子的鬼魂。最后的愿望是让这个鬼魂离开。在所有这三个故事中，关键点在于魔法力量是字面思维的；如果我们向它们祈求恩惠，我们必须请求我们真正想要的，而不是我们认为想要的。

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These physical contests and the sort of games which we have supposed the game-­playing machine to play both have the same element of learning in terms of experience of the opponent's

新的、真实的学习机器代理也是字面思维的。如果我们为一台赢得战争的机器编程，我们必须想好我们所说的"胜利"是什么意思。学习机器必须通过经验编程。

Chapter IX

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habits as well as one's own. What is true of games of physical encounter is also true of contests in which the intellectual element is stronger, such as war and the games which simulate war, by which our staff officers win the elements of their military experience. This is true for classical war both on land and at sea, and is equally true with the new and as yet untried war with atomic weapons.

一场核战争的唯一不会立即带来灾难的经验就是战争游戏的经验。如果我们要用这个经验作为我们在真正紧急情况下行动程序的指南，我们在编程游戏中所使用的胜利价值，必须是在战争实际结果中我们内心所持有的同一价值。我们只有在直接、彻底、不可挽回的危险中才能在这个问题上失败。

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Some degree of mechanization, parallel to the mechanization of checkers by learning machines, is possible in all these. There is nothing more dangerous to contemplate than World War III. It is worth considering whether part of the danger may not be intrinsic in the unguarded use of learning machines.

我们不能指望机器会追随我们那些使我们得以把毁灭称为胜利的偏见和情感妥协。如果我们要求胜利却不知道我们所说的胜利是什么意思，我们将会发现鬼魂在敲我们的门。关于学习机器就谈这么多。现在让我谈谈自我传播机器。

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Again and again I have heard the statement that learning machines cannot subject us to any new dangers, because we can turn them off when we feel like it. But can we? To turn a machine off effectively, we must be in possession of information as to whether the danger point has come.

在这里，机器和自我传播这两个词都很重要。机器不仅是一种物质形式，而且是完成某种确定目的的工具。自我传播不仅是创造一个有形的复制品；它还是创造能够执行相同功能的复制品。

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The mere fact that we have made the machine does not guarantee that we shall have the proper information to do this. This is already implicit in the statement that the checker-­playing machine can defeat the man who has programmed it, and this after a very limited time of working in. Moreover, the very speed of operation of modern digital machines stands in the way of our ability to perceive and think through the indications of danger.

在这里，两种不同的观点显现出来。一种是纯粹组合性的，涉及一个机器是否可以有足够的部件和足够复杂的结构以使自我复制成为其功能之一。这个问题的答案已经被已故的约翰·冯·诺依曼肯定地回答了。另一个问题涉及构建自我复制机器的实际操作程序。

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The idea of non-­human devices of great power and great ability to carry through a policy, and of their dangers, is nothing new. All that is new is that now we possess effective devices of this kind. In the past, similar possibilities were postulated for the techniques of magic, which forms the theme for so many legends and folk tales.

在这里，我将把我的注意力集中在一类机器上——虽然它不涵盖所有机器，但具有很大的一般性。我指的是非线性换能器。这样的机器是以时间的单一函数作为输入，并以另一个时间函数作为输出的装置。输出完全由输入的过去决定；但一般来说，输入的相加并不对应输出的相加。这类装置被称为换能器。

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These tales have thoroughly explored the moral situation of the magician. I have already discussed some

所有换能器——线性或非线性——的一个性质是对时间平移的不变性。如果一台机器执行某种函数，那么当输入在时间上向后平移时，输出也向后平移相同的量。自我复制机器理论的基础是非线性换能器表示的一种标准形式。

On Learning and Self-­Reproducing Machines

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aspects of the legendary ethics of magic in an earlier book entitled The Human Use of Human Beings.6 I here repeat some of the material which I have discussed there, in order to bring it out more precisely in its new context of learning machines. One of the best-­known tales of magic is Goethe's "The Sorcerer's Apprentice." In this, the sorcerer leaves his apprentice and factotum alone with the chore of fetching water. As the boy is lazy and ingenious, he passes the work over to a broom, to which he has uttered the words of magic which he has heard from his master.

在这里，在线性装置理论中如此重要的阻抗和导纳概念并不完全适用。我们将不得不参考某些较新的方法来实现这种表示——部分由我本人、部分由伦敦大学的丹尼斯·伽柏教授发展的方法。虽然伽柏教授的方法和我自己的方法都导致了非线性换能器的构建，但它们在以下范围内是线性的：非线性换能器被表示为其输出是一组具有相同输入的非线性换能器输出的总和。

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The broom obligingly does the work for him and will not stop. The boy is on the verge of being drowned out. He finds that he has not learned, or has forgotten, the second incantation which is to stop the broom.

这些输出以不同的线性系数组合。这允许我们在非线性换能器的设计和规范中使用线性展开理论。特别是，这种方法允许我们通过最小二乘法获得组成元素的系数。

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In desperation, he takes the broomstick, breaks it over his knee, and finds to his consternation that each half of the broom continues to fetch water. Luckily, before he is completely destroyed, the master returns, says the Words of Power to stop the broom, and administers a good scolding to the apprentice. Another story is the Arabian Nights tale of the fisherman and the genie.

如果我们将此与对装置所有输入的统计平均方法结合起来，我们就有了正交展开理论的一个分支。非线性换能器理论的这种统计基础，可以通过对每种特定情况下所用输入的过去统计数据的实际研究来获得。这是对伽柏教授方法的粗略描述。

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The fisherman has dredged up in his net a jug closed with the seal of Solomon. It is one of the vessels in which Solomon has imprisoned the rebellious genie. The genie emerges in a cloud of smoke, and the gigantic figure tells the fisherman that, whereas in his first years of imprisonment he had resolved to reward his rescuer with power and fortune, he has now decided to slay him out of hand.

而我的方法在本质上类似，但我工作的统计基础略有不同。众所周知，电流不是连续传导的，而是通过必须具有统计偏差的电子流来实现的。

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Luckily for himself, the fisherman finds a way to talk the genie back into the bottle, upon which he casts the jar to the bottom of the ocean. More terrible than either of these two tales is the fable of the monkey's paw, written by W. Jacobs, an English writer of the beginning of the century.

这些统计波动可以通过布朗运动理论来相当好地表示，或者通过类似的散粒效应或管噪声理论——我将在下一章中对此进行讨论。无论如何，可以制造装置来生成具有高度特定统计分布的标准化散粒效应，这种装置正在商业上生产。

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A retired English workingman is

注意，管噪声在某种意义上是一种通用输入，因为它在足够长时间内的波动迟早会近似于任何给定曲线。这种管噪声具有非常简单的积分和平均理论。根据管噪声的统计，我们可以容易地确定一封闭的正交非线性运算集合。

Chapter IX

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sitting at his table with his wife and a friend, a returned British sergeant-­major from India. The sergeant-­major shows his hosts an amulet in the form of a dried, wizened monkey's paw. This has been endowed by an Indian holy man, who has wished to show the folly of defying fate, with the power of granting three wishes to each of three people.

如果受这些运算支配的输入具有适当的管噪声统计分布，则我们的装置的两个组件输出的平均乘积——其中该平均值关于管噪声的统计分布取——将为零。此外，每个装置的均方输出可以归一化为1。结果是，一般非线性换能器在这些组件方面的展开，来源于熟悉的正交函数理论的应用。

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The soldier says that he knows nothing of the first two wishes of the first owner, but the last one was for death. He himself, as he tells his friends, was the second owner but will not talk of the horror of his own experiences. He casts the paw into the fire, but his friend retrieves it and wishes to test its powers.

具体来说，我们的各个装置给出的输出是输入的拉盖尔系数中的埃尔米特多项式的乘积。这在《随机理论中的非线性问题》中有详细阐述。当然，首先在一组可能输入上求平均是困难的。

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His first is for £200. Shortly thereafter there is a knock at the door, and an official of the company by which his son is employed enters the room. The father learns that his son has been killed in the machinery, but that the company, without recognizing any responsibility or legal obligation, wishes to pay the father the sum of £200 as a solatium.

使这一困难任务可实现的是：散粒效应输入具有所谓的度量传递性或遍历性。散粒效应输入分布参数的几乎任何可积函数，在几乎所有情况下，其时间平均值等于其在集合上的平均值。

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The grief-­stricken father makes his second wish--­that his son may return--­and when there is another knock at the door and it is opened, something appears which, we are not told in so many words, is the ghost of the son. The final wish is that this ghost should go away. In all these stories the point is that the agencies of magic are literal-­minded; and that if we ask for a boon from them, we must ask for what we really want and not for what we think we want.

这使得我们可以取两个具有共同散粒效应输入的装置，并确定其输出在全部可能输入集合上的平均乘积，方法是将它们的输出相乘并在时间上取平均。所有这些过程所需的操作集合，只涉及电位的加法、电位的乘法以及时间平均操作。

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The new and real agencies of the learning machine are also literal-­minded. If we program a machine for winning a war, we must think well what we mean by winning. A learning machine must be programmed by experience.

所有这些装置都存在。事实上，伽柏教授方法所需的基本装置与我的方法所需的是相同的。他的一名学生发明了一种特别有效且廉价的乘法装置，依赖于两个磁线圈吸引的晶体上的压电效应。

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The only experience of a nuclear war which is not immediately catastrophic is the experience of a war game. If we are to use this experience as a guide for our procedure in a real emergency, the values of winning which

这实质上意味着，我们可以用一组线性项的和来模拟任何未知的非线性换能器——每一项具有固定的特性和可调节的系数。这个系数可以确定为未知换能器的输出与特定已知换能器的输出之间的平均乘积——当相同的散粒效应发生器连接到两者的输入端时。

On Learning and Self-­Reproducing Machines

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we have employed in the programming games must be the same values which we hold at heart in the actual outcome of a war. We can fail in this only at our immediate, utter, and irretrievable peril. We cannot expect the machine to follow us in those prejudices and emotional compromises by which we enable ourselves to call destruction by the name of victory.

更有甚者，我们无需按仪表比例计算结果并手工将其转移到相应的换能器——从而产生装置的碎片化模拟——而是自动地将系数转移到反馈装置上完全没有问题。

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If we ask for victory and do not know what we mean by it, we shall find the ghost knocking at our door. So much for learning machines. Now let me say a word or two about self-­propagating machines.

我们成功做到的是制造了一个白箱，它可以潜在地呈现任何非线性换能器的特性，然后通过将两者置于相同的随机输入下，并以适当方式连接结构的输出，将其拉入给定的黑箱换能器的相似性中，

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Here both the words machine and self-­propagating are important. The machine is not only a form of matter, but an agency for accomplishing certain definite purposes. And self-­propagation is not merely the creation of a tangible replica; it is the creation of a replica capable of the same functions.

从而在没有任何我们干预的情况下得出合适的组合。我要问，这与以下情况在哲学上有很大不同吗——基因作为模板，从不明确的氨基酸和核酸混合物中形成相同基因的其他分子；或者病毒引导其宿主组织和汁液中相同病毒的其他分子塑造成其自身形式？我丝毫不声称这些过程的细节相同，但我确实声称它们是哲学上非常相似的现象。

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Here, two different points of view come into evidence. One of these is purely combinatorial and concerns the question whether a machine can have enough parts and sufficiently complicated structure to enable self-­reproduction to be among its functions. This question has been answered in the affirmative by the late John von Neumann.

在上一章中，我讨论了学习和自我传播的问题——既适用于机器，也——至少通过类比——适用于生命系统。在这里，我将重复我在序言中做出的某些评论，并打算立即加以运用。正如我已经指出的，这两种现象密切相关，因为前者是个体通过经验（我们可称之为个体发育学习）适应其环境的基础，而后者——因为它提供了变异和自然选择可以运作的材料——是系统发育学习的基础。

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The other question concerns an actual operative procedure for building self-reproducing machines. Here I shall confine my attentions to a class of machines which, while it does not embrace all machines, is of great generality. I refer to the non-­linear transducer.

正如我已经提到的，哺乳动物——尤其是人类——通过个体发育学习完成了大部分对环境的适应，而鸟类——具有高度多样的行为模式，这些不是在个体生命中学到的——则更多地致力于系统发育学习。我们已经看到了非线性反馈在两种过程的起源中的重要性。本章致力于研究一个具体的自组织系统——在其中非线性现象起着很大作用。

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Such machines are apparatuses which have as an input a single function of time and which have as their output another function of time. The output is completely determined by the past of the input; but in general, the adding of inputs does not add the corresponding outputs. Such pieces of apparatus are known as transducers.

我在这里描述的是我认为在脑电图或脑波的自组织中发生的事情。

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One property of all transducers, linear

要明智地讨论这个问题，我必须先谈谈脑波是什么，以及如何对其结构进行精确的数学处理。多年来人们就知道神经系统的活动伴随着某些电位的产生。这一领域的首次观察可以追溯到上世纪初，由伏打和伽伐尼在青蛙腿的神经肌肉标本中进行。

Chapter IX

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or non-­linear, is an invariance with respect to a translation in time. If a machine performs a certain function, then, if the input is shifted back in time, the output is shifted back by the same amount. Basic to our theory of self-­reproducing machines is a canonical form of the representation of non-­linear transducers.

这是电生理学科学的诞生。然而，这门科学直到本世纪头二十五年末才发展得较为缓慢。值得反思的是，生理学这一分支的发展为何如此缓慢。

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Here the notions of impedance and admittance, which are so essential in the theory of linear apparatus, are not fully appropriate. We shall have to refer to certain newer methods of carrying out this representation, methods developed partly by me7 and partly by Professor Dennis Gabor8 of the University of London. While both Professor Gabor's methods and my own lead to the construction of non-­linear transducers, they are linear to the extent that the non-­linear transducer is represented with an output which is the sum of the outputs of a set of non-­linear transducers with the same input.

用于研究生理电位的原始装置由电流计组成。这些有两个弱点。第一个是，用于移动电流计线圈或指针的全部能量来自神经本身，且极为微小。

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These outputs are combined with varying linear coefficients. This allows us to employ the theory of linear developments in the design and specification of the non-linear transducer. And in particular, this method allows us to obtain coefficients of the constituent elements by a least-­square process.

第二个困难是，那个时代的电流计是一种其可动部分具有相当大惯性的仪器，并且需要非常明确的恢复力才能将指针带到明确的位置；也就是说，根据情况的性质，电流计不仅是一种记录仪器，也是一种扭曲仪器。最早的优秀生理电流计是艾因托文的弦线电流计，其可动部分被简化为一根导线。尽管这种仪器以当时的标准来看已经很出色，但它不足以在没有严重扭曲的情况下记录微小的电位。

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If we join this to a method of statistically averaging over the set of all inputs to our apparatus, we have essentially a branch of the theory of orthogonal development. Such a statistical basis of the theory of non-­linear transducers can be obtained from an actual study of the past statistics of the inputs used in each particular case. This is a rough account of Professor Gabor's methods.

因此，电生理学必须等待一项新技术。这项技术就是电子学，有两种形式。一种基于爱迪生关于气体传导的某些现象的发现，由此产生了

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While mine are essentially similar, the statistical basis for my work is slightly different. It is well known that electrical currents are not conducted continuously but by a stream of electrons which must have

真空管或电子阀用于放大。这使得将弱电位相当忠实地转换为强电位成为可能。因此，它允许我们使用并非来自神经而是受其控制的能量来移动记录装置的最终元件。

On Learning and Self-­Reproducing Machines

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statistical variations from uniformity. These statistical fluctuations can be represented fairly by the theory of the Brownian motion, or by the similar theory of shot effect or tube noise, about which I am going to say something in the next chapter. At any rate, apparatus can be made to generate a standardized shot effect with highly specific statistical distribution, and such apparatus is being manufactured commercially.

第二个发明也涉及真空中的电传导，被称为阴极射线示波器。这使得使用比任何以前的电流计的可动部分都轻得多的电枢成为可能——即电子流。借助这两种装置——单独或结合——本世纪的生理学家已能忠实地追踪微小电位的时间过程——这些电位完全超出了19世纪准确仪器化的范围。

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Note that tube noise is in a sense a universal input in that its fluctuations over a sufficiently long time will sooner or later approximate to any given curve. This tube noise possesses a very simple theory of integration and averaging. In terms of the statistics of tube noise, we can easily determine a closed set of normal and orthogonal non-­linear operations.

通过这些手段，我们已经能够获得放置在头皮上或植入大脑的两个电极之间产生的微小电位的准确时间过程记录。虽然这些电位在19世纪就已经被观察到，但新的准确记录的可用性在二三十年前引起了生理学家的巨大希望。

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If the inputs subject to these operations have the statistical distribution appropriate to tube noise, the average product of the output of two component pieces of our apparatus, where this average is taken with respect to the statistical distribution of tube noise, will be zero. Moreover, the mean square output of each apparatus can be normalized to one. The result is that the development of the general non-­linear transducer in terms of these components results from an application of the familiar theory of orthonormal functions.

至于利用这些装置直接研究大脑活动的可能性，这一领域的领导者包括德国的贝格尔、英国的阿德里安和马修斯，以及美国的贾斯珀、戴维斯和吉布斯夫妇。必须承认，脑电图学的后续发展至今未能实现该领域早期工作者所抱有的美好希望。

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To be specific, our individual pieces of apparatus give outputs which are products of Hermite polynomials in the Laguerre coefficients of the past of the input. This is presented in detail in my Nonlinear Problems in Random Theory. It is of course difficult to average in the first instance over a set of possible inputs.

他们获得的数据是由墨水记录器记录的。这些是非常复杂和不规则的曲线；虽然可以辨别某些主导频率——如约每秒10次振荡的α节律——但墨水记录不适合进一步数学处理。

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What makes this difficult task realizable is that the shot-­effect inputs possess the property known as metric transitivity, or the ergodic property. Any integrable function of the parameter of distribution of shot-­effect inputs has in

结果是，脑电图学更像一门艺术而非科学，依赖于训练有素的观察者基于大量经验识别墨水记录某些特性的能力。这有一个非常根本的缺陷：使脑电图的解释在很大程度上成为主观的事情。

Chapter IX

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almost every instance a time average equal to its average over the ensemble. This permits us to take two pieces of apparatus with a common shot-­effect input, and to determine the average of their product over the entire ensemble of the possible inputs, by taking their product and averaging it over the time. The repertory of operations needed for all these processes involves nothing more than the addition of potentials, the multiplication of potentials, and the operation of averaging over time.

在20世纪20年代末和30年代初，我对连续过程的调和分析产生了兴趣。虽然物理学家以前考虑过这样的过程，但调和分析的数学几乎局限于研究周期性过程或在时间变大（正或负）时趋近于零的过程。我的工作是最早尝试将连续过程的调和分析建立在坚实的数学基础之上的研究之一。

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Devices exist for all these. As a matter of fact, the elementary devices needed in Professor Gabor's methodology are the same as those needed in mine. One of his students has invented a particularly effective and inexpensive multiplying device depending on the piezoelectric effect on a crystal of the attraction of two magnetic coils.

在这方面，我发现基本概念是自相关——这已经被G·泰勒（现为杰弗里·泰勒爵士）用于湍流研究中。对于时间函数f(t)，这个自相关由f(t+τ)乘以f(t)的时间平均表示。引入时间复函数是有利的——尽管在我们研究的实际情况中我们处理的是实函数。

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What this amounts to is that we can imitate any unknown non-­linear transducer by a sum of linear terms, each of fixed characteristics and with an adjustable coefficient. This coefficient can be determined as the average product of the outputs of the unknown transducer and a particular known transducer, when the same shot-­effect generator is connected to the input of both. What is more, instead of computing this result on the scale of an instrument and then transferring it by hand to the appropriate transducer, thus producing a piecemeal simulation of the apparatus, there is no particular problem in automatically effecting the transfer of the coefficients to the pieces of feedback apparatus.

现在，自相关变为f(t+τ)与f(t)的共轭的乘积的平均。无论我们处理的是实函数还是复函数，f(t)的功率谱由自相关的傅里叶变换给出。我已经谈到过墨水记录不适合进一步数学处理的缺点。在自相关概念产生任何重要成果之前，有必要用更适合仪器处理的记录取代这些墨水记录。

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What we have succeeded in doing is to make a white box which can potentially assume the characteristics of any non-­linear transducer whatever, and then to draw it into the similitude of a given black-­box transducer by subjecting the two to the same random input and connecting the outputs of the

记录微小波动电位以供进一步处理的最佳方法之一是使用磁带。这允许将波动电位以一种永久形式存储，以后方便时使用。大约十年前，麻省理工学院电子研究实验室在沃尔特·A·罗森布利斯教授和玛丽·A·布雷热博士的指导下设计了一种这样的仪器。

On Learning and Self-­Reproducing Machines

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structures in the proper manner, so as to arrive at the suitable combination without any intervention on our part. I ask if this is philosophically very different from what is done when a gene acts as a template to form other molecules of the same gene from an indeterminate mixture of amino and nucleic acids, or when a virus guides into its own form other molecules of the same virus out of the tissues and juices of its host. I do not in the least claim that the details of these processes are the same, but I do claim that they are philosophically very similar phenomena.

在这种装置中，磁带以调频形式使用。原因是读取磁带总是涉及一定量的擦除。

X Brain Waves and Self-­Organizing Systems

Notes

Notes

Notes

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Foreword by Doug Hill 1. John Pfeiffer, "Man's Brain Child," New York Times, April 18, 1965, https://tinyurl.com/y9xccjpu. 2. Kai-Fu Lee, "Tech Companies Should Stop Pretending AI Won't Destroy Jobs," MIT Technology Review, February 21, 2018, https://tinyurl .com/ya7spngu.

Gabor, D., "Electronic Inventions and Their Impact on Civilization," Inaugural Lecture, March 3, 1959, Imperial College of Science and Technology, University of London, England. 7. Wiener, N., and P. Masani, "The Prediction Theory of Multivariate Stochastic Processes," Part I, Acta Mathematica, 98, 111-150 (1957); Part II, ibid., 99, 93-137 (1958).

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In September 2018, Lee published AI Superpowers: China, Silicon Valley, and the New World Order. 3. See Matthew Desmond, "Americans Want to Believe Jobs Are the Solution to Poverty. They're Not." New York Times Magazine, September 11, 2018, https://tinyurl.com/y7ghzuqp; Eduardo Porter, "Tech Is Splitting the U.S.

Also Wiener, N., and E. Akutowicz, "The Definition and Ergodic Properties of the Stochastic Adjoint of a Unitary Transformation," Rendiconti del Circolo Matematico di Palermo, Ser. II, VI, 205-217 (1957). 8.

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Workforce in Two," New York Times, February 4, 2019, https://nyti.ms/2DSI2KZ. 4. Amy Bernstein and Anand Raman, "The Great Decoupling: An Interview with Erik Byrnjolfsson and Andrew McAfee," Harvard Business Review, June 2015, https://hbr.org/2015/06/the-great-decoupling 5. Norbert Wiener, "Some Moral and Technical Consequences of Automation," Science, New Series 131, no. 3410 (May 6, 1960), 1355. 6.

Samuel, A. L., "Some Studies in Machine Learning, Using the Game of Checkers," IBM Journal of Research and Development, 3, 210-229 (1959). 9. Watanabe, S., "Information Theoretical Analysis of Multivariate Correlation," IBM Journal of Research and Development, 4, 66-82 (1960). 10.

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On the 1965 blackout, see James Burke, Connections (Boston: Little, Brown, 1978), 1&ndash;­2; David E. Sanger, "Russian Hackers Appear to Shift Focus to U.S. Power Grid," New York Times, July 27, 2018, https:// tinyurl.com/y94f4egl.

Stanley-Jones, D., and K. Stanley-Jones, Kybernetics of Natural Systems, A Study in Patterns of Control, Pergamon Press, London, 1960. 导言 1.

Notes

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Nelson D. Schwartz and Louise Story, "High-­Speed Trading Glitch Costs Investors Billions," New York Times, May 6, 2010, http://nyti.ms/ aAzXcc; Thomas Heath, "The Warning From JPMorgan about Flash Crashes Ahead," Washington Post, September 5, 2018, https://tinyurl .com/ychvmcve. 8. Norbert Wiener, The Human Use of Human Beings, Houghton Mifflin, 1950, 37. 9.

MacColl, L. A., Fundamental Theory of Servomechanisms, Van Nostrand, New York, 1946. 2. Rosenblueth, A., N. Wiener, and J. Bigelow, "Behavior, Purpose, and Teleology," Philosophy of Science, 10, 18-24 (1943). 3. Kolmogoroff, A.

▶

Flo Conway and Jim Siegelman, Dark Hero of the Information Age: In Search of Nobert Wiener, the Father of Cybernetics (New York: Basic Books, 2004), 4. 10. See the joint edition of his two-volume autobiography, Norbert Wiener: A Life in Cybernetics (Cambridge, MA: MIT Press, 2017), 55, 57. Ronald R.

N., "Interpolation und Extrapolation von stationären Zufälligen Folgen," Bull. U.S.S.R., Ser. Math. 5, 3-14 (1941).

▶

Kline's introduction to that edition mentions the original title of Ex-­Prodigy on p. xii. 11. Conway and Siegelman, Dark Hero, p. 5. 12. Wiener, A Life in Cybernetics, 284. 13.

Schrödinger, Erwin, What is Life?, Cambridge University Press, Cambridge, England, 1945. 5. Maxwell, J. C., Proc. Soc. (London), 16, 270-283 (1868). 6.

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Steve J. Heims, John von Neumann and Norbert Wiener: From Mathematics to the Technologies of Life and Death (Cambridge, MA: MIT Press, 1980), 140. 14. Katherine Hayles, How We Became Posthuman: Virtual Bodies in Cybernetics, Literature, and Informatics (Chicago: University of Chicago Press, 1999), 18. 15.

Turing, A. M., "On Computable Numbers, with an Application to the Entscheidungsproblem," Proceedings of the London Mathematical Society, Ser. 2, 42, 230-265 (1936). 7. McCulloch, W.

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The conviction that Wiener's ideas have become increasingly relevant in the digital era inspired the IEEE to sponsor two "Reintroducing Norbert Wiener in the 21st Century" conferences, one in 2014 and the second in 2016. See http://21stcenturywiener.org. 16. Conway and Siegelman, Dark Hero, 243. 17.

S., and W. Pitts, "A logical calculus of the ideas immanent in nervous activity," Bull. Biophys, 5, 115-133 (1943). 8.

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Drew Harwell, "Google to Drop Pentagon AI Contract after Employee Objections to the 'Business of War,'" Washington Post, June 1, 2018, https://tinyurl.com/y75e6bn9.

Levinson, N., J. Math. and Physics, 25, 261-278; 26, 110-119 (1947). 9. Lee, Y.

Notes

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Wiener, Human Use, 17. 19. Conway and Siegelman, Dark Hero, 93&ndash;­98, 217&ndash;­230; Heims, John von Neumann and Norbert Wiener, 379&ndash;­389. 20. Heims, 377. 21.

W., J. Math. and Physics, 11, 261-278 (1932). 10. Wiener, N., Extrapolation, Interpolation, and Smoothing of Stationary Time Series, Technology Press and Wiley, New York, 1949. 11.

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Conway and Siegelman, Dark Hero, 16; Wiener, A Life in Cybernetics, 459&ndash;­460; Heims, 155. 22. See, for example, David Streitfeld, "Tech Giants, Once Seen as Saviors, Are Now Viewed as Threats," New York Times, October 12, 2017, https://tinyurl.com/y8y4qdl2; Noam Cohen, "Silicon Valley Is Not Your Friend," New York Times, October 13, 2017, https://tinyurl.com/ y9omhyoe; Jamie Doward, "The Big Tech Backlash," The Guardian, January 27, 2018, https://tinyurl.com/y77vku5j; and Noah Kulwin, "The Internet Apologizes," New York Magazine, April 13, 2018, https://tinyurl .com/ybtml5d6. Foreword by Sanjoy K.

Wiener, N., and A. Rosenblueth, "The Mathematical Formulation of the Problem of Conduction of Impulses in a Network of Connected Excitable Elements, Specifically in Cardiac Muscle," Arch. Cardiol. Méx., 16, 205-265 (1946). 12. 来自墨西哥国立心脏病学研究所关于阵挛的未发表文章。13. Fortune, 32, 139-147 (October); 163-169 (November, 1945).

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Mitter 1. Claude E. Shannon, "A Mathematical Theory of Communication," Bell System Technical Journal 27, no. 3 (1948): 379&ndash;­423, https://doi.org/ 10.1002/j.1538-7305.1948.tb01338.x. 2.

第二章 1. Oxtoby, J. C., and S. M. Ulam, "Measure-Preserving Homeomorphisms and Metrical Transitivity." Ann. of Math., Ser. 2, 42, 874-920 (1941). 2. 然而，奥斯古德的某些早期工作代表了向勒贝格积分方向的重要一步。3. Hopf, E., "Ergodentheorie," Ergeb. Math., 5, No. 2, Springer, Berlin (1937).

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Shockley, "The Theory of p-­n Junctions in Semiconductors and p-­n Junction Transistors," Bell System Technical Journal 28 (1949): 435&ndash;489, https://doi.org/10.1002/j.1538-7305.1949.tb03645.x. 3. Turing, "On Computable Numbers, with an Application to the Entscheidungsproblem," Proceedings of the London Mathematical Society S2-42 (January 1937): 230&ndash;265, https://doi.org/10.1112/plms/ s2-42.1.230; John von Neumann, The Computer and the Brain (New Haven, CT: Yale University Press, 1958). 4. Norbert Wiener, Cybernetics, or Control and Communication in the Animal and the Machine (Cambridge, MA: MIT Press, 1948), 42. 5.

Wiener, N., The Fourier Integral and Certain of Its Applications, The University Press, Cambridge, England, 1933; Dover Publications, Inc., N.Y. 5. Haar, H., "Der Massbegriff in der Theorie der Kontinuierlichen Gruppen." Ann. of Math., Ser. 2, 34, 147-169 (1933). 第四章 1.

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Wiener, Cybernetics, 162.

此处作者利用了J. von Neumann的个人通信。2. Paley, R. C., and N. Wiener, "Fourier Transforms in the Complex Domain," Colloquium Publications, Vol. 19, American Mathematical Society, New York, 1934, Chapter 10. 3. Stieltjes, T. Annales de la Fac. des Sc. de Toulouse, 1894, p. 165; Lebesgue, H., Leçons sur l'Intégration, Gauthier-Villars et Cie, Paris, 1928. 4.

Notes

▶

See, for example, Mark Davis and Alison Etheridge, Louis Bachelier's Theory of Speculation: The Origins of Modern Finance (Princeton, NJ: Princeton University Press, 2006). 7. See Norbert Wiener, Extrapolation, Interpolation, and Smoothing of Time Series, with Engineering Applications (Cambridge, MA: MIT Press, 1949). 8. Wiener, Cybernetics, 10, 11. 9.

这是库普曼的混合性质，是证明统计力学合理的必要且充分的遍历假设。5. 我们特别参考李博士近年来的论文。6.

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See R. Liptser and A. Shiryaev, "Computation of Mutual Information and Channel Capacity of a Gaussian Channel with Feedback," in Statistics of Random Processes, vol. 2 (Berlin: Springer, 1978), 190&ndash;­194. 10.

见R. Fisher和J. von Neumann的著作。1. Poincaré, H., Les Méthodes Nouvelles de la Mécanique Céleste, Gauthier-Villars et fils, Paris, 1892-1899. 2.

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Feller, An Introduction to Probability Theory and Its Applications, vol. 2 (New York: Wiley, 1971). 11. Kalman and R. Bucy, "New Results in Linear Filtering and Predication Theory," Journal of Basic Engineering 83 (1961): 95&ndash;108, https://doi.org/10.1115/1.3658902. 12.

Cannon, W., The Wisdom of the Body, W. Norton & Company, Inc., New York, 1932; Henderson, L. J., The Fitness of the Environment, The Macmillan Company, New York, 1913.

▶

For an information theoretic interpretation of the Kalman&ndash;Bucy filter, see S. Mitter and N. Newton, "Information and Entropy Flow in the Kalman&ndash;­Bucy Filter," Journal of Statistical Physics 118, nos. 1&ndash;­2 (2005): 145&ndash;­176, https://doi.org/10.1007/s10955-004-8781-9; and S.

第五章 1. Journal of the Franklin Institute, various papers, 1930 on. 2. Turing, A. M., "On Computable Numbers with an Application to the Entscheidungsproblem," Proceedings of the London Mathematical Society, Ser. 2, 42, 230-265 (1936).

▶

Mitter, "Filtering and Stochastic Control: A Historical Perspective," IEEE Control Systems 16 (1996): 67&ndash;76, https://doi.org/10.1109/37.506400. 13. Mitter, "Filtering and Stochastic Control." 14. Wiener's suggestions have been further developed by G.

第六章 1. 英国布里斯托尔的W. Grey Walter博士的个人通信。

▶

Newton, L. Gould, and J. Kaiser in Analytical Design of Linear Feedback Controls (New York: Wiley, 1957). 15.

第七章 1. Thompson, D'Arcy, On Growth and Form, Amer. ed., The Macmillan Company, New York, 1942. 第九章 1.

▶

See Mitter, "Filtering and Stochastic Control." 16. Wiener, Cybernetics, 113. 17. Wiener, 112. 18.

Huxley, J., Evolution: The Modern Synthesis, Harper Bros., New York, 1943. 2. von Neumann, J., and O. Morgenstern, Theory of Games and Economic Behavior, Princeton University Press, Princeton, N.J., 1944. 3. Wiener, N., Extrapolation, Interpolation, and Smoothing of Stationary Time Series with Engineering Applications, The Technology Press of M.I.T. and John Wiley & Sons, New York, 1949. 4.

▶

Wiener, 57, 58.

Samuel, A. L., "Some Studies in Machine Learning, Using the Game of Checkers," IBM Journal of Research and Development, 3, 210-229 (1959). 5. Watanabe, S., "Information Theoretical Analysis of Multivariate Correlation," IBM Journal of Research and Development, 4, 66-82 (1960). 6.

Notes

▶

Sandberg, J.-­C. Delvenne, N. Newton, and S.

Wiener, N., The Human Use of Human Beings; Cybernetics and Society, Houghton Mifflin Company, Boston, 1950. 7. Wiener, N., Nonlinear Problems in Random Theory, The Technology Press of M.I.T. and John Wiley & Sons, Inc., New York, 1958. 8. Gabor, D., "Electronic Inventions and Their Impact on Civilization," Inaugural Lecture, March 3, 1959, Imperial College of Science and Technology, University of London, England.

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Mitter, "Maximum Work Extraction and Implementation Costs for Nonequilibrium Maxwell's Demon," Physical Review E 90 (2014): 042119, https://doi.org/ 10.1103/PhysRevE.90.042119. 20. Mitter, "Filtering and Stochastic Control." 21. Wiener, Nonlinear Problems in Random Theory (Cambridge, MA: MIT Press, 1966). 22.

第十章 1. Taylor, G. I., "Diffusion by Continuous Movements," Proceedings of the London Mathematical Society, Ser. 2, 20, 196-212 (1921-1922). 2.

▶

Ito, "Multiple Wiener Integrals," Journal of the Mathematical Society of Japan 3 (1951): 157&ndash;­169, https://doi.org/10.2969/jmsj/00310157. 23. Wiener, Cybernetics, 178&ndash;­180. 24. Wiener, "Generalized Harmonic Analysis," Acta Mathematica 55 (1930): 117&ndash;­258; Wiener, Nonlinear Problems in Random Theory. 25.

Barlow, J. S., and R. Brown, An Analog Correlator System for Brain Potentials, Technical Report 300, Research Laboratory of Electronics, M.I.T., Cambridge, Mass. (1955). 3.

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Wiener, 192. Preface to the Second Edition 1. Wiener, N., The Human Use of Human Beings; Cybernetics and Society, Houghton Mifflin Company, Boston, 1950. 2.

这项工作是在麻省总医院神经生理学实验室和麻省理工学院通信生物物理学实验室的合作下进行的。4. 使用了麻省理工学院计算中心的IBM-709计算机。5.

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Wiener, N., Nonlinear Problems in Random Theory, The Technology Press of M.I.T. and John Wiley & Sons, Inc., New York, 1958. 3. Here I am using the term "non-­linear system" not to exclude linear systems but to include a larger category of systems. The analysis of non-linear systems by means of random noise is also applicable to linear systems and has been so used. 4.

Wiener, N., "Generalized Harmonic Analysis," Acta Mathematica, 55, 117-258 (1930); Nonlinear Problems in Random Theory, The Technology Press of M.I.T. and John Wiley & Sons, Inc., New York, 1958. 6. Wiener, N., "The Ergodic Theorem," Duke Mathematical Journal, 5, 1-39 (1939); 亦见Modern Mathematics for the Engineer, E. Beckenbach (Ed.), McGraw-Hill, New York, 1956, pp. 166-168. 7.

▶

The terms "black box" and "white box" are convenient and figurative expressions of not very well-determined usage. I shall understand by a black box a piece of apparatus, such as four-­terminal networks with two input and two output terminals, which performs a definite operation on the present and past of the input potential, but for which we do not necessarily have any information of the structure by which this operation is performed. On the other hand, a white box will be a

Wiener, N., "Plancherel's Theorem," The Fourier Integral and Certain of Its Applications, The University Press, Cambridge, England, 1933, pp. 46-71; Dover Publications, Inc., New York. 8. 这是对实际情况的简化描述，尤其是在皮层中，因为神经元的全或无操作取决于它们是否具有足够的长度，以使神经元本身中传入脉冲形式的重建接近渐近形式。然而，例如在皮层中，由于神经元较短，同步的必要性仍然存在，尽管过程的细节要复杂得多。9.

Notes

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similar network in which we have built in the relation between input and output potentials in accordance with a definite structural plan for securing a previously determined input-­output relation. 5. Bose, A. G., "Nonlinear System Characterization and Optimization," IRE Transactions on Information Theory, IT&ndash;­5, 30&ndash;40 (1959) (Special supplement to IRE Transactions). 6.

我必须说，英国布里斯托尔伯登神经学研究所的W. Grey Walter博士已经获得了关于存在狭窄中心节律的一些证据。我不完全了解他的方法论的细节；然而，我理解

▶

Gabor, D., "Electronic Inventions and Their Impact on Civilization," Inaugural Lecture, March 3, 1959, Imperial College of Science and Technology, University of London, England. 7. Wiener, N., and P. Masani, "The Prediction Theory of Multivariate Stochastic Processes," Part I, Acta Mathematica, 98, 111&ndash;­150 (1957); Part II, ibid., 99, 93&ndash;­137 (1958).

他所指的现象在于，在他的脑波拓扑图中，当从中心向外时，指示频率的射线被限制在相对狭窄的扇形中。10. Barlow, J. S., "Rhythmic Activity Induced by Photic Stimulation in Relation to Intrinsic Alpha Activity of the Brain in Man," EEG Clin. Neurophysiol., 12, 317-326 (1960).

▶

Also Wiener, N., and E. Akutowicz, "The Definition and Ergodic Properties of the Stochastic Adjoint of a Unitary Transformation," Rendiconti del Circolo Matematico di Palermo, Ser. II, VI, 205&ndash;­217 (1957). 8.

11. Cold Spring Harbor Symposium on Quantitative Biology, Volume XXV (Biological Clocks), The Biological Laboratory, Cold Spring Harbor, L.I., N.Y., 1960.

▶

Samuel, A. L., "Some Studies in Machine Learning, Using the Game of Checkers," IBM Journal of Research and Development, 3, 210&ndash;­229 (1959). 9. Watanabe, S., "Information Theoretical Analysis of Multivariate Correlation," IBM Journal of Research and Development, 4, 66&ndash;­82 (1960). 10.

Samuel, A. L., "Some Studies in Machine Learning, Using the Game of Checkers," IBM Journal of Research and Development, 3, 210-229 (1959).

▶

Stanley-­Jones, D., and K. Stanley-­Jones, Kybernetics of Natural Systems, A Study in Patterns of Control, Pergamon Press, London, 1960. Introduction 1.

Stanley-Jones, D., and K. Stanley-Jones, Kybernetics of Natural Systems, A Study in Patterns of Control, Pergamon Press, London, 1960. 导言

▶

MacColl, L. A., Fundamental Theory of Servomechanisms, Van Nostrand, New York, 1946. 2. Rosenblueth, A., N.

MacColl, L. A., Fundamental Theory of Servomechanisms, Van Nostrand, New York, 1946. 2. Rosenblueth, A., N.

▶

Wiener, and J. Bigelow, "Behavior, Purpose, and Teleology," Philosophy of Science, 10, 18&ndash;­24 (1943). 3. Kolmogoroff, A.

Wiener, and J. Bigelow, "Behavior, Purpose, and Teleology," Philosophy of Science, 10, 18-24 (1943). 3. Kolmogoroff, A.

▶

N., "Interpolation und Extrapolation von stationären Zufälligen Folgen," Bull. U.S.S.R., Ser. Math. 5, 3&ndash;­14 (1941).

N., "Interpolation und Extrapolation von stationaren Zufalligen Folgen," Bull. U.S.S.R., Ser. Math. 5, 3-14 (1941).

Notes

▶

Schrödinger, Erwin, What is Life?, Cambridge University Press, Cambridge, England, 1945. 5. Maxwell, J, C., Proc. Soc. (London), 16, 270&ndash;­283, (1868). 6.

Schrodinger, Erwin, What is Life?, Cambridge University Press, Cambridge, England, 1945. 5. Maxwell, J. C., Proc. Soc. (London), 16, 270-283 (1868). 6.

▶

Turing, A. M., "On Computable Numbers, with an Application to the Entscheidungsproblem," Proceedings of the London Mathematical Society, Ser. 2, 42, 230&ndash;­265 (1936). 7. McCulloch, W.

Turing, A. M., "On Computable Numbers, with an Application to the Entscheidungsproblem," Proceedings of the London Mathematical Society, Ser. 2, 42, 230-265 (1936). 7. McCulloch, W.

▶

S., and W. Pitts, "A logical calculus of the ideas immanent in nervous activity," Bull. Biophys, 5, 115&ndash;­133 (1943). 8.

S., and W. Pitts, "A logical calculus of the ideas immanent in nervous activity," Bull. Biophys, 5, 115-133 (1943). 8.

▶

Levinson, N., J. Math. and Physics, 25, 261&ndash;­278; 26, 110&ndash;­119 (1947). 9. Lee, Y.

Levinson, N., J. Math. and Physics, 25, 261-278; 26, 110-119 (1947). 9. Lee, Y.

▶

W., J. Math. and Physics, 11, 261&ndash;­278 (1932). 10. Wiener, N., Extrapolation, Interpolation, and Smoothing of Stationary Time Series, Technology Press and Wiley, New York, 1949. 11.

W., J. Math. and Physics, 11, 261-278 (1932). 10. Wiener, N., Extrapolation, Interpolation, and Smoothing of Stationary Time Series, Technology Press and Wiley, New York, 1949. 11.

▶

Wiener, N., and A. Rosenblueth, "The Mathematical Formulation of the Problem of Conduction of Impulses in a Network of Connected Excitable Elements, Specifically in Cardiac Muscle," Arch. Cardiol.

Wiener, N., and A. Rosenblueth, "The Mathematical Formulation of the Problem of Conduction of Impulses in a Network of Connected Excitable Elements, Specifically in Cardiac Muscle," Arch. Cardiol. Mex., 16, 205-265 (1946). 12. 来自墨西哥国立心脏病学研究所关于阵挛的未发表文章。13. Fortune, 32, 139-147 (October); 163-169 (November, 1945).

▶

Méx., 16, 205&ndash;­265 (1946). 12. Unpublished articles on clonus from the Instituto Nacional de Cardiología, Mexico. 13. Fortune, 32, 139&ndash;­147 (October); 163&ndash;­169 (November, 1945).

第二章 1. Oxtoby, J. C., and S. M. Ulam, "Measure-Preserving Homeomorphisms and Metrical Transitivity." Ann. of Math., Ser. 2, 42, 874-920 (1941). 2. 然而，奥斯古德的某些早期工作代表了向勒贝格积分方向的重要一步。3. Hopf, E., "Ergodentheorie," Ergeb.

▶

Chapter II 1. Oxtoby, J. C., and S.

Math., 5, No. 2, Springer, Berlin (1937).

▶

Ulam, "Measure-Preserving Homeomorphisms and Metrical Transitivity." Ann. of Math., Ser. 2, 42, 874&ndash;­920 (1941). 2. Nevertheless some of Osgood's early work represented an important step in the direction of the Lebesgue integral. 3. Hopf, E., "Ergodentheorie," Ergeb.

Ulam, "Measure-Preserving Homeomorphisms and Metrical Transitivity." Ann. of Math., Ser. 2, 42, 874-920 (1941). 2. 然而，奥斯古德的某些早期工作代表了向勒贝格积分方向的重要一步。3. Hopf, E., "Ergodentheorie," Ergeb. Math., 5, No. 2, Springer, Berlin (1937).

▶

Math., 5, No. 2, Springer, Berlin (1937).

Math., 5, No. 2, Springer, Berlin (1937).

Notes

▶

Wiener, N., The Fourier Integral and Certain of Its Applications, The University Press, Cambridge, England, 1933; Dover Publications, Inc., N.Y. 5. Haar, H., "Der Massbegriff in der Theorie der Kontinuierlichen Gruppen." Ann. of Math., Ser. 2, 34, 147&ndash;­169 (1933). Chapter IV 1.

Wiener, N., The Fourier Integral and Certain of Its Applications, The University Press, Cambridge, England, 1933; Dover Publications, Inc., N.Y. 5. Haar, H., "Der Massbegriff in der Theorie der Kontinuierlichen Gruppen." Ann. of Math., Ser. 2, 34, 147-169 (1933). 第四章 1.

▶

Here the author makes use of a personal communication of J. von Neumann. 2. Paley, R. C., and N.

此处作者利用了J. von Neumann的个人通信。2. Paley, R. C., and N. Wiener, "Fourier Transforms in the Complex Domain," Colloquium Publications, Vol. 19, American Mathematical Society, New York, 1934, Chapter 10. 3. Stieltjes, T. Annales de la Fac. des Sc. de Toulouse, 1894, p. 165; Lebesgue, H., Lecons sur l'Integration, Gauthier-Villars et Cie, Paris, 1928. 4.

▶

Wiener, "Fourier Transforms in the Complex Domain," Colloquium Publications, Vol. 19, American Mathematical Society, New York, 1934, Chapter 10. 3. Stieltjes, T. Annales de la Fae. des Sc. de Toulouse, 1894, p. 165; Lebesgue, H., Leçons sur l'Intégration, Gauthier-­Villars et Cie, Paris, 1928. 4.

Wiener, "Fourier Transforms in the Complex Domain," Colloquium Publications, Vol. 19, American Mathematical Society, New York, 1934, Chapter 10. 3. Stieltjes, T. Annales de la Fac. des Sc. de Toulouse, 1894, p. 165; Lebesgue, H., Lecons sur l'Integration, Gauthier-Villars et Cie, Paris, 1928. 4.

▶

This is the mixing property of Koopman, which is the necessary and sufficient ergodic assumption to justify statistical mechanics. 5. We refer especially to recent papers by Dr. Lee. 6.

这是库普曼的混合性质，是证明统计力学合理的必要且充分的遍历假设。5. 我们特别参考李博士近年来的论文。6.

▶

See writings of R. Fisher and J. von Neumann. 1. Poincaré, H., Les Méthodes Nouvelles de la Mécanique Céleste, Gauthier-Villars et fils, Paris, 1892&ndash;­1899. 2.

见R. Fisher和J. von Neumann的著作。1. Poincare, H., Les Methodes Nouvelles de la Mecanique Celeste, Gauthier-Villars et fils, Paris, 1892-1899. 2.

▶

Cannon, W., The Wisdom of the Body, W. Norton & Company, Inc., New York, 1932; Henderson, L. J., The Fitness of the Environment, The Macmillan Company, New York, 1913.

Cannon, W., The Wisdom of the Body, W. Norton & Company, Inc., New York, 1932; Henderson, L. J., The Fitness of the Environment, The Macmillan Company, New York, 1913.

▶

Chapter V 1. Journal of the Franklin Institute, various papers, 1930 on. 2. Turing, A.

第五章 1. Journal of the Franklin Institute, various papers, 1930 on. 2. Turing, A.

▶

M., "On Computable Numbers with an Application to the Entscheidungsproblem," Proceedings of the London Mathematical Society, Ser. 2, 42, 230&ndash;­265 (1936).

M., "On Computable Numbers with an Application to the Entscheidungsproblem," Proceedings of the London Mathematical Society, Ser. 2, 42, 230-265 (1936).

Notes

▶

Chapter VI 1. Personal communication of Dr. Grey Walter, of Bristol, England.

第六章 1. 英国布里斯托尔的W. Grey Walter博士的个人通信。

▶

Chapter VII 1. Thompson, D'Arcy, On Growth and Form, Amer. ed., The Macmillan Company, New York, 1942. Chapter IX 1.

第七章 1. Thompson, D'Arcy, On Growth and Form, Amer. ed., The Macmillan Company, New York, 1942. 第九章 1.

▶

Huxley, J., Evolution: The Modern Synthesis, Harper Bros., New York, 1943. 2. von Neumann, J., and O. Morgenstern, Theory of Games and Economic Behavior, Princeton University Press, Princeton, N.J., 1944. 3. Wiener, N., Extrapolation, Interpolation, and Smoothing of Stationary Time Series with Engineering Applications, The Technology Press of M.I.T. and John Wiley & Sons, New York, 1949. 4.

Huxley, J., Evolution: The Modern Synthesis, Harper Bros., New York, 1943. 2. von Neumann, J., and O. Morgenstern, Theory of Games and Economic Behavior, Princeton University Press, Princeton, N.J., 1944. 3. Wiener, N., Extrapolation, Interpolation, and Smoothing of Stationary Time Series with Engineering Applications, The Technology Press of M.I.T. and John Wiley & Sons, New York, 1949. 4.

▶

Samuel, A. L., "Some Studies in Machine Learning, Using the Game of Checkers," IBM Journal of Research and Development, 3, 210&ndash;­229 (1959). 5. Watanabe, S., "Information Theoretical Analysis of Multivariate Correlation," IBM Journal of Research and Development, 4, 66&ndash;­82 (1960). 6.

Samuel, A. L., "Some Studies in Machine Learning, Using the Game of Checkers," IBM Journal of Research and Development, 3, 210-229 (1959). 5. Watanabe, S., "Information Theoretical Analysis of Multivariate Correlation," IBM Journal of Research and Development, 4, 66-82 (1960). 6.

▶

Wiener, N., The Human Use of Human Beings; Cybernetics and Society, Houghton Mifflin Company, Boston, 1950. 7. Wiener, N., Nonlinear Problems in Random Theory, The Technology Press of M.I.T. and John Wiley & Sons, Inc., New York, 1958. 8. Gabor, D., "Electronic Inventions and Their Impact on Civilization," Inaugural Lecture, March 3, 1959, Imperial College of Science and Technology, University of London, England.

Wiener, N., The Human Use of Human Beings; Cybernetics and Society, Houghton Mifflin Company, Boston, 1950. 7. Wiener, N., Nonlinear Problems in Random Theory, The Technology Press of M.I.T. and John Wiley & Sons, Inc., New York, 1958. 8. Gabor, D., "Electronic Inventions and Their Impact on Civilization," Inaugural Lecture, March 3, 1959, Imperial College of Science and Technology, University of London, England.

Notes

▶

Chapter X 1. Taylor, G. I., "Diffusion by Continuous Movements," Proceedings of the London Mathematical Society, Ser. 2, 20, 196&ndash;­212 (1921&ndash;­1922). 2.

第十章 1. Taylor, G. I., "Diffusion by Continuous Movements," Proceedings of the London Mathematical Society, Ser. 2, 20, 196-212 (1921-1922). 2.

▶

Barlow, J. S., and R. Brown, An Analog Correlator System for Brain Potentials, Technical Report 300, Research Laboratory of Electronics, M.I.T., Cambridge, Mass. (1955). 3.

Barlow, J. S., and R. Brown, An Analog Correlator System for Brain Potentials, Technical Report 300, Research Laboratory of Electronics, M.I.T., Cambridge, Mass. (1955). 3.

▶

This work was undertaken with the cooperation of the Neurophysiology Laboratory of the Massachusetts General Hospital and the Communications Biophysics Laboratory of M.I.T. 4. The IBM-­709 at the M.I.T. Computation Center was used. 5.

这项工作是在麻省总医院神经生理学实验室和麻省理工学院通信生物物理学实验室的合作下进行的。4. 使用了麻省理工学院计算中心的IBM-709计算机。5.

▶

Wiener, N., "Generalized Harmonic Analysis," Acta Mathematica, 55, 117&ndash;­258 (1930); Nonlinear Problems in Random Theory, The Technology Press of M.I.T. and John Wiley & Sons, Inc., New York, 1958. 6. Wiener, N., "The Ergodic Theorem," Duke Mathematical Journal, 5, 1&ndash;­39 (1939); also in Modern Mathematics for the Engineer, E. Beckenbach (Ed.), McGraw-­Hill, New York, 1956, pp. 166&ndash;­168. 7.

Wiener, N., "Generalized Harmonic Analysis," Acta Mathematica, 55, 117-258 (1930); Nonlinear Problems in Random Theory, The Technology Press of M.I.T. and John Wiley & Sons, Inc., New York, 1958. 6. Wiener, N., "The Ergodic Theorem," Duke Mathematical Journal, 5, 1-39 (1939); 亦见Modern Mathematics for the Engineer, E. Beckenbach (Ed.), McGraw-Hill, New York, 1956, pp. 166-168. 7.

▶

Wiener, N., "Plancherel's Theorem," The Fourier Integral and Certain of Its Applications, The University Press, Cambridge, England, 1933, pp. 46&ndash;­71; Dover Publications, Inc., New York. 8. This is a simplified picture of what happens, especially in the cortex, since the all-­or-­none operation of neurons depends on their being of a sufficient length so that the remaking of the form of the incoming impulses in the neuron itself approaches an asymptotic form. However, in the cortex for example, owing to the shortness of the neurons, the necessity of synchronization still exists, although the details of the process are much more complicated. 9.

Wiener, N., "Plancherel's Theorem," The Fourier Integral and Certain of Its Applications, The University Press, Cambridge, England, 1933, pp. 46-71; Dover Publications, Inc., New York. 8. 这是对实际情况的简化描述，尤其是在皮层中，因为神经元的全或无操作取决于它们是否具有足够的长度，以使神经元本身中传入脉冲形式的重建接近渐近形式。然而，例如在皮层中，由于神经元较短，同步的必要性仍然存在，尽管过程的细节要复杂得多。9.

▶

I must say that some evidence of the existence of narrow central rhythms has been obtained by Dr. Grey Walter of the Burden Neurological Institute in Bristol, England. I am not acquainted with the full details of his methodology; however, I understand that the phenomenon

我必须说，英国布里斯托尔伯登神经学研究所的W. Grey Walter博士已经获得了关于存在狭窄中心节律的一些证据。我不完全了解他的方法论的细节；然而，我理解他所指的现象在于，在他的脑波拓扑图中，当从中心向外时，指示频率的射线被限制在相对狭窄的扇形中。

Notes

▶

to which he refers consists in the fact that in his toposcopic pictures of brain waves, as one goes out from the center, the rays indicating the frequency are confined to relatively narrow sectors. 10. Barlow, J. S., "Rhythmic Activity Induced by Photic Stimulation in Relation to Intrinsic Alpha Activity of the Brain in Man," EEG Clin.

to which he refers consists in the fact that in his toposcopic pictures of brain waves, as one goes out from the center, the rays indicating the frequency are confined to relatively narrow sectors. 10. Barlow, J. S., "Rhythmic Activity Induced by Photic Stimulation in Relation to Intrinsic Alpha Activity of the Brain in Man," EEG Clin.

▶

Neurophysiol., 12, 317&ndash;­326 (1960). 11. Cold Spring Harbor Symposium on Quantitative Biology, Volume XXV (Biological Clocks), The Biological Laboratory, Cold Spring Harbor, L.I., N.Y., 1960.

Neurophysiol., 12, 317-326 (1960). 11. Cold Spring Harbor Symposium on Quantitative Biology, Volume XXV (Biological Clocks), The Biological Laboratory, Cold Spring Harbor, L.I., N.Y., 1960.

Index

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

A

• Affective tone, 175–177, 207
• Aircraft, military, 8–11
• Alpha rhythm of brain, 34, 195,
• “A Mathematical Theory of
• Amazon, xviii
• Amount of information, 86–91, 127–128
• Analogy machines, 161, 165–166
• Anthropology, 27–28
• Anticipatory feedback, 153
• A posteriori knowledge, 87
• A priori probability, 86–87
• Artificial intelligence and neuroscience, xvi, xxxiii–xxxiv
• Artificial limbs, 38
• Astronomy, 43–50 gravitational, 51
• Astrophysics, 48–49
• Ataxia, 12–13, 129–130
• Autocorrelation, 254–259 of brain waves, 259–265
• Automata, 57–62 coupled to the external world, 60–61
• Automation, x–xi, 39 in early science, 56–57 literal-minded computers and, xii speed of, xii

B

• Background noise, 16
• Barlow, John S., xlvii
• Bartlett, F. C., 34
• Bateson, Gregory, 36
• Bergson, Henri, 62–63
• Bigelow, Julian H., 10, 11, 13, 14, 18, 23
• Blind persons, reading by, 33, 191–192
• Blueprints, xliv–xlvi
• Bohr, Niels, 53
• Borel, Emile, 65
• Bose, Amar, xli
• Boyd, Constance D., xlvi
• Braille, 33, 191–192
• Brain. See also Nervous system alpha rhythm of, 34, 195, 273 comparison of human versus lower mammal, 210–214 death effects on, 205 functional and organic disorders of, 202–203 handedness and, 211–213 higher mental functions in, injury to, 13, 212 neurons of, 165–166, 203–204, 209–210 power consumed by, 181–182 shock treatment of, 205–206 sleep effects on, 205 synapses of, 20–22, 25, 29, 165–166, 171, 271–272
• Brain waves autocorrelation of, 259–265 defined, 251–252 fireflies experiment and, 275–276 harmonic analysis of, 254, 263, magnetic tape for recording, 254–255 oscillators of frequencies, 273–274 sampling problem, 265–271 self-organization of, 251, 277–279 technology for measurement of, 252–254
• Brazier, Mary A. B., 255
• Bread-and-Butter Fly, 176
• British empirical school of philosophy, 174
• Brownian motion, xxv, xxvi, 120 time series, 98–105
• Brynjolfsson, Erik, x
• Bulletin of Atomic Scientists, xvi
• Bush, Vannevar, 6, 8, 10, 22, 219
• Bush differential analyzer, 161
• Butler, Samuel, 39–40
• Brownian motion, 98–105, 120 conditional probabilities and, 96–97 defined, 94–95 filtering problem, 114–121

C

• Communication,” xxi
• Calculus ratiocinator, 19
• Caldwell, Samuel, 10
• Cannon, Walter B., 3, 25
• Cantor, Georg, 67
• Carroll, Lewis, 176
• Cars, automated, xii
• Cathode-ray oscillographs, 253
• Chain of transmission and return of information, 129–131
• Channel capacity, xxii
• Character groups, 75–76
• Chávez, Ignacio, 25, 32
• Checkers, 238
• Chess-playing machines, 228–230, 236–237
• Chess theory, 236
• Clerk Maxwell, James, 18, 132
• Clonic oscillation, 30–31
• Collation mechanisms, 200–201
• Colonies. See Communities
• Communal information, 219–221
• Communication, methods of, 223–224 triple constriction of, 224–225
• Communication engineering, 14–17 message-noise problem in, 93–94
• Communication technologies, xi
• Communities, 215–216 group information in, 219–221 homeostasis in small, closely knit, 222–223 intercommunication in, 216–217 social sciences and, 227–228
• Computation errors, correction of, 200
• Computing machines, 7, 8, 19–21, 34, 39, 56, 61, 85, as analogy machines, 161, 165–166 brain as, 20–22, 25, 29, 165–166, 171 conditioned reflexes in, 178–179 contingencies affecting operation of, 163–164 data inserted at beginning in ideal, 162–163 defined, 159 as essential for the war effort, 22–23 game-playing, 228–230, 234–239, 241–242 induction by, 172–173 learning apparatus in, 179–181 logic of, 173–174 mathematical logic and, xxiii–xxiv, 19–20 memory and, 166–169 numerical, 161–162, 194 pathological processes in, 204 power consumed by, 181–182 for recording information, 159–161 relays used in, 164 for solution of partial differential equations, 6, 161, 180–181 telegraph-type repeaters, 168–169 two great types of, 161
• Conditional probabilities, 96–97
• Conditioned reflexes in computing machines, 178–179
• Conductivity, phenomena of, 25–26
• Conscience, 205
• Control by informative feedback, 154–155
• Control systems, 132–133
• Conway, Flo, xiv, xvii
• Cybernetics, or Control and
• Communication in the Animal and the Machine on cybernetics as lingua franca of animals and machines, xv–xvi, xxi–xxii first reissue of, ix
• Cybernetics, ix–xi recognition of uncertainty, xviii, stances against science taken by, xvi–xvii statistical mechanics and, xxix–xxxii

D

• Dark Hero of the Information Age, xiv
• Darwin, Charles, 51–53
• Darwin, George, 50, 52
• Davis, James W., xlvii
• Death effects on the brain, 205
• De Santillana, G., 35
• Descartes, René, 57–58
• Discrete time series, theory of, 121–125
• Dubé, Georges, 42
• Durchmusterung, 44–45
• Dynamics, 174–175

E

• Effective boundary, 137
• Electrical currents and circuits, xxxvi, xxxvii, 29, 246–247
• Electroencephalography, 253–254
• Electrophysiology, 252–253
• Energy computing machine, 181–182 human, 59–60, 181–182
• Engineering, ancient, 54–55
• Entropy, 80–83, 88, 90
• Ergodic hypothesis, 71, 77–80
• Ergodic transformations, 78–80
• Ericsson, M., 27
• Evolution, Darwinian, 51–52
• Ex-Prodigy: My Childhood and
• Exterior points, 137
• Entscheidungsproblem,” xxi

F

• Facebook, xi, xii, xviii
• Feedback control, xxx, 11–12, double system of, 146
• Feedback(s) affective tone as, 176–177 anticipatory, 153 chain of transmission and return of information as, 129–131 compensator and effector, 153–155 complicated system stabilized by two, 144–145 control by informative, 154–155 differential operators and ranges of, 139–143 double system of control and, eye-muscle, 184–185 homeostatic, 156–157 in human animal reflexes, 153–154 infinity and, 137–138 information and, 132–133 interior points and, 137–139 mathematics of, 133–137 mechanical systems of, 132–133 negative, 132 oscillations due to excessive amount of, 148 of voluntary activity, 132, 146–147
• Feedback systems, information, xxviii–xxix
• Ferromagnetism, 169–170
• Filtering problem, time series, 114–121
• Fireflies, 275–276
• First-order programming, 238–239
• Fisher, R. A., 17
• Fourier transformation, 105–108, 115–119
• Fremont-Smith, Frank, 26–27
• Frequency modulation, 255
• Freud, Sigmund, 178
• Functional disorders, 202–203
• Fourier transformation, 105–108, 115–119 multiple, 97–98 prediction problem for, 110–114, 120 theory of amount of information and, 127–128 theory of discrete, 121–125 zeros in, 109–110

G

• God and, 58–59 nineteenth-century study of, 59–60
• Greek origin of name Cybernetics and, 18 moral position of, 41–42 preface to second edition of, xxxv–xlvii
• Gabor, Dennis, xli, xliii–xliv, 246,
• Game-playing machines, 228–230, 234–239, 241
• Games checkers, 238 chess, 228–230, 236–237 magic, 242–244 physical contests as, 241–242 struggle activities as, 239–241 war as, 235–236, 242, 245
• Game theory, 235–236
• Gas flow rates, 149–150
• Gauss–Markov processes, xxvii
• Generators, output of, 276–277
• Gestalt, 27, 33, 37, 191, 194
• Gibbs, Willard, xviii, 53–54, 70 ergodic hypothesis of, 71 statistical mechanics work of, 65–67, 70–71 on transformation groups, 71–76
• God, 57–59
• Goethe, Johann Wolfgang von, xix, 243
• Google, xviii
• Greed, xiii
• Group information, 219–221
• Group scanning, 189–191
• Gibbs’ work on, 65–67

H

• Haldane, J. B. S., 34, 128
• Handedness, 211–213
• Harmonic analysis, 34–35, 254, 263, 275
• Harrison, George, 32
• Harvard Business Review, x
• Hayles, N. Katherine, xvi
• Hearing, sight replaced by, 196–197
• Heims, Steve J., xvi, xviii
• Heisenberg, Werner, 53
• Hey, W., 43
• Homeostasis, 156–157 in small, closely knit communities, 222–223
• Human body, energy of, 59–60
• Human logic, 173–174
• Hume, David, 174, 183
• Huxley, Julian, 234

I

• Index
• Index
• Index
• Index
• I Am a Mathematician, xv
• Ikehara, Shikao, xlvi
• Induction, 172–173
• Industrial revolutions, 40–41
• Infinity, 137–138
• Information amount of, 86–91, 127–128 chain of transmission and return of, 129–131 and communication as mechanisms of organization, 27–28 conveyed in odors, 217
• Index
• Information (cont.) group, 219–221 statistical theory of amount of, 16–17 storage of, 166–171 various forms of communication of, 217–219
• Information feedback, xxviii–xxix
• Intercommunication in organizations, 216–217
• Interior points, 137–139
• Internal noise of receiving system,
• Invariants of the group, 74
• Ito, xxvi
• Index loss of, 203–204 sensory prosthesis and, 195–196
• Index
• Index
• Index concentration of visual information in, 185–186 eye-muscle feedbacks in, 184–185 group scanning in, 189–191 outline drawing recognition and, 186–187 reading by persons without, 33, 191–192 replaced by hearing, 196–197 sensory prosthesis and, 191, 195–196 stages in diagrammatization of impressions in, 187–188 transformations in, 188–189
• Index contributions to mathematics by, xxiii–xxiv, 19–21 depression experienced by, xvii–xviii design of linear control system and, xxvii–xxix on greed, xiii information defined by, xxiv–xxv introduction by, x on mass media of his day, xi non-linear systems and, xxxii–xxxiii, xxxvi–xxxvii overt warnings about technology, xi, xviii prophecy of, through

J

• Jacobs, W. W., xix, 243

K

• Kalman, R. E., xxvii
• Kalman–Bucy filter, xxvii
• Kipling, Rudyard, xviii, 239–240
• Koopman, 77, 79
• Kotelly, John C., xlvii

L

• Lettvin, J., 21, 178
• Lewin, Kurt, 27
• Lies, 221–222
• Limbs, artificial, 38
• Lindsley, Donald B., 272
• Linear control system design, xxvii–xxix
• Linear invariants, 74, 77
• Linear operations, 238–239
• Linear prediction, theory of, xliii–xliv
• Lobotomy, 205–206
• Locke, John, 174, 175, 183, 187,
• Logic, human, 173–174
• Lorente de Nó, Rafael, 23
• Learning machines, xlii–xlv, 179–181 games and, 228–245 magic and, 242–244
• Lebesgue, Henri, 65, 69 work on theory of trigonometric series, 67–68
• Lee, Kai-Fu, x
• Lee, Yuk Wing, xlvi, 6, 24
• Leibniz, Gottfried Wilhelm, 4, 19, 58–59, 215
• Lebegue’s work on trigonometric series and, 67–68, 69
• Lebesgue’s work on, 67–68

M

• MacColl, L. A., 12, 144
• Machina ratiocinatrix, 19
• Magic, 57, 242–244
• Magnetic tape, 254–255
• Markov processes, theory of, xxvi
• Mathematical logic, xxiii–xxiv, 19–21
• Maxwell demons, xxix–xxx, 17, 81–83
• McAfee, Andrew, x
• McCulloch, Warren, 18, 20–21, 23, 27, 33, 37–38, 193, 194
• Mead, Margaret, 28, 36
• Measurement precision, 86–87
• Mechanical feedback, 132–133
• Memory, 166–170 functional and organic disorders and, 202–203
• Message–noise problem, 93–94
• Messages, theory of, 120
• Meteorology, 44–47 cosmic, 50 tidal evolution and, 50–52
• Metrically transitive transformations, 78–79
• Michelson interferometer, 257–258
• Mind, content of the human, 174
• Minimization problems, 15
• Momentum, 126
• Moral position of Wiener on science, xvi–xvii, 41–42
• Multiple time series, 97–98
• Muscle action, 12–13, 25 artificial limbs and, 38 feedback and, 146–147
• Mutual information, xxii
• Maxwel demons in, 81–83 time average in, 70 transformation groups in, 71–76

N

• Negative feedbacks, 132
• Nervous system. See also Brain affective tone and, 175–177, 207 artificial intelligence and, xvi, xxxiii–xxxiv ataxia of, 12–13, 129–130 chain of transmission and return of information in, 129–131 limits to organization of, 207 mathematical logic and, 20–22 memory and, 166–170 messages to, 177–178 neurons in, 165–166 synapses in, 20–22, 25, 29, 165–166, 171, 179, 271–272 tabes dorsalis of, 13, 129–130 treatment of discrepancies by, 201–202 vision and (See Vision)
• Neurons, 165–166 lengths of chains of, 209–210 memory loss and, 203–204
• Newtonian mechanics, 53–54 in astronomy, 45–50
• New York Times, ix, xii
• Nikodym, theorem of, 96
• Noisy-channel coding theorem, xxiii
• Non-linear prediction, xliii–xliv
• Nonlinear Problems in Random
• Non-linear systems, xxxii–xxxiii, xxxvi–xli, 239 oscillations of frequencies in, 273–274
• Non-linear systems of relaxation oscillations, 150–151
• Non-linear transducers, 246–249
• Northrup, F. C. S., 28
• Numerical machines, 161–162,

O

• “On Computable Numbers, with an Application to the
• Ontogenetic learning, 233–234
• Organic disorders, 202–203
• Organisms, multicellular, 215–216
• Organizations. See Communities
• Organ pipes, 148–149
• Oscillation, 29, 30–31 of frequencies in non-linear mechanisms, 273–274 mathematics symbolism of, 133–137 non-sinusoidal, 148 in organ pipes, 148–149 relaxation, 149–150
• Osgood, W. F., 70
• Outline drawing recognition, 186–187

P

• Paleontology, 51–52
• Parkinsonism, 146
• Partial differential equations, 6, 161, 180–181
• Pascal, Blaise, 19
• Pavlov, Ivan, 175
• Pfeiffer, John, ix
• Phase average, 95–96
• Phosphorescence, 170
• Photocells, 193
• Photography, 169, 170, 187
• Phylogenetic learning, 233–234,
• Physical contests as games, 241–242
• Pitts, Walter, 20–21, 23, 26, 33, 42
• Planck’s law, 53
• Prediction linear and non-linear, xliii–xliv time series problem, 110–114,
• Prefrontal lobotomy, 205
• Principle of Uncertainty, xviii, 15
• Probabilities, conditional, 96–97
• Probability, a priori versus a posteriori, 86–87
• Probability density, 90–93
• Probability zero, 66–67, 96
• Proofs, logical, 173
• Psychology, 171–172
• Psychopathology commonalities between the brain and computing machines and, 199–200 distinction between functional and organic disorders in, 202–203 traffic jams and, 207–209
• Ptolemaic geocentric system, xxxvii
• Purpose tremor, 13, 146

Q

• Quantum degeneracy, 170
• Quantum mechanics, 125–126

R

• Raisbeck, Gordon, xlvi
• Ramos, F. Garcia, 26
• Random noise, xxxix–xl
• Reading by blind persons, 33, 191–192
• Reflexes, feedback in, 153–154
• Relaxation oscillation, 149–150 non-linear systems of, 150–151
• Robinson, Charles E., xlvii
• Rosenblith, Walter A., 255, 274
• Rosenblueth, Arturo, 3, 4–6, 8, 13–14, 17–19, 23, 25–26, 31
• Royce, Josiah, 4
• Russell, Bertrand, 173

S

• Salivation, 175
• Samuel, A. L., xliv
• Sandberg, Henrik, xxx
• Scanning process, 7, 168–169, 189–190
• Science, xii
• Scientific fields, Wiener on boundaries of, 4–6
• Scientific judgment, 36–37
• Second law of thermodynamics, xxxii
• Second-order programming, 238–239
• Self-organization of brain waves, 251, 277–279
• Self-organization of genes, xlii, xlvi
• Self-propagating machines defined, 245–246 electrical currents and, 246–247 non-linear transducers and, 246–249 shot-effect inputs and, 247–248
• Selfridge, Oliver G., 26, 42, 178
• Senses, human. See Smell, sense of; Vision
• Sensory prosthesis, 191, 195–196
• Servomechanisms, 29
• Shannon, Claude, xv–xvi, xxi, xxii–xxiii, 17, 20–21, 119
• Shockley, William, xxi
• Shock treatment, 205–206
• Shot-effect inputs, 247–248
• Siegelman, Jim, xiv, xvii
• Similarity, theory of, 183, 187
• Skyscrapers, 207–208
• Sleep, 205
• Smell, sense of, 217
• Social sciences, 227–228
• Social systems, communication within, 35–36
• Sociology, 27–28
• Statistical mechanics, xxix–xxxii character groups in, 75–76 entropy and, 80–83
• Steam engines, 56
• Stock market, xii–xiii, 228
• Storage of information, 166–171
• Struggle activities as games, 239–241
• Symbolism of mathematics, 133–137
• Synapses, 20–22, 25, 29, 165–166, 171, 179 nerve fibers carrying, 271–272
• Szent-Györgyi, Albert, 128

T

• Theory, xxxvii–xxxix, 247
• Tabes dorsalis, 13, 129–130
• Taylor, G. I., 254
• Telegraph-type repeaters, 168, 187
• Telephone circuits, 85–86, 94,
• Tesla, xii
• The Computer and the Brain, xxi
• The Human Use of Human Beings, xiii, xvii, xxxvi, 243
• “The Sorcerer’s Apprentice,” xix,
• Tidal evolution, 50–53
• Time, 47–48, 54
• Time average, 70
• Time series applications of, 85–86
• Traffic jams, 207–209
• Transformation groups, 71–76 visual perspective, 188–191
• Transformations, ergodic, 78–80
• Trigonometric functions, xxxvii–xxxix, 65
• Trump, Donald, xix
• Tube noise, 247
• Turing, Alan, xxi, 34, 173

U

• Uber, xii

V

• Vallarta, Manuel Sandoval, 4, 25
• Vision
• Visual flicker, 273
• Vitalism, 54, 63
• Vocoder system, 85–86, 94
• Volta and Galvani, 252
• Voluntary activity, 12–13 feedback of, 132, 146–147
• Von Neumann, John, xxi, 28, 77, 79, 180, 220–221, 245 game theory of, 235–236

W

• Wiener’s definition of, xxiv–xxv
• Wallace, Alfred, 52
• War as game, 235–236, 242,
• Watanabe, S., xliv, 239
• Wave problems, 23–24
• Weaver, Warren, 23
• Webster, Frederic, 42
• Wiener, Leo, xiv
• Wiener, Norbert as child prodigy, xiv–xv collaborators with, xv, 3–8
• Wiener filtering, xxv–xxvii
• Wiener–Hopf equation, xxvi, 239
• Wiener measure, xxiii–xxiv
• World War III, 242

Y

• Youth, xiv, xvii
• YouTube, xviii

Z

• Zuckerberg, Mark, xi

Cybernetics · Second Edition (1961) · Norbert Wiener

Forewords by Doug Hill & Sanjoy K. Mitter · 10 章 + 导论