Computation in Neural Nets - Understanding Understanding: Essays on Cybernetics and Cognition - page 48

TABLE 3.
q=0

f ( T ) = 1/D t

q=1 f (v) = f 1 + f 2 - tf 1 f 2

q=2 f (•) =D tf 1 f 2

q=3 f ( C ) = 0

taking more and more cross-products of intensities into consideration until
for the strongest logical function being short of contradiction—the logical
“AND”—the single cross-product of all stimuli is computed.
We have carefully avoided associating with “ p ” or with “ f ” the actual
output frequency. We called f the “internal frequency”. The reason will
become obvious in a moment. It is well known that after the production of
each pulse a physiological neuron requires a certain moment of time D t R —
the so-called “refractory period”—to recover from its effort and to be ready
for another pulse (see also fig. 14). But in table 3 the resulting frequency
for zero threshold is the reciprocal of the pulse duration D t , which, of course,
is unmanageably high for a neuron whose refractory period is clearly much
longer than the duration of its pulse

(29)

DD t

R >

t .

It is very easy indeed to accommodate this difficulty in our calculations, if
we only realize that the actual output frequency f o of the element is the fre-
quency f at which it “wants” to fire, reduced by the relative time span in
which it cannot fire:

( ) (30)

f =- f 1 f D t R .

o o

Solving for the output frequency in terms of internal frequency and refrac-
tory period we have:

f
ft R

f

o =

. (31)

1 + D

From this is easily seen that the ultimate frequency at which an element
can fire is asymptotically approached for f Æ 1/D t , and is given by:

+ 1 1

f

omax =

DD D ,

(32)

t t t

R

which is in perfect agreement with our concept of the physiological behav-
ior of this element. The actual values for pulse duration and refractory
period may be taken from appropriate sources (Eccles, 1952; Katz, 1959).

3.2. The Neuron as an “Integrating Element”
The element discussed in the previous paragraphs is an “All or Nothing
Device” par excellence , and in the two subtitles “Synchronism” and “Asyn-
chronism” we investigated only how this element behaves when subjected