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Here, some back-of-an-envelope calculations produced interesting results.
Suppose that any individual unit had a probablity
p
of finding an equilibrium
state in one second. Then the time for such a unit to reach equilibrium would
be of the order of 1/
p
. And if one had a large number of units,
N
of them, act-
ing quite independently of one another, the time to equilibrium for the whole
assemblage would still be 1/
p
. But what if the units were fully interconnected
with one another, like the four units in the prototypical four-homeostat setup?
Then each of the units would have to find an equilibrium state in the same
trial as all the others, otherwise the nonequilibrium homeostats would keep
changing state and thus upsetting the homeostats that had been fortunate
enough already to reach equilibrium. In this configuration, the time to equi-
librium would be of the order of 1/
p
N
. Ashby also considered an intermediate
case in which the units were interconnected, but in which it was possible for
them to come into equilibrium sequentially: once unit 1 had found an equilib-
rium condition it would stay there, while 2 hunted around for the same, and
so on. In this case, the time to equilibrium would be
N
/
p
.
Ashby then put some numbers in:
p
= 1/2;
N
= 1,000 units. This leads to
the following estimates for
T
, the time for whole system to adapt (1952, 142):
for the fully interconnected network:
T
1
= 2
1000
seconds;
for interconnected but sequentially adapting units,
T
2
= 2,000 seconds;
for the system of entirely independent units,
T
3
= 2 seconds.
24
Two seconds or 2,000 seconds are plausible figures for biological adapta-
tion. According to Ashby, 2
1000
seconds is 3 × 10
291
centuries, a number vastly
greater than the age of the universe. This last hyperastronomical number was
crucial to Ashby's subsequent thinking on the brain and how to go beyond the
homeostat, and the conclusion he drew was that if the brain were composed
of many ultrastable units, they had better be only
sparsely connected
to one
another if adaptation were going to take a realistic time. At this point he began
the construction of a new machine, but before we come to that, let me note
again the ontological dimension of Ashby's cybernetics.
The brain that adapted fastest would be composed of fully independent
units, but Ashby noted that such a brain “cannot represent a complex biologi-
cal system” (1952, 144). Our brains do not have completely autonomous sub-
systems each set to adapt to a single feature of the world we inhabit, on the one
hand; the neurons of the brain are observably very densely interconnected,
on the other. The question of achieving a reasonable speed of adaptation thus
resolved itself, for Ashby, into the question of whether some kind of serial ad-
