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more light makes the windows bigger, perhaps, but thereby makes the house
more likely to collapse” (1964, 42).
The details here are not important, but I want to note the distinctly Ashby-
ite way in which Alexander frames the problem in order to set up his own
solution of it, a solution which is arguably at the heart of Alexander's subse-
quent career. As discussed earlier, in a key passage of
Design for a Brain
Ashby
gave estimates of the time for multihomeostat systems to achieve equilib-
rium, ranging from short to impossibly long, depending upon the density of
interconnections between the homeostats. In the second edition of
Design
,
he illustrated these estimates by thinking about a set of rotors, each with two
positions labeled A and B, and asking how long it would take various spinning
strategies to achieve a distribution of, say, all As showing and no Bs (Ashby
1960, 151). In
Notes on the Synthesis of Form
, Alexander simply translates this
illustration into his own terms, with ample acknowledgment to Ashby but
with an interesting twist.
Alexander invites the reader to consider an array of one hundred lightbulbs
that can be either on, standing for a misfit in the design process, or off, for no
misfit. This array evolves in time steps according to certain rules. Any light
that is on has a 50-50 chance of going off at the next step. Any light that is off
has a 50-50 chance of coming back on if at least one light to which it is con-
nected is on, but no chance if the connected lights are all off. And then one
can see how the argument goes. The destiny of any such system is eventually
to become dark: once all the lights are off—all the misfits have been dealt
with—none of them can ever, according to the rules, come back on again. So,
following Ashby exactly, Alexander remarks, “The only question that remains
is, how long will it take for this to happen? It is not hard to see that apart
from chance this depends only on the pattern of interconnection between the
lights” (1964, 40).
61
Alexander then follows Ashby again in providing three estimates for the
time to darkness. The first is the situation of independent adaptation. If the
lights have no meaningful connections to one another, then this time is basi-
cally the time required for any single light to go dark: 2 seconds, if each time
step is 1 second. At the other extreme, if each light is connected to all the
others, then the only way in which the lights that remain on can be prevented
from reexciting the lights that have gone off is by all of the lights happening to
go off in the same time step, which one can estimate will take of the order of
2
100
seconds, or 10
22
years—one of those hyperastronomical times that were
crucial to the development of Ashby's project. Alexander then considers a
third possibility which differs in an important way from Ashby's third possibil-
