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Design for a brain
We can return to the technicalities of Ashby's cybernetics. The homeostat was
the centerpiece of his irst topic,
Design for a Brain
, which was published in
1952 (and, much revised, in a second edition, in 1960). I want to discuss some
of the principal features of the topic, as a way both to clarify the substance of
Ashby's work in this period and to point the way to subsequent developments.
First, we should note that Ashby had developed an entire mathematical
apparatus for the analysis of complex systems, and, as he put it, “the thesis
[of the topic] is stated twice: at irst in plain words and then in mathematical
form” (1952, vi). The mathematics is, in fact, relegated to a forty-eight-page
appendix at the end of the topic, and, following Ashby's lead, I, too, postpone
discussion of it to a later section. The remainder of the topic, however, is not
just “plain words.” The text is accompanied by a distinctive repertoire of dia-
grams aimed to assist Ashby and the reader in thinking about the behavior of
complex systems. Let me discuss just one diagram to convey something of the
flavor of Ashby's approach.
In figure 4.5
Ashby schematizes the behavior of a system characterized by
just two variables, labeled
A
and
B
. Any state of the system can thus be denoted
by a “representative point,” indicated by a black dot, in the
A-B
plane, and the
arrows in the plane denote how the system will change with time after finding
itself at one point or another. In the unshaded central portions of the plane,
the essential variables of the system are supposed to be within their assigned
limits; in the outer shaded portions, they travel beyond those limits. Thus, in
panel I, Ashby imagines that the system starts with its representative point at
X
and travels to point
Y
, where the essential variables exceed their limits. At
this point, the parameters of the system change discontinuously in a “step-
function”—think of a band breaking in the bead-and-elastic machine of 1943,
or a uniselector moving to its next position in the homeostat—and the “field” of
system behavior thus itself changes discontinuously to that shown in panel II.
In this new field, the state of the system is again shown as point
Y
, and it is then
swept along the trajectory that leads to
Z
, followed by another reconfiguration
leading to state field III. Here the system has a chance of reaching equilibrium:
there are trajectories within field III that swirl into a “stable state,” denoted by
the dot on which the arrows converge. But Ashby imagines that the system in
question lies on a trajectory that again sweeps into the forbidden margin at
Z
.
The system then transmogrifies again into state IV and at last ceases its devel-
opment, since all the trajectories in that field configuration converge on the
central dot in a region where the essential variables are within their limits.
