Source
Ashby, Design for a Brain (2nd ed., 1960), LIT-787, read in NOTE-851: Ss. 5/8, 6/8–6/9, 7/2–7/26 and Ch. 8, with the formal statement in S. 22/6.
What was actually shown
Adaptation as stability. Behaviour is adaptive if it “maintains the essential variables … within physiological limits” (S. 5/3), which is stability of the organism–environment system in the region where they stay within limits (S. 5/8).
Necessity (Ss. 7/4–7/8). If the reacting part does not know how the environment acts on the essential variables, only trial and error can find out. The rule “if the trial is unsuccessful, change the way of behaving; when and only when it is successful, retain the way of behaving” requires that the parameters of the reacting part be unsettled exactly when an essential variable is outside its limits. So there must be a channel from the essential variables to those parameters, “formally identical (isomorphic)” in any adaptive system, living or mechanical (S. 7/8).
Sufficiency (S. 7/11). A whole is at equilibrium only where every part is (S. 6/8). The parameter system is at equilibrium only when the essential variables are within limits. So every equilibrium of the whole is adapted, whatever the reacting part’s construction and however the new parameter values are drawn, “at random” included (S. 7/25).
Demonstration (Ch. 8). The Homeostat, four magnets coupled through uniselector-set weights drawn from random-number tables, recovers stability after an operator reverses a connection, by finding a compensating reversal, and adapts to a constraint it was not built for.
What could have failed: the veto argument needs the parameter system to be at rest only within limits; a machine built otherwise (S. 8/13) seeks the wrong goal, which the Homeostat with mis-set relays would show.
What this does not say
- Not that adaptation is fast. The search is blind. Ashby’s own calculation (S. 11/2) gives 2¹⁰⁰ trials for 100 independent essential variables. How it becomes practicable is THEORY-307.
- Not that the step-mechanisms choose. They change “at random” and are kept only if the essential variables do not veto them. The second feedback alters the parameters of regulation without directing the alteration.
- Not that the brain is a Homeostat. Ashby says of the step-mechanisms “we have at present practically no idea of where to look” (S. 9/4), and that the ultrastable form is “only one of a large class of related forms” (S. 7/26).
- Not about environments the repertoire cannot meet. With no stable configuration available, an ultrastable system, like an organism, fails (S. 8/11).
- Necessity holds under the stated case. Where the reacting part already knows how the environment acts on its essential variables, or can act on them directly, the deduction does not apply (Ss. 7/3–7/4).
Connections
- THEORY-217 (Barandiaran) uses Ashby’s essential variables and regime switches; its “second-order regulation that shifts the system to another regime” is this account’s second feedback, and its claim that malfunction needs no second order of norms is compatible with Ashby, whose second feedback is a mechanism, not a norm.
- THEORY-153 (Beer) rests its regulation on Ashby’s law of requisite variety, which Ashby applies to the ancillary regulations (S. 17/13).
- THEORY-134. Viability theory takes the constraint set as given; Ashby likewise takes the essential variables and their limits from the species (S. 3/14).
Note of 2026-10-19: the two deductions, re-derived
Take the whole as a state-determined system with four blocks of variables: environment E, reacting part R, essential variables V and the parameters S of R. Its transition is x’ = F(x), with one component map per block. R acts on V only through E and does not know how E is coupled to V (Ss. 7/3–7/4). A state is adapted when every essential variable is within its limits there (S. 5/8).
Sufficiency. x is an equilibrium of the whole iff F(x) = x, which holds iff each component map leaves its own block fixed at x, given the other blocks’ values there. That is the veto (S. 6/8), and it needs nothing beyond state-determinacy. If S changes at every state where some essential variable is outside its limits, then at an equilibrium, where S does not change, every essential variable is within its limits. This holds whatever R’s construction and however the new values of S are drawn (S. 7/25). If no configuration of S is stable, the whole has no equilibrium and the statement is vacuous (S. 8/11). The condition must hold for as long as V is outside, as in the Homeostat, whose relay stays closed and keeps advancing the uniselector while a needle is past its limit (S. 8/2). A step-mechanism that jumps only on crossing out of the limits can land in a field with an equilibrium outside them and then stay there.
Necessity. S depends on V, in Ashby’s operational sense (S. 12/3), if two states differing only in V can be followed by different values of S. The trial-and-error rule (S. 7/7) keeps the way of behaving, which S sets (S. 6/3), when the trial succeeds, and changes it when it fails. Success is judged by V. Take two states that agree in E, R and S, with V within its limits in one and outside in the other. Such pairs exist, because V is a coordinate of its own, whenever V can leave its limits at all. The rule keeps S in the first and changes it in the second. So S depends on V, and there is a channel from V to S, direct or through intermediates. With S → R → E → V, this closes a second loop beside the primary R ⇄ E. The deduction fixes no form for the loop, which is why Ashby calls the ultrastable form “only one of a large class of related forms” (S. 7/26). Once the rule is assumed, the necessity is close to definitional. A regulator whose one fixed setting is stable in every environment of the class needs no such channel, but it does not adapt by trial and error. Whether systems that do need different settings can do without the channel is QUESTION-170.