Source
Ashby, Design for a Brain (2nd ed., 1960), LIT-787, read in NOTE-851: Ss. 10/5–10/9, 11/2–11/12, 12/10–12/17, 13/8–13/13, 15/4–15/11, 16/7–16/15, 17/3, and the proof in S. 22/14.
What was actually shown
Exponential against linear (Ss. 11/2–11/6). With N jointly required successes each of probability p per trial: all at once, (1/p)ᴺ trials; one after another, about N/p; all tried, failures retried, a little more than 1/p. For p = ½, N = 1,000, at one trial a second: about 10²⁹³ years, about 8 minutes, a few seconds. “What had made the processes … so excessively time-consuming is that partial successes go for nothing.” Crystallisation is the physical case: impossible if every molecule must fall into place at once, routine by succession (S. 11/8).
Retention needs disconnection (S. 11/10). If adapting one essential variable leaves others adapted, the step-mechanisms that changed can have no channel to the parts that serve the others. “For the accumulation of adaptations to be possible the system must not be fully joined.”
Constancies separate (Ss. 12/10, 22/14). Two subsystems joined only through a third are independent and each state-determined if and only if the third is constant: “a wall of constancies”. Parts that go constant over a threshold give temporary independence; enough of them “can cut a system to pieces” (S. 12/17). In a richly joined system a near-complete equilibrium “will almost certainly fall back”; in a poorly joined one the number of parts at equilibrium “cannot fall with time” (Ss. 13/9–13/10).
Separate stores for separate situations (Ss. 10/8–10/9, 16/12–16/15). For an adaptation to A to survive learning B and be ready when A recurs, the step-mechanisms must split into non-overlapping sets, with the situation selecting which set is on the second feedback. In a multistable system with few parts active per stimulus, different stimuli use largely different parts, which does this without a dedicated gate; similar stimuli share parts, and then “new learning does tend to destroy old”, more as the learnings resemble each other (Robinson’s numbers, Skaggs’s chess positions). Accumulation and retroactive inhibition are opposed, and an intermediate degree of connection shows both partially.
The environment allows it (Ss. 15/2–15/11). Ordinary environments are mostly part-functions, constant most of the time and each affecting few others, so they can be adapted to piece by piece, in their natural order where they form a chain, provided the links carry little.
What could have come out otherwise: the calculations could have shown the brain’s speed compatible with rich joining. They show it is not, for independent probabilities.
What this does not say
- Not measured. The times are computed for type-cases with independent successes. The match to habituation, ablation and interference is qualitative; Ashby leaves measurement to experimenters (S. 16/11).
- Not that less connection is always better. Joining adds repertoire and early warning (Ss. 17/5–17/6); connection must lie “between certain limits” (S. 17/7).
- Not a mechanism for the gate. How the right store is selected is shown only for the random-dispersion case.
- Not specific to brains. The results are about state-determined systems with step-mechanisms; any system of that kind is covered, and nothing more is claimed about which ones the brain uses.
Connections
- THEORY-324 is the mechanism whose speed this account limits.
- CLAIM-185. Its thesis, that complex structure grows only on persistent anchors, is this account’s in another domain, down to the crystal. This account adds the condition the claim leaves implicit: a retained part must be cut off from what is still changing, or it does not stay retained. The transfer to arguments is analogy.
- QUESTION-038. Ashby’s answer to what makes a kept structure usable again is a store closed to new trials and opened by its own situation.
- CLAIM-180. Interference grows with similarity, because similar inputs use the same parts: a near restatement is the one most likely to overwrite, which is the other side of drift.
- CLAIM-176. Recurrence is exploitable only where the recurring situation reaches its own store (Ch. 10).
- CLAIM-179’s note on May (LIT-930). Ashby’s sampled matrices (S. 20/10) give the earlier, empirical form of the size limit on stability, and Chapters 13 and 16 give the escape: weak joining and many constancies.