Volume 11 of W. Ross Ashby's Journal
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1948



Volume 11



2429+03	2429+04



2429+05	2430

Summary: Full equations and approximations of the machine. (see below).
Homeostat circuit
Hover mouse here to display note
2431	2432



Hover mouse here to display note
2432+01	2432+02

Summary: Reporting progress in the machine. 2435
Summary: Social example of instability. Society [18]: Actual example of unstable equilibrium in a country, 1851, two more examples, 2434.
2433	2434

Homeostat works

2435	2436



2437	2438


Summary: Method for investigating friction coefficients in my machine. (2432)
2439	2440


Summary: How well does the machine's actual behavior correspond with the settings? (see also 2448, 2452)
2441	2442

Summary: Memory and multistability.
Summary: Trying to make a system give assigned roots. Higher geometry of fields and matrix theory [20]: Forming system with given roots 1818, 2444.
2443	2444



2445	2446

Summary: If there are no feedbacks, a linear dynamic system cannot develope steady oscillations, but more general systems can. Linear system feedback and oscillations Oscillation in linear system
Homeostat possible bias
2447	2448

Summary: Relations between stability of the machine and its supposed stability of setting. j→∞ is sufficient to make the behavior tend to the theoretical form. (see 2452)

2449	2450

Summary: In a multistable system with multiple subsystems, the number of stable subsystems rises exponentially with the time towards its limit.

2451	2452


Higher geometry of fields and matrix theory [22]: If one variable is made more self-stable, the whole may become unstable, 2423, 2454, 2463, 2458, 2460.
2453	2454



2455	2456

Summary: Two much stability gives rigidity and loss of control over other systems stability has an optimum. (Generalised in next two sections).
Higher geometry of fields and matrix theory [22]: If one variable is made more self-stable, the whole may become unstable, 2423, 2454, 2463, 2458, 2460.
2457	2458


Summary: The fault of too much stability proved more generally. Over stability just means slavery. Higher geometry of fields and matrix theory [22]: If one variable is made more self-stable, the whole may become unstable, 2423, 2454, 2463, 2458, 2460.
2459	2460

Summary: Multistable system point.

2461	2462

Higher geometry of fields and matrix theory [22]: If one variable is made more self-stable, the whole may become unstable, 2423, 2454, 2463, 2458, 2460.
Absolute system with infinity of variables Canonical equations with infinity of variables Variable system with infinite
2463	2464


Summary: Equations [x'=f(x)] and x=F(x^o;t) when n→∞.
2465	2466

Gestalt recognition Pattern (in general) as stimulus

2467	2468

Summary: Definition and test for two patterns of initial displacement, differently sited to be equal. 4148
Amoeba habituation in Habituation in Protozoa
2469	2470

Pain distinct from pain Paramecium habituation in Pleasure nature of

2471	2472



2473	2474



2475	2476



2477	2478



2479	2480



2481	2482

Resolution of physiological states Jennings

2483	2484

Summary: One factor in multistable systems tend to decrease interaction when two lines are activated simultaneously. The Multistable System [8]: A factor which tends to lessen interaction between lines in a multistable system, 2485.
Summary: Concept of a "stimulus".
2485	2486



2487	2488


Summary: The conditioned reflex and association possibly solved. The Conditioned Reflex [3]: Simple conditioned reflex as an elementary property of the commutive system, 1621. Still unsolved, 1943. Solved with multistable system, 1982. Further observations, 2064, 2490. Still unsolved, with reasons, 2192, 2243.
2489	2490

Summary: The diagram of immediate effects must conform to the type of experiment.

2491	2492



2493	2494


Null-function can be added to or removed from absolute system
2495	2496

Summary: When null-functions are present we can get absolute systems by either including them or excluding them.
Summary: On "fixing" and "releasing" a variable. Oddments [13]: Parametric form of "fixing" a variable, 2498.
2497	2498

Forcing a variable Habituation mechanism of
Association explanation The Conditioned Reflex [10]: Forcing a variable in an U.S. repeatedly to one value tends to make the resting state go towards that value 2500.
2499	2500



2501	2501+01



2501+02	2502


Summary: The ultrastable system shows a tendency to stabilize a variable at a value to which it is repeatedly forced. Cf. 2690
2503	2504



2505	2506

Summary: Whenever possible, postulate many independent ultrastable systems rather than one multistable system.
Association explanation Reflex, conditioned and ultrastability
2507	2508


Summary: Yet another attempt at the conditioned reflex and association. Cf. 2691
2509	2510

Feedback of the simple concept
Summary: The concept of "negative feedback" is just too simple to be worth anything. (See also 2524)
2511	2512



2513	2514



2515	2515+01



2515+02	2516

Ergodism Ergodic systems Information Wiener on

2517	2518



2519	2520

Computing machines Computing machines To work as homeostat
Homeostat copied by ACE
2521	2522

Summary: The ACE, if the operator knows the trick, can imitate the homeostat.
Summary: This concept of negative feedback is most unsuitable as a fundamental concept.
2523	2524



2525	2526

Summary: Theorem on f's and F's invariant under transformation Φ.
Summary: Biographical note.
2527	2528

Higher geometry of fields and matrix theory [8]: Numerical arrangement for maximal stability, 2529.
Summary: Systems of (almost) maximal stability (and see below)
2529	2530

Summary: Systems of maximal stability.

2531	2532



2533	2534



2535	2536


Summary: My theory explains why nerve cells cannot regenerate.
2537	2538


Training of ultrastable system
2539	2540

Summary: One part of an ultrastable system can act as "trainer" to another part. The Multistable System [9]: Replicated arcs cannot be corrected individually by the environment - 2541 - but if sample combinations of arcs are used, there is a tendency to correction, 2647.
Summary: A snag in the multistable system, which must be answered. (see 2647)
2541	2542

Instinct and homeostasis

2543	2544



2545	2546

Summary: Exposition.
Stimulus compound
2547	2548



2549	2550

Summary: In general, if a series of related compound stimuli evoke a series of patterns of activations, we can expect a priori no particular relation between the patterns of activations. Any special relation found to exist must be due to some special arrangement in the machine.

2551	2552

Society [23]: Systems of predators and prey 2553. Society [24]: Ecological system of Daphnia population, 2553.
Summary: On "memory" in society. Society [25]: Law in a society as part-function, 2554. Society [26]: Memory in society by Standing Orders. 2554.
2553	2554



2555	2556

Organisation concept abandoned Parameter as variable outside system
Constraint reaction of homeostat to
2557	2558



2559	2560

1949

Broadcast on 29 Dec 1948
Homeostat faster model
2561	2562



2563	2564


Summary: Ideas for new homeostat. (continued 2568)
2565	2566



2567	2568



2569	2570



2571	2572



2573	2574



2575	2576


Diagram of immediate effects (D.I.E.) part-function in Part-function effect on D.I.E. (diagram of immediate effects)
2577	2578



2579	2580

Summary: Constancy is by no means necessary for independence. The latter can be obtained even with gross fluctuation provided it is forced.

2581	2582

Summary: A system of step-functions reaches a resting state or cycle instantaneously
Summary: Define the parts and predict the behavior of the whole, not vice versa. Oddments [12]: An absolute system can always be regarded as made by the assembly of parts, 2584.
2583	2584

Summary: Any absolute system can be regarded as built of parts. Summary: Constancies are conserved when parts are joined or separated.
Summary: Fields may, and should, be thought of as bounded and finite in extent.
2585	2586



2587	2588



2589	2590



2591	2592



2593	2594

Summary: Discussion of the stability of a system formed by joining an infinite number of part-functions. Equilibrium of system of part functions

2595	2596

Summary: Response of linear system to an input when its response to a step-function is known. Interaction Poincaré on Output to given input
Statistical mechanics Poincaré on
2597	2598

Canonical equations of Laplace transform Laplace transformation Solution of linear equations by Linear system and Laplace transform Output to given input
Summary: Solution of linear differential equations by Laplace transforms. Linear system input of simple harmonic motion Oscillation forced
2599	2600

Transmission ratio
Transfer function of system described by differential equations
2601	2602

Summary: Transfer functions and my equations.
Summary: Stability of a chain with feedback. (See also 2621)
2603	2604

Summary: Nyquist's criterion is merely a convenience. Routh is fundamental
Summary: Transfer function of a single variable. Feedback and cycle Resting cycle implies feedback
2605	2606

Oscillation implies feedback
Summary: Oscillation necessarily implies feedback. Extrapolation and prediction Habituation to moving stimulus The Conditioned Reflex [7]: Habituation to a moving stimulus 2608.
2607	2608


The Conditioned Reflex [12]: Prediction, nature of, 2609.
2608-A	2609

The Conditioned Reflex [13]: Ultrastable process tending to correct prediction, 2610.

2610	2611

The Conditioned Reflex [4]: Conditioned reflex might be due to feedback depending on a "match" 2612.
Summary: Habituation to a moving stimulus, prediction, and the conditioned reflex. Reflex, conditioned and ultrastability
2612	2613

Reflex, conditioned machine built The Conditioned Reflex [5]: Conditioned reflex machine built. 2614. Seems to be original, 2623.
Summary: A mechanism for conditioned reflex. Made: 16 Aug '49. Learning gets fixed Memory gets fixed
2614	2615

Summary: Evidence that neurons learn and then "fix". Feedback binary counter turned to decimal
Summary: An extremely simple example of feedback modifying behavior. (See 2729)
2616	2617


Summary: Properties of the relaxation oscillator.
2619	2620


Summary: Weiner's example (2604) amplified. (See next section)
2621	2622

Summary: Stability of a chain-circuit of variables. (See also 2604) The Conditioned Reflex [5]: Conditioned reflex machine built. 2614. Seems to be original, 2623.
Summary: Inaugural meeting of the Ratio Club at the National Hospital for Nervous Diseases. Information in time series
2623	2624


Memory and selectivity Selection needs memory Selection of wave length
2625	2626

Summary: Systems with high selectivity must have long dieaway by cybernetic necessity.
Summary: Memory in the dogs of the "Tinder Box". Memory in the 'Tinder Box' dogs
2627	2628

Part-function necessary in environment

2629	2630



2631	2632

Universe multistable system and the rest
Summary: The multistable system much clarified. Goal without feedback
2633	2634

Summary: Goal-seeking behavior does not necessarily imply feedback. (Continued, 2643) Feedback not necessary for goal-seeking
Conduction, nerve short circuit Psychiatric applications [11]: Causalgia as due to vicious circle 2636.
2635	2636

Vicious circle causalgia as
Summary: Granit on causalgia.
2637	2638



2639	2640

Summary: The main properties of the multistable system are proved necessary.
Summary: Canonical equations from the transfer function. Transfer function converse
2641	2642



2643	2644

Summary: Goal-seeking behavior does not necessarily imply feedback. (Continued, 2650, 2654)

2645	2646

Natural Selection [9]: Parallel with the correction of arcs in multistable system by environment 2647. The Multistable System [9]: Replicated arcs cannot be corrected individually by the environment - 2541 - but if sample combinations of arcs are used, there is a tendency to correction, 2647.
Summary: The problem of 2541 ─ that with replicated arcs there is no longer individual correction of the wrong ones ─ may be solved statistically if the brain uses combinations obtained by sampling. 4216
2647	2648

Summary: Memories may perhaps float. 4155 Memory floating Oddments [34]: Memories might 'float' 2649.
Feedback not necessary for goal-seeking Goal without feedback Servo-mechanism as stabiliser
2649	2650

Summary: Strong goal-seeking usually needs a servo-mechanism. (Continued 2654)
Psychiatric applications [13]: Collected list 2652.
2651	2652



2653	2654

Higher geometry of fields and matrix theory [13]: M=MATRIX If latent roots of M equal none of those of A, neither B nor C can be wholly zero, 2655.
Summary: If a part is to behave with more stability than it has intrinsically, then feedback is necessary.
2655	2656

Statistical mechanics in brain
Summary: Meditations on a new statistical mechanics.
2657	2658


Quotations [27]: Quotation on regarding the brain as a factory and trying to study it by seeing the main events of input and output but being unable to see the small details in the workshops, 2660.
2659	2660

Boolean algebra and logic - machines Logic machine

2661	2662



2663	2664



2665	2666

Summary: Machine for Boole's logic.

2667	2668

Summary: If one or more variables are unobserved, a cycle of parameter-values need not elicit a cycle of observed values.
Summary: An essential feature of the development of the conditional reflex is that an independence changes to dependence. The Conditioned Reflex [19]: A fresh start at the conditioned reflex, 2670.
2669	2670



2671	2672

The Conditioned Reflex [20]: A possible mechanism for the conditioned reflex examined but rejected, 2673.
Summary: The conditioned reflex cannot be explained this way.
2673	2674


Summary: A parameter can be localised in action by part-functions.
2675	2676

Summary: If the observer tries to control a variable he may be forming part of the whole system. Oddments [20]: Status of an observer who holds a variable constant, 2677.
Summary: A "stimulus"is one of a pair of initial states. Higher geometry of fields and matrix theory [25]: If A dominates B, the latent roots of the whole are just those of A and those of B, 2678.
2677	2678

Summary: If systems are joined by dominance, the latent roots are unmoved.
Summary: Two possible ways of proving feedback between two sub-systems. Feedback is also proved present if we can find in A a single frequency not found in A + B. Feedback test for
2679	2680



2681	2682


Summary: Some properties of a system of part-functions when a single parameter causes activations by its alternation.
2683	2684


Summary: A theorem on localised absoluteness.
2685	2686


Summary: A second stimulation can not only break a field but can save it.
2687	2688

The Conditioned Reflex [22]: An ultrastable system is immune to a disturbance ß if the U.S. was going to act as ß anyway, 2689. This gives a new clue to the conditioned reflex, 2691.
Summary: Briefly, an adapted system cannot be broken by forcing it to do what it was going to do anyway. This idea only restates what was said 18 months ago on 2503!
2689	2690

Forcing a variable The Conditioned Reflex [22]: An ultrastable system is immune to a disturbance ß if the U.S. was going to act as ß anyway, 2689. This gives a new clue to the conditioned reflex, 2691.

2691	2692

Summary: The conditioned reflex again! Yet another mechanism! This time in iterated ultrastable systems. 4596. No! Just the same old one rediscovered yet again.
Summary: Note on the previous note. The Conditioned Reflex [23]: In some circumstances, not reinforcing a conditioned reflex may give a large response, 2694.
2693	2694

The Conditioned Reflex [24]: Two ways of getting a conditioned reflex: they are closely related, 2695.
Summary: The two ways of getting a conditioned reflex are almost identical.
2695	2696



2696+01	2696+02

These images are reproduced courtesy of The Estate of W. Ross Ashby. Copyright 1972, 2008 © The Estate of W. Ross Ashby