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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
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2431 2432
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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(xo;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 β if the U.S. was going to act as β 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 β if the U.S. was going to act as β 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

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