Volume 17 of W. Ross Ashby's Journal
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1952



Volume 17



4291+03	4291+04

Knowing means 'controlling' DAMS (Dispersive and Multistable System) [86]: 'Knowing' means controlling, 4292.

4292	4293

DAMS (Dispersive and Multistable System) [87]: Ultrastable system cannot stop until "Cortex" "knows" environment. 4294.
Summary: What 'knowing' a system means. Contrast 4315. 4429, 4438. Better stated in transitions 4305
4294	4295

Black box, problem of the Black box by differences Difference replacing variable Memory and unobservables Unobservables replacement by other observations Variable replaced by difference

4296	4297

Summary: Differences, at a finite time later, can replace variables. 4301, 5206 Personal notes [21]: I decide to write Introduction to Cybernetics 4298. Personal notes [26]: The "Introduction to Cybernetics" was, apparently, written at Dad's suggestion. 4298.

4298	4299

Summary: Shannon's theory in its relation to the theory of the absolute system. 4312, 4396. Review 4345
Epistemology [16]: No one is a proper judge of whether he has or has not obtained "knowledge" 4301.
4300	4301

Summary: Effectiveness of parameters with finite substitution. Applied 4414 Dimension of parametric control History examples Memory in system Parameter control exerted by
Summary: Examples of states that include history. Summary: Knowledge must be tested by control. 4438 Information at runaway Epistemology [17]: Knowledge must mean 'control' if it is to be objective, 4303.
4302	4303

Triunique mapping
Summary: One-one-one relation between parameter and transition. 4396
4304	4305

Circularity of my brain studying "the brain" Epistemology [18]: Circularity of my theory, 4306.
Summary: My theory must become more circular, showing how an ultrastable brain is bound to work via the absolute system, etc. 4814
4306	4307


Design for a Brain Citizen's review Personal notes [20]: Reviews of "Design": 4258 Observer, 4309 Citizen, 4380 British Medical Journal, 4423 Journal of Consulting Psychology, 4423 McCulloch, 4446. Hibbert Journal, 4595 Galaxy, 4595 Scientific American, 4643 Occupational Psychology.
4308	4309

Summary: Entropy with two outputs, and the transmission of information from system to system. 4312, 4429 Transmission from system to system Epistemology [19]: "Knowing" as being at the right memory-state 4310.
Summary: Scientific knowledge is knowledge of a transformation. 4344, 4454 Group (mathematical) not all science Epistemology [20]: All knowledge is knowledge of transformation, 4311.
4310	4311

Parameter dominating system Transmission from system to system Variety defined

4312	4313


Summary: 'Variety' in systems.
4314	4315

Summary: 'Variety' in systems. See page 4327

4316	4317



4318	4319



4320	4321



4322	4323



4324	4325


Transformation Monograph
4326	4327

Transformation Monograph
Closure defined Group (mathematical) origin of Transformation Monograph
4328	4329

Transformation Monograph Variable defined
Transformation Monograph Variety in image
4330	4331

Joining of systems Transformation Monograph
Transformation Monograph
4332	4333

Transformation Monograph
Set or Ensemble of machines Transformation Monograph
4334	4335

Capacity information Transformation Monograph Variety in state

4336	4336+01


Transformation Monograph
4336+02	4337

Transformation Monograph Variety theorem on limits
Transformation Monograph
4338	4339

Impulse disturbances reduced to Transformation Monograph
Transformation Monograph
4340	4341

Transformation Monograph
Transformation Monograph
4342	4343

Machine definition Transformation Monograph
Set or Ensemble of machines Transformation Monograph
4344	4345

Entropy limit of Transformation Monograph
Transformation Monograph
4346	4347

Transformation Monograph Epistemology [21]: Nature of knowledge and control, Review { 4348 - 4364 }
Answer nature of Transformation Monograph Epistemology [21]: Nature of knowledge and control, Review { 4348 - 4364 }
4348	4349

Control nature of Transformation Monograph Epistemology [21]: Nature of knowledge and control, Review { 4348 - 4364 }
Transformation Monograph Epistemology [21]: Nature of knowledge and control, Review { 4348 - 4364 }
4350	4351

Transformation Monograph Epistemology [21]: Nature of knowledge and control, Review { 4348 - 4364 }
Transformation Monograph Epistemology [21]: Nature of knowledge and control, Review { 4348 - 4364 }
4352	4353

Memory during control Transformation Monograph Epistemology [21]: Nature of knowledge and control, Review { 4348 - 4364 }
Transformation Monograph Epistemology [21]: Nature of knowledge and control, Review { 4348 - 4364 }
4354	4355

Transformation Monograph Epistemology [21]: Nature of knowledge and control, Review { 4348 - 4364 }
Transformation Monograph Epistemology [21]: Nature of knowledge and control, Review { 4348 - 4364 }
4356	4357

Transformation Monograph Epistemology [21]: Nature of knowledge and control, Review { 4348 - 4364 }
Transformation Monograph Epistemology [21]: Nature of knowledge and control, Review { 4348 - 4364 }
4358	4359

Transformation Monograph Epistemology [21]: Nature of knowledge and control, Review { 4348 - 4364 }
Transformation Monograph Epistemology [21]: Nature of knowledge and control, Review { 4348 - 4364 }
4360	4361

Transformation Monograph Epistemology [21]: Nature of knowledge and control, Review { 4348 - 4364 }
Transformation Monograph Epistemology [21]: Nature of knowledge and control, Review { 4348 - 4364 }
4362	4363

Transformation Monograph Epistemology [21]: Nature of knowledge and control, Review { 4348 - 4364 }
Feedback and spread of variety Transformation Monograph
4364	4365

Transformation Monograph Triunique = bilinear
Bilinear system Transformation Monograph
4366	4367

Transformation Monograph
Transformation Monograph
4368	4369

Transformation Monograph

4370	4371

1953

Transmission from system to system
Summary: Variety in state accumulates.
4372	4373

Summary: Uniform activity in the parameters drives down variety in state. Homogeneity by parameters Society [48]: An evolving system needs long-term memories as well as short, 4374. The Multistable System [76]: An evolving system requires long term memories as well as short, 4374.
Summary: Long-term memories. Basin
4374	4375

Summary: On basins.
Summary: 'Delay' need not be rejected as a basic concept. Delay (in substitution) as basic concepts Natural Selection [76]: Evolution as progression to independance of Brownian movement, 4377.
4376	4377

Summary: Note on Darwinism. Summary: 'Experiment' = 'competition'. 4384 Competition equals trials Design for a Brain British Medical Journal review Experiment = competition Trial and error equals competition Society [49]: Trial = competition = experiment, 4380. Personal notes [20]: Reviews of "Design": 4258 Observer, 4309 Citizen, 4380 British Medical Journal, 4423 Journal of Consulting Psychology, 4423 McCulloch, 4446. Hibbert Journal, 4595 Galaxy, 4595 Scientific American, 4643 Occupational Psychology.

4380	4381

Adaptation speeding up adaptation Speed (of adaptation)
Summary: There is a maximal speed at which evolution or adaptation can proceed. The best one can do is to get near the maximum. 4384 Alpha rhythm and cell's activities Threshold and a-rhythm
4382	4383

Summary: The α-rhythm. Dispersion and alpha rhythm
Summary: Speed of adaptation can be achieved only by trials and comparisons. Homeostasis basic theory Regulation basic theory DAMS (Dispersive and Multistable System) [88]: Speed of adaptation demands trials, 4385.
4384	4385

Requisite Variety, Law of proof by inverse
Summary: Regulation (destruction of information) requires extra information. Continuous form 4395, 4658
4386	4387

Summary: Lack of variety and step-function are equivalent. 4439, 4440 Constraint and step-function Protocol constraint in Step function = lack of variety
Summary: Apparent inertia in adaptation. Homeostasis transients [no] Regulation transients in Transient defined Natural Selection [77]: Fisher's explanation of apparent inertia in evolution, 4389.
4388	4389

Transient maximal length

4390	4391

Summary: 'Transient' translated into non-metric terms. 4644 (vol.18)
Summary: Gödel's coding. Theorem 5086 Summary: Digital and analogue. Computing machines digital and analogue
4392	4393

Summary: Quotation showing gross ignorance of the principles of organisation, by one who should know better. Society [50]: Example showing present ignorance about organisation, 4394.
Summary: Two functions combining to an invariant. 4658 Homeostasis continuous form Invariant [no] homeostasis Regulation continuous form
4394	4395

Transducer inverse of
Machine non-singular Transducer non-singular
4396	4397



4398	4399

Coding theory of
Summary: The absolute system as coder and decoder. Extended 4414, 4461
4400	4401


Immunity defined Self-locking system conditions for
4402	4403

Habituation theory of

4404	4405

Basin selection of

4406	4407



4408	4409

Summary: Limiting basin when determinate machine is affected occasionally by impulse-operate. 4524, 5512
Summary: Proof of theorem Summary: When many related theorems are possible, pick on one and prove it quite rigorously; the exact details will then show the exact effect of each proposed variation. Oddments [42]: When many variations are possible, pick on one to prove it vigorously; the effect of modifications can then easily be seen. 4411.
4410	4411

Summary: (An addendum) Fixation Maier on
Input trasition as input Transition probability as input
4412	4413



4414	4415

Summary: Canonical equations of the decoder. Shorthand started Personal notes [22]: I start shorthand, 4416, I stop it, 4446, List of symbols, 5108.
Amplifier and loss of information DAMS (Dispersive and Multistable System) [62]: Magnification causes loss of information, 4417.
4416	4417

Summary: Magnification and dispersion from the point of view of information. 4422 Summary: If information is to be conserved, linearity must be achieved everywhere. Dispersion theory of Linear system importance The Multistable System [78]: Dispersion changes variety in value to variety in position. 4418.
Psychiatric applications [23]: Messages heavily contaminated with noise may be best ignored. 4419.
4418	4419

Summary: Proof that messages that are heavily contaminated with noise are best ignored.
Summary: Necessary conditions for a system to have resting states that differ only at a few variables.
4420	4421

DAMS (Dispersive and Multistable System) [63]: Effect of magnification in DAMS, 4422.
Summary: Effect of magnification on behaviour. Design for a Brain review Self-locking system as invariant Personal notes [20]: Reviews of "Design": 4258 Observer, 4309 Citizen, 4380 British Medical Journal, 4423 Journal of Consulting Psychology, 4423 McCulloch, 4446. Hibbert Journal, 4595 Galaxy, 4595 Scientific American, 4643 Occupational Psychology.
4422	4423

Summary: Invariants of a dynamic system with parameters. Summary: The Conditioned Reflex as a loss of power to transmit. 4430 Invariant "self-locking" as Invariant "stable" as Reflex, conditioned as loss of transmission The Conditioned Reflex [43]: Conditioned reflex as loss of transmition, 4424.
Summary: Distinguish variety in design from variety during performance. Continued 4427 top, 4427, 4428, 4431 Genes more fundamental
4424	4425

Arc competition among Order of time Organisation implies constancy The Conditioned Reflex [42]: The multistable system probably promotes competition between it's component arcs, 4426.
Design amount of
4426	4427

Summary: A system can "know" by having the right values of variables or parameters. 4438 Knowing as selection of vector
Summary: When a designer makes a machine of n states and a parameter-combinations, he puts in variety of a.n.log n This is its intrinsic content. 4463, 4704 Information in machine
4428	4429

Summary: Information that can come from a machine. Graph definition Machine falls in capacity Epistemology [22]: Estimates of how fast knowledge can be got from a machine 4430.
Entropy and information
4430	4431

Summary: Trial and error in reaction to shock. Summary: Information in printed English. Information per word Memory information in

4432	4433



4434	4435

Relation binary
Summary: Riguet on binary relations. 4470, 4498, 4566, 4581, 4604, 4632
4436	4437

Prediction as regulation Epistemology [23]: 'Prediction' and 'control' are forms of regulation, 4438.
Summary: Prediction and control are just forms of regulation. Summary: Wave as constraint; travelling immobility. 4440, 4943 Constraint wave as Thing as constraint Waves as entity
4438	4439


Summary: Way of behaving, constraint, thing, part-function. Constraint examples Dimension and constraint Rank and constraint
4440	4441

Constraint meaning of
Summary: More on "constraint". 4553, 4564
4442	4443

Entropy computing Information computing
Summary: Computing entropy.
4444	4445

Summary: Shorthand has more disadvantages than advantages. List of symbols:- End of this volume and 5108 Design for a Brain review Shorthand stopped Personal notes [20]: Reviews of "Design": 4258 Observer, 4309 Citizen, 4380 British Medical Journal, 4423 Journal of Consulting Psychology, 4423 McCulloch, 4446. Hibbert Journal, 4595 Galaxy, 4595 Scientific American, 4643 Occupational Psychology. Personal notes [22]: I start shorthand, 4416, I stop it, 4446, List of symbols, 5108.
Summary: ~~Every material system is equivalent to a transducer and a noise-source.~~ [deleted]
4446	4447

Summary: One formulation covers "design" "input" and "noise". (Next section) 4449 Design nature of Information in machine
Epistemology [24]: Distinction between 'design' and 'input' 4449.
4448	4449

Black box, problem of the first considered Input nature of

4450	4451



4452	4453

Summary: Information in a machine. 4701, 4847 Black box, problem of the theory of
Quantum theory and Black Box Epistemology [25]: Theory of Black Box, 4455.
4454	4455


Algebra Black Box as Machine as an algebra
4456	4457

Black box, problem of the isomorphism Invariant of Black Box Isomorphism in Black Box
Group (mathematical) not all science
4458	4459


Design within Black Box Transducer inverse of
4460	4461

Summary: Outline of the theory of the Black Box. 4480
Design nature of
4462	4463


Summary: What "designing" a machine means abstractly.
4464	4465



4466	4467


Summary: The variation of the essential variables must be supplemented. 4482, 4581
4468	4469

Summary: A single machine contains many "informations", most of which do not interact with the others. Example 4577 Information two need not interact
Summary: Joining absolute systems without metric. Example 4473, 4498, 4733 Joining general theory
4470	4471

Summary: Must every system drift to the condition of maximal internal separation? 4500, 4524 Summary: Cap or intersection as selective operator. Summary: Unsolved problem. Solved 5009 Operator ∩ (intersection) as selector Selection by ∩ (intersection operator)

4472	4473

Summary: Anything that can have variety is really a set. Variety implies a set
Distinguishability equivalence relation Epistemology [26]: Indistinguishability is an equivalence relationship, 4475.
4474	4475



4476	4477

Algebra Black Box as Black box, problem of the homomorphism in Compatibility machine and equivalence relation Equivalence relation in machine Homomorphism applied incorrectly Quotient machine by indistinguishability Epistemology [27]: Black Box may admit a homomorphism 4478.
Summary: The relation "observer A cannot distinguish x from y"; homomorphism. 4501, 6254
4478	4479

Summary: Are there "levels" of design? 4595 Design nature of
Summary: The Black Box is a set. Summary: Randomisation as a way of passing a message that is no message. Black box, problem of the is a set Random coding Set or Ensemble Black Box as Epistemology [28]: The Black Box is a set 4481. Epistemology [52]: Dispersion is used by the experimenter in recording his results, 4481.
4480	4481

Summary: The whole cannot be at a resting state unless every part is are a resting state. 4508, 4581, Example 2916.7, Markov chain 4904
Summary: How the homeostat works. 4520, 4538, 4581, 4701 Veto in equilibria
4482	4483

Quotient machine by indistinguishability Epistemology [29]: Homomorphisms in the Black Box, 4484.

4484	4485



4486	4487


Ideal (mathematical) homomorphism in machines
4488	4489



4490	4491

Lattice of homomorphisms
Summary: Partial knowledge; equivalent relation between machines. 4729, 4777, 5001
4492	4493

Summary: More constraints means fewer possibilities but more discoverable patterns, 4504 Summary: In set theory, remember that inequalities are likely to have cybernetic applications. 4503 Asymmetry importance of Constraint generates pattern Pattern (in general) as constraint
Summary: Set theory and its use. Set or Ensemble set theory
4494	4495

Summary: 'Large' and 'small' machines. Oddments [43]: Large small machines, and small large machines 4496.
Summary: Logic and theory. Quotient machine gas laws
4496	4497

Summary: Homomorphism in machines. Mapping joining systems

4498	4499

Summary: Joining machines.
Continuity is non-metrical Metric by clasification Set or Ensemble set theory Topology in machines
4500	4501

Distinguishability in brain
Information conservation in chain
4502	4503

Summary: Observations on set theory. Structure by constraint
Algebra Black Box as Ultrastability formal proof
4504	4505



4506	4507

Veto in equilibria
Summary: Principle of ultrastability stated more vigorously. Better still 4581 Ergodism and experience Ergodism von Neumann's theorem
4508	4509

Summary: Ergodicity and loss of information. DAMS (Dispersive and Multistable System) [64]: DAMS described as a shuffling machine 4510.
Summary: Tactics for getting DAMS better aligned. DAMS (Dispersive and Multistable System) [65]: Strategy for getting DAMS better aligned 4511.
4510	4511

Algebra machine and internal composition
Summary: Machines are related to the algebraic laws of internal composition, as well as those of external.
4512	4513

Constraint and departments
Structure as partial knowledge Society [51]: Organisation between departments as partial solution of the problem 4515.
4514	4515



4516	4517


Summary: Built-in structure in an adapting system implies that part of the solution has already been obtained. 4599, 4600
4518	4519

Selection amplifier
Summary: Amount of selection and ultrastability. 4582.6, 4904 Unsolved problems [15]: Paradox of which is the more important, permanence or change 4521.
4520	4521

Genes reproduction of Information on chromosomes
Summary: How chromosomes reproduce themselves. High survival power. Natural Selection [78]: Reproduction of genes; extra survival power given by combination in pairs 4523.
4522	4523

Disturbance habituation to Habituation theory of
Habituation theory of
4524	4525

Habituation theory of
Habituation theory of
4526	4527

Habituation theory of
Habituation theory of DAMS (Dispersive and Multistable System) [66]: Habituation in DAMS, theory of, 4529.
4528	4529

Habituation theory of
Habituation theory of
4530	4531

Habituation theory of
Essential variables relation to selection amplifier Habituation theory of
4532	4533

Habituation theory of
Summary: Habituation. 4559, 4596, 4609, 4762, 5512 Habituation theory of
4534	4535

Summary: Formal proof that, if a set is stable, no state in it can lead ever to a state outside the set.
Summary: Power for adaptation. (See next page) 4583 Adaptation motive power for Entropy as prime mover
4536	4537


Summary: Adaptation needs a transducer between the prime (statistical) mover and the useful result. 4583 Summary: Markov processes in machines. Markov process / chain in machine
4538	4539

Markov process / chain in chain of machines Markov process / chain in machine
Markov process / chain in machine
4540	4541

Markov process / chain in machine
Markov process / chain in machine
4542	4543

Markov process / chain in machine
Summary: Markoff process in machinery. 4671 Summary: The human brain may not be optimal for inclusion in computer. Markov process / chain in machine Society [52]: The human brain may not be an optimal component 4545.
4544	4545

Trial and error sub-trials The Multistable System [79]: Trials within trials are an important advanced method 4546.
Summary: Trials within trials, or the admission of variation into sub-units of an ultrastable system. Society [53]: Trials may [be] conducted as details within larger trial only if functionally disconnected while they are going on. 4547.
4546	4547

Reducibility example DAMS (Dispersive and Multistable System) [89]: Example of how the existence of a constraint can shorten a search, 4548.
Summary: Examples of how reducibility shortens time of search. 4552, 4563, 4650, 4948
4548	4549

Canonical form all problems Problems canonical form Epistemology [30]: Reduction of all problems to canonical form 4550.

4550	4551

Summary: All problems can be reduced to a canonical form. 4560, 4585
Model speed of Society [54]: Value of using models 4555.
4552	4555


Summary: The method of models, for quicker searching. Review 4560-4575 Isomorphism use of Pattern (in general) use of
4556	4557

Summary: Isomorphism between machines.
Summary: Distinguishability correspond to dependence. Dependence = distinguishability Distinguishability and dependence Distinguishability tends to fall The Multistable System [80]: The theory dependencies is that of distinguishabilities 4559. Epistemology [31]: Distinguishability is related to dependence 4559.
4558	4559

Summary: A Review on "Speed of Adaptation" with special reference to that of a Problem-Solving System. ... it is now possble to build a system, or machine, of more than human intelligence. Summary: Contents §1 Introduction 4560 §2 The method of models 4562 §3 Constraints on the operands 4563 §4 Constraints on the transformation: (i) Reducibility (a) What is Reducibility? 4564 (b) The effect of Reducibility 4567 (ii) Continuity (a) What is Continuity?4568 (b) The effect of Continuity 4569 §5 Selection by components 4570 §6 The Maximal Speed 4574 Adaptation speeding up adaptation Constraint effects of Speed (of adaptation) of learning Society [55]: Methods of getting solution more quickly { 4560 - 4575 }
Adaptation speeding up adaptation Constraint effects of Speed (of adaptation) of learning Society [55]: Methods of getting solution more quickly { 4560 - 4575 }
4560	4561

Summary: §2 The method of models Adaptation speeding up adaptation Constraint effects of Speed (of adaptation) of learning Society [55]: Methods of getting solution more quickly { 4560 - 4575 }
Summary: §3 Constraints on the operands A and B Adaptation speeding up adaptation Constraint effects of Relation defines subset Speed (of adaptation) of learning Society [55]: Methods of getting solution more quickly { 4560 - 4575 }
4562	4563

Summary: §4 Constraints on the transformation: (i) Reducibility (a) What is reducibility? Adaptation speeding up adaptation Constraint effects of Reducibility reviewed Speed (of adaptation) of learning Society [55]: Methods of getting solution more quickly { 4560 - 4575 }
Adaptation speeding up adaptation Constraint effects of Reducibility reviewed Speed (of adaptation) of learning Society [55]: Methods of getting solution more quickly { 4560 - 4575 }
4564	4565

Adaptation speeding up adaptation Constraint effects of Reducibility reviewed Reducibility in set theory Speed (of adaptation) of learning Society [55]: Methods of getting solution more quickly { 4560 - 4575 }
Summary: (b) The use of reducibility Adaptation speeding up adaptation Constraint effects of Reducibility reviewed Speed (of adaptation) of learning Society [55]: Methods of getting solution more quickly { 4560 - 4575 }
4566	4567

Summary: (ii)Continuity (a) What is continuity? Adaptation speeding up adaptation Constraint effects of Continuity as constraint Reducibility reviewed Speed (of adaptation) of learning Society [55]: Methods of getting solution more quickly { 4560 - 4575 }
Summary: (b) Value of continuity Adaptation speeding up adaptation Chess discontinuity in Constraint effects of Speed (of adaptation) of learning Society [55]: Methods of getting solution more quickly { 4560 - 4575 }
4568	4569

Summary: §5 Selection by components Adaptation speeding up adaptation Constraint effects of Speed (of adaptation) of learning Society [55]: Methods of getting solution more quickly { 4560 - 4575 }
Adaptation speeding up adaptation Constraint effects of Selection as application Speed (of adaptation) of learning Society [55]: Methods of getting solution more quickly { 4560 - 4575 }
4570	4571

Adaptation speeding up adaptation Constraint effects of Speed (of adaptation) of learning Society [55]: Methods of getting solution more quickly { 4560 - 4575 }
Adaptation speeding up adaptation Constraint effects of Speed (of adaptation) of learning Society [55]: Methods of getting solution more quickly { 4560 - 4575 }
4572	4573

Summary: §6 The Maximal Speed of Adaptation Adaptation speeding up adaptation Constraint effects of Speed (of adaptation) of learning Society [55]: Methods of getting solution more quickly { 4560 - 4575 }
Summary: (1) A first estimate of how long a problem will take in the solving might be given by the product of the possibilities in its components, assuming independence. (2) This is a bad estimator, being biassed. It is in fact an upper bound of the true value. (3) By the use of models the process of search can often be hastened. (4) Often the components are not independent, and only a portion of the product-space need be searched. Various factors (described) may have this effect. (5) Selection by components may be possible. It reduces the time to its logarithm. (6) There is a minimal time for the solution of a problem (or adaptation): it is the time that the fastest isomorphic system can get the answer out in binary notation. 4650, 4668 Adaptation speeding up adaptation Constraint effects of Speed (of adaptation) of learning Society [55]: Methods of getting solution more quickly { 4560 - 4575 }
4574	4575

Topology necessity for
Summary: Poincaré on the study of functions. Information two need not interact Linkage Meccano linkage
4576	4577

Summary: Two messages in a channel need not interact. 4641 Random movements giving trigonometrical equation
Summary: Emission of "cos²x + sin²x =1" randomly. Selection quantity of
4578	4579

Summary: Two agents may select the same element, yet differ widely in their degrees of selection. 4583, 4598 Amplifier and selection
Summary: An even more rigorous statement of ultrastablity. 4882 4467 4508 4520 Ultrastability formal proof
4580	4581

Summary: Rigorous statement of ultrastablity. 4881, 4904, 5046

4582	4583

Summary: Relation of essential variables to selection-amplifier. 4586
Problems solving problems Selection of solution Solution (to a problem) finding
4584	4585


Summary: What is 'problem solving'?
4586	4587

Set or Ensemble real object as element

4588	4588+01


Summary: Every real object is an element in an indefinitely large number of sets. Which sets are to be considered must first be defined.
4588+02	4589



4590	4591

Dynamic system game as dynamic system Games as dynamic system Strategy in dynamic system The Multistable System [85]: The theory of games as a chapter in that of the multistable system. 4592.
Summary: Neumann's theory of games translated into my theory of systems. 4650
4592	4593

Summary: Stability checked.
Summary: Review of the book. [Design for a Brain] Design as input Design for a Brain review in 'Galaxy' Equilibrium proper definition Personal notes [20]: Reviews of "Design": 4258 Observer, 4309 Citizen, 4380 British Medical Journal, 4423 Journal of Consulting Psychology, 4423 McCulloch, 4446. Hibbert Journal, 4595 Galaxy, 4595 Scientific American, 4643 Occupational Psychology.
4594	4595

Summary: 'Equilibrium' refers to a state, 'stability' to the region around the state. Basin Traffic principle nature
Summary: Properties of metric-less system. 4623 Continuity as constraint Information in stimulus Stimulus information in
4596	4597

Summary: The fullest description of a 'stimulus' is still inadequate to define its content of information.
Summary: In comparing an ultrastable (mechanical) solver with Man we must take care that they start with comparable amounts of prior knowledge. Oddments [44]: The ultrstable system studied by me is one that starts by knowing almost nothing; it starts therefore somewhat handicapped 4599.
4598	4599

Summary: Ways of getting effective discriminative feedback are to be found specially, for each type of system, not as a general problem. 4613, 4641, 5548
Control in set theory Dimension and constraint
4600	4601

Summary: Control, and part-function, in terms of set theory. 4604 Part-function in set theory Step function in set-theory
Summary: Incentives in the ultrastable system. Incentive in society Variable can be non-metric Society [57]: Incentives in social organisation 4603.
4602	4603

Summary: Practically all my concepts are non-metrical. Canonical equations in set theory Independence non-metric form Null-function can be non-metric Set or Ensemble my concepts in set-theory
Summary: Having several basins has nothing to do with being divisible into parts. Noticed again 5502 Basin General Staff history of Reducibility and basins Society [58]: The German General Staff 4605.
4604	4605

Summary: Organisation of the German General Staff. 6534 Evolution reviewed Natural Selection [80]: Relation between multistable systems and evolving genetic system reviewed, { 4606 - 4620 } Personal notes [23]: Re-read my notes completely from page 1000 on, 4606.
Summary: Is the Darwinian system a specialised one? 4608, 4613 Evolution reviewed Natural Selection [80]: Relation between multistable systems and evolving genetic system reviewed, { 4606 - 4620 }
4606	4607

Summary: How much of a field should be known? Essential variables in Darwinian system Evolution reviewed Natural Selection [80]: Relation between multistable systems and evolving genetic system reviewed, { 4606 - 4620 }
Summary: In Darwinian evolution; the part of essential variables is played by those parts whose disequilibrium leads to widespread disturbance around them. Evolution reviewed Natural Selection [80]: Relation between multistable systems and evolving genetic system reviewed, { 4606 - 4620 }
4608	4609

Evolution reviewed Natural Selection [80]: Relation between multistable systems and evolving genetic system reviewed, { 4606 - 4620 }
Evolution reviewed Self-locking system in set theory Natural Selection [80]: Relation between multistable systems and evolving genetic system reviewed, { 4606 - 4620 }
4610	4611

Summary: Self locking and self-reproducing systems in the terms of set theory. Evolution reviewed Property reproducing Reproduction in set-theory Natural Selection [80]: Relation between multistable systems and evolving genetic system reviewed, { 4606 - 4620 }
Summary: Precise statement of the fact that instability is infectious. Summary: The general solution of the problem of the least discriminative feedback is - that there is no general solution. Every problem has its own optimum, and finding the optimum is a part of the problem. 4600, 5548 Summary: Am still totally unable to write Darwinian ideas in any rigorous way, in spite of many motes ever since 4051. Evolution reviewed Natural Selection [80]: Relation between multistable systems and evolving genetic system reviewed, { 4606 - 4620 }
4612	4613

Evolution reviewed Natural Selection [80]: Relation between multistable systems and evolving genetic system reviewed, { 4606 - 4620 }
Summary: What Darwin really did do. 4618 Evolution reviewed Natural Selection [80]: Relation between multistable systems and evolving genetic system reviewed, { 4606 - 4620 }
4614	4615

Summary: Darwin's actual theory. Evolution reviewed Natural Selection [80]: Relation between multistable systems and evolving genetic system reviewed, { 4606 - 4620 }
Summary: What does "endurance" mean? Evolution reviewed Natural Selection [80]: Relation between multistable systems and evolving genetic system reviewed, { 4606 - 4620 }
4616	4617

Evolution reviewed Natural Selection [80]: Relation between multistable systems and evolving genetic system reviewed, { 4606 - 4620 }
Summary: Darwin's method for the study of complex systems. 4655 Evolution reviewed Natural Selection [80]: Relation between multistable systems and evolving genetic system reviewed, { 4606 - 4620 } Epistemology [33]: Darwin's method for the study of complex systems 4619.
4618	4619

Summary: Darwin's theory and that of the multistable system are related by intersecting in a set of theorems that contains both. Summary: How to develop the theory of "knowing". Evolution reviewed Knowing theory of Natural Selection [80]: Relation between multistable systems and evolving genetic system reviewed, { 4606 - 4620 } Natural Selection [81]: Darwinian systems and the multistable system both use some of the theorums in the theory of large systems, 4620. The Multistable System [86]: The multistable system resembles the Darwinian because both share large numbers of common theorums in the much larger theory of systems. 4620.

4620	4621

Summary: How a machine transforms a set of representative points in its field. Equilibrium proper definition Stability defined in set theory Stable set defined
Dynamic system as a stable set
4622	4623

Summary: "Stability"defined. A "machine" is a stable sub-set. 4630, 4632, 4643, 4656, 4795 Summary: Every set in a machine generates a stable set that contains it. 4630 Accessible state Stable set generated by set
Variety in set theory
4624	4625


Summary: Studying variety with the methods of the theory of sets.
4626	4627

Mapping stimulus as Operator stimulus as Stimulus as application
Summary: Repetition of a well-defined stimulus simply creates a new, compound, operator, that has stable sets with new, interesting, properties. 4630, 4632
4628	4629

Mapping product mapping Operator product operator Stimulus compound
Summary: Stable sets of a product application. 4762
4630	4631

Basin algebraic definition Basin algebraic form
Summary: "Basin" defined algebraically. Better 4743 Constitution (political) need for Society [59]: Cromwell on the necessity for a constitution, 4633.
4632	4633

Summary: Strategy. 4640 Optimum Yates' principle Strategy money in research
Additive adaptation costing and Costing as strategy Society [60]: Costing as method 4635.
4634	4635

Homeostasis 'costing' as method Regulation "costing" as method

4636	4637

Quotations [7]: "Out of the mass of interesting data which is available in any business, how much is worth collecting? The answer: Only that which can influence policy" Edwards, 4638.
Null-function ignorable
4638	4639

Summary: The costing accountant and the strategy of control. Discrimination in selection Model in accountancy
Summary: Mechanism for simultaneous adaptation. 4577, 5417 Adaptation of parts The Multistable System [87]: Parts of multistable system can adapt simultaneously provided channel width is adequate and a disperser is provided. 4641.
4640	4641

Summary: "Maximising profits" as a "keeping within limits." Essential variables maximising Society [61]: When limits of essential variables are 0 and + 8, and random disturbances are likely, best strategy is to make the value maximal, as with profits, 4642. Society [62]: Self locking by, Standing Orders 4642.
Summary: Self-locking in society. Group (mathematical) not all science Self-locking system in Parliament Stable set in science Standing Orders self-locking Personal notes [20]: Reviews of "Design": 4258 Observer, 4309 Citizen, 4380 British Medical Journal, 4423 Journal of Consulting Psychology, 4423 McCulloch, 4446. Hibbert Journal, 4595 Galaxy, 4595 Scientific American, 4643 Occupational Psychology.
4642	4643



4643+01	4643+02



4643+03	4643+04

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