Volume 18 of W. Ross Ashby's Journal
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1953



Volume 18



4643+05	4643+06



4644	4645

Transient maximal length
Summary: Theorems on transients. 4761 Summary: System in which x chases α. Chasing equation of
4646	4647

Summary: Of what use is neurophysiology to me? Summary: Drugs of addiction. Addiction nature of Neuron ?determinate
Summary: If the environment offers constraint, the cortex can profit. Environment constrained Hunt and stick optimal strategy Strategy in adaptation The Multistable System [88]: If the environment is not constrained, cortex can do nothing better than search at random 4649.
4648	4649

Adaptation strategy of Estimation and adaptation Maximal likelihood and adaptation Trial and error optimal method

4650	4651

Summary: Strategy of trial and error. 4797, 4822, 4844, 4947, 4941

4652	4653

Diagram of immediate effects (D.I.E.) with "boxes"
Summary: Box-diagrams are not precise. Summary: Evolution as habituation. Evolution as habituation Habituation evolution as Natural Selection [82]: Evolution can be regarded as a "becoming immune to mutation" 4655.
4654	4655

Closure defined Equilibrium proper definition
Summary: Meaning of 'stability'. 4741, 4785, 4795 Habituation and stability
4656	4657

Homeostasis variety is necessary Regulation variety is necessary Requisite Variety, Law of stated
Summary: Only variation can force variation down - exact conditions necessary. 4662, 4674, 4750 Entropy necessary for regulation Output variety in Variety necessary for regulation
4658	4659

Homeostasis in homeostat Homeostat two regulators in Levels in homeostat Regulation in homeostat
Summary: ~~All regulations are included in the Markov chain's progression to an absorbing state.~~ [deleted] 4676, 4678, 4683, 4695, 4701 Markov process / chain in machine
4660	4661



4662	4663


Summary: Entropies in regulation. 4666, 4722, 4971 Capacity for control Information and entropy
4664	4665

Summary: Entropy and information. Entropy as missing information

4666	4667

Summary: An organism cab control an environment of its own size (channel capacity), but not more. Constraint in environment

4668	4669


Summary: An error-controlling regulator cannot reduce the incoming variation to less than a half. But see 4688
4670	4671

Markov process / chain dominating Markov process Transition probability with Markov parameter
Summary: Markovian parameters to Markov chain. 4700 Summary: Meaning of "output". Output meaning of
4672	4673

Constraint regulation as Regulation basic nature

4674	4675

Transient in regulation

4676	4677

Equilibrium in regulation
Summary: On regulation. 4709, 4795
4678	4679


Noise regulation versus Regulation regulation, several inputs
4680	4681

Summary: Regulation when several inputs disturb. Initial state in regulation
Homeostat variety via relay Relay regulation via relay Transient in regulation
4682	4683



4684	4685

Trial and error number of trials necessary
Summary: Regulation in the homeostat's second order feedback. 4695, 4701, 4709
4686	4687

Error control by Regulation by error

4688	4689

Summary: Error-controlled regulation is possible only by blocking conduction.
Information and observer Epistemology [34]: When variety arrives, the observer who sees all sees unity changing to diversity; the element in the set sees diversity change to unity. 4691.
4690	4691


Question variety in Selection and variety Trial and error variety in Variety in set v. in element
4692	4693

Summary: In information, the point of view of the element is very different from that of the set. Searching variety in
Homeostat its discontinuous 2nd order process can be changed through intermediates to that of thermostat Markov process / chain can be modified to give a field Regulation discontinuous and continuous are related Trial and error relation to continuous stability
4694	4695



4696	4697


Summary: Progression to an absorbing state in a Markov chain and progression along a line of behaviour in a stable, continuous system are two extremes of a continuous scale. 4842
4698	4699

Homeostat and Markov process Joining two Markov chains Markov process / chain building 'machine of'
Summary: Markov chains as component parts for building a machine. 4703, 4770
4700	4701

Design amount of, partitioned
Summary: If a designer is only partly responsible for the determination of a machine, the fraction (implied by "partly") can be given meaning only if there is no loss of variety in the transduction.
4702	4703

Summary: A determinate machine, with single-valued field, can be formed only by supplying variety of n log n bits. 4722 Homeostat quantity of design in
Homeostat flow of variety in
4704	4705

Information flows in homeostat Selection and variety
Switching switching off
4706	4707

Summary: Quality in design. 4725, 4733, 4788

4708	4709



4710	4710+01



4710+02	4711



4712	4713



4714	4715


Homeostat as designer
4716	4717



4718	4719

Design standardised form
Regulation standard form
4720	4721

Summary: Regulations at various levels reduced to standard and common form. 4737, 4906 Amplifier homeostat as Homeostat amplification in

4722	4723



4724	4725

Amplifier works by robbery
Summary: The homeostat does not amplify. Contradicted 4792
4726	4727

Summary: ~~How many environments can the cortex adapt to ?~~ [deleted]
Lattice of homomorphisms Quotient machine of absolute system Epistemology [35]: Homomorphism may result from states becoming indistinguishable. 4729.
4728	4729

Summary: More ~~homomorphisms~~ quotient machines (4778) 4777
Markov process / chain not provided by determinate machines Variety in Braille
4730	4731

Summary: A set of determinate machines do not give a Markov chain.
Design in joining Joining design in Part joining Variety in joining
4732	4733



4734	4735

Variety in a vector
Summary: Information going into a system to design two parts. 5006 Behaviour and design Design and behaviour Genes as ultimate regulator Regulation by genes
4736	4737

Essential light of retina in dream
Introspection unreliability of
4738	4739

Summary: The unreliability of introspective evidence.
Equilibrium Riguet's definition
4740	4741

Trajectory Riguet's definition
Basin algebraic definition
4742	4743

Isomorphism and equiformality Part in set theory Tensor product of two machines

4744	4745

Algebra machine and internal composition Variable defined

4746	4747


Summary: Riguet's statement of "relational mechanics." 4751 Regulation implies both activity and non-activity
4748	4749

Summary: Regulation implies both activity of the regulator and inactivity of the essential variable.

4750	4751



4752	4753


Projection in set theory
4754	4755


Summary: Coordinates and projections in relational form. Dependence Riguet's definition Independence Riguet's definition
4756	4757


Summary: Riguet's definition of "dependance". 4813, 4992
4758	4759


Summary: Riguet's "trajectory" is practically my "transient". Trajectory Riguet's definition
4760	4761

Habituation further theory

4762	4763


Summary: More on habituation. 4917
4764	4765

1954

Joining tensor calculus of Machine Riguet's definition Tensor product of two machines

4766	4767

Dynamic system stochastic Machine stochastic machine Stochastic processes in machine
Input defined Markov process / chain the Markov machine Output defined Transition probability in Markov machine
4768	4769

Joining stochastic machines

4770	4771



4771+01	4771+02



4772	4772+01


Summary: Stochastic machines. 4847, 4876, 4868, 4904, 5097
4772+02	4773



4773+01	4773+02

Tensor properties collected
Summary: Properties of tensor product.
4774	4775

Summary: Equilibrium of Markov chain. Markov process / chain finding equilibrium density
Dynamic system compatible with equivalence relation Lattice Riguer on Machine compatible with equivalence relation
4776	4777

Compatibility machine and equivalence relation Dynamic system "quotient" machine Equivalence relation in machine Homomorphism corrected Machine quotient machine Quotient machine by indistinguishability
Summary: Quotient machines. 4937, 5001, 5165, 5148
4778	4779

Control of system that learns Learning during regulation
Summary: Observations on controlling a system that can learn. Design and variety Information variety is sufficient Variety and information
4780	4781

Summary: Set theory in machines can dispense with the idea of "information". 4795
Survival in set theory
4782	4783



4784	4785

Disturbance and survival
Summary: "Survival in spite of disturbance" in the terms of set theory. 4790, 4795
4786	4787

Summary: "Output to an input" is a relation of order, and may give a lattice. Arc as partly ordered set Cortex partly ordered arcs in Input input to output as order Lattice input to output lattice Order among arcs Output output to input, as order Partly ordered set arcs as partly ordered set
Summary: Complex taps can be easily built by mere conjunction of many simple. 4792 Design of complex tap Dynamic system for repetitive work Machine for repetitive regulation Relay design of
4788	4789

Summary: I am able to approach the subject of the origin of intelligence, i.e. regulation, from two points of view, but do not seem to be able to relate them.
Summary: Why regulation?
4790	4791

Summary: The homeostat does amplify. 4794> Amplifier homeostat as Homeostat amplification in Relay design of
Summary: Designing a machine to build a machine. 4808 (top), 5070, 5072 Dynamic system dynamic system that "designs" another dynamic system Machine designed mediately Machine that designs machine Epistemology [37]: Machine that builds a machine 4793.
4792	4793

Summary: The limit of progressive regulation. Amplifier limit of Regulation limit of
Control as reduction Equilibrium and information Information as reduction Regulation and information Selection and information Survival in set theory
4794	4795

Summary: Many concepts include that of "reduction". 4880, 4950, 4963 Design and information Machine as reduction Prediction as reduction Problems solving problems Property as information Reduction many forms Relation as information
Code military Coding theory of Strategy of trial and error Trial and error optimal method
4796	4797

Summary: Strategy of trial and error. 4844, 4949 Machine is a selector Selection by machine Statistic trial and error as statistic
Mapping tensor power of
4798	4799

Variety in product-machine
Summary: Every machine on states M defies "machines" on states in Mⁿ (n=1,2,...). Only in the latter is variety bound to fall. (Its "tensor powers") 4869 Summary: "Transformation". Disturbance repetitive disturbance Mapping and transformation Transformation definition of
4800	4801

Regulation repetitive disturbance Triunique mapping

4802	4803



4804	4805


Homeostat amplification in
4806	4807

Amplifier of regulation Design with repetition
Summary: Gain in regulation when the sequence has repetition. 4831, 5002, 5070 Design machine showing design Design rate of change of design Regulation of design Epistemology [36]: A machine of n states requires n steps before the observer can know its design 4809.
4808	4809

Summary: Change of state and change of design. Summary: The "tracker" as regulator. Regulation "tracker" as example
Summary: Error controlled regulation. Regulation by error
4810	4811

Summary: Levels in regulation. Regulation levels in regulation
Summary: Learning is worth while only when the disturbance will be repeated. Learning useful against repetition
4812	4813

Summary: The diagram of immediate effects as a higher relation. Circularity of my brain studying "the brain" Diagram of immediate effects (D.I.E.) as relation
Implication Logic cannot be proved Epistemology [38]: The circularity of a brain that is itself a machine trying to study a machine 4815.
4814	4815

Summary: The circularity of reasoning about reasoning. 4835, 4897 Mapping and implication

4816	4817


Summary: Slowing down a machine, and sleep. Diffuse system as source of variety
4818	4819

DAMS (Dispersive and Multistable System) [90]: The variety may perhaps be supplied in the mammalian brain by its "diffuse" system 4820.
Noise destroying information
4820	4821

Strategy of trial and error
Summary: Getting the disruptive feedback from the distant environment. 4844, 4927 Memory in black box
4822	4823

Black box, problem of the first considered Constraint in black box Degrees of freedom in machine

4824	4825



4826	4827


Epistemology [39]: Proving the existence of hidden variables 4829.
4828	4829

Summary: Proving the existence of hidden variables. Discrimination in feedback Feedback discriminative
Arc active and inactive Memory in discriminative feedback The Multistable System [89]: In the multistable system there must be parts not activated in each reaction. 4831.
4830	4831

Summary: Discriminative feedback. 4834, 5345 Attention nature of Secretary and attention
Summary: On attention, and vigilance. Environment constrained
4832	4833

Discrimination is it a problem? Feedback discriminative
Summary: The "problem" of discriminative feedback must be shown to exist in the real environment.
4834	4835

Isomorphism in set theory Relation nature of
Implication in set theory
4836	4837


Summary: Nature of relations and sets. 4897 Set or Ensemble set theory The Multistable System [90]: Set theory may play a part in the workings of the multistable system. 4839.
4838	4839

Black box, problem of the first considered Control partial
Summary: More on the Black Box. 4951 Epistemology [40]: The Black Box that can be only partially controlled 4841. Epistemology [41]: I can study either the Black Box, or a set of observers studying black boxes. 4841.
4840	4841

Hunt and stick in machine Markov process / chain producing one state
Summary: Hunt-and-stick is a more general form of stability. 4881, 5046 Equilibrium "hunt and stick" as Hunt and stick as stability Regulation fundamental process
4842	4843

Searching random is more general
Summary: Strategy of trial and distribution of probabilities. 4849 Summary: Two ways of regarding "design". Design nature of
4844	4845

Requisite Variety, Law of re-stated Variety requisite
Summary: Law of Requisite Variety stated with respect to a rectangular table. Stated purely in terms of set theory 4850 Input saturation of
4846	4847


Summary: An input can be saturated i.e. has a capacity as a channel. Theory of nature of Trial and error determine of trial by theory
4848	4849

Requisite Variety, Law of in set theory
Summary: The Law of Requisite Variety in full rigours of set theory. 5002, 5047
4850	4851

Machine defined again

4852	4853

Transducer Shannon's

4854	4855



4856	4857



4858	4859

Summary: Machines, with inputs and outputs, treated wholly by mappings. All this is, in substance, identical with Riguet's form. 4867. Simpler 4876, 4991
Summary: Feeding a machine with input and output back into itself. Evolution as process Natural Selection [83]: Huxley and Fisher on Evolution (extracts from book) 4861.
4860	4861

Arc tend to separate Species origin of
Exponential rate of increase
4862	4863


Discrimination in selection
4864	4865

Summary: Adaptation in evolution. Constraint and natural law Information Goldman on Quotations [53]: Goldman on Science as a use of Constraints 4866.
Summary: Quotations. Quotations [54]: "A study of the real world thus becomes a study of transducers." 4867.
4866	4867

Summary: "A machine" implies three sets and two mappings. 4871 Simpler 4876 Best 5097

4868	4869

Summary: A set of replicate machines.
Epistemology [42]: A machine observed at every n-th step is still a machine. 4871.
4870	4871

Summary: The machine of intermittent observation. Initial state as source of variety
Summary: Initial states may appear simply as a source of variety. Mapping and machine Variety due to initial state
4872	4873

Summary: Re-entrant chain of mappings. 4876

4874	4875

Summary: What is a scientific "theory"? 4948
Summary: A "machine" implies two sets and a mapping; coupling requires an extra mapping. 4932, 4952, Formal statement 5097 Machine defined finally Mapping machine as
4876	4877


Design for "keeping moving" Variety of "keep moving"
4878	4879

Summary: The amount of design in "keep moving". Reduction in machine Step-mechanism proposed
Summary: There are two distinct reasons why a machine may be used in regulation. 5046 Regulation machine and regulation
4880	4881

Homeostat theory of
Summary: "Independence" is a special case of "incomplete transmission of variety". Independence as non-transmission of variety Variety and independence
4882	4883

Ultrastability corrected

4884	4885



4886	4887



4888	4889



4890	4891



4892	4893

Summary: Why the uniselectors have many values. 5046
Summary: Specifying the second-order feedback rigorously.
4894	4895

Church's theorem
Summary: Church's theorem. Lattice Piaget on Structure Piaget on
4896	4897


Summary: Logic in the multistable system. 5305, 5313 Logic in the multistable system The Multistable System [91]: Multistable system developing the structure of the world around it. 4899.
4898	4899

Regulation multiplicity of aims
Summary: Speed is merely one of many demands that can made to qualify simple adaptation. 4964 Optimum selecting efficiently Selection definition of object by reference to others
4900	4901

Squeedunk problem of
Max( ) (function) selecting by
4902	4903

Summary: On identifying an optimum in a set. Absorbing state, in Markov chain coupled Markov process / chain ultrastability in Ultrastability with Markov systems Veto in Markov machine
Summary: Equilibrium in coupled Markov systems. Homeostat other forms of Ultrastability with mixed systems
4904	4905

DAMS (Dispersive and Multistable System) [91]: Ultrastability can be shown with various types of system, discrete, two-valved, determinate etc 4906.

4906	4907



4908	4909


Experimenter receiving information
4910	4911


Summary: All sorts of continuous and discontinuous systems put together to make all sorts of ultrastable systems.
4912	4913

Differential equation stability theory of Equilibrium Bellman on Equilibrium complexity of Information partial Knowledge partial Stability stability theory of differential equations
Summary: Bellman on 'stability'. Trajectory stability of
4914	4915

Aging (as process) Experience law of History aging processes Machine Markovian, aging in Markov process / chain aging in Variety in Markov machines
Habituation in Markov machines
4916	4917

Summary: Statistical laws in the Markov chain. 4919, 4946 Basin and 'closure' Closure and 'basin' Experience example
Aging (as process) and entropy Entropy in physics
4918	4919

Statistical mechanics Tolman on

4920	4921

Variety and entropy
Knowledge and equal probability Probability equal, and ignorance
4922	4923

Ergodism nature of
Degrees of freedom Tolman's definition Reversible process in dynamic system Time reversal of
4924	4925


Summary: Relation of the physicist's "entropy" to my work.
4926	4927

Summary: Supplementary information and its mode of use. Variety source of
Evolution as process
4928	4929

Adaptation as by-product Evolution the proper study of Natural Selection [84]: The study of evolution must not be "to explain adaptation" but simply to deduce "what will happen?" 4930.
Summary: Evolution and psychology must study the basic question "what will in fact happen?" 5535 Isomorphism and equiformality
4930	4931



4932	4933

Summary: Isomorphism and equiformality. 4990, 5000
Hierarchy (of Bourbaki) machine in hierarchy Machine in hierarchy of sets
4934	4935

Summary: The theoretical structure of the theory of machines, according to Bourbaki. 4970, 5904, 5907
Homomorphism justified
4936	4937

Summary: Homomorphism returns.
Black box, problem of the inaccessible states Epistemology [43]: States that become inaccessible during the testing, 4939, and especially 4968.
4938	4939


Summary: Closed sets of states in a black box. 4951, 4968, 4989 Discrimination in feedback
4940	4941

Summary: Trials are good, for they bring information. 4945, 4948, 4965, 4963 Information by trials Trial and error gives information
Behaviour all reducible to behaviour Thing as way of behaving
4942	4943

Summary: A "thing" is a way of behaving.
Summary: Proof of 4871 Discrimination example
4944	4945

Summary: Discriminative feedback. 4963 Summary: Information repair. Information "repair" (MacKay) Information and discriminative feedback
Summary: Letters as Markov chain. Adaptation strategy of Markov process / chain English as Maximal likelihood and adaptation
4946	4947

Reducibility value of Trial and error nature of Epistemology [44]: The strategy of putting questions 4948.

4948	4949

Summary: The strategy of adaptation. 4962, 4964, 4980 Reduction in code-solving
Summary: The Black Box is built. [see photos: Description \| Black Box \| Details] Black box, problem of the My Black Box built
4950	4951

Summary: On the accessibility of states. 4953, 4968 Accessible state Control of system Initial state control over Machine partly observable
Summary: The "partly observable machine with input." 4956 Epistemology [45]: "Observing" or "studying" a machine means getting sequence of inputs and outputs alternately, 4953.
4952	4953

Protocol primary observation

4954	4955

Summary: What "examining a machine with input" means. 5055
Experience example
4956	4957



4958	4959

Epistemology [46]: The method of getting absoluteness by using past values is essentially second-rate 4960.
Summary: When a system is partly unobservable, the method of trying to restore absoluteness by taking earlier values into account is fundamentally second-rate; it will succeed only when the case is peculiarly favourable. 4979
4960	4961

Discrimination feedback for discimination Feedback third order
Summary: All necessary improvements to the basic ultrastable system can be had by the addition of further orders of feedback. Chess organisation for
4962	4963

Summary: More on the chess-playing team. Dichotomy achieving
Summary: Efficiency of solving is adaptation at a higher level than solving. Efficiency in solving
4964	4965

Continuity in measurement Measurement nature of Metric systems with
Summary: Scales of measurement. Variable metric form
4966	4967

Black box, problem of the inaccessible states Epistemology [43]: States that become inaccessible during the testing, 4939, and especially 4968.

4968	4969

Summary: Science is interested chiefly in the case where the parameters and states are so related that every state is accessible at will. 4989 Equilibrium in the hierarchy Hierarchy (of Bourbaki) equilibrium
Summary: "State of equilibrium" in the hierarchy or sets. Summary: Orthogonality of actions in regulation. Capacity for control Channel capacity for control Orthogonality of control
4970	4971

Summary: We live by the incorporation of pieces that are already keepers-out of noise. Determinate why important
Summary: Living organisms surround themselves with invariants. Summary: Example of an adequate channel. Pantagruel, l.iii,ch.xxix Invariant utility of
4972	4973

Convergence (of lines of behaviour) in random transformation Information in random machine Transformation random Variety and random transformation

4974	4975



4976	4977

Summary: With a random transformation the variety tends to fall to two thirds at each step. Qualified 5158
Information blocking
4978	4979

Summary: "Time" can be treated as a disturber of a machine, like an input. Time as disturber
Summary: Research and the strategy of adaptation.
4980	4981

Summary: "Integrating" and transformation. Integration (mathematical) and set theory
Summary: Nature of "invariance." Determinate and 'closed' Invariant nature of Noise and closure
4982	4983

Summary: Notes on "closure" of a transformation. 4989 Summary: Getting from the discrete to the continuous. Closure and 'basin' Discrete to continuous Transformation closed
Emergent properties
4984	4985

Organisation emergent properties
Summary: Whether properties "emerge" or not depends on our knowledge of the parts. Summary: Why information? Energy an old question Information and energy
4986	4987

Summary: "How to dichotomise" takes time to be learned. Dichotomy achieving
Black box, problem of the "suitable" sets of states
4988	4989

Epistemology [47]: A set of states suitable for investigation must satisfy EXPRESSION 4990.
Summary: However many states are available, the experimenter confines himself to some set satisfying certain conditions.
4990	4991

Dependence Riguet's definition Diagram of immediate effects (D.I.E.) Riguet's formulation Independence Riguet's definition

4992	4993



4993+01	4993+02

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