Vol. 23 of Ross Ashby's Journal

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1962



Volume 23



6393+03	6393+04

Habituation theorem of

6394	6395

Mapping composition of random mapping Random mappings Summary: The hard core of "habituation", rigorously. Summary: Two random mappings in succession do not give a random mapping. Nor one used twice, similarly.
Anticipation how fast?
6396	6397


Summary: The unit that develops anticipation must be tiny.
6398	6399

Anticipation improving The Conditioned Reflex [50]: Allowable specialisations, for better performance. ●.
Summary: Specialising the anticipation, may properly go into μ. 6457, 6588
6400	6401



6402	6403

Summary: The designer (or planner) must select among the equilibria.
Adaptation anti-adaptation Faculty list of
6404	6405

1963

Summary: Every faculty is good or bad according to the environment.

6406	6407



6408	6408+01


Summary: The number of circuits traceable round n fully joint parts increases as \|n (approx). 6426
6408+02	6409

Atom simplest functional Neuron simplest possible Unit simplest

6410	6411



6412	6413



6414	6415


Summary: The theoretical unit is simply a mixer.
6416	6417

Summary: To build any machine, only a mixer is sufficient.

6418	6419

Summary: The Pitts-McCullock neuron from my atom.

6420	6421


Summary: Stability of a mixed net of Ashby atoms.
6422	6423

Combinatorics orders of magnitude Factorial order of magnitude Magnitude orders of Order of magnitude

6424	6425

Diagram of immediate effects (D.I.E.) how many Property how many Summary: How big numbers arrive. 6438
Self-awareness impossible
6426	6427

Summary: Some peculiarities of the "self" relationship.
Summary: Some problems become non-trivial only when much detailed specification is added.
6428	6429

Genius
Directive correlation (Sommerhoff) and noise-correction Noise and directive correlation
6430	6431

Summary: Sannon to Sommerhoff.

6432	6433

Regulation differential equation expressing
Genius Summary: How two functions f and g must be related if they transmit the value x independently of the value of y. [DIAGRAM] Summary: Some "geniuses" are just the people who happen to be right. 6570
6434	6435

Thing as constraint
Auto-correlation as constraint Summary: "Thing" and auto-correlation.
6436	6437

Topology how many
Science a cooperative effort Summary: The topologies on n points number about exp(n²). (Size No. 7 on 6424) 6454
6438	6439

Canalisation (Waddington) a local equilibrium Heredity Waddington on
Intelligence Waddington's mistake Learning genetic readiness
6440	6441

Summary: Review of Waddington's "Nature of life".
Independence algebraic form Summary: Algebraic form of "the behaviour doesn't depend on variables Z".
6442	6443

Equilibrium and liquid state Liquid state
Memory as halucination Remembering as hallucination Summary: "Remembering" as hallucination.
6444	6445

Memory disadvantage of Summary: Example of how too much memory can be disadvantageous.
Philosophy writings on Tabula rasa theory
6446	6447



6448	6449

Amasia example Summary: Some details about binary relations from B. Russell.
He and She dynamics, example Marriage dynamics, example
6450	6451


Dynamic system logical dynamic system Summary: Logical dynamics. 6455
6452	6453

Currency and topology Topology how learned Summary: Example of how a topology is learned.
Amasia example Politics Amasian example
6454	6455


Anticipation achieved on cards Order of magnitude
6456	6457

Localisation not necessary Memory non-stored example Summary: A memory of a pattern does not have to be stored anywhere.

6458	6459

Machine Gill on Machine Ginsburg on Summary: Proofs the orders of size.
Memory infinitely far back Summary: Indefinitely long memory in simple machine. 6470
6460	6461

Equilibrium and long trajectory Trajectory long, with equilibrium

6462	6463

Homeostat Grodins' book Servo-mechanism biological Summary: A practical way of getting fairly long trajectories with all ending in states of equilibrium. 6485 says joins need not be invariant in time.
Constraint analysis Cylindrance introduced Summary: The start of ~~Relation~~ and Constraint Analysis. 6467, 6473, 6476
6464	6465

1964

Heuristic Searching exponential growth
Searching back from goal
6466	6467

Information Reza's book Topology Bushaw's book
Evolution ensures extinction! Genes no unique pattern Survival evolution prevents! Natural Selection [89]: Selection intensifies selection. Simpson, ●.
6468	6469


Liquid state
6470	6471


Axiom and cylindrance Cylindrance introduced Dream as re-organisation
6472	6473


Organisation new properties Summary: Much in "Computers and Thought" is relevant to cylindrance.
6474	6475

Cylindrance increase with time Dynamic system cylindrance rises
Summary: In the system that is not richly joined, the cylindrance of the set of initial and terminal states tends to increase exponentially with time. 6485, 6549
6476	6477

Cylindrance in everyday life
Summary: Examples of low cylindrance in everyday life.
6478	6479

Amoeba movement at

6480	6481


Learning amoeboid movement Summary: Movement of Amoeba: parts and whole. 6703
6482	6483

Summary: Contractile molecules in an Amoeba can readily get coordinated for movement. 6789
Cylindrance of dynamic system Dynamic system cylindrance rises Input changing subsets
6484	6485



6486	6487

Summary: If every unit has only k inputs, but may move the k around over all the variables, the cylindrance in the 2n-space X'x X is restricted to k + 1. 6493
Summary: If the inputs are changed infinitely fast, the restriction on cylindrance holds, but no trajectory can be found. 6491
6488	6489

Summary: Simpler proof that seeing k keeps cylindrance, in the 2n space, down to k.
Interaction in set theory Semi-group Ljapin's book Transformation and semi-groups
6490	6491

Summary: "Interaction" corresponds to the last elements removed as C_p-1R shrinks to R.
Cylindrance and adaptation Cylindrance of machine with input
6492	6493

Cylindrance of projection Projection cylindrance of
Meaning ambiguous Summary: A set may increase in cylindrance if a variable is ignored. 6522 Generalised to n dimensions: 6531 Footnote 6502
6494	6495

Summary: Meaning of "meaning".
Cylindrance and union
6496	6497

Summary: If the distinction between two values of a variable is lost (and the relation re-formed by union, i.e. + and 0 counts as +), then cylindrance may increase. 6504
Cylindrance algorithm for finding
6498	6499


Cylindrance adding values
6500	6501

Summary: Effect on cylindrance of adding new values to variables (values that did not occur before in R)
Cylindrance removal of plane
6502	6503

Summary: Cutting out a slice cannot make cylindrance rise.
Equivalence relation and cylindrance
6504	6505

Summary: Effect on cylindrance of an equivalence relation when the sections combine by intersection.

6506	6507


Summary: If only g variables vary, the cylindrance cannot exceed g. 6509 (foot)
6508	6509

Cylindrance of t points

6510	6511

Summary: Rigorous proof that a set with t points cannot exceed t in cylindrance.

6512	6513


Summary: Theorem.
6514	6515


Cylindrance composition and
6516	6517

Cylindrance composition and Summary: When they are cylindrance-one sets, composition does not raise the cylindrance. 6519 Summary: Combining sets to form their product does not raise cylindrance. 6824
Cylindrance composition and
6518	6519

Cylindrance composition and
Cylindrance composition and
6520	6521

Cylindrance composition and
Cylindrance composition and Summary: Composition (or elimination) will not raise cylindrance unless the implied projection raises it. And a proof that projection can raise it. 6826
6522	6523


Cylindrance section and Summary: Section will not raise cylindrance unless the implied projection raises it. And a proof that section can raise it.
6524	6525


Summary: Proof of: As base, so cylinder. Better: 6825 Example of 6494
6526	6527

Cylindrance and reducibility Reducibility and cylindrance Summary: Cylindrance is a generalisation of reducibility.
Summary: Defeated. Not this time - see page 6531
6528	6529

Cylindrance and stability Stability and cylindrance Summary: There is no obvious relation between cylindrance and stability.

6530	6531

1965


Cylindrance and determinate system Dynamic system determinate and cylindrance Summary: Example showing how projection may jump the cylindrance up from 2 to any given number. Another example 6829 Summary: The theory of the determinate dynamic system leads naturally to set theory and cylindrance.
6532	6533

Directive Moltke's system General Staff history of Summary: The man who understands.

6534	6535


Talandic quantities
6536	6537


Summary: Goodwin's results are magnificent, and rigorous; but dangerously specialised.
6538	6539



6540	6541

Memory permanence Z-transform Jury's book Summary: Estes on the permanence of many traces.
Cylindrance of a theorem
6542	6543

Pattern (in general) examples of how many Summary: All the maths we know has low cylindrance. 6551

6544	6545

Bremermann's limit another form Summary: Any selection of 1 from more than 10^{1000...(47 zeros)...0} is physically impossible.
Information in a mapping
6546	6547

Non-linear systems information in Summary: How information-quality can explode when complicated at the sensory side. 6549
Information when input is a sequence Summary: Length of sequence increases the uncertainty exponentially.
6548	6549

Learning pleasure versus pain Pain simpler than pleasure Summary: Learning by pleasure is sophisticated.
Cylindrance of a theorem Theorem proving, and cylindrance Summary: Almost all the operations used in proving theorems do not raise cylindrance.
6550	6551

Equilibrium coordination at
Cylindrance an improved proof Summary: Simpler proof of Lemma.
6552	6553

Amplification in evolution Evolution delegation in

6554	6555

Gene interaction between genes Interaction between genes
Display extravagant, in polygamous birds Evolution polygamy forces extravagant display
6556	6557

Projection not independent Summary: Extracts from Huxley.
Summary: p-dimensional projections may not be allowed arbitrarily (if n>2)
6558	6559


Summary: A relation can always be found that has projections including, or not including, in arbitrary fashion, those of a given point.
6560	6561


Self-describing system can be reformulated in simpler form Summary: The idea of a system reporting on its own behaviour is better replaced by some much simpler equivalent.
6562	6563



6564	6565

1966

Reproduction a mathematical virus Virus mathematical example Summary: A mathematical virus.
Cylindrance excessive
6566	6567

Cylindrance reduction of, example Summary: Reduction of high cylindrance to low; examples. 6611
Group (mathematical) Lie L(x+y)
6568	6569

Fleet, problem of the Genius Transmission by subset
Constraint forces "transmission" Subset forces "transmission"
6570	6571

Summary: Every subset (of a product set) implies a quantity of internal transmission of information.

6572	6573

Broadcast gives interaction Summary: A woeful special case in transmission. 6579 Solved again 7006!
Transformation and complexity
6574	6575


Summary: Analyses of data or relations (Fourier, of variance, into partial correlations, etc) are of use only if the first few terms collect all that is significant. 6615
6576	6577

Cylindrance using low cylindrance Summary: Transforming sets of low cylindrance to a "simpler form". 6679
Fleet, problem of the
6578	6579

Summary: Problem of the Fleet, solved. 6662, 6912

6580	6581


Cause in complex system Localisation of meaning of "cat" Summary: Two examples of internal communications.
6582	6583

Bremermann's limit and cylindrance Cylindrance and Bremermann's limit Summary: The classic test for "cause" becomes invalid in the complex system. Summary: We cannot study any arbitrary relation of cylindrance higher than 270
Memory on pin-table Pin table as mapping
6584	6585


State on pin-table Summary: A "pin-table" machine.
6586	6587

Anticipation on pin-table

6588	6589

Summary: Anticipation forced on the "pin-table". 6594
Summary: Though the designer of an anticipator must look at it in detail, its demonstration demands a great and deliberate reduction in the quantity of information emitted. 6596
6590	6591

Archer dream of Dream and "self" Self-awareness impossible Summary: "I", in a dream, is not necessarily the site of intellectual activity.
Markov process / chain all operators Matrix all operators Operator all as transition matrices
6592	6593

Forcing a variable generalised Veto in Markov machine
Pin table as mapping Summary: All the operators, made uniform. 6596
6594	6595

Anticipation on pin-table

6596	6597

Retroactive inhibition quantative estimate
ASP
6598	6599

Adaptation rate of Genes optimal number Summary: Anticipation embodied again. Discrimination and retro-active inhibition. 6602, 6811
Summary: Quotations from Bremermann.
6600	6601

Reflex, conditioned Pavlov's 'p.197'

6602	6603



6604	6605

Adaptation evolutionary Evolution adapts genetic pool, not individual Summary: [Pavlov's] Page 197 solved? 6608.9, 6726, 6727 Summary: What natural selection really preserves.
Probability varying in time Summary: A stochastic series of varying probability.
6606	6607


Summary: At first, ignore the internal relations between stimuli. 6727, 6767
6608	6609

Summary: Some items that must be dealt with in an adequate theory of the Conditioned Response 6726
Cylindrance and reducibility
6610	6611

Information in continuous waveform Summary: To be able to compute a function by a few variables at a time is a (non-trivial) restriction.
Summary: Information in a continuous waveform.
6612	6613

Helm incident
Geiger counter as randomiser Random generator Summary: The Helm incident.
6614	6615

Memory without record

6616	6617

Summary: Extracts from book.

6618	6619

Aggression Lorenz on

6620	6621



6622	6623



6624	6625


Summary: What wholly new features come in with more dimensions?
6626	6627

Pendulum Lotka's set

6628	6629

Summary: Solution of the paradox of the pendulums.
Pattern (in general) stored as mechanism Redundancy storage of
6630	6631

Habituation spread of Reynolds' number and habituation Summary: Patterns must not be stored in the brain!
Summary: Speed of habituation and Reynold's number.
6632	6633

Feedback equivalent net without Summary: Every system with feedback is equivalent to a chain of systems without feedback.

6634	6635

Mapping obtaining
Evolution Mayr on evolution Summary: Getting all possible mapping electrically.
6636	6637

1967

Mesa phenomenon in percolation Network probabilistic Step function and percolation
Mapping random Step function "mesa" phenomenon
6638	6639



6640	6641


Information loss, in "mesa" phenomenon Mapping destroying information
6642	6643

Entropy second law and heterogeneity Thermodynamics second law Summary: The "mesa" phenomenon as decay of information. But see 6784

6644	6645



6646	6647



6648	6649

Summary: How children recognise patterns.
Summary: A usable approximation.
6650	6651

Summary: Consequences of H(A)=0. 6657.7
Transmission in a net Unsolved problems [24]: Can all the pair-wise direct transmission T_I-AB(A:B) be given arbitrarily? ●. Summary: Two problems in information theory.
6652	6653



6654	6655


Diagram of immediate effects (D.I.E.) and transmissions T_g-x(X:Y')
6656	6657



6658	6659


Summary: Information in machines. 6663, 6772
6660	6661

Coordination requires transmission Summary: Communication is to suppress the unwanted. 6742

6662	6663

Interaction in machine
Summary: Total constraint over trajections analysed in the state-determined machine. 6772
6664	6665



6666	6667

Summary: Only when the higher order interactions (of the types specified) are zero can the qualities of the DIE be used additively.

6668	6669

Summary: Proof of 6667
Order as handicap, Mr More Structure as handicap, Mr More Summary: Structure of thinking machinery.
6670	6671

Summary: Powers' theorem

6672	6673

Organisation and parts Part and whole, independent Summary: Parts isolated (with an experimenter) and parts in a whole (with other parts as disturbers) are not directly comparable.
Stirling numbers
6674	6675

Transmission how many?
Summary: Ways of analysing a total transmission are so many that the worker must be guided by outside reasons. 6678, 6721
6676	6677



6677+01	6677+02

Volume 23

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