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Volume 23 of W. Ross Ashby's Journal
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1962
Volume 23
6393+03 6393+04
Habituation theorem of
6394 6395
Summary: The hard core of "habituation", rigorously.
Summary: Two random mappings in succession do not give a random mapping. Nor one used twice, similarly.
Mapping composition of random mapping
Random mappings
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. 6400.
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-McCulloch 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
Summary: How big numbers arrive. 6438
Diagram of immediate effects (D.I.E.) how many
Property how many
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: Shannon to Sommerhoff.
6432 6433
Regulation differential equation expressing
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
Genius
6434 6435
Thing as constraint
Summary: "Thing" and auto-correlation.
Auto-correlation as constraint
6436 6437
Topology how many
Summary: The topologies on n points number about exp(n2). (Size No. 7 on 6424) 6454
Science a cooperative effort
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".
Summary: Algebraic form of "the behaviour doesn't depend on variables Z".
Independence algebraic form
6442 6443
Equilibrium and liquid state
Liquid state
Summary: "Remembering" as hallucination.
Memory as halucination
Remembering as hallucination
6444 6445
Summary: Example of how too much memory can be disadvantageous.
Memory disadvantage of
Philosophy writings on
Tabula rasa theory
6446 6447
6448 6449
Summary: Some details about binary relations from B. Russell.
Amasia example
He and She dynamics, example
Marriage dynamics, example
6450 6451
Summary: Logical dynamics. 6455
Dynamic system logical dynamic system
6452 6453
Summary: Example of how a topology is learned.
Currency and topology
Topology how learned
Amasia example
Politics Amasian example
6454 6455
Summary: A memory of a pattern does not have to be stored anywhere.
Anticipation achieved on cards
Order of magnitude
6456 6457
Localisation not necessary
Memory non-stored example
6458 6459
Summary: Proofs the orders of size.
Machine Gill on
Machine Ginsburg on
Summary: Indefinitely long memory in simple machine. 6470
Memory infinitely far back
6460 6461
Equilibrium and long trajectory
Trajectory long, with equilibrium
6462 6463
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.
Homeostat Grodins' book
Servo-mechanism biological
Summary: The start of Relation and Constraint Analysis. 6467, 6473, 6476
Constraint analysis
Cylindrance introduced
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, 6469.
6468 6469
Liquid state
6470 6471
Axiom and cylindrance
Cylindrance introduced
Dream as re-organisation
6472 6473
Summary: Much in "Computers and Thought" is relevant to cylindrance.
Organisation new properties
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
Summary: Movement of Amoeba: parts and whole. 6703
Learning amoeboid movement
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 Cp-1R shrinks to R.
Cylindrance and adaptation
Cylindrance of machine with input
6492 6493
Cylindrance of projection
Projection cylindrance of
Summary: A set may increase in cylindrance if a variable is ignored. 6522 Generalised to n dimensions: 6531 Footnote 6502
Meaning ambiguous
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
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
Cylindrance composition and
6518 6519
Cylindrance composition and
Cylindrance composition and
6520 6521
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
Cylindrance composition and
6522 6523
Summary: Section will not raise cylindrance unless the implied projection raises it. And a proof that section can raise it.
Cylindrance section and
6524 6525
Summary: Proof of: As base, so cylinder. Better: 6825 Example of 6494
6526 6527
Summary: Cylindrance is a generalisation of reducibility.
Cylindrance and reducibility
Reducibility and cylindrance
Summary: Defeated. Not this time - see page 6531
6528 6529
Summary: There is no obvious relation between cylindrance and stability.
Cylindrance and stability
Stability and cylindrance
6530 6531
1965
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.
Cylindrance and determinate system
Dynamic system determinate and cylindrance
6532 6533
Summary: The man who understands.
Directive Moltke's system
General Staff history of
6534 6535
Talandic quantities
6536 6537
Summary: Goodwin's results are magnificent, and rigorous; but dangerously specialised.
6538 6539
6540 6541
Summary: Estes on the permanence of many traces.
Memory permanence
Z-transform Jury's book
Cylindrance of a theorem
6542 6543
Summary: All the maths we know has low cylindrance. 6551
Pattern (in general) examples of how many
6544 6545
Summary: Any selection of 1 from more than 101000...(47 zeros)...0 is physically impossible.
Bremermann's limit another form
Information in a mapping
6546 6547
Summary: How information-quality can explode when complicated at the sensory side. 6549
Non-linear systems information in
Summary: Length of sequence increases the uncertainty exponentially.
Information when input is a sequence
6548 6549
Summary: Learning by pleasure is sophisticated.
Learning pleasure versus pain
Pain simpler than pleasure
Summary: Almost all the operations used in proving theorems do not raise cylindrance.
Cylindrance of a theorem
Theorem proving, and cylindrance
6550 6551
Equilibrium coordination at
Summary: Simpler proof of Lemma.
Cylindrance an improved proof
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
Summary: Extracts from Huxley.
Projection not independent
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
Summary: The idea of a system reporting on its own behaviour is better replaced by some much simpler equivalent.
Self-describing system can be reformulated in simpler form
6562 6563
6564 6565
1966
Summary: A mathematical virus.
Reproduction a mathematical virus
Virus mathematical example
Cylindrance excessive
6566 6567
Summary: Reduction of high cylindrance to low; examples. 6611
Cylindrance reduction of, example
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
Summary: A woeful special case in transmission. 6579 Solved again 7006!
Broadcast gives interaction
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
Summary: Transforming sets of low cylindrance to a "simpler form". 6679
Cylindrance using low cylindrance
Fleet, problem of the
6578 6579
Summary: Problem of the Fleet, solved. 6662, 6912
6580 6581
Summary: Two examples of internal communications.
Cause in complex system
Localisation of meaning of "cat"
6582 6583
Summary: The classic test for "cause" becomes invalid in the complex system.
Summary: We cannot study any arbitrary relation of cylindrance higher than 270
Bremermann's limit and cylindrance
Cylindrance and Bremermann's limit
Memory on pin-table
Pin table as mapping
6584 6585
Summary: A "pin-table" machine.
State on pin-table
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
Summary: "I", in a dream, is not necessarily the site of intellectual activity.
Archer dream of
Dream and "self"
Self-awareness impossible
Markov process / chain all operators
Matrix all operators
Operator all as transition matrices
6592 6593
Forcing a variable generalised
Veto in Markov machine
Summary: All the operators, made uniform. 6596
Pin table as mapping
6594 6595
Anticipation on pin-table
6596 6597
Retroactive inhibition quantative estimate
ASP
6598 6599
Summary: Anticipation embodied again. Discrimination and retro-active inhibition. 6602, 6811
Adaptation rate of
Genes optimal number
Summary: Quotations from Bremermann.
6600 6601
Reflex, conditioned Pavlov's 'p.197'
6602 6603
6604 6605
Summary: [Pavlov's] Page 197 solved? 6608.9, 6726, 6727
Summary: What natural selection really preserves.
Adaptation evolutionary
Evolution adapts genetic pool, not individual
Summary: A stochastic series of varying probability.
Probability varying in time
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
Summary: To be able to compute a function by a few variables at a time is a (non-trivial) restriction.
Information in continuous waveform
Summary: Information in a continuous waveform.
6612 6613
Helm incident
Summary: The Helm incident.
Geiger counter as randomiser
Random generator
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
Summary: Patterns must not be stored in the brain!
Habituation spread of
Reynolds' number and habituation
Summary: Speed of habituation and Reynold's number.
6632 6633
Summary: Every system with feedback is equivalent to a chain of systems without feedback.
Feedback equivalent net without
6634 6635
Mapping obtaining
Summary: Getting all possible mapping electrically.
Evolution Mayr on evolution
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
Summary: The "mesa" phenomenon as decay of information. But see 6784
Entropy second law and heterogeneity
Thermodynamics second law
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
Summary: Two problems in information theory.
Transmission in a net
Unsolved problems [24]: Can all the pair-wise direct transmission TI-AB(A:B) be given arbitrarily? 6653.
6652 6653
6654 6655
Diagram of immediate effects (D.I.E.) and transmissions Tg-x(X:Y')
6656 6657
6658 6659
Summary: Information in machines. 6663, 6772
6660 6661
Summary: Communication is to suppress the unwanted. 6742
Coordination requires transmission
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
Summary: Structure of thinking machinery.
Order as handicap, Mr More
Structure as handicap, Mr More
6670 6671
Summary: Powers' theorem
6672 6673
Summary: Parts isolated (with an experimenter) and parts in a whole (with other parts as disturbers) are not directly comparable.
Organisation and parts
Part and whole, independent
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

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