Volume 22 of W. Ross Ashby's Journal

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1958

Volume 22

6043+03 6043+04

Summary: Number of atoms in the brain, and the maximal information it can store. 6179 Brain variety in Summary: Distinguish between the qualities, in the brain, of information and of memory. Sample space importance of 6044 6045

6046 6047

Summary: Finding how much information there is in a brain. Information how much in brain? 6048 6049

Memory as transmission from past Memory how much in the brain? 6050 6051

Channel capacity and memory 6052 6053

6054 6055

Summary: "Memory capacity" is basically channel capacity between times in the same system. Any Black Box provides an infinite number of capacities. 6069 Capacity for memory 6056 6057

Summary: Of all the !memory capacities", the maximal value may be of physical interest. 6179 Summary: Build devices for demonstration. DAMS Mark II (Dispersive and Multistable System) [14]: Why not a new model for demonstration? 6059. 6058 6059

Summary: Build small specialist machines, each devised to show one fact with perfect clarity. Immunity conditioned reflex in Reflex, conditioned in serology The Conditioned Reflex [47]: Conditioned reflex of alcohol causing production of anti-toxin. 6060. Treatment a form of war Psychiatric applications [96]: Blitz-therapy. 6061. 6060 6061

Summary: Blitz-therapy. Summary: Two sorts of memory are identifiable. 6068 Hypnosis (mesmerism) Kelsey's work Memory two types of 6062 6063

Atom proposition in logic Complexity irreducible Logic atom proposition Proposition atomic Reducibility irreducible systems 6064 6065

Summary: A proposition is "atomic" if its user does not propose to break it up. Summary: The brain may be like a digital computer in being error-free by going from equilibrium to equilibrium. 6126 Equilibrium give error-free action Summary: Irreducible complexity. Summary: Simple "relations". Relation simple examples 6066 6067

Summary: To test whether memory really is permanent. Hypnosis (mesmerism) memory under Memory ?eternal Diagram of immediate effects (D.I.E.) among memories Localisation principles of Memory principles for localisation 6068 6069

Summary: Effect of "memory" is studied by the usual method for studying effect, but the two variables are separated in time (as well, usually, as in space) Independence and number of equation 6070 6071

Summary: A DIE can be demonstrated rigorously in a machine with memory, and by the same basic operations as when there is no delay. Continued 6105 Summary: Learning by pain is fundamentally simpler (demands less communication ) than learning by reward. Algedonic pain and pleasure different Learning pleasure versus pain Pain distinct from pleasure Pleasure different from pain 6072 6073

1959

Summary: The theory of machines may help with interpolation rather than with long range prediction. 6076 Theory of for interpolation Summary: The physicists are not yet clear about what they mean by 'casual' and 'determinate'. Cause Born on Determinate and Born on 6074 6075

Organisation Simon on Set or Ensemble theory over-valued 6076 6077

Summary: The value of the new logic of mechanism can easily be over-rated. Pattern (in general) transmission of Transition constraint on Transmission of pattern 6078 6078+01

Confluant and input Equilibrium selected by input 6078+02 6079

Anticipation of adaptations Tilde ~ operation 6080 6081

6081+01 6081-A

Summary: Equilibria attract. 6267 Equilibrium two attract Resolution of physiological states Jennings Topology of equilibria Summary: The process of inscription is much weaker than I thought on 5844. Continued: 6092 Inscription very weak 6082 6083

Equilibrium Tilde-operation Tilde ~ operation Summary: Operation "go to your basin". 6267 6084 6085

Basin and tilde operation Kernal relation (Riguet), =Noyau 6086 6087

Summary: Habituation with cycles allowed. 6108 Habituation tilde-operation Machine generating properties Selection by machine 6088 6089

Summary: A general method for solving problems in combination dynamics. 6108, 6349, 6334 Closure giving property Property as stability Stability generating a property Summary: Closure under a sequence imposes little restriction on the closures at intermediate stages. Closure under two operators 6090 6091

6092 6093

6094 6095

6096 6097

Summary: "Inscription" goes. How a pattern of equilibria is related to the pattern of transitions at the input. 6143 6098 6099

6100 6101

Resolution of physiological states in detail Summary: Final conclusions (to date!) about my explanation of Jennings' law. 6347, 6137, 6108, 6143, 6127, 6128, 6269 6102 6103

Summary: Another way of writing Sommerhoff's directive correlation. 6105, 6284 Summary: Are isomorphisms denser around equilibrium? Directive correlation (Sommerhoff) in set theory Equilibrium generates isomorphisms Isomorphism cluster at equilibrium Summary: Isolating a pure concept is like isolating a pure element. Localisation principles of Memory principles for localisation 6104 6105

Diagram of immediate effects (D.I.E.) and theory of graphs Grundy function of graph Kinematic graph and graph theory Summary: Berge's book shows me I must develop my combinatorial dynamics myself. Combinatorial dynamics and theory of graphs Graph theory of 6106 6107

Domain change of Function change of domain Operator change of domain 6108 6109

Summary: Restriction of an operator to a selected domain may make evident a property that is otherwise inconspicuous. 6137, 6350 Summary: Quantum mechanics is moulded chiefly by specific atomic peculiarities, not by general epistemological principles. 6179, 6303 Quantum theory too specific 6110 6111

Set or Ensemble two books on set Oscillation two coupled 6112 6113

6114 6115

Summary: Oscillating systems, when coupled, do not necessarily pull together in frequency. Compatibility machine and equivalence relation Equivalence relation and machine Machine and equivalence relation Summary: When a simplification is permissible. 6148, Better: 6254 Summary: Today I can say I have solved the problem I set out to solve on 7 May 1928 [31 years prior]. I asked, roughly, whence came the patterning properties of the nervous system. The answer is now clear... 6116 6117

Summary: ... As the selection gets more intense, and the closed set smaller, so does the relation show more intensely. But also, so does it become more degenerate, until finally, at a state of equilibrium, the degeneracy is complete. Then all - disturbances and responses - meet at zero. The adaptation is perfect, intelligence infallible, all in Nirvana. The final statement. Summary: General, abstract, nature of "induction", Induction (physiological) nature of 6118 6119

Summary: Threshold combines lots of equilibria with continuity. Alpha rhythm as mutation Polystable and threshold Threshold purpose of Unsolved problems [19]: Does the thalamus exist to teach in childhood, becoming functionless later on? 6121. 6120 6121

Sub-system "size" of Summary: Possible function for the "functionless" parts of the mid-brain. Summary: The "size" of a system had no unique meaning. 6122 6123

Isomorphism generalised Summary: Isomorphism, homomorphism and now protomorphism. 6150, 6260 Protomorphism defined Structure protomorphism defined 6124 6125

Delay (in substitution) and equilibrium Equilibrium and interruption Interruption immunity from Summary: The environment goes much from equilibrium to equilibrium, constant on route but noisy in timing. The brain, appropriately, also goes much from equilibrium to equilibrium. 6126 6127

Summary: Any part of the brain that behaves, with a characteristic pattern will tend to send that pattern to other parts. 6137, 6143, 6248 Break becoming memory Memory evolution of 6128 6129

Amines and memory Memory and amines Spraying Summary: How the amines may come in. 6130 6131

Summary: Rapid adaptation in an irreducible whole implies many equilibria in the parts. Adaptation rapid adaptation demands equilibria Equilibrium many necessary 6132 6133

Memory by aggregation of molecules Step-mechanism by aggregation Forcing a variable forcing homeostat 6134 6135

Summary: Simultaneous forcing of two variables may give a slight tendency to association. 6140, 6197 Association by simultaneous forcing Reflex, conditioned by simultaneous forcing The Conditioned Reflex [48]: Simultaneous forcing may give a trace of conditioned reflex. 6136. Summary: Closure under a sequence, and a property of one operator, implies a corresponding property on the other operators. 6143, 6269 Resolution of physiological states general principle 6136 6137

Coordination in time Directive correlation (Sommerhoff) in time Input selection by Property selection for Selection by input-sequence 6138 6139

Summary: A more general type of "forcing" operator". 6269, 6247, 6312, 6322 Forcing a variable generalised Summary: Razran's review reviewed. 6269 Reflex, conditioned Razran's review 6140 6141

1960

Summary: Set theory: model or language? Set or Ensemble and brain Pattern (in general) transmission of Transition constraint on 6142 6143

6144 6145

Summary: Given a machine, an input restricted to certain transitions, and a subset closed under all sequences (words) restricted to such transitions, to find the properties of the pattern of transitions at the output. 6152 Summary: The outcome of an infinitely long input can be predicted from a finite number of steps. 6146 6147

Homomorphism only simplification Machine and equivalence relation Simplicity meaning of 6148 6149

Summary: Measuring how much a machine has been simplified. Summary: 'Relations' between patterns. Structure Bourbaki's Chapter 4 6150 6151

6152 6153

6154 6155

Summary: Input pattern of transition showing as output pattern. Summary: Nearness in time encourages similarity in response. Equilibrium case of many Nearness in time, and output Topology of time and behaviour 6156 6157

Summary: ... no regulator can be more effective than the state-determined system. Determinate is best regulator Regulation determinate is best 6158 6159

Summary: No regulator (other things being equal) can give performance better than the machine with input. Entropy zero entropy Markov process / chain of zero entropy 6160 6161

Summary: Meaning of H(A)=0. Congruence in matrix Coordination example in matrix equilibrium Directive correlation (Sommerhoff) example in matrix Equilibrium example of coordination at Higher geometry of fields and matrix theory [30]: (Mod 12) MATRIX has VECTOR as equilibrium (and 23 other, given, vectors), 6163. 6162 6163

Summary: Example of the coordination that exists at a state of equilibrium. 6350 Accumulation (of adaptations) may demand chance localisation Dispersion must be random (!) Gating necessary Localisation must be random Memory must be random Quotations [60]: Claude Bernard, 6165. 6164 6165

Requisite Variety, Law of application to accumulation Summary: When there is no information about the problems that recur, accumulation demands that the activations are small and that the "chance" method be used. 6227 Equivalence relation are arbitory Pattern (in general) all are arbitrary Perceptron 6166 6167

Summary: What are grouped together as "equivalent" must be specified; information is required. 6181, 6222, 6305 6168 6169

Equivalence relation information in Homomorphism variety of Information in equivalence relation 6170 6171

Summary: When a particular equivalence relation is to be specified, the variety to be suppressed is of the order of |n. 6182 6172 6173

Difference equation solved Dynamic system difference equation solved 6175 6176

Summary: The concept of feedback being positive or negative is usefully simple only when the system is continuous. 6184 [Goes in small steps - Riguet 6184] 6177 6178

Summary: Solution of the linear difference equation. Electron has number of states possible Relay has infinite states possible 6179 6179A

Summary: More on self-reproduction. Pattern (in general) recognition of Reproduction more examples 6180 6181

6182 6183

Summary: Selfridge's Pandemonium and pattern recognition. 6222 Requisite Variety, Law of in Pandemonium Oddments [46]: Carry out the program of pages 6184 (foot) and 6185 (top). Summary: I should re-read my Notes, Vol. 5 or so onwards, reading "lots of step-functions" as the more general "lots of equilibria", and lots of step-surfaces" as "lots of boundaries of confluents". Confluant generalisation of step-function Step function what matters is the confluent Oddments [46]: Carry out the program of pages 6184 (foot) and 6185 (top). 6184 6185

Digital computer is specialised Summary: The "general purpose" computer of today is in fact extremely specialised. 6186 6187

Digital computer is a table-user Summary: The general purpose computer, to become a really general machine must simply become a table-searcher. Table computer uses table 6188 6189

6190 6191

Summary: Rubin and Sitgreaves' results summarised. 6199 Pandemonium (of Selfridge) Summary: I must demonstrate, some day, that a heap of manure has as high an organisation as a man. Manure organisations of Organisation of manure or silo Reflex, conditioned in manure Reproduction self reproduction, impossible Silo organisation of 6192 6193

Summary: In a lot of ways a system cannot, strictly, be "self-.....ing". 6566 Organisation self organisation, impossible Self-awareness impossible Set or Ensemble undefined universe Connexion independent Feedback long, for independence Independence at input Loop long, for independence 6194 6195

Summary: Independence of probabilities of equilibrium demands that all loops of connexion be long. 6199, 6333 Equilibrium independence of probability Polystable confluents similar 6196 6197

Summary: Can two fields be very different if both have lots of equilibria? 6248 Polystable forest fire in polystable Polystable several properties polystable 6198 6199

6200 6201

6202 6203

6204 6205

Summary: Properties of the polystable system. 6243, 6248, 6342, 6363 Step-mechanism in learning (Estes) Summary: Estes finds learning to go in jumps. 6542 Learning in all-or-nothing steps 6206 6207

Zato-coding described 6208 6209

6210 6211

Efficiency in Zato-coding 6212 6213

6214 6215

6216 6217

6218 6219

Chess Zato-coding in 6220 6221

Summary: Zato-coding. 6222 6222+01

6222+02 6222+03

Coding of pattern, ρ-1Sρ Equivalence relation and pattern Pattern (in general) after coding, ρ-1Sρ Transformation of a pattern, ρ-1Sρ 6222+04 6223

Summary: Pattern-recognising after coding. 6260, 6346 6224 6225

Summary: Form all mappings, and you are performing all pattern-recognitions. 6346 Mapping and pattern recognition Vacillant of mapping Accumulation (of adaptations) demands separate channels 6226 6227

Summary: Adaptation to the recurrent situation demands step-mechanisms with a multiplicity of channels. Channel necessary Adaptation faculties as adaptation Faculty list of Phrenology faculties of 6228 6229

6230 6231

Summary: What properties of a brain are specialisation to terrestrial life and what are good absolutely? 6404 Constraint discovering Laws of nature value of discovery 6232 6233

Machine as constraint Fibonacci's series as example 6234 6235

6236 6237

6238 6239

6240 6241

Summary: We study "machines" that depend on their immediately preceding states because experience has shown them to be very common in the world around us. 6246 Equilibrium complement of ergodicity Ergodism complement of equilibrium Summary: I must write a text book on the Theory of Equilibrium. 6350 6242 6243

Habituation tilde-operation Topology natural, of machine Summary: Why systems prefer small responses. 6248, 6250 Continuity and habituation 6244 6245

Set or Ensemble undefined universe Universe if undefined Summary: Only restricted types of trajectory or process are suitable for cybernetic studies. Expectation operational form Operational principle "expectation" and 6246 6247

Summary: "Association" clarified further. 6269 Association operational form Diffusion of pattern Topology transfer of 6248 6249

Summary: Sketch of a theory that two coupled systems, in going to equilibrium, tend to prefer regions in their phase-spaces that are topologically similar. Equilibrium when topologies match Summary: At equilibrium, with suitable metric, the responses have a bias towards smallness. 6250 6251

6252 6253

Equivalence relation and machine Machine and equivalence relation Simplification of machine 6254 6255

Homomorphism [=?µ?-1] Summary: Machine Σ may be simplified by equivalence Relation [formula] 6260 6256 6257

Genius Campbell on genius Induction (gaining knowledge by induction) by genius Trial and error by genius Summary: Campbell won't allow "genius". 6289 Ignorance field of ignorance 6258 6259

Projection of relation Transformation meaning of SRS-1 Transformation when invertible 6260 6261

Summary: [SRS-1] is the "shadow" of R when "projected" by S. It can be inverted back to R if and only if [S-1S=Δ]. 6265 Dependence better Diagram of immediate effects (D.I.E.) algebraic form Immediate effect algebraic definition 6262 6263

Summary: Immediate effect is a reality-shadow reaction. Machine as transformation of succession Time machine as coding of Summary: A machine is a "shadow" of simple progression. 6264 6265

Summary: Meaning of [formula] Reflex, conditioned and confluants Resolution of physiological states general principle 6266 6267

6268 6269

Summary: A better statement of the equilibrium theory of the Conditioned Reflex and Jennings' law. 6295, 6312, 6323, 6333, 6338, 6347 Tilde ~ operation 6270 6271

Summary: Theory of Conditioned Reflex and Jennings' law without equilibria under each operator. 6316, 6338 6272 6273

Solipsism A. Huxley on solipsism 6274 6275

Summary: Review of Suppes' book. Neighborhood (in topology) Relation Wiener's suggestion Metric by clubbing Topology by clubbing Topology of brain and machine 6276 6277

6278 6279

6280 6281

1961

Summary: There is no difficulty in getting from a structure of mere clubbing to a full topology. Equilibrium homomorphism of equilibria Homomorphism of equilibria 6282 6283

Summary: Extension of homomorphism. 6284 6285

Directive correlation (Sommerhoff) algebraic form Environment for brain ? (Rho) 6286 6287

Summary: Directive correlation quite simply. 6297 Adaptation anti-adaptation Summary: Specifying the "worst" brain. Genius Gauss' method 6288 6289

Summary: The genius searches. 6335, 6339, 6430, 6570 Summary: Unsolved problem: must systems grow in a way that is grossly self limiting in organisational possibilities? Organisation growth 6290 6291

Summary: The Hamiltonian is a constraint on the field, therefore uninteresting. Field (of substitution) Hamiltonian in field Hamiltonian function nature Summary: The Hamiltonian is not for me. 6321 6292 6293

Energy and equilibrium irrelevant Equilibrium and energy Max( ) (function) energy and equilibrium Minimum energy and equilibrium Summary: Energy flow is neither maximal nor minimal at equilibrium; it is just irrelevant. 6321, 6345, 6350, 6365 Constraint through relation Relation transmits constraint Selection through relation 6294 6295

Summary: If a set is diminished, any set tied to it by any relation will be diminished. Summary: Getting from simple equilibrium to directive correlation. 6350 Directive correlation (Sommerhoff) in machine at equilibrium Equilibrium and directive correlation 6296 6297

Summary: What a species can do, it can recognise. Genes making recogniser Recognition control by genes Localisation of adaptation (niche) Niche (ecological) mathematical example 6298 6299

Summary: So we have exemplified the fact that laws that are functions of their place of action, will develop different adaptations in different places. 6350 Competition mathematical examples Selection by machine 6300 6301

Summary: A species that needs its competitors. 6350, 6355 Quantum theory is of deterministic system! 6302 6303

Waves wave-function as determinate system Summary: The dynamics of the wave-function is that of a state-determined system. Pattern (in general) are arbitrary 6304 6305

Summary: Pattern recognition is arbitrary. 6346 Summary: The "anatomical" body is only one way of identifying the boundary of a system. Anatomy as D.I.E. (diagram of immediate effects) Connexion mechanical 6306 6307

Diagram of immediate effects (D.I.E.) of isolated system Isolation algebraic form Natural system as communication net Organisation as communication organisation net 6308 6309

Summary: What "isolated" means. 6349 Summary: Natural systems, observation, and experiment. Experimenter and system Observable meaning 6310 6311

6312 6313

Summary: Five properties necessary for the conditioned reflex. [deleted] Summary: New layout for the conditioned reflex. [deleted] 6314 6315

Reflex, conditioned modes of display Summary: More on Conditioned Reflex 6323, 6347 6316 6317

Reflex, conditioned ?Solution of problem [on Pavlov's page 197] 6318 6319

Summary: I read the riddle of [Pavlov's] page 197. 6338 Summary: Clear example of how a Newtonian system, with no convergence by Liouville, may show strong convergence if seen by a simpler observer. 6627 Convergence (of lines of behaviour) and Liouville's theorem Liouville's theorem effect of simplifying Pendulum Lotka's set 6320 6321

Summary: "Forcing" does not imply "one confluent." Forcing a variable generalised 6322 6323

Summary: Final (?) statement of the lae of anticipation. 6334, 6342, 6347 Communication in conditioned reflex Reflex, conditioned as communication between operations Selection and conditioned reflex 6324 6325

Confluant ways of changing Reflex, conditioned ways of forcing 6326 6327

Anticipation machine for Reflex, conditioned machine for 6328 6329

Summary: Mechanical layout for showing law of anticipation. 6333, 6334, 6342, 6347, 6352 6330 6331

Summary: To show anticipation. 6334 Anticipation machine for Feedback getting long Loop getting long loop 6332 6333

Summary: Mixing network, one way. Equilibrium forces relation Summary: "Transmission" of selection among the components of equilibria. 6347, 6350 Searching from both ends 6334 6335

Chess two-way search Efficiency in searching Goal two-way search Trial and error efficiency of Summary: In a process of search, knowing the goal, and especially of intermediate goals, can cut the time fabulously. Constraint in environment's transitions 6336 6337

Homeostat conditioned reflex on Reflex, conditioned on Homeostat Summary: Dickens says eloquence comes from thinking about the subject. Genius Dickens on 6338 6339

Summary: Information when two inputs try to get through one output. 6340 6341

Confluant getting smaller confluants Design for small confluents 6342 6343

Summary: Construction to get many compact confluents. 6347, 6362.9 Dispersion small confluents Summary: Convergence to equilibrium in Markov chain. Convergence (of lines of behaviour) Markov non-convergence Equilibrium even distribution, Markov Markov process / chain convergence (or bunching) 6344 6345

Summary: Pattern recognition is arbitrary. Pattern (in general) are arbitrary Anticipation theory 6346 6347

Summary: Theory of anticipation. 6352, 6374, 6389 Isolation as stability Survival as equilibrium 6348 6349

Coordination compound equilibria Equilibrium list of compound equilibria Mapping compound equilibria Operator compound eqilibria Summary: Equilibria and their properties. 6373, 6389 6350 6351

Summary: The elementary conditioned reflex processes only about 2 bits of information, and needs a mechanism of only that capacity. 6363 Arc optimal size Reflex, conditioned machine for Achondroplasia Dickens' memory Localisation principles of Memory principles for localisation 6352 6353

Summary: Notes on: Finding stored information. 6362 Equilibrium as survival Selection mathematical examples Survival mathematical examples 6354 6355

Equilibrium as survival Selection mathematical examples Survival mathematical examples Summary: Example of natural selection and evolution in a computer. 6358 Equilibrium as survival Selection mathematical examples Survival mathematical examples 6356 6357

Equilibrium as survival Selection mathematical examples Survival mathematical examples Summary: Survival of the fittest in a computer. Equilibrium as survival Selection mathematical examples Survival mathematical examples 6358 6359

Equilibrium as survival Selection mathematical examples Survival mathematical examples Summary: Survival of the fittest in a computer. Equilibrium as survival Selection mathematical examples Survival mathematical examples 6360 6361

Summary: For economy, the brain must store memories at the site of use. 6383 Localisation principles of Requisite Variety, Law of localisation of memory Confluant getting smaller confluants Equilibrium getting neutral equilibrium 6362 6363

Summary: How to make a multistable system. Energy and equilibrium irrelevant Equilibrium irrelevance of energy Homeostasis and energy 6364 6365

Summary: The physicist's equilibrium at zero free-energy and the biologist's homeostasis. Chess three "organisations" Organisation and redundancy Redundancy three in chess 6366 6367

Summary: A game of chess shows three "organisations" simultaneously. One goes down, one up, and one does not change. 6379 6368 6369

Summary: The great difference between teaching by pain and teaching by pleasure. 6550 Summary: To feel sympathy is to have no assurance that the other entity is really feeling. 6384 Pain distinct from pleasure Pleasure different from pain Sympathy proof of feeling? Summary: It is often forgotten that planning must have a goal. 6401 Directive correlation (Sommerhoff) need for goal Goal necessity for Memory nitrous oxide on memory Plan must have a goal Retroactive inhibition by nitrous oxide 6370 6371

Constraint polystable system finds Polystable finds constraint The Multistable System [131]: Polystable system finds constraint automatically(?) 6372. Summary: The polystable system tends automatically to find and to use the constraints. Anticipation theory 6372 6373

1962

Summary: To show anticipation, the operations must be such as lead to a unique state; by what route, whether quickly or slowly, are irrelevant 6389 Markov process / chain uncertainty analysis Uncertainty analysis of Markov chain Summary: How a Markov chain shows in Uncertainty Analysis of the triples. 6374 6375

Summary: How many parts produce this trajectory? Part how many? Parts how many? Trajectory how many parts? Summary: Proof of previous note. 6376 6377

Organisation and redundancy Redundancy and organisation 6378 6379

Summary: Organisation and redundancy should be defined, in set theory, as [RR-1'R]. Constraint in set theory Organisation in set theory Summary: [RR-1'R≠0] is a sensitive test for the existence of constraint, but [RR-1'R] does not equal it. 6380 6381

Summary: On the subjective. 6384, 6427 Memory held on a relation Summary: Memory held on constraints. Knowledge communicable and uncomunicable 6382 6383

Unsolved problems [23]: What can a machine transmit? 6384. Summary: A machine can transmit only ......what? 6384 6385

Summary: When [x'=Φ(x)], no convergence anywhere implies div Φ=0 everywhere. Convergence (of lines of behaviour) and [div F (=?F)] Divergence in phase-space Stability and [?F] Uncertainty analysis of 1,m Complexity of basic assumptions 6386 6387

Summary: Examples of ideas that demand the pre-existence of other ideas. Anticipation theory 6388 6389

6390 6391

Summary: Theorem on anticipation. 6394 6392 6393

6393+01 6393+02

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

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