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Isomorphism
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Ross indexed the following pages under the keyword: "Isomorphism".


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1941
Summary: Suppose the cortex is a 'representation' of the environment, i.e. corresponding to events in the periphery (stimuli, reactions) there are events in the cortex. Nothing new in this idea. But suppose that the cortex is more 'sensitive', so that if the periphery is being driven out of its range of stability the corresponding variable in the cortex will break first, i.e. get outside its range of stability, and thus switch to another portion of the field (817), and change partially to another organisation.
Cortex as 'sensitive'
Reactions right and wrong
Reflex, conditioned
Equilibrium by cortex 'breaking'
Isomorphism of cortex and environment
Neuron death of
Pain and organisation
Reflex, conditioned
0859 0860
Cortex, visual
Signal vision as
Structure interlocking
Vision mostly signals
Isomorphism ? group necessary
0863 0864
Break of organisation
Energy free energy
Organisation break of
Group (mathematical) of groups
Isomorphism and representations
0865 0866
Group (mathematical) basic
Hallucination and isomorphism
Isomorphism and neurosis
Pattern (in general) and neurosis
0871 0872
Dream isomorphism in
Isomorphism in dream
0873 0874
Isomorphism almost isomorphism
Vision binocular
0875 0876
Entropy and sensory adaptation
Differential equation turned to operator
Group (mathematical) and machine
Isomorphism in machine
Operator = differential equation
Substitution (mathematical) as differential equation
0917 0918
Isomorphism exact definition
Stimulus pattern and equilibrium
Environment as parameter
Organisation and its environment
0933 0934
Summary: One stage in our long journey is finished and solved: the 'exact' case, i.e. an organisation where we are given full and exact information about every little detail.
Differential equation and linear partial differential equations
Group (mathematical) and isomorphism
Isomorphism ? group necessary
1059 1060

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1944
Summary: Two machines may form a whole which is stable if they were joined one way, and unstable if joined the other.
Summary: Two stable machines may be unstable when joined if either contains more than one variable.
Isomorphism Craik's book on
1665 1666

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1946
Summary: Effect on latent roots of adding constant to main diagonal, how to move all latent roots to right or left, and a new test for stability.
Equilibrium dominant root
Higher geometry of fields and matrix theory [18]: Test for stability by dominant root, 2072.
Homeostat design
Isomorphism making machine
2072 2073
Summary: Principles and details for a machine to be absolute, show ultrastability, etc. (see 2095, 2161, 2182 etc)
Summary: Experiment.
Isomorphism making machine
2080 2081
Summary: Simple units with output a linear function of the inputs are sufficiently general provided we can control also their general speed of working.
Homeostat design
Isomorphism making machine
2082 2083
Homeostat design
Isomorphism making machine
2094 2095

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1947
Isomorphism not always in chemical form
Equilibrium in chemical systems
2166 2167
Summary: A number of interesting points from Richardson's book.
Summary: The various "constancies" of the body, so carefully maintained (homeostasis), are also separations and independencies. This needs further investigation. (See 2314)
Homeostat design
Isomorphism making machine
Natural Selection [48]: Homeostasis = constancy = independence, why the latter? 2181. Answered 2314, to preserve the gene pattern.
2180 2181

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1952
Isomorphism of science
Information chain of systems
3802 3803
Isomorphism multistable systems and mathematics
Mathematics as dynamic system
The Multistable System [31]: Contained in the multistable system should be all mathematics, 3926.
Summary: All maths should be expressible in terms of dynamic systems.
3926 3927

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1953
Black box, problem of the isomorphism
Invariant of Black Box
Isomorphism in Black Box
Group (mathematical) not all science
4458 4459
Summary: The method of models, for quicker searching. Review 4560-4575
Isomorphism use of
Pattern (in general) use of
4556 4557
Isomorphism and equiformality
Part in set theory
Tensor product of two machines
4744 4745

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1954
Isomorphism in set theory
Relation nature of
Implication in set theory
4836 4837
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
Isomorphism electromechanical example
Higher geometry of fields and matrix theory [17]: An electromechanical analogy (spring and mass / condenser etc) in detail 4998.
Summary: An exact electromechanical analogy.
4998 4999
Summary: Isomorphism.
Isomorphism formal definition
Machine isomorphism defined
Summary: Homomorphism.
Homomorphism example
5000 5001
Summary: Example of the effect of continuity as a constraint. Caution: See 5054. 5636
Diagram of immediate effects (D.I.E.) and memory
Isomorphism in memory
Memory isomporphism in
5024 5025
Summary: Requisite variety stated algebraically. 5075
Isomorphism in memory
Memory isomporphism in
5048 5049

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1955
Summary: Machine with input and binary relation.
Isomorphism and prediction
Prediction why important
5184 5185

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1956
Summary: Raiffa et al. describe maths as isomorphic with real systems. 5298, 6260
Canonical equations found by Lotka
Delay (in substitution) Lotka on
Isomorphism real system and maths
5272 5273
Ultrastability bias to efficiency
The Multistable System [107]: The multistable system has a bias towards becoming efficient and quickly adapting. 5342.
Summary: The ultrastable system has an intrinsic bias towards efficiency and quickness in learning.
Black box, problem of the poorly observable black box
Isomorphism Moore's definition equals mine
5342 5343

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1957
Conditionality in set theory
Organisation in set theory
Organisation as conditionality
Reducibility in set theory
Summary: Basic meanings of organisation, reducibility, conditionality. 5537, 5675, 5993
Isomorphism example in differential equations
5532 5533

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1958
Summary: Survival of the fittest, demonstrated in a computer. 5801, 5828, 5961
Isomorphism in mathmatical physics
Model in physics, Synge on
5798 5799
Confluant and conditioned reflex
Diffusion of pattern
Equilibrium under regular transitions
Input pattern in
Inscription defined
Isomorphism transitions and confluents
Learning without feedback
Pattern (in general) transmission of
Summary: The pattern in the confluents tends to copy the pattern in the input-transitions. Stochastic case: 5873, 5892
Anticipation automatic
Confluant and conditioned reflex
Continuity learning the structure
Dimension learning it empirically
Equilibrium under regular transitions
Prediction automatic
5844 5845
Summary: A new form of independence and the "proxy" relation.
Proxy relation
Relation "proxy" relation
Isomorphism Hilton's extension
Relation isomorphism generalised
5914 5915
Isomorphism Bourbaki's extended
6012 6013

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1959
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
Isomorphism generalised
Summary: Isomorphism, homomorphism and now protomorphism. 6150, 6260
Protomorphism defined
Structure protomorphism defined
6124 6125

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