Volume 09 of W. Ross Ashby's Journal
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1945



Volume 09



1959+02	1959+03



1959+04	1959+05



1960	1961



1962	1963



1964	1965

Summary: My misunderstandings, taken from my own notes, which must be well explained lest they become the reader's, too.
Summary: Some points after reading all my back notes. Personal notes [3]: Whole notes re-read from the beginning, 1967.
1966	1967

Summary: A very practical note on nomenclature in exposition. (Continued next note)

1968	1969



1970	1971

Summary: New nomenclature and slogans.

1972	1973


Summary: Better to think of constancy than activation; and of separation rather than distribution. The idea of a "movement dying out" is shown due to the fact that a common region of constancy is a resting region.
1974	1975

Psychiatric applications [30]: Alcohol, if it raises threshold, will tend to split up complex adaptations into simpler ones 1976.

1976	1977

Summary: A theorem that if a variable, properly joined to others, does not transmit an effect it must be constant (or possibly, changing uniformly). (Converse of 1921)

1978	1979

Summary: Handling part-functions.
The Multistable System [6]: The Traffic Principle, 1981. Unsolved problems [3]: Can I demonstrate, on any of my machines, the Traffic principle? 1981.
1980	1981

The Conditioned Reflex [3]: Simple conditioned reflex as an elementary property of the commutive system, 1621. Still unsolved, 1943. Solved with multistable system, 1982. Further observations, 2064, 2490. Still unsolved, with reasons, 2192, 2243.
Summary: Explanation of the simple conditioned reflex. "Traffic" Principle. (2240, 4596) Traffic principle stated
1982	1983

Summary: "Signals" and Jennings' "Law of the resolution of physiological states" are now explained. Resolution of physiological states Jennings Signal nature of

1984	1985

Summary: An improvement on the theorem about what is necessary in a multistable system.

1986	1987

Summary: For independence test, we must find ∑_ρ=1..n-1[f]^ρ. The old method of Lim_ρ→∞[f]^ρ is rejected. See 2054

1988	1989


Summary: It is decided that a 1st Jacobian matrix (J.M.) cannot be accepted as physically real unless, for each i, not all a_ii , a_iσ a_σi , ... are zero. This is necessary and sufficient that the 2nd J.M. has all main-diagonal elements non-zero and this is the simplest test for it. It follows that a more correct form of the relation is ∑_1..n[f]^ρ=[F], the sum including the n-th power. This last power adds any missing diagonal terms. See 2056
1990	1991



1992	1993

Summary: A clarification of interaction where one reaction uses another. "Dominance" is really a negative concept. Ultrastability is not enough, we must have multistability. A "helping" B, and B "using" A are really the same thing.
Summary: More extended tests of the chance of stability. Oddments [14]: Effect on equilibrium of fixing a variablle, 1808. Numerical test of proportion which become unstable, 1995.
1994	1995

Summary: Empirical study of the effect of fixing variables in stable systems.

1996	1997



1998	1999

Summary: Multistable system defined in new form. Theorem in modern form proves possibility of adaptation by parts.

2000	2001

Summary: A very crude estimate of the chance, in a multistable system, of getting an adaptation without upsetting previously established adaptations. It suggests the great importance of low activations and the gross disturbance which might follow even a small increase in it. 5416 The Multistable System [5]: Marked effect on multistable system of a small change in level of activation, 2002.

2002	2003

Summary: Standard symbols: General mathematical, complete systems, and for general repeated use. Symbols standardised
Step function symbols for
2004	2005


Summary: Modern proof of the basic theorem of the multistable system.
2006	2007



2008	2009


Summary: Elementary rigorous properties of the multistable system, and of part-functions. Summary: When bounds in a multistable system are altering, a line's chance of destruction is proportional to the number of variables it activates, and therefore also to its length. (See next note) The Multistable System [4]: In a multistable system with bounds changing at random, a line's endurance is inversley proportional to its length, 2011.
2010	2011



2012	2013

Summary: In a multistable system, with bounds changing at random, shorter lines have greater survival. Under parameter change, resting states have maximal endurance if they coalesce. Hence Habituation. (See below)
The Conditioned Reflex [11]: In a multistable system, if variables are repeatedly forced to certain values they will tend to become stabilised there, 1943. Improved statement, 2015, 2240.
2014	2015

Summary: A more rigorous statement and proof of the theorem that repeated constraints on a multistable system lead to the system becoming stable at that state.

2016	2017

Oddments [7]: New-born turtle going to the sea as example of a reaction which looks complex but is simple, 2018. Masserman also, 2046. Morgan's examples, 2184.
Summary: On play. Also on reactions which look complete and turn out to be simple.
2018	2019

Pendulum equations of

2020	2021



2022	2023

1946

Summary: Some calculated lines of behaviour of a pendulum from different starting configurations and with various parameter values.

2024	2025


Summary: As working hypothesis it is assumed that "coordination" always means "arranging things so that we get (1) stability (2) where we want it.
2026	2027

Oddments [18]: Simple method for calculating with x = ab^y, 2028.

2028	2029

Higher geometry of fields and matrix theory [21]: Test for stability of EQUATION [x'=Ax] by complex variable theory, 2030. An example 2267.
Summary: Non-instant systems, those with delay, may easily be converted to complete and instant by including derivatives.
2030	2031

Valve thermionic valve, details Oddments [17]: Values, thermionic tubes, details on, 2032.

2032	2033

Summary: Details about values, for reference.
Summary: If A dominates B, and B dominates C, in one complete system, then A must dominate C.
2034	2035

Summary: The case of the top shoot of a tree dominating the growth of lateral shoots fits into my formulation of "dominance" quite naturally.
Independence types of
2036	2037



2038	2039

Summary: Clarification of the position when dependence itself depends on other variables.
Equilibrium of coupled systems
2040	2041


Summary: An over-all theorem on the stabilities of joined systems.
2042	2043


Psychiatric applications [6]: Masserman's principle of Deviation and Substitution, 2045. Unsolved problems [4]: Can Masserman's principles (2045) be demonstrated?
2044	2045

Oddments [7]: New-born turtle going to the sea as example of a reaction which looks complex but is simple, 2018. Masserman also, 2046. Morgan's examples, 2184.

2046	2047



2048	2049

Oddments [48]: Effect of alcohol on complex behaviour, 2050.
Summary: Extracts from Masserman.
2050	2051


Summary: A simple example of the substitution equation of a complete system, suitable as an elementary exercise.
2052	2053



2054	2055

Summary: An improved statement of the main theorems on independence.
Field (of substitution) of linear system Linear system field of
2056	2057


Summary: Answer to "how general is the field of linear equations [x'=Ax] ?"
2058	2059


The Conditioned Reflex [16]: Importance of averaging in the conditioned reflex, 2061.
2060	2061

Summary: By dealing with averages of many ultrastable systems we arrive at a new order or level of phenomena.

2062	2063

The Multistable System [7]: The principle of "minimal bounds" 2064. The Conditioned Reflex [3]: Simple conditioned reflex as an elementary property of the commutive system, 1621. Still unsolved, 1943. Solved with multistable system, 1982. Further observations, 2064, 2490. Still unsolved, with reasons, 2192, 2243.
Summary: An important, though imprecise observation on requirements for a solution of the conditioned reflex problem.
2064	2065

Summary: Detailed example showing the roots moving with change of one coefficient in [x'=Ax] Higher geometry of fields and matrix theory [15]: If EQUATION, with roots r₁,...,r_n, to find ?r_p/?a_St, 0750, 1824. i.e. effect of coefficient on a root. Example 2066, 2401.
Group (mathematical) theory of one-parameter
2066	2067

Equilibrium as invariant
Equilibrium neutral, in group theory
2068	2069

Summary: Notes on one parameter groups.

2070	2071

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



2074	2075



2076	2077



2078	2079

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


Summary: I suspect that any change in timing of a reaction really means learning a new reaction, i.e. new arcs developed.
2084	2085



2086	2087



2088	2089

Summary: Electro-mechanical equiformality.
Summary: The important thing is to push to the limit and then make this a new starting point.
2090	2091


Summary: Latent roots of [2x2 matrix: 0 I a 0].
2092	2093

Homeostat design Isomorphism making machine

2094	2095



2096	2097



2098	2099

Summary: A theoretical study of a Unit devised, and part built, by myself. (Further, 2161, 2182)

2100	2101

1947

Summary: Details for setting the machine of 2094 to correspond to assigned set of coefficients in [x'=Ax].
Summary: Importance of echo impulses.
2102	2103

Summary: To demonstrate importance of echo impulses

2104	2105


Summary: Practical notes for use when converting known systems to differential equations in absolute form.
2106	2107



2108	2109



2110	2111


Summary: Notes the effect of altering the general speed of reaction of one variable.
2112	2113

Summary: Example of stability in the non-linear case.

2114	2115


Summary: Equations of a simple dynamic system.
2116	2117

Half-time of decay Q to find
Homeostasis of pH Regulation of pH
2118	2119



2120	2121

Summary: The dynamic system which controls the pH of the blood exhibited in my form, as illustration.

2122	2123

Summary: A method of getting an approximate solution to non-linear differential equations.

2124	2125

Summary: A physical example of the principle that when a change needs a rare combination to make it possible, it will usually occur by some other way, in stages. (Cf. 2329)
Canonical equations of chemical reaction Chemical dynamics equations
2126	2127



2128	2129

Equilibrium in chemical systems
Summary: The dynamics of chemical systems.
2130	2131

Homeostat design
Steady state Bunsen burner, waterfall
2132	2133



2134	2135



2136	2137



2138	2139



2140	2141



2142	2143

Summary: A study of dynamic systems which are themselves processes, like the Bunsen burner.
Summary: A new way in which one absolute system can be derived from another.
2144	2145

Chemical dynamics relation to molecular processes
Summary: In the study of enzyme systems and chemical dynamics, the equations of 2130 are the ultimate foundation: they are the bricks out of which further knowledge is to be built.
2146	2147



2148	2149

Canonical equations of chemical reaction Chemical dynamics linkage in equations

2150	2151

Summary: Equations tying the variables in the systems of chemical dynamics.
Chemical dynamics principles
2152	2153



2154	2155



2156	2157

Summary: Principles for the experimental study of the dynamics of chemical systems. Society [7]: Processes as absolute systems in society 2158.
Summary: Example of coordination and training as equilibrium in a dynamic system.
2158	2159


Homeostat design
2160	2161

Summary: Further practical details for making a unit. (See 2182)
Natural Selection [13]: In adaptation by heredity there is the recombination effect 1254. Quotation 2163.
2162	2163

Servo-mechanism theory
Summary: Chemical dynamics and thermodynamics. Chemical dynamics equations
2164	2165

Isomorphism not always in chemical form
Equilibrium in chemical systems
2166	2167


Summary: Instability and threshold in chemical dynamics with catalysts. Step-mechanism example
2168	2169

Differential equation numerical solution Solution (to a problem) numerical

2170	2171



2172	2173

Summary: The Adams- Bashforth method for numerical integration of ant simultaneous ordinary differential equations.
Summary: Exposition. Clear ideas can be transmitted to a listener who does not know the argument by language only simple and direct. (What a sentence!)
2174	2175

Society [27]: Richardson treats foreign politics by my methods, i.e. as absolute systems, 2176.

2176	2177


Higher geometry of fields and matrix theory [10]: Method for finding EXPRESSION [Lim x_i, t?8], 2179. Higher geometry of fields and matrix theory [19]: Finding latent roots by Mallock machine, 2179.
2178	2179

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


Summary: A workable unit has actually been made (second system, other was 2094). (Improved, 2432) Learning speed of Speed of learning
2182	2183

Oddments [7]: New-born turtle going to the sea as example of a reaction which looks complex but is simple, 2018. Masserman also, 2046. Morgan's examples, 2184. Oddments [8]: Example of non-adaptive organisation, 2184. (Amblystoma's limb walking backwards).
The Conditioned Reflex [17]: Conditioned reflex can occur outside cerebral cortex, 2185.
2184	2185

The Conditioned Reflex [6]: List of properties of conditioned reflex for checking theory, 2186.
Summary: Extracts from book.
2186	2187


Summary: Coordination and keeping within limits.
2188	2189



2190	2191

The Conditioned Reflex [3]: Simple conditioned reflex as an elementary property of the commutive system, 1621. Still unsolved, 1943. Solved with multistable system, 1982. Further observations, 2064, 2490. Still unsolved, with reasons, 2192, 2243.

2192	2193

Summary: Pavlov and the conditioned reflex seems to make little contact with my work, chiefly because he allows the dog no interaction with the environment.
Homeostasis Cannon applied it to social and industrial systems Homeostasis defined Homeostasis review of Cannon on Society [3]: As man in society is analogous to the neurone in the brain, the same solution will do for both. Cannon thinks the same, 2195, 2198.
2194	2195



2196	2197

Infant homeostasis in Society [3]: As man in society is analogous to the neurone in the brain, the same solution will do for both. Cannon thinks the same, 2195, 2198.

2198	2198+01


Summary: Review of "The wisdom of the body."
2198+02	2199



2199+01	2199+02

Learning some classical facts to be explained The Multistable System [33]: Several examples from animal psychology of apparent multistability. { 2200 - 2209 }
Learning some classical facts to be explained The Multistable System [33]: Several examples from animal psychology of apparent multistability. { 2200 - 2209 }
2200	2201

Learning some classical facts to be explained The Multistable System [33]: Several examples from animal psychology of apparent multistability. { 2200 - 2209 }
Learning some classical facts to be explained The Multistable System [33]: Several examples from animal psychology of apparent multistability. { 2200 - 2209 }
2202	2203

Learning some classical facts to be explained Pleasure nature of The Multistable System [33]: Several examples from animal psychology of apparent multistability. { 2200 - 2209 }
Association various experts on Learning some classical facts to be explained The Multistable System [33]: Several examples from animal psychology of apparent multistability. { 2200 - 2209 }
2204	2205

Learning some classical facts to be explained The Multistable System [33]: Several examples from animal psychology of apparent multistability. { 2200 - 2209 }
Learning some classical facts to be explained The Multistable System [33]: Several examples from animal psychology of apparent multistability. { 2200 - 2209 }
2206	2207

Learning some classical facts to be explained Signal learning by The Multistable System [33]: Several examples from animal psychology of apparent multistability. { 2200 - 2209 }
Summary: Experiments in learning compared with my theory. Learning some classical facts to be explained The Multistable System [33]: Several examples from animal psychology of apparent multistability. { 2200 - 2209 }
2208	2209


Association explanation
2210	2211

Summary: The formulation of "signal", "symbol", "association" given vaguely on 786 is confirmed and given more precision. Coordination Bartlett's definition Signal nature of

2212	2213


Meanings of words in my form stimulus, compound stimulus Stimulus nature of
2214	2215



2216	2217

Summary: Clarification of "stimulus" and some collected types. (See 2486) Pattern (in general) as stimulus
Constraint at input Input variety in Reflex, conditioned fusion of parameters
2218	2219


Summary: Look out for linkages in experimental dynamic systems. There are often much closer linkages in the structure of the experiment than seems at first sight. Several parameter often turn out to be one parameter.
2220	2221

Linear system matrix solution Matrix solution of x'=Ax

2222	2223


Delay (in substitution) defined Delay (in substitution) independence by
2224	2225


Summary: Independence by delay. (See below) (Another example 2229) Society [15]: Examples in society of independence by delay 2227.
2226	2227



2228	2229


Summary: The mathematical core of "association". (Example next page) Association explanation The Conditioned Reflex [18]: The "two-parameter" explanation of "association" 2231, 2234.
2230	2231



2232	2233

Association explanation The Conditioned Reflex [18]: The "two-parameter" explanation of "association" 2231, 2234.
Summary: An attempted explanation of "association" on an actual experiment. Meanings of words in my form receptors and effectors
2234	2235


Complex equilibria with snake charming as example
2236	2237

Summary: Some elementary observations on the organism-environment relation.
Summary: A stimulus is many stimuli. Stimulus mutiplicity
2238	2239

Forcing a variable The Conditioned Reflex [8]: If a variable is repeatedly displaced to a value X, then the system tends to a field with resting state at X, 2240. The Conditioned Reflex [11]: In a multistable system, if variables are repeatedly forced to certain values they will tend to become stabilised there, 1943. Improved statement, 2015, 2240.
Summary: If a variable of an ultrastable system is repeatedly forced to take a particular value arbitrarily, then the resting state tends to develop with the variable at that value.
2240	2241

Summary: It is dangerous for an ultrastable system to move. (4596)
The Conditioned Reflex [3]: Simple conditioned reflex as an elementary property of the commutive system, 1621. Still unsolved, 1943. Solved with multistable system, 1982. Further observations, 2064, 2490. Still unsolved, with reasons, 2192, 2243.
2242	2243

Multistable reserve defined The Conditioned Reflex [15]: The "multistable reserve" 2244.
Summary: The multistable reserve.
2244	2245

Summary: A clear example of my concept of "independence".
Summary: Neurosis as instability. Psychiatric applications [10]: Davis' theory of neurosis as instability 2247.
2246	2247


Personal notes [4]: A dream of mine 2249.
2248	2249


Fatigue lesser stability
2250	2251



2251+01	2251+02

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