Home | Journal | Bookshelf | Index | Other | Timeline | Previous ◄ ► Next | Help | Copyright

Volume 09 of W. Ross Ashby's Journal
is loading...


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 Limρ→∞[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 aii , a aσi , ... 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 = aby, 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,...,rn, to find ∂rp/∂aSt, 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 xi, t→∞], 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

Home | Journal | Bookshelf | Index | Other | Timeline | Previous ◄ ► Next | Help | Copyright