Volume 13 of W. Ross Ashby's Journal
is loading...

Warning: Your browser does not have JavaScript enabledJavaScript has been used to implement many features on this Web site. Unless you enable JavaScript, the following things will not work for you: pop-up image previews, feedback links, random page links, the jump-to-any-page, jump-to-any-volume boxes, and much more. It will annoy you...

1950



Volume 13



3050+03	3050+04

Summary: Stability of systems whose units always tend to some function of the variables.

3051	3052

DAMS (Dispersive and Multistable System) [8]: DAMS, equations of, 2983. DAMS Mark 13, equations of, 3053.
Summary: The equations of DAMS. (Effect of neon, next page) Example next page. Summary: Control of DAMS' stability. DAMS (Dispersive and Multistable System) [10]: Factors affecting DAMS' stability 3054.
3053	3054

DAMS (Dispersive and Multistable System) [5]: Effect on DAMS' equations of a neon striking, 3055.

3055	3056

DAMS (Dispersive and Multistable System) [72]: Behaviour of dispersive system when the Essential variables emit disturbances proportional to their deviations 3057.
Summary: Essential variables may work by 'habituation'. (Review 3280) Habituation essential variables and DAMS (Dispersive and Multistable System) [92]: The essential variables may act as a gate to which the rest will habituate 3058.
3057	3058

Summary: A simple mode of action of the essential variables. 3382, 4526 DAMS (Dispersive and Multistable System) [93]: The essentail variables may work by intermittently forcing themselves to take the values they should have 3059.
Oddments [28]: Is the absolute system 'noiseless'? 2992, 3013, 3031, 3060.
3059	3060

1951


Summary: Part-functions will divide the whole more effectively if the permanent connections are few. Cycle probabilty of
3061	3062

The Multistable System [16]: Tendency of a multistable system to develop cycles, with a calculation 3063. Personal notes [11]: I meet Norbert Weiner, 3063, 3075.

3063	3064



3065	3066



3067	3068


Summary: Wiener says cycles will be common in DAMS; I say they will be few. 4892, 5461, 5472
3069	3070

Additive adaptation and 'serial' additive adaptation
Environment relation to essentail variables
3071	3072



3073	3074

Summary: Set-up necessary, in brain and DAMS, for serial learning. (3087, 3141) Personal notes [11]: I meet Norbert Weiner, 3063, 3075.
Black box, problem of the first considered Black box, problem of the theory of Epistemology [32]: Theory of Black Box first considered 3076.
Hover mouse here to display note
3075	3076



3077	3078


Summary: Functional knowledge obtainable when only some of the variables are observable. 3716
3079	3080

Absolute system Wiener on
Summary: Wiener's opinion on the 'absolute' system. The Multistable System [99]: Relation of the multistable system to its environments. 3082, 3026.
3081	3082

Markov process / chain equilibrium in ensemble
Transition probability eqilibrium of ensemble
3083	3084

Summary: The Markoff process. Cf. 3223
Summary: Stability of system of Markoff chains. DAMS (Dispersive and Multistable System) [69]: Stability of system with transition probabilities. Roots of matrix of elements all between 0 and 1 and where each row sums to 1. 3086.
3085	3086

Environment relation to essentail variables Essential variables relation to environment
Summary: Relation of essential variables to system of part-functions.
3087	3088

Additive adaptation essential
Summary: There should be many essential variables, allowing patterns to endure in proportion to their suitability, and averaging of the behaviours.
3089	3090

Summary: The elementary conditioned reflex does not need essential variables. Corollary: It is thus a by-product. The Conditioned Reflex [36]: For the elementary conditioned reflex, essential variables are not necessary. 3091.
Latent roots distribution of
3091	3092

Summary: The probability of stability. Quotations [58]: "Tous les actes aussi variés soient-ils, n'ont qu'un but, celui de maintenir constantes les conditions de la vie dans le milieu intérieur." Claude Bernard. 3093. [~ "All such various acts have only one purpose, to maintain the constant conditions of life in the internal milieu."]
Summary: If the f in the canonical equation behaves as a Markoff chain, the variable's behaviour is - Brownian movement with drift. Brownian movement canonical equations of Stochastic processes differential equations
3093	3094

Summary: Stochastic differential equations.

3095	3096



3097	3098

Summary: Systems that are partly stochastic.
Density in phase in absolute system Information and density in phase Statistical mechanics density in phase
3099	3100



3101	3102



3103	3104

Summary: The basic equations of statistical mechanics (Continued 3134) Black box, problem of the conjuring as
Information effect of threshold Threshold and information
3105	3106

Dynamic system infinite

3107	3108

Summary: Probability of stability in an infinite machine. (3121)
Summary: Two things necessary if an infinite system is to be stable. (Cf. 3200) Summary: Reactions to delay are difficult. (3138) Delay (in substitution) cause difficulty
3109	3110

The Conditioned Reflex [37]: One of the conditioned reflex's most characteristic features is recovery after extinction. 3111.
Summary: Animals react to more things than the experimenter thinks he is supplying. 4597 The Conditioned Reflex [38]: 'Pseudo'-conditioning is due to the animal reacting to more than the experimenter thinks of, 3112.
3111	3112


Serial adaptation in rats
3113	3114

Summary: Psychological facts to be explained by DAMS. Additive adaptation example
Summary: A part-function's 'degree of constancy.'
3115	3116

Brownian movement sticking does not cause bias

3117	3117+01


Summary: Variables 'sticking' does not necessarily cause a bias.
3117+02	3118

Summary: No excuse is necessary to suppose that part-functions are constant only at certain values. Perhaps the concept of 3200 may be usable.
Summary: In an absolute system one variable knows nothing of another variable's constancy.
3119	3120

Statistical mechanics density in phase Stochastic processes differential equations
Statistical mechanics density in phase Stochastic processes differential equations
3121	3122

Summary: Infinite systems of stable parts. Statistical mechanics density in phase Stochastic processes differential equations
Statistical mechanics density in phase Stochastic processes differential equations
3123	3124

Statistical mechanics density in phase Stochastic processes differential equations
Statistical mechanics density in phase Stochastic processes differential equations
3125	3126

Summary: How a variable's distribution changes after an internal dt. Statistical mechanics density in phase Stochastic processes differential equations
Statistical mechanics density in phase Stochastic processes differential equations
3127	3128

Summary: Steady states in an infinite system. Statistical mechanics density in phase Stochastic processes differential equations
Joining by [x'=e^-x2-...] Statistical mechanics density in phase Stochastic processes differential equations
3129	3130

Essential variables and pleasure Pleasure learning by pleasure Statistical mechanics density in phase Stochastic processes differential equations
Summary: I am now ready to account for learning by 'pleasure'. Statistical mechanics density in phase Stochastic processes differential equations
3131	3132

Summary: In a linear system with all variables distributed, the means of the variables behave the same as the variables would if undisturbed. Statistical mechanics density in phase Stochastic processes differential equations
Density in phase of linear system Field (of substitution) convergence in unstable system Statistical mechanics density in phase Statistical mechanics of linear system Stochastic processes differential equations
3133	3134

Statistical mechanics density in phase Stochastic processes differential equations
Statistical mechanics density in phase Stochastic processes differential equations
3135	3136

Summary: In an absolute system independent distributions don't stay independent. Independence loss of statistical independence with time Statistical mechanics density in phase Stochastic processes differential equations
Summary: 'Delay' in a machine is only behaviour of zero amplitude. Delay (in substitution) nature of
3137	3138

Summary: In a system of part-functions there are no 'parts' only distributed activations.
Additive adaptation and relation to environment Arc multiple arcs traversing environment Environment must be traversed multiply Society [36]: The various members of a society should not have to judge the efficacy of their individual efforts by watching a common indicator 3140. The Multistable System [97]: The different 'arcs' of the multistable system should traverse the environment by different routes. 3140.
3139	3140

Essential variables must be many Natural Selection [15]: Cumulative, additive, adaptation 3141.
Summary: To get cumulative adaptation, the environment must be traversed by a variety of paths. (4546, 4215) DAMS (Dispersive and Multistable System) [12]: DAMS should have plenty of informative feedback, 3142.
3141	3142

Summary: Conditions affect, in the long run, only the stable patterns. Oddments [29]: Changed conditions in the system affect, in the long run, only the stable patterns. 3143.

3143	3144

Part-function that 'locks' Resting state of a part Stimulus effect on multistable systems
Summary: On the chance that a disturbance should alter the resting state of some part. (3272) DAMS (Dispersive and Multistable System) [70]: Effect of surrounding variables on resistance of a part to a stimulus that would force it to another resting state. 3146. (Theory of DAMS.)
3145	3146

Resting state forcing system to another resting state
Summary: A system of part-functions may be easier to change if it is built in stages of assembly. Break effect of joining on resistance to break
3147	3148



3149	3150

Summary: Darwinian mechanisms are to be developed by Darwinian process.
Information gate admitting Switching as a gate admitting information
3151	3152



3153	3154



3155	3156



3157	3158

Oddments [37]: Bias introduced when S sees D through itself: DIAGRAM 3159.

3159	3160



3161	3162

Summary: Switches that see a Markoff process only through themselves: consequent bias in their settings. (Theory in metric-less states, 4527) Markov process / chain seen through a gate or switch Stochastic processes seen through a gate or switch
Information in machines
3163	3164

Information in machines
Information in machines
3165	3166

Information in machines
Information in machines
3167	3168

Information in machines
Summary: In an absolute system formed by the junction of independent parts, if a particular part can take one of ρ initial states and can show σ lines of behaviour from each initial state, then the quantity of information log₂ ρ + log₂ σ cannot be exceeded whatever part has been chosen. Information in machines
3169	3170

Density in phase in absolute system Information in machines
Information in machines
3171	3172

Summary: Information in an absolute system always falls to log₂ η* (3176) where η is the number of the system's stable states and cycles. *Allowance should be made for the fact that the resting states are not equally probable. Information in machines
Information in machines
3173	3174

Information in machines
Summary: Information in a machine. The catchment area of a resting state. Information in machines
3175	3176

Summary: Information in a conjoined system. 3274 Information in machines Information organisms aim to destroy it
Information in machines Markov process / chain passing through transducer
3177	3178

Information in machines
Information in machines
3179	3180

Summary: Example and proof of Shannon's Theorem 7 Information in machines
Information in machines DAMS (Dispersive and Multistable System) [13]: Possible patterns for joining output and inputs, 3182, 3237.
3181	3182

Information in machines
Information in machines
3183	3184

Information in machines
Information in machines
3185	3186

Information in machines
Information in machines
3187	3188

Summary: Networks for DAMS. (Cf. 3237) (Further example 3306) Information in machines
Information in machines
3189	3190

Information in machines
Information in machines
3191	3192

Summary: Information in machines. Information in machines
Information in machines
3193	3194

Information in machines
Information in machines Markov process / chain affecting a machine
3195	3196

Information in machines Markov process / chain affecting a machine
Information in machines Markov process / chain affecting a machine
3197	3198

Information in machines Markov process / chain affecting a machine
Summary: Shannon and I. Chasing equation of Coding in machine Constant intrinsic stability definition Equilibrium 'constant intrinsic' Information in machines Markov process / chain affecting a machine Output as function of input Transformation function-forming
3199	3200

Summary: A variable of constant intrinsic stability and one that always moves towards some function of its neighbours' states are identical. (Cf. 3110) (Behaviour 3134, 3239) Information in machines Markov process / chain affecting a machine
Information in a disturbed system Information in machines Markov process / chain affecting a machine Parameter as source of information
3201	3202

Summary: Passing information from parameter into machine. The previous theorem can be improved. Here is a better statement... Information in machines Markov process / chain affecting a machine
Information in machines Markov process / chain affecting a machine
3203	3204

Summary: Accurate statement of the amount of information that can be put into a machine by arbitrary interference. (3275) Information in machines Markov process / chain affecting a machine
Summary: A physical example of habituation. Habituation physical example Information in machines Markov process / chain affecting a machine
3205	3206

Summary: In the field of an absolute system, every convergent junction acts as a sink for information. Information in machines Information lost by convergence in field Markov process / chain affecting a machine
Information in machines Markov process / chain affecting a machine
3207	3208

Summary: Maximal loss at a convergent point in a field. Table of log₂[(a^a b^b)/(a+b)^a+b]. Information in machines Markov process / chain affecting a machine
Summary: We cannot measure information by finding contributions from sub-ensembles and adding. (Another example 3249) Information belongs to the whole system Information in machines Markov process / chain affecting a machine
3209	3210

Information in machines Markov process / chain affecting a machine
Summary: An absolute machine can never gain more information than is put into it. Information in machines Markov process / chain affecting a machine
3211	3212

Information in machines Markov process / chain affecting a machine
Summary: When a parameter affects a machine, the gain in information is stationary (and a maximum) if the parameter's values are distributed independently of the machine's. Information in machines Markov process / chain affecting a machine
3213	3214

Information in machines Markov process / chain affecting a machine
Summary: Passage of information as machine dominates machine. (See 3298, 3218, 3275) Information in machines Markov process / chain affecting a machine
3215	3216

Capacity information Channel capacity of absolute systems Information in machines Markov process / chain affecting a machine Transmission capacity of absolute systems
Information in machines Markov process / chain affecting a machine
3217	3218

Information in machines Markov process / chain affecting a machine
Summary: (Stated at the front - on 3218): If a machine is driven by an absolute system, the duration of coupling makes no difference to the amount of information received. Information in machines Markov process / chain affecting a machine
3219	3220

Information in machines Markov process / chain affecting a machine
Summary: An information source controlling an otherwise absolute system raises it to a definite information content at which it is in stable equilibrium. (3086) (Canonical equations next page) Information in machines Markov process / chain affecting a machine
3221	3222

Information in machines Markov process / chain affecting a machine Markov process / chain equilibrium in ensemble Parameter as source of information Resting state of system with Markoff parameter
Summary: Canonical equations of the densities in state of a system disturbed by an information source. (See 3227) Information in machines Markov process / chain affecting a machine
3223	3224

Information in machines Information of transition Markov process / chain affecting a machine
Summary: Another measure of information applicable to a machine. Information in machines Markov process / chain affecting a machine
3225	3226

Information in machines Markov process / chain affecting a machine
Summary: When driven by a steady statistical source, the information in a machine does not tend to a minimum. Information in machines Markov process / chain affecting a machine
3227	3228

Information in machines Markov process / chain affecting a machine Statistical mechanics states that cannot be escaped from
Summary: States that lock accumulate all the members of the ensemble. 3233, 3291, 4524 Information in machines Markov process / chain affecting a machine
3229	3230

Information in machines Markov process / chain affecting a machine
Information in machines Markov process / chain affecting a machine Transition probability between resting states
3231	3232



3232+01	3232+02

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