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Volume 13 of W. Ross Ashby's Journal
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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.
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[(aa bb)/(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

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