Volume 15 of W. Ross Ashby's Journal
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1951



Volume 15



3586+03	3586+04

Environment reviewed again Essential variables Reviewed again
Environment reviewed again Essential variables Reviewed again
3587	3588

Environment reviewed again Essential variables Reviewed again
Environment reviewed again Essential variables Reviewed again
3589	3590

Conflict arrangement for Environment reviewed again Essential variables Reviewed again Psychiatric applications [16]: An arrangement possibly leading to conflict, 3591.
Environment reviewed again Essential variables Reviewed again
3591	3592

Environment reviewed again Essential variables Reviewed again
Summary: How essential variables, environment, and network are to be arranged in organism and DAMS. 3603, 3825, 4600, 4613 - there is no general solution, 4832, 5737 Environment reviewed again Essential variables Reviewed again Signal multistable system responding to
3593	3594


Summary: A clearer statement about the Essential Variable. Chess theory of games Games theory of
3595	3596


Summary: A glance at the theory of games. 4589
3597	3598

Equilibrium multistable system around state of The Multistable System [81]: In a system of part-functions, all infinitesimal displacements, in whatever direction, from a resting state activate the same set of variables, 3581, 3599.
The Multistable System [82]: Arcs activated by infinitesimal displacements from a resting state - all displacements activate the same arcs 3600.
3599	3600


Summary: Getting dispersion. 3870 Dispersion to change
3601	3602

Summary: How the cortex perhaps gets selective disruption of wrong arcs. 3825, 4600, 4831 Essential variables possible mode of action Learning imprinting Learning serial learning DAMS (Dispersive and Multistable System) [47]: Possible mode for action of essential variables, 3603.

3603	3604


Summary: Long lines of behaviour in phase-space often appear in the living world as circulating between organism and environment. 3645, 3760 Detailed Balancing, Principle of Statistical mechanics Fowler on
3605	3606

Campbell's theorem Degenerance, in system definition Epistemology Campbell's theorem Observable Campbell's theorem
Summary: Statistical mechanics. Chess 'super' moves Homeostat variety on switches Information on uniselectors
3607	3608

Cleverness may be purely negative Selection of patterns
Summary: 'Positive' cleverness may be really only what is left after the elimination of nonsense. 4578 5307.3 (See 3629) Information amplifier for
3609	3610



3611	3612

Feedback in information amplifier
Summary: Evolution and the homeostat are information-amplifiers. (3616)
3613	3614

Chess number of positions
Summary: Details of chess-playing.
3615	3616

Evolution as information amplifier Natural Selection [50]: Darwin's system, as an information-amplifier, 3617. DIAGRAM

3617	3618



3619	3620



3621	3622

Chess information amplifier Evolution as information amplifier

3623	3624

Army organisation of

3625	3626

Chess information amplifier
Summary: Properties of an information-amplifier. 4155
3627	3628

Summary: The elimination of wrong moves at chess may eliminate too much. Arc multiple arcs traversing environment Chess information amplifier Environment control of Statistic as random transformation Transducer random Transformation random
Summary: Random transformations. Instinct inate releasing mechanisms in
3629	3630

Summary: How instinct is activated. Transformation of taste
Summary: Random transformation in taste. 3665 Transformation random
3631	3632

Selection example Natural Selection [37]: Illustration of the power of 'mere' selection, 3633.
Arc active and inactive Arc number of The Multistable System [92]: The number of arcs that a reaction activates; distribution and average, 3634. The Multistable System [93]: Number of reactions that will use a given arc; distribution and average, 3634. DAMS (Dispersive and Multistable System) [48]: Numerical estimates of DAMS' efficiency in dispersion, 3634.
3633	3634



3635	3636

Summary: Calculations on dispersion. The Multistable System [26]: Number of variables necessary for multi-stability, 3637. DAMS (Dispersive and Multistable System) [49]: DAMS is too small to show multistability 3637.
Dispersion in olfactory system
3637	3638

Stimulus dying out

3639	3640


Summary: The chance that inactivity will stop an effect getting into the rest of the machine. Brownian movement in DAMS (Dispersive and Multistable System) DAMS (Dispersive and Multistable System) [50]: 'Brownian' activity in DAMS, 3642.
3641	3642

Summary: Environment reducible to orthogonal subsystems. Also 3648 Additive adaptation example Environment control of Reducibility example
Summary: Innate mechanisms must be studied for their organisational properties. Amplifier nature of Instinct reason for studying
3643	3644

1952

Summary: Three ideas. Feedback importance of Operator and feedback Natural Selection [47]: Evolution is, in a sense, regenerative and unstable, 3645.
Levels involve environment
3645	3646

Summary: Functional levels may be topologically re-arranged within organism and environment. Additive adaptation example Environment control of

3647	3648

Summary: Example of an environment.
Psychiatric applications [17]: A list of possibilities, of abnormality in the brain's self-correcting parameters to the variables, 3650.
3649	3650


DAMS (Dispersive and Multistable System) [51]: Advantageous adjustment mechanisms, 3652.
3651	3652


Summary: Cybernetics and the psychoses. 3673 Step function fixity in paranoia
3653	3654

Summary: The mechanism underlying paranoia. Aggression relation to paranoia
Information and resting states Resting state and information DAMS (Dispersive and Multistable System) [52]: The resting states of DAMS are not accessible unless a rich source of information is available and a broad channel into it, 3656.
3655	3656

Summary: The number of resting states that a machine can display to an observer depends on the information that the observer can get into the machine. (Next page) Stimulus information in
Information in primary operation Primary operation information admitted
3657	3658


Information in canonical equations
3659	3660

Summary: Information in the field and in the equations of an absolute system is S log S. 3695 Summary: The homeostat's amplification factor is less than x1, but I was the first to point this out. Homeostat variety in fields
Summary: Again the necessity for achieving success by stages. Design amount of Natural Selection [6]: Selection in stages can reduce the time from 2^p to P, 3662.
3661	3662

Summary: Approximate estimate of the amount of design put into the homeostat.
Summary: How many uniselectors the homeostat should have. 3743 Transformation random
3663	3664

Summary: Example of a random transducer. 3667
Summary: Chess strategy. Chess strategy in Strategy in chess
3665	3666


Memory in multistable system
3667	3668


Summary: Chess player's manual. 4569 Summary: Amount of design in the homeostat.
3669	3670

Summary: Possible reason why psychoses are rare in children. Cf. 3650 Psychiatric applications [18]: Why are psychoses rare in children? 3672.
Oddments [31]: Isolated systems, 3673.
3672	3673

Summary: Isolating a system.
Quotations [32]: The fundamental problem of theoretical biology is discover how the behaviour of myriads of blind, stupid, and by inclination chaotic, atoms can obey the laws of physics and chemistry, and at the same become integrated into organic wholes and into activities of such purpose-like character" Sommerhoff, 3675.
3674	3675

Invariant and 'purpose'

3676	3677


Cause meaning of
3678	3679



3680	3681

Memory in multistable system Memory Sommerhoff on Serial adaptation Sommerhoff on serial adaptation

3682	3683

Summary: Extracts from Sommerhoff. 3709, 3715
Summary: When there is more than one source, how many entropies are calculable?
3684	3685


Summary: Information from multiple sources.
3686	3687

Summary: Definition of 'memory'. 3810 Memory rigorous definition

3688	3689

Experiment when it stops
Information from machine to machine
3690	3691

Summary: Experimenter and system. 3697, 3725
J - function (Ashby) defined
3692	3693

Information in partition Partition information in

3694	3695



3695+01	3695+02

Summary: A function that measures information but is free from the concept of probability. Its basis is the 'partition'. Compare Neumann and Morgenstern 67. 5027

3696	3697

Summary: Even the experimenter must be regarded as an ensemble. 3709 Set or Ensemble in experimenter
Field (of substitution) information in
3698	3699

Summary: To compute information, members having the same field must be kept together. Strategy in chess

3700	3701


Summary: Chess strategy. 4590, 4651
3702	3703

Experience law of Parameter allows information to fall Set or Ensemble parameter and information
Summary: Every parameter-change allows (or forces) the information in an ensemble to drop to a new lower level. Same applies to δ-impulse 3936. Habituation theory of
3704	3705

Summary: Habituation, and adding information to an ensemble. 3774 Ergodism in ensemble DAMS (Dispersive and Multistable System) [53]: Habituation in DAMS, 3706.
Summary: The effect of the initial state decays with time if some parametric input is active. 3954 Logic depends on trial DAMS (Dispersive and Multistable System) [54]: If an ensemble has an input, the behaviour depends less and less on the initial state, 3707.
3706	3707

Summary: Decay of information in an ensemble.
Cause meaning of
3708	3709

Summary: The concept of 'cause' implies more than one line of behaviour. 5118 Summary: Today's tip: Cleverness, by Selection out of Thermal Noise, Steady state unnecessary
Mathematics as dynamic system Unconscious, the nature of
3710	3711


Logic depends on trial
3712	3713


Summary: Mathematical knowledge is knowledge of how to control a certain environmental, physical, system. 3721, 3725, 3729
3714	3715

Black box, problem of the replacing variables Variable unobservable
Summary: Transformation of a linear absolute system. Higher geometry of fields and matrix theory [16]: The latent roots are invariant when variables are replaced by derivatives. 3717, 3719.
3716	3717


Summary: Replacing variables by derivatives. 3723, 4296, 5202 Derivative replacing variable Latent roots unobservable variables Higher geometry of fields and matrix theory [16]: The latent roots are invariant when variables are replaced by derivatives. 3717, 3719.
3718	3719

Summary: Two unstable systems joined to give a stable. Society [41]: Information as control, 3720.
Natural Selection [46]: Organisation in business, 3721.
3720	3721

Mathematics as dynamic system
Summary: More examples of mathematics as a study of real dynamic possibilities. 3729
3722	3723


Knowing means 'controlling'
3724	3725


Invariant one helps another Transducer inverse
3726	3727


Summary: 'Knowing' means 'controlling', which means 'keeping invariant'. Review 4348, 4294 Mathematics as dynamic system
3728	3729

Summary: More illustrations that maths is based on physical, empirical knowledge. 3926 Summary: Real 'dial-readings'. Summary: Itinerary in the States: London, New York, Chicago.
Summary: Itinerary in the States: Warren McCulloch. John Bowman at Mellon Institute, Pittsburgh. Koskoff. New York. Boston. MIT: [Lethrin ?], Walter Pitts, Norbert Wiener, Aitkins, Marvin Minsky, Mary Brazier. Maze maze solving machines
Hover mouse here to display note
3730	3731

Summary: Itinerary in the States: Boston: Society for the Unity of Science. New York, Warren McCulloch, New England, 9th Macy Conference, Mrs Metzger (Ruth McCulloch's mother). Cambriidge, Walter Pits, Norbert Wiener, Bell Laboratories, New Jersey, Claude Shannon Maze maze solving machines
Summary: Itinerary in the States: Richard Wallace, Philadelphia. Washngton, Mina Rees, Seymour Kety. New york, London.
3732	3733



3734	3735

Summary: To make, or not to make, a calculating machine? Computing machines worth making?

3736	3737

Summary: Wallace's Maze-solving Computer.
Transducer inverse
3738	3739


Summary: Shannon's mechanical brains.
3740	3741


Summary: Information in the homeostat.
3742	3743

Summary: Information in the homeostat.
Random searching Searching random versus systematic
3744	3745


Natural Selection [61]: A supposedly systematic search over more than 10¹⁵ is random for the portion searched 3747.
3746	3747

Memory and systematic searching

3748	3749

Amplifier nature of

3750	3751

Summary: Searching, random and systematic. Information first amplifier
Summary: Qualification to 3746.
3752	3753


Computing machines programming
3754	3755

Group (mathematical) natural unit as group
The Multistable System [71]: A system with null-functions, if observed on a new set of dials, no longer shows null-functions (Ashby 3757). The Multistable System [83]: The breaking of a whole into subsystems by part-functions is not invariant for change of coordinates. 3757.
3756	3757


Part-function transformation to Transformation to give part-functions
3758	3759

Summary: The division by part-functions is not objective. Transformation can destroy part-functions. 3767, 3799 Cortex repeated arcs
Summary: Details of dispersion. Primary operation on multistable systems Primary operation defined The Multistable System [84]: Primary operation needs special definition when applied to a system with part-functions, 3761.
3760	3761



3761+01	3762

Summary: Addendum to the definition of the primary operation. Corrected 3894
Higher geometry of fields and matrix theory [7]: Field cannot be transformed to show all the variables but one as part-functions 3764.
3763	3764


Summary: A misunderstanding about part-functions. 3868
3765	3766

Canonical equations change of coordinates Rank of system with part-function
The Multistable System [77]: The rank of the differential matrix is unaltered by changing to new variables that are linear functions of the old. Ashby 3768.
3767	3768


Natural Selection [79]: Theorum The rank of [?f/?x] is not invarient if the transformation is non-linear, Ashby 3771.
3770	3771

Summary: Rank of the differential matrix, and null-functions. Rank and reducibility Reducibility rank of
Information retention by null-function Null-function and retention of information
3772	3773


Summary: Part-function were introduced to cause retention of information. 3799
3774	3775

Summary: Example of a canonical equation of nullity 2. 3799 Substitution (mathematical) example
Independence to pattern
3776	3777

Control via constants Jacobian (determinant) rank and control Parameter independence among
Information loss in function
3778	3779


Rank and reducibility Reducibility rank of
3780	3781



3782	3783

Summary: Rank, information, effective parameters. 3780, 3799, 3788
Summary: Determination of initial states. 3789, 3847
3784	3785

Determinate meaning of Set or Ensemble relation to 'determinate'
Summary: Field + field, and determinate changes of parameter. Summary: The observer-system relation is symmetrical; so we can calculate 'information' over an ensemble of observers Experimenter information to Information to experimenter
3786	3787

Information in vector Rank and resting state Resting state rank around
Summary: Information, rank, equations. 3799 Experimenter testing independence Experimenter using primary operations Independence testing for
3788	3789



3790	3791

Summary: On the operation that brings the representative point to a particular initial state. 3846, 4628 Convergence (of lines of behaviour)
Independence and convergence Independence types of Information convergence and Invariant three types
3792	3793

Summary: Convergence of lines as invariance.
Experimenter receiving information Information transfer of
3794	3795


Summary: An absolute system cannot give to another absolute system that it dominates more information than the first one contains. 3797
3796	3797


Summary: Rank, and control effected by parameters. 3800, 3802, 4301 Control via constants Input control possible Jacobian (determinant) rank and control Parameter control by Rank of system with part-function
3798	3799

Channel capacity of absolute systems
Summary: Channel capacity in a machine. Hour glass system transmission of information
3800	3801

Isomorphism of science
Information chain of systems
3802	3803



3804	3805

Summary: Transmission of information through a chain of absolute systems.
Homogeneity and group
3806	3807

Summary: Homogeneity implies group statistical regularity implies group. 3849 Invariant implies group
Summary: Examples testing dependence of F on x^o.
3808	3809



3810	3811


Memory definition
3812	3813

Summary: (1) What is meant by 'memory'. (2) Memory does not require feedback. 3840 Transformation memory as
Summary: Memory as conjugate behaviour. Summary: Habituation implies memory. 3842 Habituation implies memory
3814	3815


Interaction and notation Problems methods for Serial adaptation Polya on serial adaptation Transformation random The Multistable System [27]: Polya's methods for solving problems correspond in detail with those of the multistable system, 3817.
3816	3817

Analogy in maths Quotations [41]: 'A method is a device you use twice'. Polya, 3818.
The Multistable System [28]: Example of how a multiplicity of tests, each of low reliability, can give a result of high reliability, 3819.
3818	3819

Habituation length of path

3820	3821



3822	3823

Summary: Habituation. 3837, 3842, 3856, 4526 Dispersion defined by information Independence definition Information and independence and dispersion
Essential variables possible mode of action
3824	3825



3826	3827


Summary: How the Essential Variables must act to be selective. 5549, 5415, 4169, 4831, 5345 Threshold function of
3828	3829


Summary: Variables in the brain should be driven actively by the environment. Receptors reason for multistable systems
3830	3831

Summary: Odd notes. Constraint at input Input variety in

3832	3833

DAMS (Dispersive and Multistable System) [55]: The critical surfaces of the neons in DAMS do not fulfil the same functions as the crit. surfaces of the relays in the homeostat 3834.
Summary: A better view of the homeostat. 3837
3834	3835


Summary: What is essential in the homeostat. 3841, 3856, 4161 Basin and habitation Habituation and basins
3836	3837


Dis-inhibition
3838	3839

Summary: On habituation. 3842, 3856, 3865, 4524
Summary: Memory implies that step-functions exist and that the system contains more than one resting state. 'Memory' is 'change of resting state'. Example 3833, 3856, 3842, 3900. Multiple resting states are necessary: they are also sufficient if we observe them through a system U, which can be the observer! Memory what is necessary
3840	3841

Habituation and memory Step function necessary for memory

3842	3843


Summary: Habituation and memory. 3865, 4524 Alarm and habituation
3844	3845

Experimenter using primary operations Primary operation relation to experimenter

3846	3847

Transition probability

3848	3849

Absolute system origin of
Dispersion proved necessary Experimenter must have dispersion The Multistable System [94]: Dispersion proved necessary, 3851.
3850	3851

Summary: Only an observer with dispersion can take advantage of a system's absoluteness.
Summary: Exploring a machine.
3852	3853

Summary: Detail of 3844.
Summary: Change full to step-functions for resting states. Equilibrium number of states of Resting state number of
3854	3855

Summary: Other things being equal, the system with more step-functions will have more resting states.
Information decay of Natural Selection [51]: Importance of the fact that the world is old, 3857.
3856	3857


Summary: The importance of the age of thing. Review 4155 Problems solved serially Serial adaptation example
3858	3859

Summary: The catchment areas define a partition. Basin as partition Equilibrium proper definition The Multistable System [29]: The multistable system's problem is to get its forgetting right! 3860.
Summary: Definition of 'stability'.
3860	3861

Summary: Return of parameter to a previous value can cause further loss of information. 3863, 3954, 4057, 4074, 4373 Information fall under change of parameter

3862	3863

Summary: A fluctuating parameter tends to lesser the number of resting states.
Dis-inhibition Habituation and basins
3864	3865

Summary: The reactive condition is the more probable, from which the system may diverge under habituation.
Summary: The channel from step-function to observer must be broad if the observer is to see variety of behaviour. Channel capacity step-functions to observer DAMS (Dispersive and Multistable System) [56]: The channel from step-functions to observer must be broad if observer is to see much variety in behaviour 3867.
3866	3867

Canonical equations [y'₁=1, y'₂=0, ...]
Summary: Every system can be transformed to [y^~₁=1, y^~₂=...=y^~_n=0] Cf. 1151
3868	3869

Control infinitesimal
Summary: All control is based on the infinitesimal. 3930, 4015
3870	3871


Resting state in chain of levels DAMS (Dispersive and Multistable System) [57]: Number of resting states when arranged DIAGRAM without neons, 3873.
3872	3873



3874	3875

Summary: Stability of a circuit of levels. Another interesting system...
DAMS (Dispersive and Multistable System) [58]: Number of resting states of the 'clover leaf', DIAGRAM 3877.
3876	3877



3878	3879

Summary: Behaviour of the 'clover' system.
Feedback via single wire
3880	3881

Summary: Feedback can occur along a single channel.
Latent roots distribution of
3882	3883



3884	3885



3886	3887



3888	3889


Summary: An incomplete solution of the problem of the probability of stability.
3890	3891

Summary: A variable 'is' whatever a particular system, perhaps ourselves, sees it as. (But see 4000) and 3896, Relation equivalence relation
Summary: "interacts with" is an equivalence relation.
3892	3893

Summary: A likely mechanism for the conditioned reflex. 3897 Essential variables limits and conditioned reflex The Conditioned Reflex [41]: Another contribution to the basic mechanism 3894.
Primary operation defined
3894	3895

Summary: The primary operation, and testing absoluteness.

3896	3897


Summary: More on the Conditioned Reflex
3898	3899

Step function mixed form
Summary: A hybrid step-full-function. By 4000 it is in (2), a full function.
3900	3901



3902	3903



3904	3905



3906	3907



3908	3909


Absolute system with complex variables Complex (Freudian) complex variable machine Complex variable machine
3910	3911



3912	3913

Summary: n complex variables are equivalent to 2n real variables. Complex 'machinery'.

3914	3915

Summary: n arcs can control n complex variables.
Higher geometry of fields and matrix theory [26]: If a_jk=a_jk + ib_jk, and [a_jk] has roots ?₁...?_n, then MATRIX has roots ?₁...?_n , ?₁* ... ?_n* 3917.
3916	3917

Summary: Resting states and latent roots of complex-variable systems.
Summary: Volterra's book. Competition equations of Delay (in substitution) introduces memory Memory by delay Survival Volterra's equations
3918	3919



3920	3921


Summary: Arcs that are simple as complex variables do not stay so as real variables.
3922	3923

Mathematics as dynamic system The Multistable System [30]: It may happen that part talks to part through the environment 3924.
Summary: In the brain, part often talks to part via the environment. 5424 Experiment as communication
3924	3925

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

Summary: Topology of absolute system.
Summary: 'Stability' must be re-stated in terms of information. 3963, 3980, 3975 Genes should receive no information Information genes should get none Unsolved problems [13]: 'Stability' should be re-stated in terms of information, so as not to raise the unwanted 'unstable' equilibria. 3929.
3928	3929

Primary operation using
Summary: The disturbances of most interest are those that are infinitesimal and the system becomes linear.
3930	3931

Summary: Self-reproducing arcs are of very great importance, for good or evil. Review 4154 The Multistable System [40]: Self-reproducing arcs are of high importance, for good or evil 3932.
Information in partition Partition information in
3932	3933


Summary: A derivation of the partition-function.
3934	3935

Basin and habitation
Summary: Administering a determinate impulse to an ensemble can only cause its information to fall. 3954 Basin defined Information and d-impulse
3936	3937

Step function topology of
Summary: Unsolved problem. 3959, 3962 Information must be destroyed
3938	3939

Adaptation as destruction of information Homeostasis as destruction of information

3940	3941



3941+01	3941+02

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