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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 2p 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 xo.
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 αjk=ajk + ibjk, and [αjk] has roots ρ1...ρn, then MATRIX has roots ρ1...ρn , ρ1* ... ρn* 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

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