Volume 24 of W. Ross Ashby's Journal
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1967



Volume 24



6677+03	6677+04



6677+05	6677+06

Analysis of variance Complexity irreducible Factorial experiment, and uncertainty
Summary: The Fisherian factorial experiment in uncertainty analysis. 6719, 7172 Cylindrance and reducibility
6678	6679


Summary: Merely thinking of two axes as becoming a new, single (vector) axis is profoundly disturbing to cylindrance. 6683, 6686, 7141
6680	6681


Summary: ~~Every set of cylindrance p may be transformed to a set of cylindrance 1 by a transformation of cylindrance not exceeding p+1.~~ [deleted] 6686
6682	6683



6684	6685

Summary: Transforming a space with a subset in it, so that the subset takes a new form, in the new space, with lowered cylindrance. 6683, 6680

6686	6687



6688	6689



6690	6691



6692	6693

Amoeba movement at Kinematics of Amoeba

6694	6695



6696	6697



6698	6699



6700	6701


Summary: Amoeboid coherence.
6702	6703



6704	6705



6706	6707


Summary: Amoeboid coherence (kinematics) in three dimensions.
6708	6709



6710	6711



6712	6713



6714	6715


Summary: Rigorous formation of the Amoeba's kinematics.
6716	6717


Summary: Rigorous kinematics of the Amoeba in 3 dimensions. Coordination requires, example Pianist coordination in
6718	6719



6720	6721


Memory allocation of
6722	6723

Summary: The analysis of uncertainty in dynamic systems. { 6786 6787 6788 6789 6790 6791 } 6845 Aberrations analysis of
Summary: Optical aberrations may be analysed in various ways at the analyst's choice.
6724	6725

Information loss, in conditioned reflex Reflex, conditioned information loss
Summary: Pavlov, p.197 Summary: Events that show mutual exclusion in their behaviours may be called a "variable". Variable nature of
6726	6727

Needle theorem of

6728	6729



6730	6731



6732	6733

Cylindrance definition
Summary: Forms of definition of "cylindrance".
6734	6735



6736	6737



6738	6739



6740	6740+1

Summary: Theorem of stacked cylindrances. (The sliced loaf) 6753 Summary: Dictum: The function of the brain is to find the complicated ways of stopping information from flowing. But see 6832!

6741	6741+01



6742	6743

Summary: Outline of method giving work for the next twenty years. 6767
Homeostat conditioning in Reflex, conditioned on Homeostat
6744	6745



6746	6747



6748	6749


Summary: The Homeostat's conditioning, modernised. 6761
6750	6751

Summary: Conditioning seen as habituation. 6754 Reflex, conditioned as habituation Stimulus nature of
Summary: Analogy still holds strongly between "interaction" set and "interaction" entropies. 6818 Interaction on stacking sets
6752	6753

Summary: Importance of alternation of operators. Alternation as operator Anticipation alternation in Habituation aternation in Habituation conditioned reflex as Reflex, conditioned alterations, forcing Trajectory long, with equilibrium
Forcing a variable theorem of Insistance theorem of Operator forcing Operator insistence Polystable forcing of
6754	6755


Summary: The theorems of Insistence and Forcing. Moulding operation
6756	6757


Summary: Independence of the two fields: all free and one variable fixed.
6758	6759

Summary: Double Insistence.
Homeostat conditioning in Reflex, conditioned on Homeostat
6760	6761



6762	6763


Summary: Conditioning in the homeostat, in terms of set theory. Insisting on two properties simultaneously does not tend to make the one evoke the other.
6764	6765

Summary: Effects of selecting two properties simultaneously. Excitation and organisation
Topology in nerve net
6766	6767

Summary: To get predictions from kinematic topology, use repetitive structured inputs. 6773 Absolute system use in theory
ASP Group (mathematical) in machines with input
6768	6769

Summary: Group therapy in kinematic graphs. 6811 Information axioms of
Summary: Axioms of information theory. Cylindrance and reducibility Explanation cylindrance of Relation Five-fold
6770	6771

Entropy fall in state-determined-system
Constraint increase with time Laws of nature increase with time Pattern (in general) increase with time Planet growth of law on Steady state on planet, and law Time makes law increase
6772	6773

Summary: When a mapping operates (a state-determined system) either: activity goes down or internal pattering increases. 6850, 6835. Examples: 6854 Summary: Under any (one) sequence of mappings either activity decreases or internal patterning increases. 6777
Convergence (of lines of behaviour) random Entropy rate of fall Mapping random, convergence
6774	6775

Summary: The Poisson distribution has entropy (just under) 1 bit less than the even distribution. 6780, 6814 Summary: Entropy of ½ ± y. Entropy H(½+y,½-y)

6776	6777


Summary: One random mapping on an even (rectangular) distribution with many variables goes almost wholly to internal constraint (transmission).
6778	6779



6780	6781


Summary: How a random mapping increases the convergence.
6782	6783


Summary: Under a random mapping, the internal transmission will rise rapidly at first, as the distribution leaves the rectangular form; but it will soon stop increasing, and can be expected to show no further interesting degree of increase. 6802 Entropy Bent's book Second Law (of thermodynamics) Bent's book
6784	6785

Coordination requires, example

6786	6787

Memory in coordination Transmission for coordination
Summary: Another example of coordination by information-flow internally. 6792
6788	6789

Oyster tendency Vulnerability trend to minimum
Summary: The tendency of the oyster, rigorised.
6790	6791

Coordination requires coordination Memory in coordination Pianist coordination in Transmission for coordination

6792	6793

Summary: Another example of the relativity of memory.
Entropy non-exclusive events
6794	6795



6796	6797



6798	6799

Summary: Cox' book is worth long thought. 6801, 6938

6800	6801


Summary: Thinly connected nets converge faster. If... Nothing can be inferred about two being easier than three unless we add an assumption about the zeroness of higher order interactions (independence of higher order probabilities.) Convergence (of lines of behaviour) in net Mapping convergence in net Network convergence in
6802	6803

Diagram of immediate effects (D.I.E.) and convergence Mapping and D.I.E.

6804	6804+01



6804+02	6805

Summary: How the deletion of one arrow from a full DIE (diagram of immediate effects) makes the number of possible mappings fall. 6884
Summary: Deletion of the DIE-arrows does not imply that the convergence must increase necessarily. Entropy sampling distribution of
6806	6807

Machine relations compatible Relation compatible with machine
Summary: If two binary relations are each compatible with a machine, then so is their composition.
6808	6809

Pattern (in general) generates a set Set or Ensemble generated by pattern
Summary: Example of the message generating the set it comes from. ASP how succeed faster Prediction ASP
6810	6811



6812	6813



6814	6815

Summary: Speeding up ASP.
Habituation theories in the literature Reflex, conditioned literature searched
6816	6817

Summary: There is no such thing as the mechanism of the conditioned reflex.
Summary: Intersection cannot raise cylindrance. Cylindrance and intersection
6818	6819

Cylindrance and transformation of space

6820	6821


Summary: Projections of product sets.
6822	6823


Summary: Cylindrical closure of a product set. Proof: As base, so cylinder.
6824	6825

Summary: [formula]
Summary: Closures of projections and vice versa. Example: 6830
6826	6827



6828	6829

1968

Summary: Exchanging variables for cylindrance. Information in regulation, Conant
Summary: Collection of some ways of transforming a space and affecting cylindrance.
6830	6831

Error Conant's theorem Regulation Conant's study
Summary: Conant's theorem that the error controlled feedback regulator conserves information. 6942 Collapsing theorems Conant's Continuity and information Discrimination effect of loss, on H,T,Q Interaction effects of collapsing Transmission after collapsing
6832	6833

Relation and transmission Transmission with constraint
Channel capacity of machine Noise just another input Sub-system finding, by Conant
6834	6835

Summary: The main features of Conant's thesis.
Cylindrance of differential equation
6836	6837


Differential equation cylindrance of
6838	6839



6840	6841


Summary: Cylindrance of constraints provided by different equations.
6842	6843


Stability and internal transmission Transmission internal, and stability
6844	6845


Ergodism complement of equilibrium
6846	6847


Summary: "Stability" and "amount of internal transmission" are not related in any simple way. 7107
6848	6849

Memory must develop
Summary: Any memory-determined system (more than one state back) must show ever-increasing constraint over the successive memory spans. Memory and increase Pattern (in general) exchange with memory
6850	6851


Summary: How to generalise the theorem
6852	6853



6854	6855



6856	6857

Summary: State-determined systems converging and developing structure.
Summary: Effect of union on cylindrance.
6858	6859

Degenerance, in system in set theory Reducibility set theory form of ?F/?x=0

6860	6861



6862	6863

Summary: Set theory's way of saying "∂Φ/∂x = 0".

6864	6865



6866	6867


Cylindrance conservation of Transformation conserving cylindrance
6868	6869



6870	6871

Needle defined

6872	6873



6874	6875



Hover mouse here to display note
6876	6877



Hover mouse here to display note
6877+01	6879


Summary: Transformations that leave all cylindrances unchanged. 6908
Hover mouse here to display note
6879+01	6881

Cylindrance of group Group (mathematical) cylindrance of
Summary: The cylindrance of every group is 3 Summary: Cylindrance of the interaction set. Cylindrance of interaction set Interaction cylindrance of
6882	6883

Answer cylindrance of Question cylindrance of

6884	6885



6886	6887


Summary: The dimensions of question and answer must, between them, provide all the dimensions of the function-space. Complexity conservation of Conservation of Complexity Law of Epistemology [55]: Law of conservation of complexity (in question and answer) 6889.
6888	6889

Independence effect on Q Interaction with an independent variable

6890	6890+01



6890+02	6891

Summary: One independent variable in a interaction term makes it zero. 6976
Summary: Meaning of "true". Set or Ensemble "is true" in set Theorem truth of, in set theory Truth in set theory
6892	6893

Interaction rotating "probability" axes Probability rotating "axes" Rotation of "probability" axes

6894	6895



6896	6897



6898	6899


Summary: "Rotating the axes" in probabilities. 7048
6900	6901



6902	6903

Summary: Cylindrance of a needle-pierced rectangular set equals the needle's base.

6904	6905


Summary: Studying mechanisms that are "dynamic" demands far more information than those that are more of the "static" type. Dynamic system information in, v. static Information dynamic versus static systems
6906	6907

Transformation rectangular to rectangular
Rectangularity conservation of Reducibility conservation of
6908	6909

Summary: A start to the difficult problem of the mapping that conserve rectangularity. Question improper
Summary: As many people, trained on simple systems, will start by asking the wrong questions, the cybernetician must be well educated in recognising wrongness.
6910	6911

Channel forms of Coordination by direct means Coordination through dummy variable Transmission forms of
Summary: The brain's job is to carry, as information for coordination, only what cannot be carried by the environment. The size of our brain reflects only the deficiency of the environment.
6912	6913


Summary: Worked out examples of how to make the enemy work as ship-to-ship transmitter.
6914	6915

Summary: Coordination is possible without nerves.
Coordination and regulation Regulation and coordination Transmission in regulation and coordination
6916	6917



6918	6919


Summary: Transmission, coordination, and regulation, their relations clarified by numerical examples. 6943
6920	6921

Holography and the brain
Summary: Holography does only what the nervous system has done for 100 million years.
6922	6923


Summary: (See previous note) Summary: On consciousness. Conscious mind proves physics insuffient Entropy Conant's H^L Materialism inadequate
6924	6925

Summary: Conant's measures H^L,T^L,Q^L have the freedom from absolute value called for in the "Bio Science" paper. Information Conant's H^L,T^L,Q^L Library retrieval equals theorem-proving Theorem theorem proving equals information retrieval Transmission Conant's T^L
Homomorphism of machines with input Machine homomorphic
6926	6927



6928	6929

Summary: Algebraic form of homomorphism between two machines with input.

6930	6931

Summary: For best regulation, the environment must be a homomorphism of the regulator. But see 6934 Homomorphism proved necessary Regulation homomorphism for maximal
Summary: Definition of homomorphic machines with input. 6936 Machine algebraic theory
6932	6933



6934	6935

Summary: Optimal regulation and homomorphism. Linearly dependent process defined Machine Turing-type Markov process / chain and linearly dependent process Turing machine and machine with input
Transmission in real systems
6936	6937


Summary: Constraints may involve a variable through its components.
6938	6939

Coding of machine to machine Coordination machinery for coordination Information in regulation, Conant Transducer for coordination
Summary: Machinery for coordination.
6940	6941

Summary: The linear-controlled feedback regulator does not lose information. Error Conant's theorem Feedback information in error-control
Coordination minimal information for Transmission minimal, in coordination
6942	6943

Coordination minimal information for Transmission minimal, in coordination
Summary: Coordinate more units with less communication! Coordination minimal information for Transmission minimal, in coordination
6944	6945

Coordination minimal information for Transmission minimal, in coordination
Coding Ashby's method Coordination minimal information for Transducer Ashby's form Transmission minimal, in coordination
6946	6947

Coordination minimal information for Transmission minimal, in coordination
Coordination minimal information for Transmission minimal, in coordination
6948	6949

Summary: (1) The "transmissions" require for coordination can always be achieved - method given. (2) The whole flow of information can be analysed by the methods of book-keeping. Another analysis: 6997 Analysis of information flow Coordination minimal information for Information partitioned Partition of information flows Transmission minimal, in coordination
Summary: High order interactions can readily occur in physical systems. 7006 Coordination minimal information for Interaction in physical systems Transmission minimal, in coordination
6950	6951

Coordination minimal information for Transmission minimal, in coordination
Coordination minimal information for Transmission minimal, in coordination
6952	6953

Coordination minimal information for Transmission minimal, in coordination
Coordination minimal information for Transmission minimal, in coordination
6954	6955

Summary: Fuller example of coordinating several bodies by information. Coordination minimal information for Transmission minimal, in coordination
Coordination minimal information for Randomiser use of Transmission minimal, in coordination
6956	6957

Coordination minimal information for Transmission minimal, in coordination
Coordination minimal information for Transmission minimal, in coordination
6958	6959

Coordination minimal information for Transmission minimal, in coordination
Coordination minimal information for Transmission minimal, in coordination
6960	6961

Analysis of information flow Coordination minimal information for Information partitioned Partition of information flows Transmission minimal, in coordination
Summary: Information flow for control and coordination. Cf. 7165 Coordination minimal information for Transmission minimal, in coordination
6962	6963

Coordination minimal information for Transmission minimal, in coordination
Coordination minimal information for Transmission minimal, in coordination
6964	6965

Summary: The cases of 1 and 3 vehicles, to make certain. Coordination minimal information for Transmission minimal, in coordination
Coordination minimal information for Transmission minimal, in coordination
6966	6967

Channel what is a channel? Coordination minimal information for Transmission minimal, in coordination
Coordination minimal information for Transmission minimal, in coordination
6968	6969

Coordination minimal information for Transmission minimal, in coordination
Coordination minimal information for Ignorance ensuring Noise use of Transmission minimal, in coordination
6970	6971

Coordination minimal information for Transmission minimal, in coordination
Summary: Problem of the Two Trucks:- Coordination minimal information for Transmission minimal, in coordination
6972	6973

ASS (Automatic Self-Strategizer) information flow in Information flow in ASS
Summary: The flow of information, control, and decision when ASS (automatic self-strategizer) produces a legal and winning play. 6989, 6996
Hover mouse here to display note
6974	6975



6975+01	6975+02

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