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Step function
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Ross indexed the following pages under the keyword: "Step function".

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Summary: A break may be treated as a mere incident in the development (in time) of one machine. Also one machine may be considered as split into two parts with a break between if one of the variables is a step-function of the time (see next paragraph). A break is a change of organisation. Changes of organisation have two causes: (1) Due to conditions outside the machine, which are arbitary parameter changes, and are my doing. (2) Due to conditions inside the machine - a break if we ignore the cause.
Step function defined
0995 0996
Step function all linear functions of one
Summary: All step-functions can be expressed as a linear function of one basic step-function, stp (x), "step-x", here defined. (Not true)
1019 1020
Step function collected properties
1029 1030
Summary: In the specification of a system with step-functions present, the latter cannot be specified by differential equation form. It seems that our equations for the system must be in form { dxi/dt = fi(x;y), y'i = ai+bistp{Vi(x;y)} } or { xi = Fi(x0;y;t), y'i = ai+bistp{Vi(x;y)} }. And as these define the future behaviour of the x's, and as in any case they can usually be solved only numerically, we might as well leave them in this state. (Compare 1048) (Better 1086)
Step function in differential equations
1041 1042
Summary: The idea that "orderliness" or "intelligence" spreads like crystallisation is probably covered more correctly by the more precise idea that it is "reaching neutral point and stopping still" which spreads along a chain of dominance.
Break equations for
Dominance chain of
Equilibrium spread of
Organisation spread of
Step function in differential equations
1047 1048

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Summary: The question of "dominance" is still further clarified. I define "immediate", "distant" and "ultimate" dependance. Also "completed matrix of an organisation". "Dominance" (two equivalent definitions). "Parameter" is defined as "dominant and constant". It is proved that if a dominates b, and b dominates c, then a dominates c.
Break continuous approximation
Step function eqivalent continuous form
Substitution (mathematical) change to differantial equation form
1083 1084

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Summary: A property of step-functions.
Step function (not)
1219 1220
Summary: We have a right to expect that normal equilibrium will be commoner than other sorts
Part-function further discussion
Step function in substitution
Substitution (mathematical) part-function in
1259 1260
Part-function defined
Step function defined
Summary: We have got a grip of "part-function", finding that it depends simply on zero values of dxi/dt.
1281 1282

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Summary: Standard symbols: General mathematical, complete systems, and for general repeated use.
Symbols standardised
Step function symbols for
2004 2005

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Summary: A multistable system tends to lose reactivity, which will often be restored by applying some strong, but unrelated, stimulus, at the cost of some forgetting. ? Action of E.C.T. (Corollary 3464). ? Explanation of 'induction'. 3656, 4628, 4524.
Induction (physiological) explanation of
Reynolds' number
Step function laminar and turbulent flow
The Multistable System [41]: Eddies resemble the subsystems of a multistable system. 3438.
3437 3438
Code inverse
Environment as transducer
Transducer inverse
Transformation inverse
Oddments [36]: If the environment is operator E, the brain must become -E-1. 3499.
Summary: If the environment is E the brain must become -E-1 4294
Environment must be non-singular
Essential variables information from
Step function carries information
3499 3500
Learning must use step-functions
Step function necessary in central nervous system
3523 3524

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Summary: Cybernetics and the psychoses. 3673
Step function fixity in paranoia
3653 3654
Habituation and memory
Step function necessary for memory
3842 3843
Step function mixed form
Summary: A hybrid step-full-function. By 4000 it is in (2), a full function.
3900 3901
Step function topology of
Summary: Unsolved problem. 3959, 3962
Information must be destroyed
3938 3939
Summary: States and metric give field.
Summary: Ultrastability does not need step-functions!
Metric step-function and
Step function in set-theory
3964 3965
Summary: 'Step-functions' topologically. 4000, 4005, 4602
Step function topology of
3992 3993
Part-function definition
Step function improved definition
4000 4001
Step function necessary for memory
4124 4125
Step function and information
Threshold and step-functions
4128 4129
Summary: Adaptation of essential variables, (next page) 4163
Epistemology [12]: The observer must be present to disturb the system if ultrastability is to be demonstrated 4160.
Adaptation new formulation
Basin and step-function
Step function ultrastability without step function
The Multistable System [57]: Adaptation can use either step-function or basins, 4161.
4160 4161

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Summary: Lack of variety and step-function are equivalent. 4439, 4440
Constraint and step-function
Protocol constraint in
Step function = lack of variety
Summary: Apparent inertia in adaptation.
Homeostasis transients [no]
Regulation transients in
Transient defined
Natural Selection [77]: Fisher's explanation of apparent inertia in evolution, 4389.
4388 4389
Summary: Control, and part-function, in terms of set theory. 4604
Part-function in set theory
Step function in set-theory
Summary: Incentives in the ultrastable system.
Incentive in society
Variable can be non-metric
Society [57]: Incentives in social organisation 4603.
4602 4603

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Summary: Selfridge's Pandemonium and pattern recognition. 6222
Requisite Variety, Law of in Pandemonium
Oddments [46]: Carry out the program of pages 6184 (foot) and 6185 (top).
Summary: I should re-read my Notes, Vol. 5 or so onwards, reading "lots of step-functions" as the more general "lots of equilibria", and lots of step-surfaces" as "lots of boundaries of confluents".
Confluant generalisation of step-function
Step function what matters is the confluent
Oddments [46]: Carry out the program of pages 6184 (foot) and 6185 (top).
6184 6185

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Mesa phenomenon in percolation
Network probabilistic
Step function and percolation
Mapping random
Step function "mesa" phenomenon
6638 6639

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