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

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

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

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

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

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

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

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

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

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