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

 Previous | Next | Cards | Index | Cloud 1941
 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 forDominance chain ofEquilibrium spread ofOrganisation spread ofStep function in differential equations 1047 1048

 Previous | Next | Cards | Index | Cloud 1942
 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 approximationStep function eqivalent continuous formSubstitution (mathematical) change to differantial equation form 1083 1084

 Previous | Next | Cards | Index | Cloud 1943
 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 discussionStep function in substitutionSubstitution (mathematical) part-function in 1259 1260
 Part-function definedStep function defined Summary: We have got a grip of "part-function", finding that it depends simply on zero values of dxi/dt. 1281 1282

 Previous | Next | Cards | Index | Cloud 1945
 Summary: Standard symbols: General mathematical, complete systems, and for general repeated use. Symbols standardised Step function symbols for 2004 2005

 Previous | Next | Cards | Index | Cloud 1951
 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 inverseEnvironment Transducer inverseTransformation 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 4294Environment must be non-singularEssential variables information fromStep function carries information 3499 3500
 Learning must use step-functionsStep function necessary in central nervous system 3523 3524

 Previous | Next | Cards | Index | Cloud 1952
 Summary: Cybernetics and the psychoses. 3673Step function fixity in paranoia 3653 3654
 Habituation and memoryStep 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, 3962Information must be destroyed 3938 3939
 Summary: States and metric give field. Summary: Ultrastability does not need step-functions!Metric Step function 3964 3965
 Summary: 'Step-functions' topologically. 4000, 4005, 4602Step function topology of 3992 3993
 Part-function definitionStep function improved definition 4000 4001
 Step function necessary for memory 4124 4125
 Step function and information Threshold 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 formulationBasin Step function ultrastability without step function The Multistable System [57]: Adaptation can use either step-function or basins, 4161. 4160 4161

 Previous | Next | Cards | Index | Cloud 1953
 Summary: Lack of variety and step-function are equivalent. 4439, 4440Constraint Protocol constraint inStep function = lack of variety Summary: Apparent inertia in adaptation.Homeostasis transients [no]Regulation transients inTransient 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. 4604Part-function Step function Summary: Incentives in the ultrastable system.Incentive in societyVariable can be non-metric Society [57]: Incentives in social organisation 4603. 4602 4603

 Previous | Next | Cards | Index | Cloud 1960
 Summary: Selfridge's Pandemonium and pattern recognition. 6222Requisite 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-functionStep function what matters is the confluent Oddments [46]: Carry out the program of pages 6184 (foot) and 6185 (top). 6184 6185

 Previous | Next | Cards | Index | Cloud 1967
 Mesa phenomenon in percolationNetwork probabilisticStep function and percolation Mapping randomStep function "mesa" phenomenon 6638 6639
 These images are reproduced courtesy of The Estate of W. Ross Ashby. Copyright 1972, 2008 © The Estate of W. Ross Ashby

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