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Summary of W. Ross Ashby's Journal Entries
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In July 1941 Ross decided to end his journal entries with a summary:

The following table lists and links to all of the summaries, covering volumes 4-25 over the period 1941-1972. Text that is in [square brackets] was either an editorial comment, difficult to read, impossible to type, or a case where Ross used square brackets himself! Because the summaries appear at the end of sections, when you use the link to jump to the page where the summary is, you generally have to flip back a few pages to find the start of the section. The dates listed are often actually associated with a following journal entry on the same page as the summary.

     Date      Page Summary
4-May-39 0586 Nirvanophilia is identical with stable equilibrium.
20-Jun-39 0588 A great idea... organisation must spread from the environment inwards.
4-Jan-41 0858 Had my severe illness here. Was it febrile reaction to enormous cortical readjustment? I don't know. But it felt as if I had "swallowed a rainbow". And the next page contains the essential discovery.
4-Jan-41 0859 Suppose the cortex is a 'representation' of the environment, i.e. corresponding to events in the periphery (stimuli, reactions) there are events in the cortex. Nothing new in this idea. But suppose that the cortex is more 'sensitive', so that if the periphery is being driven out of its range of stability the corresponding variable in the cortex will break first, i.e. get outside its range of stability, and thus switch to another portion of the field (817), and change partially to another organisation.
  0960 (1) It is impossible to say how much one variable depends on another. (2) The meaning of "dx'i/dxk" is given. (3) The Question "Does xi depend on xk" is meaningless. (4) New form of matrix test for dominance is given. (5) Definitions given of (a) xi-t curve depends on x0k, (b) xi-t curve is independant of x0k, (c) xi dominates xk, (d) "parameter".
  0960 I have decided in future to end the Sections with a Summary. It may perhaps force rather more tidiness into the ideas and will be useful for reference.
22-Jul-41 0963 Three methods are given for exploring a system of equations like 957 (top) in order to find parameters, and dominances using basically the method of 958 (top).
22-Jul-41 0966 If a field should alter its organisation, and particularly its dominances and independences, reversibly when a variable exceeds a given value, we may either look on it in this way, or (preferably) we may set up new and more comprehensive field equations treating it as one constant organisation. But see 1038 for a much improved statement.
22-Jul-41 0967 After a lot of breaking and final reaching of a neutral point, if we test it by displacing it a little and ask 'will it be stable' the answer is that if it is stable O.K., and if it is no longer stable, we've broken it. So who cares?
24-Jul-41 0969 The use of diagrams like those of 940, 946, 967 are permissible only if they represent (a) immediate dependencies as given by the substitutions and subject to its restrictions, or (b) as completed diagrams (961) to represent final dominances etc, but not as both haphazardly. Completed diagrams may be used to typify an organisation (contrary to 928). Also an addendum to the method of 962.
24-Jul-41 0970 Our substitutions deal quite adequately with the idea of the free energy available to the brain and body - by ignoring it.
24-Jul-41 0971 A higher level must usually change more slowly than a lower level, in order that the lower level may be given time to catch its neutral point.
25-Jul-41 0972 If, from a given system, we remove knowledge of a variable, we must introduce probability to replace it. (But see next paragraph)
25-Jul-41 0974 If initial conditions are unknown we must replace them with probability.
25-Jul-41 0976 The idea is suggested that the old memories, as organisations, may be present implicitly rather than explicitly.
27-Jul-41 0978 The lower animals, at any rate, with their environment may be much simplified for our purpose by noting that one animal may be considered to be split into several, or many, parts, each of which has its own environment. So animal and environment = several machines, not one.
27-Jul-41 0982 We have discussed the situation: p's dominate x's, and x's dominate y's. Under these conditions we can get a stability of organisation. Also we can get y-point in y-space moving twice through the same point in different directions. If the x's react rapidly they will tend to disappear functionally. A succession of such gives transmission through a series of organisations. If one level has only a few, or a single, variable this introduces an essential simplicity into all subsequent levels. A large organisation may be 'simple' because it depends on only one or a few parameters.
  0983 Details are given showing that it is possible to explore, experimentally, a given field or organisation. To do this parameters are necessary, and it may be necessary to introduce new ones not mentioned before.
  0985 An organisation with n variables and m parameters has two separate complexities. Subject to conditions, m describes the number of coordinates in the space in which the neutral point moves, when m=n we have a 'transative' state.
  0987 A (better) restatement of the theorem of 680.
  0989 Mathematical definition and test is given for 'neutral point' and 'neutral cycle' when the substitution is given as a differentil equation. (Actual example next paragraph).
  0990 An example of neutral cycle in a differential equation is given.
13-Aug-41 0995 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.
  1004 "Step-function" is defined. An analytic formula given for one. If a function in a substitution is a step function of the variables, the corresponding variable in the solved equations is a step-function of the time. The effect in a field of a step-function is discussed, The essential conditions for a break are a cloud of dots, each of which has a number associated with it saying "change one of the step-functions to this new value" and not a surface as suggested on 898.
22-Aug-41 1009 (1) Brain activity will sometimes conduct an animal, with great ingenuity, to its death. (2) Survival is a by-product of brain activity.
22-Aug-41 1009 It is agreed, with 928, that a reversible system is of no interest from our point of view and does not exist in nature anyway.
22-Aug-41 1010 We show how to calculate the shift of a neutral point for a small change of parameter when the substitution is given as differential equations, (if finite substitution 927) (if several parameters, 1023)
  1016 The general principle of "pressures", that difference means movement, suggests a method of combining sustitutions, or stimuli, to form a "product". If the number of parameters is greater than the number of variables, this product exists always, and powers are associative. The inverse in not unique. But the whole suggests a way in which groups might get in.
  1018 In general, after a break has occurred due to the x- point touching a break point, not only the field changes but also the break points.
28-Aug-41 1020 All step-functions can be expressed as a linear function of one basic step-function, stp (x), "step-x", here defined. (Not true)
  1022 The behaviour of break-surfaces.
28-Aug-41 1023 Another example of the conclusion of 1006.
28-Aug-41 1024 Equations are given for determining the shift in a neutral point if several parameters are altered a little. The change in each coordinate is a linear function of the changes of parameters.
29-Aug-41 1026 A carefully calculated field is given, with four neutral points. Useful for experimenting. (Others are on 817, 828, 839, 885, 941, 990, 1021)
  1028 An example is given, in all detail, of a substitution with two step-functions. It confirms the theorum of 1021. The existence of "false neutral points" is noted.
3-Sep-41 1038 A much better statement is given of the idea of varying patterns of dominance etc in a system.
3-Sep-41 1038 "Break" does not involve "irreversibility".
  1041 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)
  1043 Later we shall have to show how we can break down the minute rigidity of our dynamic systems, where the minutest change has to be put in and may lead to something profoundly different. Suggested way of doing it.
15-Sep-41 1044 The V-surface of a step-function cannot have a free edge.
15-Sep-41 1045 Substitutions may, perhaps, define an infinite continuous group.
  1046 "Simplicity", "wholeness", etc are perhaps clarified by the discussion above.
26-Sep-41 1047 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.
29-Sep-41 1051 Differential equations with step-functions are fundamentally unsolvable.
  1053 The concept of "breaks" by itself is not sufficient to cause any emergence of adaptation or intelligence. Brain, i.e. a machine of particular type, is necessary. (See 1063)
29-Sep-41 1055 Examples are given in ordinary machinery of "change of organisation" and "break". Both are rare.
2-Oct-41 1056 Our definition of "dominance" of 960 is correct. See 1077 for a fuller survey.
4-Oct-41 1057 The idea of a system, like the brain, altering its own organisation necessarily implies the presence of step-functions and breaks.
24-Oct-41 1059 One stage in our long journey is finished and solved: the 'exact' case, i.e. an organisation where we are given full and exact information about every little detail.
18-Nov-41 1061 It is shown conclusively that "isomorphism" does not necessarily imply "group".
19-Nov-41 1062 Some examples are given showing how a statement may be quite true about the whole and yet quite untrue of all the parts.
2-Dec-41 1064 Although a general system has no tendency to survival by adaptive behaviour, yet a "brain" has. Details are given. (see 1068)
  1065 A definition of 'organisation' is given which covers both dynamic, machine, organisations, and static, pattern ones.
1-Dec-41 1066 An "organisation", by the definition of the previous page, need not be a group.
  1067 Formulae are given in the special case where one variable always moves towards some function of the other variables.
8-Mar-42 1074 Actual equations are constructed giving the theoretical views of the nervous system in mathematical form. (See 1092)
8-Mar-42 1077 A discussion is given of the meaning of the "change of organisation" (if any) which occurs when a system settles at a new neutral point without change of the field. i.e. a variable, without change of field, going outside the "range of stability" of one neutral point. A complete clarification is given, together with its relation to my previous ideas of "breaks".
22-Mar-42 1083 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.
  1086 A method is given for changing the abrupt h'=... method of defining a break to an equivalent dh/dt method. This puts the whole system into ordinary differential equation form. The equations are in "normal" form.
  1090 An example of a break is given in substitution form, like 991.
  1092 "Equilibrium" means not moving out of a given region. (But see 1143)
25-Apr-42 1095 "Break-surfaces" are examined and some properties noted.
  1098 A statement is given of the theorem that a multilayer of break surfaces "encourages" the representative point to stay in that region.
15-May-42 1099 It might be suggested that with a million neurons the chance of getting them all properly adjusted is negligibly small. The answer is that there is usually no such thing as the right solution. We count as suitable any organisation whatsoever so long as it gets the equilibrium where we want it.
18-May-42 1100 After studying the fixed points in a dynamic world (i.e. neutral points) I presume the next step would be to take a lot of neutral points and set them moving.
4-Jun-42 1102 A layer of break surfaces keeps within bounds not only the variables concerned, but any other variable which is a direct function of them.
7-Jun-42 1106 A variable may add further break-surfaces for its further protection by deputising, i.e. by controlling another variable so that the latter breaks if the first goes too far. And this leads to the important observation that it does not matter where or why a break occurs as long as it occurs. From my point of view, all that is wanted is some change of organisation and it doesn't matter how or why it is done. Any change is as good as any other change.
  1109 We discover how to join and unjoin two machines. Also we notice that if a machine is at a neutral point it is possible, under restricted conditions, to separate and rejoin without disturbing the state of equilibrium.
8-Jun-42 1111 A red letter day. A problem in the application to the brain is solved.
  1114 If a machine with variables x has break-variables h with V-surfaces which surround an x region, and if we join this to any machine y, then the presence of the h's and the V's will tend to keep the x's within the V-region. And when the machine has settled to equilibrium, disconnecting the machine y and putting on another one, z (or changing parameters R) merely starts the x-machine changing its organisation again until it has found a new equilibrium, with the x's still inside the V-region. O.K., O.K!
  1118 A list of examples of equilibrium in biology.
9-Jul-42 1122 If two environments keep occurring, a system will break till it finds an organisation making it stable to both.
9-Jul-42 1123 "Reaction" is divided into "response" and "variation".
9-Jul-42 1123 The intrinsic form of a substitution might prove interesting.
16-Jul-42 1127 It is concluded that if a whole is to be (almost) separated into two parts, the variables concerned at the "join" must be (almost) constant. Delay is not an important factor.
16-Jul-42 1127 After all these years I conclude that "vectors" are not what I want.
  1132 Some musings on bicycle riding.
6-Sep-42 1134 Preliminary discussion of a machine falling, temporarily, into parts.
2-Oct-42 1135 We want to get adaptation on a scale, so that we can show that systems, under certain conditions, will move from lesser to greater adaptation.
14-Oct-42 1136 A statement of my present emotional position.
  1140 If an organisation stops at a field which is only partly stable this does not really matter; for if the danger of breaking is large, it will soon break and try new fields, while if the danger is small then there is little to worry about.
31-Oct-42 1141 n breaks provide 2n organisations. To give 10 different organisations every second throughout a man's life we need only 35 breaks!
  1142 Does the acquisition of a new reaction upset all the older one's as demanded by my theory? The answer seems to be "yes" but it may in some cases be of zero extent.
31-Oct-42 1143 Each single environment is a (hyper) complex number.
  1148 The definition of "equilibrium" is taken up from 1092, and made much more precise. It is concluded that it belongs to a path A special type of common occurrence is defined and given the name of "normal" equilibrium.
  1153 (1) Changing coordinates in two machines is apt to make one of them. (2) Changing to normal coordinates splits a machine into independent parts. (Cf. 3868)
19-Nov-42 1155 A review of Jennings' book.
20-Nov-42 1156 The "constants" i.e. variables whose changes make observed behaviour may themselves be activities composed of other variables. And these "constants" whose changes make.... This needs specifying from the organisational point of view. (See 1193)
22-Nov-42 1157 A refinement of the definition of "organisation".
22-Nov-42 1157 "Memory" equals change of organisation.
22-Nov-42 1158 "Adapted" behaviour equals the behaviour of any system around a point of normal equilibrium. (1148)
24-Nov-42 1159 All my theory explains the "trial and error" method in terms of non-living matter. All that, but nothing more.
  1160 Courant's definition of equilibrium. On closer reading, as R and ρ may be small to any degree, it appears that Courant's definition does not allow finite cycles like that of 1144.
  1174 The sheets give the mathematical theory up to about Oct '42; but, of cource, not at all completely.
28-Nov-42 1176 A clarification of the concept of a "break-surface".
28-Nov-42 1176 The conditioned reflex is not clear yet.
28-Nov-42 1177 A field can be explored easily, but break-surfaces are destroyed by their discovery. This may involve curious philosophical properties.
  1180 Dynamic systems are, in general, fundamentally irreversible.
1-Feb-43 1181 The concept of "break" does not need that of "irreversibility".
8-Feb-43 1182 Theory has been submitted for publication for the third time.
  1187 The concept of "a reflex" is translated into my organisational terminology.
20-Feb-43 1189 A dominating system can control the position of break-surfaces of a second system.
  1198 It has been shown that a representative point, staying within a region bounded by a layer of break-surfaces, can act as a "variable" in a substitution composed of n such points provided the representative points move with a velocity of a higher "order" than that of the substitution. "Order" is defined and explained. The ordinary substitution can be considered as the limit of this type.
  1200 A discussion of a simple reflex along my lines.
25-Feb-43 1201 "Adaptation" is more properly divided into: the adapted state after this has been reached, and the process of finding this state.
8-Apr-43 1209 We study how adaptation can increase qualitatively, and are led to define and examine "part-function" and "part-surface". (Continued 1219)
  1217 The number of possible ways of organising n variables is at last answered. It is of the order of |n
  1218 An interesting elementary substitution is described. It demonstrates paths going to infinity and neutral cycles. (Better 3776)
15-Apr-43 1219 A property of step-functions.
18-Apr-43 1226 A method is described by which a machine can show increasing adaptation, by one part after another getting into equilibrium. A clear explanation of "threshold" and "summation" in the Central Nervous System follows. It is concluded that between a sense organ and the adaptive part a "distributor" must occur. 5345
  1233 An attempt is made to classify and exhaust the causes of non-adaptation; but it seems that non- adaptation must be taken as fundamental, adaptation occuring only if there is some special reason for it.
  1244 Arrangement and collected materials for my book.
  1247 Discusses the application of the concept of the "invariant" of a substitution.
  1254 Notes on adaptation to "internal" environment; and an example of how a set of adaptations can collapse.
  1257 Huxley's book reviewed, and proof that a holistic set must be altered by infinitesimal steps.
4-Jun-43 1259 We have a right to expect that normal equilibrium will be commoner than other sorts
9-Jun-43 1265 Part-functions and step-functions should be defined as special types of path in a field.
  1267 Whittaker defines "equilibrium" and also a "neutral cycle".
16-Jun-43 1282 We have got a grip of "part-function", finding that it depends simply on zero values of dxi/dt.
30-Jun-43 1283 Some points from a book.
  1292 A description is given of relations between differential equations and solutions when certain variables are not present in some of the equations. Two matrices |f| and |F| are defined. Particularly it is shown that the "independence" test of p applies to either.
  1295 A view of Levy's book. He specifically notices that breaks are an essential feature of matter and not a trivial one.
20-Jul-43 1297 The concept of "dominance" involves an inverted way of looking at things, and is better replaced by the same variables being "independent of the others" in a system.
21-Jul-43 1298 We may not write arbitrary functions in the solutions xi=Fi(xo;t), for the f's are to be free from t. This means that there are restrictions on the F's, and it is shown that suitable F's will satisfy certain equations. (Cf. 1315)(and 1341)
  1299 Definition of the First and Second Jacobian matrices of a dynamic system, with a note that "completion" applies to the Second and not the First.
23-Jul-43 1304 A review of Carrel's "Man, the unknown".
24-Jul-43 1306 The concept of "parameter" should be replaced, (except in simple cases), by the idea of a variable having some special properties, These are given. The fundamental is [x-k=0]. (But see 1324)
  1316 Exploring the interaction of a given set of variables means finding the F's in xi=Fi(xo;t). (Assembling a machine gives us the [xoi=fi(x)] equations). By the independence test on the Second Jacobian Matrix applied in one stroke we eliminate what is not wanted. That its behaviour is reproducible is equivalent to the requirement that t is explicitly absent from the f's. This restricts possible F's. An equation is given which they must satisfy. It is proved that under these conditions the F's are always completed.
27-Jul-43 1318 "Step-function" in practice is not usually so restricted as on 1279.
  1320 At last an exact meaning can be given to the idea of whether one variable does, or does not, affect another. It can only be tested when the complete system containing the affected one is obtained. A set, independant of the others, contained in a complete set, must itself be complete.
  1321 Nil.
  1323 A definition of a complete system, and some elementary properties.
1-Aug-43 1324 Parameters which are regarded as constant "variables" thereby lose some freedom, perhaps too much sometimes.
  1326 A single permanent zero in [f] introduces a slight, permanent restriction in the field.
1-Aug-43 1327 The non-zero elements in [f] correspond, in a sense, to dendrons.
  1334 The chance that n variables should all independently be in equilibrium is discussed and this gives an estimate of the time required to reach equilibrium. The fastest method of getting equilibrium will be the one found in practice, for the system selects the fastest. And this suggests that the brain will automatically manifest an "analysing" tendency.
  1340 The environment (probably) consists of many small complete systems contained in larger complete systems, etc slow time changes upsetting all. Two more ways of graduating adaptation are noted. The dynamic form of "whole" and "part" is clarified.
  1344 The solutions of a complete system form a finite continuous group of order one.
  1346 Notes from Bieberbach on finite continuous groups.
  1350 Variables changing at different orders of velocity hardly interact. A study of interaction must therefore assume the variables are of the same order of velocity (Now turn to 1474!)
7-Aug-43 1353 The relations of "complete sets which contain complete sets which ..." can be shown accurately by an isomorphic diagram.
  1357 Assuming each variable has a fixed chance of getting equilibrium, it is shown that a system of n1, variables dominating n2 will in 1-pn2 cases get equilibrium by getting it in the n1 and then in the n2, while in pn2 cases it will get the whole simultaneously, the latter proportion being vanishingly small. Experiment will therefore demonstrate the equilibrium appearing in stages.
9-Aug-43 1359 An unsolved problem in organisation. (Now see 1420)
11-Aug-43 1367 If a complete system has n variables and r parameters [x-i=fi(x;λ)], then the λ's can, from given starting point, control the movement of the x-point within an r-dimensional space which moves with time through the n-space, but the λ's cannot control the movement of the r-space. (Now see 1376)
11-Aug-43 1370 A Permanent zero in the 1st. Jacobian Matrix, i.e. incomplete joining, means that a sudden change of the variables does not immediately alter the path as projected on to the other variable's axis. (Continued 1372)
  1371 The 1st Jacobian Matrix (1) cannot be filled in arbitrarily (2) does not accurately specify a dynamic system.
  1373 If each break (a) depends only on one variable, (b) affects, or appears in only that variables' f, then each variable will become stabilised almost independently of the others. Under these conditions the time taken by n is of the order of log n.
13-Aug-43 1376 As first approximation, the "largest of a sample of n" tends to increase as log n.
  1377 If r parameters controlling a complete system are arbitrarily under our control, then we can, by controlling the parameters, force an arbitrarily selected set of r variables to behave as we chose. The detailed control can, so to speak, be transmitted through the many other variables without any loss of control!
16-Aug-43 1378 Note from Eddington.
  1389 The problem of several complete systems joining into an interacting system without losing (entirely) their completeness is discussed and partially solved.
19-Aug-43 1392 The solutions are given of the problems of: Given the f's (or the F's), to find the F's (or the f's).
20-Aug-43 1396 A proof, with modern technique, of the old problem, showing that two stable machines can be joined to form an unstable one.
21-Aug-43 1400 A test to see whether a neutral point is stable or unstable. (Test for neutral cycle, 1494)
  1407 The old case of several variables affecting one another chain-fashion is re-examined. It is shown that if an "increase" leads back to a "decrease" the system will be stable, though probably with oscillations (of decreasing amplitude). If it leads to an "increase" the system may still be stable.
23-Aug-43 1409 Contrary to p.____ [0599], the concept of equilibrium does not depend on a circuit.
23-Aug-43 1410 Definition of an "almost" complete system.
  1414 If the study of a complete system of n variables is restricted to some of the variables only, the others being hidden, the behaviour of the visible variables can be predicted correctly when we know any n coordinate-time combinations. A machine may appear to show imagination. (Restated 1424)
  1416 The (real) environment may be absolutely anything. But we can devise theoretical systems to which a given brain could and would adapt, and we then examine the real world to see if such sorts exist.
31-Aug-43 1420 The idea of a "constraint" added to a dynamic system may have meaning with Newtonian dynamics but it has no general meaning. And the idea of thereby losing a "degree of freedom" is also of restricted applicability.
4-Sep-43 1424 It is shown that the "hour-glass" type of organisation will differ little from others in its properties of adaptation.
  1425 If, in a system of n variables complete or not, we are given n coordinate-time pairs, the particular path is fixed.
  1427 Notes from Eisenhart. (Ref. 476)
11-Sep-43 1431 Six definitions of a "complete" system are given and are all proved equivalent.
14-Sep-43 1433 Some references to amoeboid activity in nerve cells.
  1435 The brain is an equilibrium-trap. And if the equilibrium can only occur on certain conditions then the brain will trap those conditions too! 1487.
29-Sep-43 1439 Stabilising some variables almost certainly stabilises those other variables connected with them.
30-Sep-43 1441 More notes on the "hour-glass" case.
1-Oct-43 1442 A definition of transient and permanent equilibria.
  1443 The projections of a path, and the solutions xi=Fi(xo,t) are two forms of the same thing.
4-Oct-43 1447 Outline for a book.
1) Introduction
2) Theory of dynamic systems
3) Equilibrium
4) Change of organisation
5) Breaks (up to the theorem on layers)
6) Further developments.
5-Oct-43 1462 Complete systems containing complete systems etc, is the same as a chain of dominances.
  1464 Of the methods available for solving my differential equations, some apply generally, and some only to complete systems.
6-Oct-43 1466 It is believed that the theorems relating zeros in [f] and [F] to each other is still valid if the system is not complete.
6-Oct-43 1467 It is proved that, if they are complete systems, then if A dominates B and B C, then A dominates C.
  1468 It seems best to define whether one variable "affects" another as whether Fi contains (or not) xoi
8-Oct-43 1470 A simple practical example of the "hour-glass" type of organisation.
  1473 An actual numerical example showing that a path can be fixed by using later values of a few observable variables.
  1475 Orders of velocity make complete systems.
15-Oct-43 1476 The shift is calculated, of a neutral point as a result of small changes in parameters.
15-Oct-43 1477 How to use my theoretical discovery for practical purposes. "Organisers, Ltd". "You want the best organisation, we have them."
15-Oct-43 1480 The idea of "adaptation" is one which we bring to the data: it does not exist in the facts themselves. Any attempt to treat it as a reality leads to self-contradiction. It is analogous to "magnifying". 4930
19-Oct-43 1494 A superb theorem, much more general than that of 1113, and much more precise. It includes the other theorem as a sub-case.
20-Oct-43 1497 A test, and example, for stability or instability of a neutral cycle.
21-Oct-43 1498 Reasons for changing the form of the index.
23-Oct-43 1503 In a complete system variables may be changed for derivatives and the system is still complete. In this way reference to particular variables may be avoided without spoiling the completeness.
23-Oct-43 1503 "Step-function" is an official word in general use.
  1506 The theorem of 1493 is unaltered by any change of variables. The essential equilibrium facts of a field are unaltered by change of variables. (Further tested 1512)
  1511 The equations of a dynamic system with layers of break surfaces given in completely continuous form, suitable for general analytic studies.
26-Oct-43 1512 1506 is confirmed, that a change of variables does not generally affect the applicability of the theorem of 1493.
27-Oct-43 1515 Variables cannot be exchanged for derivatives when the conditions of 1493 are to hold.
28-Oct-43 1516 The substitution of derivatives for variables is apt to lead to troubles due to multiple values, and must be used with caution.
  1519 In the hour-glass type of organisation substitute variables will be set up, as required by the theorem of 1493. They are found to be just a different way of looking at the variables!
  1522 The theorem of 1493 is easily extendible to the case where there are a number of parameters altering arbitrarily from time to time. In this case we get a set of organisations as limit.
6-Nov-43 1524 James stating that a machine cannot vary its behaviour.
8-Nov-43 1525 Levy supports my view that knowledge of a real dynamic system is purely empirical.
8-Nov-43 1525 Notes from Bradley's book.
9-Nov-43 1526 The problem of the "distributor" solved, in essence.
  1529 A few notes on the important question of exposition.
3-Dec-43 1531 The presence of "velocity" or "inertia" effects in an artificial nervous system merely means that the "environment" is rather more complicated than it would appear to be.
  1532 Some details about getting a system of my type started.
11-Dec-43 1535 Fisher's book.
22-Dec-43 1538 A first attempt at a theory of selective operators.
1-Jan-44 1540 An "instant" system is defined. A non-instant system must be part of an instant and complete system, and can be made instant by adding differences, or derivatives as extra variables. (Better proof, 2031)
  1541 Two notes on exposition.
11-Jan-44 1548 The elementary ideas on systems and their behaviour is thoroughly tidied up and clarified.
  1553 The properties of non-complete systems are described.
  1554 An attempt to find the effect on the field of permanent zeros in the first Jacobian matrix.
11-Jan-44 1555 Two problems for the future are noted.
12-Jan-44 1561 A very precise statement of my basic theorems. (but see 1564)
  1562 A proof that finite continuous groups have differential equations not containing t explicitly.
22-Jan-44 1564 The word "absolute" seems better than the "complete" already used.
  1570 A very economical proof of the main elementary theorems by defining and using "commutive" systems. "Restricted" equilibrium is defined.
  1571 A useful approximation for finding p and P.
  1572 The smallest value of p ever likely to be used is estimated. Also a common value.
2-Feb-44 1573 Theorem B is rejected.
2-Feb-44 1573 A field.
2-Feb-44 1574 The study of the graduation of adaptation seems to be essentially empirical and unsystematic.
  1576 It is shown that a "spontaneous change of organisation" implies the presence of a step-function of the time. (The change defines the step-function).
18-Feb-44 1578 Absoluteness is not altered by separating or joining machines.
  1581 In an absolute system, knowing the behaviour of the parts (and the method of assembly) specifies the behaviour of the whole; and vice versa.
19-Feb-44 1582 Observation provides xi=Fi(xo;t), the derivative form is - er - derived; method given.
27-Feb-44 1585 An attempt at the analytical expression of a part-function.
27-Feb-44 1586 The least possible join of two absolute systems is that they should share a common step-function.
27-Feb-44 1587 Convenient equations in the technique of joining and separating parts and wholes.
27-Feb-44 1588 A symbolic way of writing step-functions.
27-Feb-44 1588 The whole question of the graduation of adaptaation (or equilibrium) must be realised to be really an attempt to increase the probability of the whole being adapted. It is only part of the general problem of altering the probabilities.
28-Feb-44 1589 An actual example of "distribution".
29-Feb-44 1591 The mere presence of part-functions in a system allows variables to be active in some reactions and inert in others.
  1592 In a commutive system with many part functions, distribution will occur, because it is more probable.
5-Mar-44 1593 "Equilibrium" is an invariant. It belongs only to an absolute system.
8-Mar-44 1594 If reactions are to adapt independently, the breaks must be restricted to the regions of part-functions.
18-Mar-44 1596 A better proof that chance of equilibrium, other things being equal, falls off as e-kn. This means nothing, for p means nothing definite.
  1598 Definitions are given of "part-functions", "activated" and "activation-region". It is shown that activations are localised, that different paths may cause different variables to become activated, and that a part-function can cause a break only when activated.
8-Apr-44 1602 Two or more [variables] which are always stable apart may be unstable when joined. (Inverse, 1658) (Note 1665)
  1613 The principle of Le Chatelier is examined in detail and given exact mathematical form. It appears that it is an emperical peculiarity of the equi;ibria of physical chemistry and is in no way general to all equilibria.
  1617 It is sometimes possible to fix the value of some variables in a machine. Details are given of the process of adding another machine to act as "stabiliser" to a variable.
  1620 In a commutive system, if we keep returning xρ to a we shall eventually get, and keep, a field which stabilises xρ at, or near, a.
19-Apr-44 1622 The conditioned reflex is an elementary property of a commutive system when a variable is repeatedly forced to take a given value. (Much improved 1981)
19-Apr-44 1625 The probability that a system should have an equilibrium cannot be deduced from the probabilities of the parts being in equilibrium. The case where they combine as a product is likely to be common and important but it must be introduced as a specific postulate.
19-Apr-44 1626 The layering of the cerebral cortex may be explained as required for wide distribution.
24-Apr-44 1627 A note on exposition.
28-Apr-44 1628 "Disturbance" and "ingressive" are defined.
30-Apr-44 1629 Collected notes and references on "invariance".
  1635 A proof is given that: If a random displacement y1 , y2 , ... , yn with probability distribution df=Φ(y1 , ... , yn) dy1 ... dyn is added to a point at X1, ..., Xn then the probability that it (i.e. X1+y1 , ... , Xn+yn) should still be within a space V is maximal if, and only if, X1 ... Xn satisfy the equation (8). (See next note).
2-May-44 1637 If a field (provided by a commutive system with break-surfaces) has maximal probability of not breaking after random disturbance, then it is of normal equilibrium and the paths must meet at the point X1 ... Xn (defined in the previous note).
5-May-44 1638 Equilibrial features are not the only ones in a field which persist after change of coordinates. Thus, the meeting of two paths is also invariant.
5-May-44 1639 Disturbances must usually be applied to a system at a slower order of time than its reactions.
10-May-44 1646 Adding regular random disturbances to a commutive system with layers of break-surfaces increases the probability, at any time, of finding the system with a field of normal equilibrium. [deleted] Correct, but rewritten.
  1657 K1 and K2 are defined, also "terminal", "simple" and "displacement". If the fields provided by random h values have K1 and K2 values distributed as Φ(K1 , K2), then the terminal fields have values distributed as A.K1Φ(K1 , K2). If the terminal fields are displaced from time to time the terminal fields develope distribution B.(K1/(1-K2)).Φ(K1 , K2). (Graph 1698) (Corollary 1705)
19-May-44 1659 Any number of unstable systems joined must be unstable.
31-May-44 1664 A dynamic organisation has, as a whole, the extra properties (over those possessed by the parts): that the Neutral Points can be restricted to sets; that a field may be stable though some of the units unstable; that the field has a neutral cycle. (There may be more).
31-May-44 1665 Two machines may form a whole which is stable if they were joined one way, and unstable if joined the other.
  1666 Two stable machines may be unstable when joined if either contains more than one variable.
9-Jun-44 1668 A review of Craik's book. And a statement of the present position, re publishing, of my theory.
  1671 An attempt to handle the similarity of machine to machine. "Equiformal" defined.
10-Jun-44 1673 A proof is given that the commutive process must increase the mean of K1.
15-Jun-44 1675 If K1 and K2 are uncorrelated, then disturbances give fields with K2 always increased.
15-Jun-44 1679 Proof that a non-activated variable, in contact only with other non-activated variables, cannot become activated.
  1684 A "distributive" system is defined. Three theorems are given, including one showing rigorously how adaptation can proceed by parts in such a system.
  1689 I am unable at present to get a satisfactorily rigorous test for independence when there are part-functions present. [But see 1748]
22-Jun-44 1692 A test of independence both necessary and sufficient, is deduced from xi=etXxoi. Although the rigour of application to arbitary functions is doubtful, it leads to the same results as the previous test.
  1695 A proof that non-activated variables cannot transmit effects. (Much better proof 1921)
24-Jun-44 1698 Much human behaviour is reaction to an internal environment: anxiety. (Cf. 1877)
25-Jun-44 1700 A graph of the multiplying factor K1/(1-K2). (Another aspect, 1705)
  1704 With linear equations, control of the coefficient of one variable is enough to enable us to put the roots and the neutral point where we like.
  1707 The distribution of K2 after disturbance is given in terms of the original distribution and the means of K1 at each K2-value.
19-Jul-44 1708 An example of two reactions, each quite adaptive, which are in unstable equilibrium if joined.
21-Jul-44 1710 Some details contributed by Carroll.
22-Jul-44 1715 For K2 among the terminal fields to be 1, i.e. for the fields to be immune to disturbance, it is necessary and sufficient either that K2=1 in the original fields or, if K2≠1, that Φ(K1 K2), for some value of K1 other than K1=0 should have, at K2=1, a pole of order ≥1. The most interesting corollary is that if any fields in Φ have K2=1, then these monopolise the terminal fields.
  1717 It must be carefully remembered that the physicist always tries to use knowledge from every source about a given dynamic system while I am rigorously confined to studying systems by observing only their behaviour.
30-Jul-44 1720 The possibility of giving some of the variables a fixed value and letting others vary is functionally identical with taking the machine to pieces.
  1721 Some other people's quotations on equilibrium.
  1723 Extracts from a book.
2-Aug-44 1725 In an absolute system (variables x1 ... xK ... xn) of fixed organisation [x~i = fi(x)], that a subsystem (variables x1 ... xK) should itself be absolute (the other variables xK+1 ... xn being given all random starting points in the testing) it is necessary and sufficient that f1 ... fK should not change for any or all changes of xK+1 ... xn.
3-Aug-44 1729 A proof that step-functions are necessary, as well as sufficient, to get changes of organisation of a subsystem in an absolute system.
11-Aug-44 1731 Pavlov says that adaptation and survival equals equilibrium.
14-Aug-44 1734 James describes the facts of adaptation = equilibrium without calling it such.
19-Aug-44 1736 Quotations demonstrating field experiments clearly as examples of my type of system.
  1739 Known examples in physics of my type of absolute system, one of which shows dominance.
5-Sep-44 1740 Two notes from a book.
19-Sep-44 1744 A note on exposition.
20-Sep-44 1745 Another example of selection leading automatically to adaptation.
  1746 An outline of quantum theory.
28-Oct-44 1801 Two points on applications to society.
1-Nov-44 1803 Note on exposition.
2-Nov-44 1804 The ordinary pendulum is not stable if we are referring to both position and velocity
3-Nov-44 1805 Useful quotations.
  1806 There is no limit to the number of variables which have to be fixed to get an isolated or absolute system.
5-Nov-44 1810 Notes on effect of fixing an economic variable. This may make a stable system unstable. Spur of joined machines. (see 1910) and (1995 bottom)
11-Nov-44 1811 A detailed non-linear use.
18-Nov-44 1813 Effect on a field of fixing a variable.
  1822 (Under conditions) two linear systems are equiformal if and only if they have the same characteristic equation.
  1826 Examples of a system tending to restore previous constants.
9-Dec-44 1827 Another actual absolute system.
9-Dec-44 1829 Equation of the plane which contains n consecutive points.
18-Dec-44 1836 Review of Spencer, with useful quotations.
  1839 Independence over two regions.
22-Dec-44 1840 Several parts, all unstable, can form a stable whole. (Simple example 2044)
7-Jan-45 1844 Routh's test for stability. (Ready for use, 1862)
12-Jan-45 1846 The probability of stability is in general unsolvable, but certain special cases might be attacked again later. (Continued 1868)
19-Jan-45 1848 Some facts which any organisation must stabilise.
  1849 Stability, and not mere fixity, is needed in society, even if only to deal with small errors.
  1851 Unstable equilibrium in a society.
22-Jan-45 1853 Some suggestions for a word to mean "survival-value". Note on selective operators.
  1856 A machine that learns.
22-Jan-45 1857 Part-function is now redefined.
2-Feb-45 1860 If there are many commutive systems sometimes affecting one another, and a parameter taking several values affects one of them, the fields in that one resulting have maximal survival-probability when all the neutral points are in the same place. (See next note) (see 1942)
5-Feb-45 1862 It is to be remembered that Fisher's book was highly successful though no formal proofs are given anywhere.
7-Feb-45 1864 Routh's test for stability given in immediately usable form.
9-Feb-45 1867 The relations of independences and activations of part-functions.
  1870 There is good reason to assume that the chance of stable equilibrium will often fall off as (1/2)n.
12-Feb-45 1875 For a system to get adapted by parts, it is proved necessary that most of the features of a distributive must be present; i.e. there is no other way. (Improved, 1985)
18-Feb-45 1877 Sex activity by my theory must result in a lowering of impulse-density.
18-Feb-45 1879 Two adaptations may be better than two independent adaptations.
19-Feb-45 1880 In future, I hope to effect an improvement in literary style.
  1888 Mendelian theory vs. Distributive theory.
  1892 Mendelian and neuronic adaptations compared and contrasted.
20-Feb-45 1893 "Dominant and recessive" applied to a distributive system.
28-Feb-45 1895 A dynamic system must definitely either proceed to equilibrium or to infinity.
10-Mar-45 1900 It seems that, if A dominates B, no examination of B's behaviour can reveal the organisation of A. To "examine" B means that the observer forms an hour-glass system with it.
  1905 In forming a big organisation the process must be (1) to list the main* variables, (2) to attempt stability by the same number of completely independent commutive systems, (3) with variables which refuse to get stable, add small joins, letting them be few in number and simple in type (i.e. step-functions). [* Now called 'essential', not 'main'.]
27-Mar-45 1909 Usable extracts from Sherrington's "Life's unfolding".
3-Apr-45 1916 Extract of Schrödinger.
  1919 For the world to be suitable to be adapted to, it must contain a large proportion of part-functions.
21-Apr-45 1922 Inactive variables cannot transmit effects, either from other variables or from bounds. (Converse 1977)
  1924 Masserman on what happens when an animal meets a deliberately chaotic environment.
6-May-45 1926 "Break" is better "saltus".
6-May-45 1928 Quotation from Wells. Note on the basic meaning of "organisation".
9-May-45 1934 Simple, worked-out examples for exposition.
11-May-45 1936 Distributive system vs. Genetic analogue.
11-May-45 1941 A further list of correspondences between genetic and neuronic adaptation.
12-May-45 1943 In a distributive system, if from time to time certain variables are constrained to certain values, the variables will tend to become in equilibrium at those values. (Better 2015) Also 1981, 2011, 2012
28-May-45 1946 So far I have discovered five basic operators and their variants.
17-Jun-45 1947 The peculiarities of a system (may) impose "drifts" on the field, to which any path must conform.
  1953 Exposition.
  1959 Points on exposition.
  1966 My misunderstandings, taken from my own notes, which must be well explained lest they become the reader's, too.
3-Jul-45 1967 Some points after reading all my back notes.
4-Jul-45 1968 A very practical note on nomenclature in exposition. (Continued next note)
  1972 New nomenclature and slogans.
  1975 Better to think of constancy than activation; and of separation rather than distribution. The idea of a "movement dying out" is shown due to the fact that a common region of constancy is a resting region.
  1978 A theorem that if a variable, properly joined to others, does not transmit an effect it must be constant (or possibly, changing uniformly). (Converse of 1921)
26-Jul-45 1980 Handling part-functions.
26-Jul-45 1983 Explanation of the simple conditioned reflex. "Traffic" Principle. (2240, 4596)
26-Jul-45 1984 "Signals" and Jennings' "Law of the resolution of physiological states" are now explained.
28-Jul-45 1986 An improvement on the theorem about what is necessary in a multistable system.
30-Jul-45 1988 For independence test, we must find ρ=1..n-1[f]ρ. The old method of Limρ→∞[f]ρ is rejected. See 2054
1-Aug-45 1991 It is decided that a 1st Jacobian matrix (J.M.) cannot be accepted as physically real unless, for each i, not all aii , a aσi , ... are zero. This is necessary and sufficient that the 2nd J.M. has all main-diagonal elements non-zero and this is the simplest test for it. It follows that a more correct form of the relation is 1..n[f]ρ=[F], the sum including the n-th power. This last power adds any missing diagonal terms. See 2056
5-Aug-45 1994 A clarification of interaction where one reaction uses another. "Dominance" is really a negative concept. Ultrastability is not enough, we must have multistability. A "helping" B, and B "using" A are really the same thing.
5-Aug-45 1995 More extended tests of the chance of stability.
  1996 Empirical study of the effect of fixing variables in stable systems.
  2000 Multistable system defined in new form. Theorem in modern form proves possibility of adaptation by parts.
  2002 A very crude estimate of the chance, in a multistable system, of getting an adaptation without upsetting previously established adaptations. It suggests the great importance of low activations and the gross disturbance which might follow even a small increase in it. 5416
  2004 Standard symbols: General mathematical, complete systems, and for general repeated use.
13-Sep-45 2007 Modern proof of the basic theorem of the multistable system.
13-Sep-45 2011 Elementary rigorous properties of the multistable system, and of part-functions.
13-Sep-45 2011 When bounds in a multistable system are altering, a line's chance of destruction is proportional to the number of variables it activates, and therefore also to its length. (See next note)
17-Sep-45 2014 In a multistable system, with bounds changing at random, shorter lines have greater survival. Under parameter change, resting states have maximal endurance if they coalesce. Hence Habituation. (See below)
  2016 A more rigorous statement and proof of the theorem that repeated constraints on a multistable system lead to the system becoming stable at that state.
7-Oct-45 2019 On play. Also on reactions which look complete and turn out to be simple.
23-Feb-46 2024 Some calculated lines of behaviour of a pendulum from different starting configurations and with various parameter values.
  2027 As working hypothesis it is assumed that "coordination" always means "arranging things so that we get (1) stability (2) where we want it.
24-May-46 2031 Non-instant systems, those with delay, may easily be converted to complete and instant by including derivatives.
5-Jun-46 2034 Details about values, for reference.
5-Jun-46 2035 If A dominates B, and B dominates C, in one complete system, then A must dominate C.
7-Jun-46 2036 The case of the top shoot of a tree dominating the growth of lateral shoots fits into my formulation of "dominance" quite naturally.
22-Jun-46 2040 Clarification of the position when dependence itself depends on other variables.
  2043 An over-all theorem on the stabilities of joined systems.
6-Jun-46 2051 Extracts from Masserman.
15-Jun-46 2053 A simple example of the substitution equation of a complete system, suitable as an elementary exercise.
4-Aug-46 2056 An improved statement of the main theorems on independence.
  2059 Answer to "how general is the field of linear equations [x'=Ax] ?"
3-Sep-46 2062 By dealing with averages of many ultrastable systems we arrive at a new order or level of phenomena.
14-Oct-46 2065 An important, though imprecise observation on requirements for a solution of the conditioned reflex problem.
  2066 Detailed example showing the roots moving with change of one coefficient in [x'=Ax]
  2070 Notes on one parameter groups.
19-Nov-46 2072 Effect on latent roots of adding constant to main diagonal, how to move all latent roots to right or left, and a new test for stability.
25-Nov-46 2080 Principles and details for a machine to be absolute, show ultrastability, etc. (see 2095, 2161, 2182 etc)
  2081 Experiment.
  2083 Simple units with output a linear function of the inputs are sufficiently general provided we can control also their general speed of working.
  2085 I suspect that any change in timing of a reaction really means learning a new reaction, i.e. new arcs developed.
21-Dec-46 2090 Electro-mechanical equiformality.
  2091 The important thing is to push to the limit and then make this a new starting point.
  2093 Latent roots of [2x2 matrix: 0 I a 0].
31-Dec-46 2100 A theoretical study of a Unit devised, and part built, by myself. (Further, 2161, 2182)
31-Dec-46 2102 Details for setting the machine of 2094 to correspond to assigned set of coefficients in [x'=Ax].
1-Jan-47 2103 Importance of echo impulses.
  2104 To demonstrate importance of echo impulses
9-Jan-47 2107 Practical notes for use when converting known systems to differential equations in absolute form.
14-Jan-47 2113 Notes the effect of altering the general speed of reaction of one variable.
15-Jan-47 2114 Example of stability in the non-linear case.
15-Jan-47 2117 Equations of a simple dynamic system.
22-Jan-47 2122 The dynamic system which controls the pH of the blood exhibited in my form, as illustration.
  2124 A method of getting an approximate solution to non-linear differential equations.
26-Jan-47 2126 A physical example of the principle that when a change needs a rare combination to make it possible, it will usually occur by some other way, in stages. (Cf. 2329)
  2131 The dynamics of chemical systems.
10-Feb-47 2144 A study of dynamic systems which are themselves processes, like the Bunsen burner.
10-Feb-47 2145 A new way in which one absolute system can be derived from another.
11-Feb-47 2147 In the study of enzyme systems and chemical dynamics, the equations of 2130 are the ultimate foundation: they are the bricks out of which further knowledge is to be built.
13-Feb-47 2152 Equations tying the variables in the systems of chemical dynamics.
15-Feb-47 2158 Principles for the experimental study of the dynamics of chemical systems.
  2159 Example of coordination and training as equilibrium in a dynamic system.
  2162 Further practical details for making a unit. (See 2182)
22-Mar-47 2165 Chemical dynamics and thermodynamics.
26-Mar-47 2169 Instability and threshold in chemical dynamics with catalysts.
20-Apr-47 2174 The Adams- Bashforth method for numerical integration of ant simultaneous ordinary differential equations.
  2175 Exposition. Clear ideas can be transmitted to a listener who does not know the argument by language only simple and direct. (What a sentence!)
26-Apr-47 2180 A number of interesting points from Richardson's book.
3-May-47 2181 The various "constancies" of the body, so carefully maintained (homeostasis), are also separations and independencies. This needs further investigation. (See 2314)
14-May-47 2183 A workable unit has actually been made (second system, other was 2094). (Improved, 2432)
14-May-47 2187 Extracts from book.
19-May-47 2189 Coordination and keeping within limits.
  2194 Pavlov and the conditioned reflex seems to make little contact with my work, chiefly because he allows the dog no interaction with the environment.
  2199 Review of "The wisdom of the body."
  2209 Experiments in learning compared with my theory.
23-Jun-47 2212 The formulation of "signal", "symbol", "association" given vaguely on 786 is confirmed and given more precision.
20-Jul-47 2218 Clarification of "stimulus" and some collected types. (See 2486)
  2221 Look out for linkages in experimental dynamic systems. There are often much closer linkages in the structure of the experiment than seems at first sight. Several parameter often turn out to be one parameter.
21-Jul-47 2227 Independence by delay. (See below) (Another example 2229)
  2231 The mathematical core of "association". (Example next page)
25-Jul-47 2235 An attempted explanation of "association" on an actual experiment.
27-Jul-47 2238 Some elementary observations on the organism-environment relation.
28-Jul-47 2239 A stimulus is many stimuli.
29-Jul-47 2241 If a variable of an ultrastable system is repeatedly forced to take a particular value arbitrarily, then the resting state tends to develop with the variable at that value.
2-Aug-47 2242 It is dangerous for an ultrastable system to move. (4596)
7-Sep-47 2245 The multistable reserve.
17-Sep-47 2246 A clear example of my concept of "independence".
17-Sep-47 2247 Neurosis as instability.
  2263 A linear dynamic system can be forced to beat at any frequency.
30-Oct-47 2270 A good example of the principle of the differential equation and its integration suitable for non-mathematicians. (See also 2278)
2-Nov-47 2271 In the exposition of scientific matter, style is even more important than usual.
5-Nov-47 2274 Notes the relations between my dynamic theory and the methods used in electrical circuit theory.
5-Nov-47 2276 Neuronic patterns are always breaking up and being laid down. The new ones are formed in relation to those persisting.
6-Nov-47 2277 A theory of G.P.I. [general paralysis of the insane] delusions.
8-Nov-47 2279 Two variations on the theme of 2269.
10-Nov-47 2280 Every vestige of claim and boast must be eliminated, being replaced by equivalent facts, or dropped.
11-Nov-47 2282 Quotations.
14-Nov-47 2284 Two points in exposition.
16-Nov-47 2287 Exposition.
18-Nov-47 2288 Exposition.
  2291 Interaction in the multistable system.
4-Dec-47 2299 The effects on stability of the intrinsic stabilities of the units forming the whole. If, as is usual, these are all stable, there tends to be an extra stabilising effect on the whole.
10-Dec-47 2302 Examples of schizophrenics being displaced further from homeostasis by chemical stimuli. And a note of an objection.
16-Dec-47 2305 An "intelligent" machine must adjust more parameters than have been specified in its design. It is not clear whether my machine passes this test. (Cf. 2315)
  2307 Some very simple "variables" do not change, i.e. [x'=0]. These are what used to be called "parameters."
21-Dec-47 2311 Null-, step-, and part-functions are, by definition, already in equilibrium and adjustment is needed only for full functions.
21-Dec-47 2313 "Joining" two machines is essentially a break and rebuild. Null-function theory is fitted.
  2315 Homeostasis is ultimately produced by the gene-pattern, and it protects the gene-pattern from the dangers of the world because the constancy means independence.
24-Dec-47 2316 Feedback.
28-Dec-47 2321 Circuit theory in its relation to my absolute systems and stability; feedback in particular.
  2322 The production of the new compounds of behavior is only interaction and has nothing to do with Intelligence.
1-Jan-48 2324 Memory is not necessarily good. Some examples to the contrary.
1-Jan-48 2326 If a stable set is to be found soon, the average number of part-functions activated should not exceed 6-10
  2327 A proof, modernised from 1724, about an absolute system within an absolute system.
3-Jan-48 2328 Absolute system defined more exactly in group form.
10-Jan-48 2330 Numerical example showing how much faster it is to adapt by parts instead of simultaneously
  2331 Chemical proof that fast reactions prevail over slow.
12-Jan-48 2334 The clock recording time must go uniformly though there are special cases where this could be modified.
  2394 Joining units never adds to the system's stability unless they want to "borrow" stability.
19-Jan-48 2395 Matrix representation of part-functions.
  2397 Correction to independence tests.
3-Feb-48 2399 Quotation on the CNS betraying its blindness.
7-Feb-48 2400 Richter believes the basic drives are homeostatic.
8-Feb-48 2401 In large systems the intrinsic stabilities of the units may become less important while the effect of joinings become dominant.
26-Feb-48 2422 Quotation of echo impulses which seem to be absent but are shown present.
29-Feb-48 2424 Making one unit more stable intrinsically may make the whole system less stable or actually unstable. Worked out example. (Fuller discussion 2454, 2458, 2463)
3-Mar-48 2431 Full equations and approximations of the machine. (see below).
13-Mar-48 2433 Reporting progress in the machine. 2435
  2434 Social example of instability.
20-Mar-48 2440 Method for investigating friction coefficients in my machine. (2432)
24-Mar-48 2442 How well does the machine's actual behavior correspond with the settings? (see also 2448, 2452)
28-Mar-48 2443 Memory and multistability.
  2444 Trying to make a system give assigned roots.
14-Apr-48 2447 If there are no feedbacks, a linear dynamic system cannot develope steady oscillations, but more general systems can.
  2449 Relations between stability of the machine and its supposed stability of setting. j→∞ is sufficient to make the behavior tend to the theoretical form. (see 2452)
14-Apr-48 2451 In a multistable system with multiple subsystems, the number of stable subsystems rises exponentially with the time towards its limit.
23-Apr-48 2457 Two much stability gives rigidity and loss of control over other systems stability has an optimum. (Generalised in next two sections).
24-Apr-48 2460 The fault of too much stability proved more generally. Over stability just means slavery.
  2461 Multistable system point.
5-May-48 2466 Equations [x'=f(x)] and x=F(xo;t) when n→∞.
6-May-48 2469 Definition and test for two patterns of initial displacement, differently sited to be equal. 4148
10-May-48 2485 One factor in multistable systems tend to decrease interaction when two lines are activated simultaneously.
10-May-48 2486 Concept of a "stimulus".
14-May-48 2490 The conditioned reflex and association possibly solved.
  2491 The diagram of immediate effects must conform to the type of experiment.
16-May-48 2497 When null-functions are present we can get absolute systems by either including them or excluding them.
  2498 On "fixing" and "releasing" a variable.
  2504 The ultrastable system shows a tendency to stabilize a variable at a value to which it is repeatedly forced. Cf. 2690
17-May-48 2507 Whenever possible, postulate many independent ultrastable systems rather than one multistable system.
21-May-48 2510 Yet another attempt at the conditioned reflex and association. Cf. 2691
  2512 The concept of "negative feedback" is just too simple to be worth anything. (See also 2524)
3-Jun-48 2523 The ACE, if the operator knows the trick, can imitate the homeostat.
  2524 This concept of negative feedback is most unsuitable as a fundamental concept.
19-Jul-48 2527 Theorem on f's and F's invariant under transformation Φ.
  2528 Biographical note.
20-Jul-48 2530 Systems of (almost) maximal stability (and see below)
27-Jul-48 2531 Systems of maximal stability.
16-Aug-48 2538 My theory explains why nerve cells cannot regenerate.
  3539 Neurofibrils exist.
23-Aug-48 2541 One part of an ultrastable system can act as "trainer" to another part.
23-Aug-48 2542 A snag in the multistable system, which must be answered. (see 2647)
  2547 Exposition.
  2551 In general, if a series of related compound stimuli evoke a series of patterns of activations, we can expect a priori no particular relation between the patterns of activations. Any special relation found to exist must be due to some special arrangement in the machine.
  2554 On "memory" in society.
  2566 Ideas for new homeostat. (continued 2568)
  2581 Constancy is by no means necessary for independence. The latter can be obtained even with gross fluctuation provided it is forced.
14-Jun-49 2583 A system of step-functions reaches a resting state or cycle instantaneously
14-Jun-49 2584 Define the parts and predict the behavior of the whole, not vice versa.
14-Jun-49 2585 Any absolute system can be regarded as built of parts.
14-Jun-49 2585 Constancies are conserved when parts are joined or separated.
17-Jun-49 2586 Fields may, and should, be thought of as bounded and finite in extent.
  2595 Discussion of the stability of a system formed by joining an infinite number of part-functions.
  2597 Response of linear system to an input when its response to a step-function is known.
  2600 Solution of linear differential equations by Laplace transforms.
  2603 Transfer functions and my equations.
  2604 Stability of a chain with feedback. (See also 2621)
13-Jul-49 2605 Nyquist's criterion is merely a convenience. Routh is fundamental
15-Jul-49 2606 Transfer function of a single variable.
16-Jul-49 2608 Oscillation necessarily implies feedback.
  2613 Habituation to a moving stimulus, prediction, and the conditioned reflex.
18-Jul-49 2615 A mechanism for conditioned reflex. Made: 16 Aug '49.
  2616 Evidence that neurons learn and then "fix".
  2617 An extremely simple example of feedback modifying behavior. (See 2729)
  2620 Properties of the relaxation oscillator.
  2622 Weiner's example (2604) amplified. (See next section)
20-Sep-49 2623 Stability of a chain-circuit of variables. (See also 2604)
20-Sep-49 2624 Inaugural meeting of the Ratio Club at the National Hospital for Nervous Diseases.
29-Sep-49 2627 Systems with high selectivity must have long dieaway by cybernetic necessity.
2-Oct-49 2628 Memory in the dogs of the "Tinder Box".
2-Oct-49 2634 The multistable system much clarified.
3-Oct-49 2635 Goal-seeking behavior does not necessarily imply feedback. (Continued, 2643)
  2638 Granit on causalgia.
5-Oct-49 2641 The main properties of the multistable system are proved necessary.
  2642 Canonical equations from the transfer function.
  2645 Goal-seeking behavior does not necessarily imply feedback. (Continued, 2650, 2654)
10-Oct-49 2648 The problem of 2541 ─ that with replicated arcs there is no longer individual correction of the wrong ones ─ may be solved statistically if the brain uses combinations obtained by sampling. 4216
10-Oct-49 2649 Memories may perhaps float. 4155
  2651 Strong goal-seeking usually needs a servo-mechanism. (Continued 2654)
  2656 If a part is to behave with more stability than it has intrinsically, then feedback is necessary.
  2658 Meditations on a new statistical mechanics.
  2667 Machine for Boole's logic.
21-Nov-49 2669 If one or more variables are unobserved, a cycle of parameter-values need not elicit a cycle of observed values.
  2670 An essential feature of the development of the conditional reflex is that an independence changes to dependence.
22-Nov-49 2674 The conditioned reflex cannot be explained this way.
22-Nov-49 2676 A parameter can be localised in action by part-functions.
22-Nov-49 2677 If the observer tries to control a variable he may be forming part of the whole system.
  2678 A "stimulus"is one of a pair of initial states.
  2679 If systems are joined by dominance, the latent roots are unmoved.
  2680 Two possible ways of proving feedback between two sub-systems. Feedback is also proved present if we can find in A a single frequency not found in A + B.
  2684 Some properties of a system of part-functions when a single parameter causes activations by its alternation.
6-Dec-49 2686 A theorem on localised absoluteness.
6-Dec-49 2688 A second stimulation can not only break a field but can save it.
6-Dec-49 2690 Briefly, an adapted system cannot be broken by forcing it to do what it was going to do anyway. This idea only restates what was said 18 months ago on 2503!
  2693 The conditioned reflex again! Yet another mechanism! This time in iterated ultrastable systems. 4596. No! Just the same old one rediscovered yet again.
7-Dec-49 2694 Note on the previous note.
7-Dec-49 2696 The two ways of getting a conditioned reflex are almost identical.
  2698 Better definition of a system which shows extinction of its conditioned reflex. (Continued over)
12-Dec-49 2700 A possible mechanism for conditioned reflexes of the second order.
12-Dec-49 2701 A slight tendency within the nervous system can easily be magnified to a maximal change in the effectors.
  2703 We must distinguish in a conditioned reflex experiment between the pattern represented by the experimenter's controls and the pattern of what arrives at the cortex.
  2704 Example of preceeding section.
19-Dec-49 2710 A system for relating stimuli given to arcs activated.
31-Dec-49 2714 The effects of selection on the distribution of a statistic.
31-Dec-49 2716 Numerical example of the solution of [x'=Ax] by x=etAx0.
  2718 Example of equations solved by Laplace transformations.
  2722 An enumeration of the possible types of organisation. Summarised 2736
21-Jan-50 2725 In a given absolute system, if n-1 variables follow a given line of behaviour and the initial state of the n-th is given, then the behaviour of the n-th is also determined. 5051
  2727 Predicting behaviour of unobservable variables. (Continued 2732)
  2731 Binary counters.
  2734 A new way of getting information about unobservable variables in an absolute system. 5051
  2736 Examples.
28-Jan-50 2737 The ways of organising classified and tabulated.
1-Feb-50 2741 Proof of an entry in the previous section.
  2746 Organisation of a civil service. 2888, 2828, 4245
  2753 A conditioned reflex demonstrated on the homeostat. 2762, 5708, 5855
8-Feb-50 2754 Examples of simple substitutions.
  2755 On the nature of 'mind'. (An application 2790)
10-Feb-50 2761 Effect of diverting a variable from its path.
  2766 Conditioned reflex in ultrastable system regarded as change of resting state. 2855, 5855, 6745
  2768 Fundamental theory of relays and Boole's algebra.
28-Feb-50 2770 Emperical tests of the chance of stability collected to date.
  2772 Chance of stability. 3050
4-Mar-50 2773 Wholes whose stability differs entirely from those of the parts.
  2776 Joining unstable systems to form a stable one.
13-Apr-50 2787 Genetic inheritance as information. (See 2806)
13-Apr-50 2787 Dictionary definitions: Absolute, Behaviour, Break, Critical.
  2788 Dictionary definitions: Disperse, Essential, Field, Independence, Interaction, Iterate, Parameter, Regular.
17-Apr-50 2789 Dictionary definitions: Representative, Stability, State, System, Variable.
23-Apr-50 2792 Discovering a scientific law is like an animal getting one reaction-system adapted to more than one environment. (Summary 2797)
  2793 A set of numerical values can be, in variables, an operand, and in parameters, an operator. (See next section)
26-Apr-50 2796 The meaning of 'several' environments. (Amplified on 2801)
28-Apr-50 2801 Groups and learning.
28-Apr-50 2806 Examples of environments that can be divided into sub-environments.
  2815 A list of actions in which some object has to be avoided.
6-May-50 2816 Some items of information theory.
19-May-50 2820 Information theory.
21-May-50 2824 Example of pattern and group.
24-May-50 2825 A stochastic process and information.
25-May-50 2828 What a mammal does to an environment that cannot be adapted to.
  2830 Social systems that can change their own parameters.
26-May-50 2831 Allbutt on a type of man.
  2833 Description of a child lacking a sense of pain and often injured.
  2842 Solution of Harlow's problem.
  2847 Modern psychology and my theory.
5-Jun-50 2848 How to 'prove' a theory of the conditioned reflex.
  2854 Extracts from Hebb's book.
  2858 A paper to be returned to later.
10-Jun-50 2859 Conditioned reflex without cortex.
10-Jun-50 2860 Razran's article.
  2861 A stimulus contains, in addition to its obvious content, derived and integrated components. (Not so much the stimulus contains them as that it will affect the nervous system as if it did) This is the principle: the 'stimulus' contains everything the nervous system can transform it into. Futile, therefore, is it to worry much about the exact details of the presentation. (Continued 2878)
10-Jun-50 2862 A process, in natural selection, that cannot reach a steady state but moves like the Flying Dutchman.
11-Jun-50 2877 An empirical test on 30 cases of whether my definition of dependence agrees with what is understood by 'causation'. 5118, 3679, 3709
  2880 A 'stimulus' is not what it seems to be. It is all that happens between the experimenter and the depths of the subject's brain. 2896
  2884 A popular misunderstanding of what 'mechanistic' means.
14-Jun-50 2887 Correspondence of primative animal to machine, and object recognition.
15-Jun-50 2888 Social cybernetics. 2898
  2889 Part-environment relation in the Multistable System. 4193
20-Jun-50 2890 Example of multistable system.
28-Jun-50 2896 Comments on the books. Examples of part-functions.
  2900 The new point of view.
  2904 Axiomatic basis of the canonical equations, preliminary.
9-Jul-50 2907 I have little to learn from what is known of ecological systems.
9-Jul-50 2914 Canonical equations of a regular system. See 2922
16-Jul-50 2921 Defining and testing an absolute system.
  2925 On the canonical equations of a regular system
  2930 Some collected notes on pattern or class-recognition, and invariants.
  2933 A simple form of motor equivalent. (See 2939)
18-Jul-50 2936 'Two-stage' ultrastability.
  2949 Essay on 'motor equivalents.' See also 2989.
25-Jul-50 2951 A new principle for a new machine.
  2952 Law relating the lingering of the representative point with the density of critical states.
  2954 Elementary features of my new machine. (See 2955) (changed to 3042)
  2974 Multistable systems, essential variables, dispersion, how to alter step-functions selectively.
21-Aug-50 2978 Behaviour of systems of part-functions.
  2980 Intrinsic stability: general, and of my new machine.
  2983 The equations of the new machine, (See next page) Confirmed 2990
  2984 Chance in my machine that n active variables are stable.
  2986 Intrinsic stability of brain and my new machine. 4154
  2989 Sensory (dispersive) cortex must contain no learning mechanisms.
30-Sep-50 2991 Canonical equations of systems composed of units each of which tries to make itself (its dial value) some function of the others. (3200)
  2992 The system that does not generate information is identical with an absolute system. 3032
  2993 Redundancy and information.
  2996 For training, essential variables are not necessary. (See 3003)
3-Oct-50 2999 Serial training in the machine. (See 3004)
  3000 Note on the 'principle of continuity'.
3-Oct-50 3001 A display for the new machine.
  3002 A simple and well known example of a system of part-functions.
24-Oct-50 3005 Serial learning.
  3007 Canonical equations of the homeostat.
29-Oct-50 3013 Facts on learning.
29-Oct-50 3013 Absolute system conserves information.
30-Oct-50 3019 Multistable system gives partly additive responses. A reaction pattern can be 'strengthened' by noisy variation of parameters. 4155
31-Oct-50 3021 A better meaning for 'difficulty of finding stability.'
  3025 n part-functions of which k are active at any one time is as easy to stabilise as k, not n, full-functions.
  3027 A multistable system adapting to several environments.
7-Nov-50 3031 Necessary and sufficient conditions that a first adaptation should be still present after a second has taken place.
12-Nov-50 3034 The noiseless transducer is the absolute system.(Continued 3164)
  3035 Theorem on absolute systems. Continued next page.
  3037 Theorem on absolute systems. Here is the theorem in its final form for proving step-functions...
23-Dec-50 3041 Systems of part-functions automatically provide step-function. (N.B. This need further investigation and more rigorous formulation).
25-Dec-50 3043 Mark 13 DAMS works.
26-Dec-50 3044 Stability in the system 'number of neons lit'.
27-Dec-50 3048 Joining 'at random'.
27-Dec-50 3051 Stability of systems whose units always tend to some function of the variables.
27-Dec-50 3054 The equations of DAMS. (Effect of neon, next page) Example next page.
27-Dec-50 3054 Control of DAMS' stability.
  3058 Essential variables may work by 'habituation'. (Review 3280)
29-Dec-50 3059 A simple mode of action of the essential variables. 3382, 4526
  3062 Part-functions will divide the whole more effectively if the permanent connections are few.
16-Jan-51 3070 Wiener says cycles will be common in DAMS; I say they will be few. 4892, 5461, 5472
20-Jan-51 3075 Set-up necessary, in brain and DAMS, for serial learning. (3087, 3141)
  3080 Functional knowledge obtainable when only some of the variables are observable. 3716
28-Jan-51 3082 Wiener's opinion on the 'absolute' system.
  3085 The Markoff process. Cf. 3223
  3086 Stability of system of Markoff chains.
28-Jan-51 3088 Relation of essential variables to system of part-functions.
29-Jan-51 3090 There should be many essential variables, allowing patterns to endure in proportion to their suitability, and averaging of the behaviours.
  3091 The elementary conditioned reflex does not need essential variables. Corollary: It is thus a by-product.
5-Feb-51 3093 The probability of stability.
  3094 If the f in the canonical equation behaves as a Markoff chain, the variable's behaviour is - Brownian movement with drift.
  3095 Stochastic differential equations.
  3099 Systems that are partly stochastic.
  3105 The basic equations of statistical mechanics (Continued 3134)
  3109 Probability of stability in an infinite machine. (3121)
  3110 Two things necessary if an infinite system is to be stable. (Cf. 3200)
  3110 Reactions to delay are difficult. (3138)
  3112 Animals react to more things than the experimenter thinks he is supplying. 4597
12-Feb-51 3115 Psychological facts to be explained by DAMS.
  3116 A part-function's 'degree of constancy.'
  3118 Variables 'sticking' does not necessarily cause a bias.
14-Feb-51 3119 No excuse is necessary to suppose that part-functions are constant only at certain values. Perhaps the concept of 3200 may be usable.
14-Feb-51 3120 In an absolute system one variable knows nothing of another variable's constancy.
  3123 Infinite systems of stable parts.
19-Feb-51 3127 How a variable's distribution changes after an internal dt.
19-Feb-51 3129 Steady states in an infinite system.
23-Feb-51 3132 I am now ready to account for learning by 'pleasure'.
23-Feb-51 3133 In a linear system with all variables distributed, the means of the variables behave the same as the variables would if undisturbed.
25-Feb-51 3137 In an absolute system independent distributions don't stay independent.
27-Feb-51 3138 'Delay' in a machine is only behaviour of zero amplitude.
27-Feb-51 3139 In a system of part-functions there are no 'parts' only distributed activations.
  3142 To get cumulative adaptation, the environment must be traversed by a variety of paths. (4546, 4215)
6-Mar-51 3143 Conditions affect, in the long run, only the stable patterns.
10-Mar-51 3146 On the chance that a disturbance should alter the resting state of some part. (3272)
14-Mar-51 3148 A system of part-functions may be easier to change if it is built in stages of assembly.
  3151 Darwinian mechanisms are to be developed by Darwinian process.
19-Mar-51 3163 Switches that see a Markoff process only through themselves: consequent bias in their settings. (Theory in metric-less states, 4527)
  3170 In an absolute system formed by the junction of independent parts, if a particular part can take one of ρ initial states and can show σ lines of behaviour from each initial state, then the quantity of information log2 ρ + log2 σ cannot be exceeded whatever part has been chosen.
  3173 Information in an absolute system always falls to log2 η* (3176) where η is the number of the system's stable states and cycles. *Allowance should be made for the fact that the resting states are not equally probable.
  3176 Information in a machine. The catchment area of a resting state.
  3177 Information in a conjoined system. 3274
  3181 Example and proof of Shannon's Theorem 7
  3189 Networks for DAMS. (Cf. 3237) (Further example 3306)
6-Apr-51 3193 Information in machines.
6-Apr-51 3200 Shannon and I.
6-Apr-51 3201 A variable of constant intrinsic stability and one that always moves towards some function of its neighbours' states are identical. (Cf. 3110) (Behaviour 3134, 3239)
7-Apr-51 3203 Passing information from parameter into machine. The previous theorem can be improved. Here is a better statement...
  3205 Accurate statement of the amount of information that can be put into a machine by arbitrary interference. (3275)
7-Apr-51 3206 A physical example of habituation.
  3207 In the field of an absolute system, every convergent junction acts as a sink for information.
  3209 Maximal loss at a convergent point in a field. Table of log2[(aa bb)/(a+b)a+b].
9-Apr-51 3210 We cannot measure information by finding contributions from sub-ensembles and adding. (Another example 3249)
10-Apr-51 3212 An absolute machine can never gain more information than is put into it.
10-Apr-51 3214 When a parameter affects a machine, the gain in information is stationary (and a maximum) if the parameter's values are distributed independently of the machine's.
  3216 Passage of information as machine dominates machine. (See 3298, 3218, 3275)
11-Apr-51 3220 (Stated at the front - on 3218): If a machine is driven by an absolute system, the duration of coupling makes no difference to the amount of information received.
  3222 An information source controlling an otherwise absolute system raises it to a definite information content at which it is in stable equilibrium. (3086) (Canonical equations next page)
13-Apr-51 3224 Canonical equations of the densities in state of a system disturbed by an information source. (See 3227)
13-Apr-51 3226 Another measure of information applicable to a machine.
13-Apr-51 3228 When driven by a steady statistical source, the information in a machine does not tend to a minimum.
13-Apr-51 3230 States that lock accumulate all the members of the ensemble. 3233, 3291, 4524
14-Apr-51 3234 Information when a stochastic parameter changes infrequently.
  3235 Ways of losing information. 3274
16-Apr-51 3237 Wiring pattern of DAMS.
  3240 Conditions that a machine shall have the maximal number of resting states. This can be specified further...
19-Apr-51 3241 Maximal number of resting states. (3308)
  3242 Information when A drives B.
  3244 The inverse of the canonical equations.
23-Apr-51 3245 An experiment stops when the exchange of information has reached equilibrium. (3248, 3254, 3691)
25-Apr-51 3247 Independence does not in general cause loss of information. (3274)
25-Apr-51 3249 Entropies in the parts do not sum to that of the whole. Entropy of a part may equal that of the whole.
25-Apr-51 3250 Information and experiment.
25-Apr-51 3253 Information in an absolute machine. [deleted]
  3263 Information and the experimenting on dynamic systems.
  3266 This then is the maximal information obtainable in an absolute system of σ states by starting it at a state selected arbitrarily and then observing how it's behaviour goes from state to state.
  3270 Information always decreases, step by step, as an unknown line of behaviour unfolds.
  3271 Uncertainty about the details within a line of behaviour is independent of whether that line, or some other, will occur. 3274
1-May-51 3279 Results collected from the last hundred pages (since 3164) on the subject 'Information in absolute systems.' 3297 3500
2-May-51 3280 New layout for DAMS, and an unsolved problem.
2-May-51 3280 I have just reviewed the notes on the pages mentioned (2955, 2996, 3001, 3003, 3014, 3026, 3028, 3056, 3059, 3071, 3082, 3087, 3115, 3138, 3140, 3149 and the previous note), all dealing with the relations between environment, essential variables, and the 'red mass' of 2957, once the essential variables have been specialised and separated. Here are my conclusions...
4-May-51 3290 A review of essential variables. (3484, 3521)
  3294 Equations of density in phase of systems that tend to stick at certain states. 4153
  3297 The longer the line of behaviour, the higher the chance of step-function change.
  3301 Information in machines.
9-May-51 3303 The continuous system can gain information though absolute.
9-May-51 3303 As soon as a sub-system is isolated it starts losing information.
23-May-51 3307 Dispersion.
23-May-51 3312 How many resting states has DAMS? (Continued 3319)
  3314 Resting states in DAMS will be few. (Continued 3319)
28-May-51 3316 Pneumatic controllers.
  3318 Measuring how much one variable affect another. The part-function as a limit.
  3325 Designing parts for a system with many resting states. (3333)
  3333 How to find the distribution of values in a system of many parts.
  3346 (1) I ignore resting cycles here, as they will probably be rare.
(2) I treat only of parts of constant intrinsic stability with equations of form x-i=Kii(x1,...,*,...,xn)-xi)}.
(3) The variables in the parentheses (above) are the 'inputs' to the part, and Φi is the 'output'. (xi merely follows Φi). (3323)
(4) Just solving f(X)=0 is of little use, for an unknown, and large, number of roots may be complex. The total number of roots, real and complex, is the product of the degrees of the several f's regarded as polynomials (3308)
(5) To get the real distinct resting states, find geometrically the real intersections of the surfaces, f(X)=0.
(6) Figure of 3322 shows that, if we want to get our resting states into a certain region of phase-space then the surfaces must waggle within it, and also across it. (3325 top).
  3347 (Continued)
(7) If Φi tends to a form resembling ρi parallel planes (3334), then the number of resting states (stable and unstable) tends to Πρi. (3336)
(8) (3340: a method, of little importance, for getting the sets of planes all orthogonal.
(9) (3342: what happens when all parts are identical. (Not the case with DAMS)
(10) To get the maximal number of resting states within a given region: (a) construct each part so that the output consists of many parallel planes, (b) join them so that the sets of planes are orthogonal.
(12) If the number of resting states is increased, we can expect the number of stable states to be increased in about the same proportion. (3345)
  3348 How many resting states has a system assembled from parts of known properties? Also 3496
13-Jun-51 3351 Modifying a stable field.
13-Jun-51 3353 Ways of altering a system's sensitiveness to disturbance.
13-Jun-51 3354 Effect of richness of joining on the number of stable resting states.
13-Jun-51 3356 The nervous system should not have internal feedbacks (unless for special reasons) But see 3396. Confirm 3425, 3521
  3359 Information and adaptation. 3521
18-Jun-51 3360 How many nerve calls has an earthworm?
  3365 Conditions that one system may control another in detail.
18-Jun-51 3366 Control in systems of Constant Intrinsic Stability.
  3367 My machines are not ergodic.
19-Jun-51 3377 Information going through a transducer.
21-Jun-51 3381 Solution of the paradox of 3379.
5-Jul-51 3382 The essential variables must be able to send much information into the rest of the system. 3500
6-Jul-51 3386 Designing an essential variable that works by emitting noise. 3521.
9-Jul-51 3387 DAMS needs a complex environment, but a simple training-schedule.
11-Jul-51 3390 My work is the 'chemistry' of machines. Progress in it will be largely empirical. Review 4141
12-Jul-51 3392 That a set of step-functions should provide many resting states it is necessary that they should be uncorrelated. This can be achieved by many cross-connexions. 3521
  3393 If the number of resting states is increased by some change of design, take care that the number stable is not actually reduced.
13-Jul-51 3395 Of the resting states, the number stable can be anything from none to all.
13-Jul-51 3398 A system joined in a circuit is likely to have very few resting states. Confirmed 3426 but see 3571.
13-Jul-51 3398 To retain information in DAMS Mark 13, use output 3 and either of 1 or 2 in all cases.
16-Jul-51 3399 Thinking of the machine as having a finite number of states is the fundamentally sound method.
16-Jul-51 3400 How to integrate step by step when parts have outputs. 4498 shows how it should be done.
16-Jul-51 3402 Further data on what is required for many resting states.
17-Jul-51 3405 A machine's tendency to destroy or conserve information (as uncertainty of state) depends slightly on certain necessary factors in the parts but depends more on the holistic factor of assembly.
  3407 Two similar parts that will give many stable resting states.
26-Jul-51 3410 Design of a part and the number of resting states.
  3415 My standardised vocabulary, collected. (Standard symbols, 2004)
30-Jul-51 3417 With a new and complex system there are no 'usual' values for the parameters, and this increases the difficulty of getting to know it. 3514
1-Aug-51 3418 Law of the Invariance of Distribution.
8-Aug-51 3422 How to stop part-functions from destroying information. 5291.9
10-Aug-51 3425 The conclusion is, then, that for many resting states we must have plenty of independence.
10-Aug-51 3426 Historical note.
  3427 Complex wholes are unstudiable. 3474, 3496, 3513
11-Aug-51 3428 Information in DAMS.
  3430 Value of a determinant.
25-Aug-51 3434 The latent roots of a system formed as a circular chain of levels. Cf. 3573
  3437 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.
  3450 Ninety quotations.
8-Sep-51 3452 In the cortex the relentless necessity for survival may lead to some interesting consequences. (See 3454) (Review, 4155)
  3457 The art of war - in the cortex. Review 4155, 4589
  3459 The animal reacts to all its surroundings. Retroactive inhibition and the theory of interaction in a Multistable System.
12-Sep-51 3460 Let DAMS keep moving.
12-Sep-51 3462 Society.
  3463 How DAMS can be made neurotic. (See next section) (See 3480)
12-Sep-51 3465 Neurosis by conflict must use up a system's resources of step-functions.
14-Sep-51 3474 The question 'what is a 'statistical' machine?' answered.
14-Sep-51 3475 What makes a complex machine 'statistical'? Review 4141
14-Sep-51 3477 How does a statistical machine work?
  3478 DAMS should demonstrate that it can manage the statistics of its environment as well as the exact details.
22-Sep-51 3479 DAMS should tend to avoid activating variables with widespread effects. 4155
  3481 On neurosis.
23-Sep-51 3483 A more practical form of environment for DAMS.
24-Sep-51 3486 Details of the Essential Variables.
  3487 How long should an arc be? 3511, 3514, 3557
25-Sep-51 3489 Part-functions are apt to lead to many useless neutral equilibria. 3491 - No they are acceptable; 3495
25-Sep-51 3490 Variable of constant intrinsic stability as part-function. (See also below)
25-Sep-51 3493 Equilibria in systems of part-functions. (See below)
26-Sep-51 3495 Types of equilibria in DAMS. Conclusion: Neutral equilibria, with esential variables within limits, are acceptable.
26-Sep-51 3496 How to study a complex system.
  3498 For a small disturbance, the effects everywhere tend to be proportional to the size of the disturbance.
27-Sep-51 3500 If the environment is E the brain must become -E-1 4294
  3501 Two new types of information in the multistable system. 3521
  3503 Haldane's book.
  3503 Example of dispersion.
  3505 How many resting states has DAMS?
15-Oct-51 3509 History of DAMS.
15-Oct-51 3509 Sex and the Multistable System
  3513 Testing DAMS. 4511
21-Oct-51 3515 Designing DAMS.
  3516 More complexity means more essential variables, which then have all to be satisfied.
  3517 Improvement by the purely empirical is as old as industry.
  3521 How to arrange DAMS. DAMS can react to a 'signal' or 'symbol'.
29-Oct-51 3522 Index to Essential Variables since 3289. 3582
29-Oct-51 3522 Reduction of all variables to a common form is of no importance.
  3526 Fundamental theorem that the nervous system must contain step-functions.
3-Nov-51 3530 Fully developed form of the 'mechanical brain'; design for a chess-playing 'machine'.4563
5-Nov-51 3531 The brain should have some step-functions almost inaccessible to the environment.
  3535 Definition of a system's 'intelligence' at a resting state.
  3537 Anatomical features gives quick success but lose generality. (Next page) 4563
12-Nov-51 3538 Fixed qualities in a system.
  3545 The neon in DAMS as absolute system.
18-Nov-51 3547 Some statistical systems. Review 4141
  3552 Joining at random and by sub-systems.
  3554 We think dynamically, not logically.
21-Nov-51 3558 How to join DAMS.
21-Nov-51 3561 Joining up Essential Variables, Environment, and network. Review 3582
22-Nov-51 3563 Representation of a typical environment.
  3570 The number of circuits that passes through each valve in DAMS is large.
  3578 Proof that circuits of levels that include a one- variable level arc easy to stabilise.
27-Nov-51 3580 Processes for elementary study.
26-Nov-51 3581 Infinitesimal displacements activate a unique set of variables. (3599)
  3594 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
30-Nov-51 3596 A clearer statement about the Essential Variable.
  3598 A glance at the theory of games. 4589
  3602 Getting dispersion. 3870
1-Dec-51 3603 How the cortex perhaps gets selective disruption of wrong arcs. 3825, 4600, 4831
1-Dec-51 3606 Long lines of behaviour in phase-space often appear in the living world as circulating between organism and environment. 3645, 3760
7-Dec-51 3608 Statistical mechanics.
7-Dec-51 3610 'Positive' cleverness may be really only what is left after the elimination of nonsense. 4578 5307.3 (See 3629)
  3614 Evolution and the homeostat are information-amplifiers. (3616)
8-Dec-51 3616 Details of chess-playing.
11-Dec-51 3628 Properties of an information-amplifier. 4155
11-Dec-51 3629 The elimination of wrong moves at chess may eliminate too much.
12-Dec-51 3630 Random transformations.
12-Dec-51 3631 How instinct is activated.
  3632 Random transformation in taste. 3665
  3637 Calculations on dispersion.
17-Dec-51 3642 The chance that inactivity will stop an effect getting into the rest of the machine.
22-Dec-51 3643 Environment reducible to orthogonal subsystems. Also 3648
29-Dec-51 3644 Innate mechanisms must be studied for their organisational properties.
2-Jan-52 3645 Three ideas.
7-Jan-52 3647 Functional levels may be topologically re-arranged within organism and environment.
8-Jan-52 3649 Example of an environment.
8-Jan-52 3654 Cybernetics and the psychoses. 3673
  3655 The mechanism underlying paranoia.
  3657 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)
17-Jan-52 3661 Information in the field and in the equations of an absolute system is S log S. 3695
17-Jan-52 3661 The homeostat's amplification factor is less than x1, but I was the first to point this out.
20-Jan-52 3662 Again the necessity for achieving success by stages.
  3663 Approximate estimate of the amount of design put into the homeostat.
20-Jan-52 3664 How many uniselectors the homeostat should have. 3743
  3665 Example of a random transducer. 3667
  3666 Chess strategy.
25-Jan-52 3670 Chess player's manual. 4569
25-Jan-52 3670 Amount of design in the homeostat.
  3672 Possible reason why psychoses are rare in children. Cf. 3650
  3674 Isolating a system.
  3684 Extracts from Sommerhoff. 3709, 3715
31-Jan-52 3685 When there is more than one source, how many entropies are calculable?
  3687 Information from multiple sources.
31-Jan-52 3688 Definition of 'memory'. 3810
  3692 Experimenter and system. 3697, 3725
3-Feb-52 3696 A function that measures information but is free from the concept of probability. Its basis is the 'partition'. Compare Neumann and Morgenstern 67. 5027
3-Feb-52 3698 Even the experimenter must be regarded as an ensemble. 3709
4-Feb-52 3700 To compute information, members having the same field must be kept together.
  3703 Chess strategy. 4590, 4651
  3705 Every parameter-change allows (or forces) the information in an ensemble to drop to a new lower level. Same applies to δ-impulse 3936.
  3706 Habituation, and adding information to an ensemble. 3774
  3707 The effect of the initial state decays with time if some parametric input is active. 3954
  3708 Decay of information in an ensemble.
9-Feb-52 3710 The concept of 'cause' implies more than one line of behaviour. 5118
9-Feb-52 3710 Today's tip: Cleverness, by Selection out of Thermal Noise,
  3715 Mathematical knowledge is knowledge of how to control a certain environmental, physical, system. 3721, 3725, 3729
  3717 Transformation of a linear absolute system.
  3719 Replacing variables by derivatives. 3723, 4296, 5202
27-Feb-52 3720 Two unstable systems joined to give a stable.
3-Mar-52 3723 More examples of mathematics as a study of real dynamic possibilities. 3729
12-Mar-52 3729 'Knowing' means 'controlling', which means 'keeping invariant'. Review 4348, 4294
28-Mar-52 3730 More illustrations that maths is based on physical, empirical knowledge. 3926
28-Mar-52 3730 Real 'dial-readings'.
28-Mar-52 3730 Itinerary in the States: London, New York, Chicago.
  3731 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.
  3732 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
  3733 Itinerary in the States: Richard Wallace, Philadelphia. Washngton, Mina Rees, Seymour Kety. New york, London.
  3736 To make, or not to make, a calculating machine?
28-Mar-52 3738 Wallace's Maze-solving Computer.
  3741 Shannon's mechanical brains.
  3743 Information in the homeostat.
2-Apr-52 3744 Information in the homeostat.
  3752 Searching, random and systematic.
  3753 Qualification to 3746.
  3760 The division by part-functions is not objective. Transformation can destroy part-functions. 3767, 3799
8-Apr-52 3761 Details of dispersion.
  3763 Addendum to the definition of the primary operation. Corrected 3894
9-Apr-52 3766 A misunderstanding about part-functions. 3868
10-Apr-52 3772 Rank of the differential matrix, and null-functions.
  3775 Part-function were introduced to cause retention of information. 3799
  3776 Example of a canonical equation of nullity 2. 3799
  3784 Rank, information, effective parameters. 3780, 3799, 3788
  3785 Determination of initial states. 3789, 3847
  3787 Field + field, and determinate changes of parameter.
  3787 The observer-system relation is symmetrical; so we can calculate 'information' over an ensemble of observers
3-May-52 3789 Information, rank, equations. 3799
5-May-52 3792 On the operation that brings the representative point to a particular initial state. 3846, 4628
6-May-52 3794 Convergence of lines as invariance.
6-May-52 3797 An absolute system cannot give to another absolute system that it dominates more information than the first one contains. 3797
  3799 Rank, and control effected by parameters. 3800, 3802, 4301
  3801 Channel capacity in a machine.
10-May-52 3806 Transmission of information through a chain of absolute systems.
11-May-52 3808 Homogeneity implies group statistical regularity implies group. 3849
12-May-52 3809 Examples testing dependence of F on xo.
  3814 (1) What is meant by 'memory'. (2) Memory does not require feedback. 3840
13-May-52 3815 Memory as conjugate behaviour.
13-May-52 3815 Habituation implies memory. 3842
17-May-52 3824 Habituation. 3837, 3842, 3856, 4526
  3829 How the Essential Variables must act to be selective. 5549, 5415, 4169, 4831, 5345
  3831 Variables in the brain should be driven actively by the environment.
  3832 Odd notes.
  3835 A better view of the homeostat. 3837
22-May-52 3837 What is essential in the homeostat. 3841, 3856, 4161
23-May-52 3840 On habituation. 3842, 3856, 3865, 4524
  3841 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!
  3845 Habituation and memory. 3865, 4524
25-May-52 3852 Only an observer with dispersion can take advantage of a system's absoluteness.
  3853 Exploring a machine.
28-May-52 3854 Detail of 3844.
28-May-52 3855 Change full to step-functions for resting states.
29-May-52 3856 Other things being equal, the system with more step-functions will have more resting states.
31-May-52 3859 The importance of the age of thing. Review 4155
1-Jun-52 3860 The catchment areas define a partition.
4-Jun-52 3861 Definition of 'stability'.
  3862 Return of parameter to a previous value can cause further loss of information. 3863, 3954, 4057, 4074, 4373
  3864 A fluctuating parameter tends to lesser the number of resting states.
11-Jun-52 3866 The reactive condition is the more probable, from which the system may diverge under habituation.
  3867 The channel from step-function to observer must be broad if the observer is to see variety of behaviour.
12-Jun-52 3869 Every system can be transformed to [y~1=1, y~2=...=y~n=0] Cf. 1151
  3871 All control is based on the infinitesimal. 3930, 4015
17-Jun-52 3876 Stability of a circuit of levels. Another interesting system...
  3880 Behaviour of the 'clover' system.
  3882 Feedback can occur along a single channel.
21-Jun-52 3891 An incomplete solution of the problem of the probability of stability.
22-Jun-52 3892 A variable 'is' whatever a particular system, perhaps ourselves, sees it as. (But see 4000) and 3896,
22-Jun-52 3893 "interacts with" is an equivalence relation.
22-Jun-52 3894 A likely mechanism for the conditioned reflex. 3897
23-Jun-52 3896 The primary operation, and testing absoluteness.
23-Jun-52 3899 More on the Conditioned Reflex
24-Jun-52 3901 A hybrid step-full-function. By 4000 it is in (2), a full function.
26-Jun-52 3914 n complex variables are equivalent to 2n real variables. Complex 'machinery'.
  3916 n arcs can control n complex variables.
  3918 Resting states and latent roots of complex-variable systems.
  3919 Volterra's book.
  3923 Arcs that are simple as complex variables do not stay so as real variables.
  3925 In the brain, part often talks to part via the environment. 5424
28-Jun-52 3927 All maths should be expressible in terms of dynamic systems.
30-Jun-52 3928 Topology of absolute system.
  3929 'Stability' must be re-stated in terms of information. 3963, 3980, 3975
30-Jun-52 3931 The disturbances of most interest are those that are infinitesimal and the system becomes linear.
1-Jul-52 3932 Self-reproducing arcs are of very great importance, for good or evil. Review 4154
2-Jul-52 3935 A derivation of the partition-function.
2-Jul-52 3937 Administering a determinate impulse to an ensemble can only cause its information to fall. 3954
2-Jul-52 3939 Unsolved problem. 3959, 3962
  3943 Examples showing how 'adaptation' means 'destroying information'. 4133, 4155, 4159, 4167
3-Jul-52 3950 Partition and lattice.
  3951 Partitions in absolute ensembles.
  3953 Fault in book, to be corrected. Yes. 3966, 3986
  3953 Partitions in absolute ensembles. 3997
4-Jul-52 3959 Input makes for uniformity. 4048, 4122
  3960 A quite different way of defining and handling the absolute system. 3962, 4019. Review, 4338
  3965 States and metric give field.
  3965 Ultrastability does not need step-functions!
7-Jul-52 3968 Ultrastability can act without a metric. 3986
8-Jul-52 3979 How to get many resting states (argued without a metric).
9-Jul-52 3984 My concepts divided into the topological and the metrical. 4026
10-Jul-52 3985 The concept of 'state' does not require number or metric.
  3990 Ultrastability proved at last! Worked out example 3967 Obsolete! 4232
14-Jul-52 3993 'Step-functions' topologically. 4000, 4005, 4602
15-Jul-52 3994 Why do our brains take so much notice of a step-function? 4233
21-Jul-52 3995 'Absoluteness' is relative to an observer. 4031, 4043.
  3997 Residue classes in behaviour.
27-Jul-52 3999 A chemical dynamic system.
27-Jul-52 4002 A more rigorous definition of full, part, step, and null functions. Try it on 3900, 4604
24-Jul-52 4003 Joining parts to form a whole.
  4004 Change of direction.
  4004 Examples of a single artificial absolute system. 4486 if some states become indistinguishable.
1-Aug-52 4005 Note on the subjective.
3-Aug-52 4011 Lewin's Topological Psychology. 4026
6-Aug-52 4012 Absolute systems. Q.E.D.
6-Aug-52 4012 Panta rhei - Heraclitus [~everything flows]
6-Aug-52 4015 On memory and schizophrenia.
6-Aug-52 4015 For progressive adaptation the essential variables must be multiple. 4167
6-Aug-52 4015 On infinitesimal disturbances.
6-Aug-52 4017 Examples of systems with part functions.
6-Aug-52 4018 Two independent 'complexities' in the 'complex system'. 4167, 4189
  4019 Importance of a system's history. 4041, 4048, 4302
21-Aug-52 4021 Interaction between adaptations.
21-Aug-52 4021 My solution includes all solutions.
8-Aug-52 4022 S.8/2 should be re-worded.
10-Aug-52 4025 'Coarsening' an absolute system. 4041, 4475, 4919
12-Aug-52 4026 Field as vector.
12-Aug-52 4026 Meaning of 'topological'.
12-Aug-52 4029 Quotations
13-Aug-52 4030 The absolute system does not imply a group. 4033
14-Aug-52 4031 An absolute system is a selected projection of the world-lines. 4038, 4043, 4292
15-Aug-52 4032 The homeostat's equations.
15-Aug-52 4033 Being a one-parameter group is not sufficient to ensure absoluteness.
15-Aug-52 4034 I formally reject the concept of 'group'.
15-Aug-52 4035 The 'group property' without groups.
15-Aug-52 4037 Abstract, and objective form of 'selection'. Review: 4137. 4099, 4229
  4038 Non-metrical definition of 'stability'.
  4038 Why not two, or more, representative points? 4121
16-Aug-52 4041 Every regular system can be made to yield an absolute system. 4042, 4302
  4042 A regular system is practically an absolute system.
18-Aug-52 4043 Nature of absoluteness. 4292, 4306
18-Aug-52 4046 The joining of machines can be represented without a metric. 4332, 4471
19-Aug-52 4047 Continuity of transformation.
19-Aug-52 4050 'Observing' a system means letting the regularity of the system's behaviour lessen the scatter in the ensemble of experimenters. 4122, 4296, Review 4348
  4052 If a system is very large and its lines of behaviour very long, the 'later' ends of the lines must differ from the 'earlier' in some 'Darwinian' way. (Note on 4055) 4099, Review 4141, 4201
22-Aug-52 4053 Essential variables. 4161
22-Aug-52 4054 In exposition, use non-learning systems as examples of organisational facts.
22-Aug-52 4054 Arcs breed. ? 4151, 4065
30-Aug-52 4057 The field of the self-locking system. 4065, 4155
  4059 The 'ordinary' and the 'statistical' machine differ only in the proportions allotted to the directly functioning part and the parameter-adjusting, servo-mechanistic part. 4061
  4060 More examples of the stable and unstable. 4062, 4070, 4074
  4061 Example of 'stability' miss-used. Further examples 4062, 4070
  4062 Economic systems vary in their amounts of stabilising machinery.
1-Sep-52 4063 The organism that 'knows' a line of behaviour is better if it knows the adjustment lines as well. Answered 4608
3-Sep-52 4066 Musings on evolution and the cortex. Review: 4155, 4071
  4069 The basis of both the multistable and the evolving system is the self-locking system (and its superior, the self-reproducing). 4071, 4099, 4153, 4166, 4201, 4229
  4070 Learning that have to adapt to a fixed (reflex) mechanism.
  4070 Meteorological dynamics. 4072
6-Sep-52 4072 Self-reproducing systems. 4086, 4099, 4154
  4073 Complex systems can also be regular.
  4075 "Design for a Brain" must use methods of proof that correspond to what I hold are the natural, physiological, methods.
7-Sep-52 4076 Random transformations.
  4079 The multistable system may have no trend if wrongly devised. 4080.0, 4175, 4201
12-Sep-52 4080 Multiple faults in a machine. 4613, 4195, 4201
  4081 A possible cause of psychosis.
  4083 Waismann's book.
12-Sep-52 4084 Example for localisation.
  4085 Absolute systems within absolute systems. (Continued 4113)
  4087 More on evolution. 4610, Review 4201, 4155, 4099
13-Sep-52 4088 In discussion, force every question to be converted to an acceptable form before answering.
  4090 Judge the difficulty of "Design for a Brain" by the comprehension shown by the average worker in EEG. Adjust the difficulty so that almost all such workers show comprehension.
  4094 Entropy etc.
  4096 The demonstration of feedback requires three primary operations.
17-Sep-52 4097 How many primary operations are required to establish the diagram of immediate effects?
17-Sep-52 4098 To study an absolute system of σ states, σ elementary operations are necessary, and they yield σ log σ of information. 4112
17-Sep-52 4098 Compare 'adaptation' in the multistable system with 'adaptation' in evolution. (My aim is to show them as identical). 4086, 4071, 4064, 4056, 4036 Reviews: 4136, 4201
  4101 What is a 'thing' in my type of concepts?
  4105 A 'thing', therefore, can be said to exist in an absolute system when the observer's parametric control is insufficient for the exploration of all initial states, so that the states have to be tested in blocks.
  4106 A 'thing' corresponds to a constraint. 4233, 4439, 4388, 4440, 4943
  4106 A 'thing' means redundancy. Example 4187
  4111 We can now consider the 'isolation' that exists when a system is not surrounded by the absolute constancies previously postulated but by variables that, though not constant, are statistically constant.
21-Sep-52 4112 (a) Adaptations in multistable system and in Darwinian system compared
(b) What is a 'thing'?
(c) What is 'reproduction'? 4522
(d) A system is in a sense 'isolated' if the disturbances are statistically constant. Review 4137
21-Sep-52 4112 Two points about dreams and the cortex.
23-Sep-52 4113 The difficulty of 'delay' is identical with the 'difficulty' of having too few variables.
23-Sep-52 4117 Absolute systems in absolute systems. 4119, 4145
23-Sep-52 4119 Tests for absoluteness.
  4120 Absolute systems within absolute systems. 4145
24-Sep-52 4122 The representative point may be divided into parts, as the whole system is thought of in parts.
  4123 More on information. 4133
  4132 On the necessity for step-functions. 4158, 4161, 4238
29-Sep-52 4136 Destruction of information. 4164, 4166. Review 4151, 4385
29-Sep-52 4136 Monograph on Evolution.
  4137 Part 1: Selection.
  4141 Part 2: The study of very large systems.
  4151 Part 3: The properties of Φ(q)
  4155 Evolutionary processes. 4172. Review 4201, 4790
Part 1: Selection. 4137.
Part 2: The study of very large systems. 4141.
Part 3: The properties of Φ(q) 4151
  4156 Runaway and information. 4303
  4160 Adaptation of essential variables, (next page) 4163
  4162 Adaptation without step-functions.
  4165 The adapting system - generalised, (next section). 4166, 4225
4-Oct-52 4171 (1) The homeostat is a self-regulator that uses information instead of power, but has the usual amplifier - with - negative - feedback. (2) The environment should be divided into (a) affected by the organism, (b) independent of the organism. (3) These give the fundamental control-flow relations. 4179, 4282, 4285
  4177 Darwinian adaptation, and the multistable systems. 4197, 4201
  4178 Psychiatry of the information-block.
6-Oct-52 4181 The self-locking system will also often be internally self-locking. 4229
  4182 For rapid and successful adaptation in the Multistable System, δ, α,η and ζ must, as channels, have large capacities.
10-Oct-52 4183 Origin of depression.
10-Oct-52 4183 The regenerative abnormality as self-locking system. 4229
11-Oct-52 4185 Genes and memory. 4206
  4186 The essence of intelligence is selection. 4285
  4187 Chaos first becomes worth studying when a constancy appears.
13-Oct-52 4189 Lashley on learning.
16-Oct-52 4193 More observations on discriminative feedback. (Foot of this page) 4201 4613
16-Oct-52 4193 Sufficient to ensure high probability of'.
16-Oct-52 4195 Discriminative feedback. 4225, 4514, 4613, 4831
16-Oct-52 4196 Discriminative feedback. 4216, 4201
17-Oct-52 4197 Trial and error by model has advantages, if the system can achieve it.
  4201 Various ideas on Darwinian and multistable evolution.
23-Oct-52 4207 Review of the relation of Darwinian to multistable system. 4216, 4239
  4210 The conditioned reflex. 4424
  4215 Assume that the number of essential variables is large and given, and is much the same for all species. 4225
  4215 Feedback through the environment.
  4222 Discriminative selection in poultry. 4233, 4239
  4222 The 'essential variable' of a watch that is to undergo trial for the Kew 'A' certificate.
  4223 Maths is not logical. 4539
22-Nov-52 4224 The necessity for selecting variables.
23-Nov-52 4227 The multistable system as merely one of many.
23-Nov-52 4228 Definition of system 'independent' of a parameter.
  4232 Precise conditions under which a system is self-locking. 4242, 4275
  4232 Better proof of ultrastability.
  4233 We take 'things' invariants, and null-functions as fundamental because we must. 4146.2, 4235.9, 4943
  4235 With 'state' as fundamental, canonical equations exist and parts can be joined, by parameters. 4604
  4235 With 'state' as fundamental, 'independence' can be defined.
28-Nov-52 4239 The field of [DIAGRAM]
29-Nov-52 4241 Darwinian and multistable systems. 4425, 4655
1-Dec-52 4244 How to get the time of adaptation to be reduced by the machine automatically. (Also) An ad hoc design is equivalent to a feedback loop with selection amplifier. 4246
2-Dec-52 4245 The diagram is more general than it looks.
2-Dec-52 4245 Getting information from a system.
  4257 On the time taken by a large system to get adapted. 4264, 4515, 4560
3-Dec-52 4260 Building an exceptionally un-intelligent machine.
3-Dec-52 4261 Building a machine to display its powers of self adjustment.
  4262 Orders or levels of essential variables.
  4263 Levels in social organisations and in the multistable system.
7-Dec-52 4267 Precise instructions for commercial organisation. 4269, 4273
7-Dec-52 4267 Is the power of abstraction the same as the power of developing an hysterical blindness?
8-Dec-52 4269 Play is an investment of surplus adaptation. 4271 (13), 4425
  4272 Explicit instructions for commercial or social organisation. 4273
14-Dec-52 4275 Building a society for chess-playing.
15-Dec-52 4276 A better way of stating my 'limit' theorems, and 'trend' theorems.
  4278 Power and I.Q. have many similar properties. 4285
14-Dec-52 4280 Appearance of a super-clever machine.
14-Dec-52 4281 'Noise' when an Ultrastable System is built of Ultrastable Systems.
18-Dec-52 4282 By serial adaptation, time falls to its logarithm.
21-Dec-52 4283 The entropies of the variation-amplifier. 4285
  4284 Multiple, competing, essential variables lead to the same problem, whether occurring in one person or scattered among many. 4289
22-Dec-52 4289 A selection-amplifier, in the multiplying sense, is not wanted; but a selection-supplementer is. 4520
  4290 Therapeutic possibilities.
  4291 Converting [x~=Ax] to x'=A'x
  4295 What 'knowing' a system means. Contrast 4315. 4429, 4438. Better stated in transitions 4305
24-Dec-52 4298 Differences, at a finite time later, can replace variables. 4301, 5206
  4300 Shannon's theory in its relation to the theory of the absolute system. 4312, 4396. Review 4345
27-Dec-52 4302 Effectiveness of parameters with finite substitution. Applied 4414
28-Dec-52 4303 Examples of states that include history.
28-Dec-52 4303 Knowledge must be tested by control. 4438
  4305 One-one-one relation between parameter and transition. 4396
30-Dec-52 4307 My theory must become more circular, showing how an ultrastable brain is bound to work via the absolute system, etc. 4814
  4310 Entropy with two outputs, and the transmission of information from system to system. 4312, 4429
30-Dec-52 4311 Scientific knowledge is knowledge of a transformation. 4344, 4454
  4315 'Variety' in systems.
  4316 'Variety' in systems. See page 4327
14-Jan-53 4373 Variety in state accumulates.
14-Jan-53 4374 Uniform activity in the parameters drives down variety in state.
14-Jan-53 4375 Long-term memories.
14-Jan-53 4376 On basins.
20-Jan-53 4377 'Delay' need not be rejected as a basic concept.
1-Feb-53 4380 Note on Darwinism.
1-Feb-53 4380 'Experiment' = 'competition'. 4384
  4383 There is a maximal speed at which evolution or adaptation can proceed. The best one can do is to get near the maximum. 4384
9-Feb-53 4384 The α-rhythm.
12-Feb-53 4385 Speed of adaptation can be achieved only by trials and comparisons.
  4387 Regulation (destruction of information) requires extra information. Continuous form 4395, 4658
17-Feb-53 4388 Lack of variety and step-function are equivalent. 4439, 4440
18-Feb-53 4389 Apparent inertia in adaptation.
  4392 'Transient' translated into non-metric terms. 4644 (vol.18)
19-Feb-53 4393 Gödel's coding. Theorem 5086
19-Feb-53 4393 Digital and analogue.
26-Feb-53 4394 Quotation showing gross ignorance of the principles of organisation, by one who should know better.
  4395 Two functions combining to an invariant. 4658
27-Feb-53 4401 The absolute system as coder and decoder. Extended 4414, 4461
  4410 Limiting basin when determinate machine is affected occasionally by impulse-operate. 4524, 5512
1-Mar-53 4411 Proof of theorem
1-Mar-53 4411 When many related theorems are possible, pick on one and prove it quite rigorously; the exact details will then show the exact effect of each proposed variation.
  4412 (An addendum)
  4416 Canonical equations of the decoder.
  4418 Magnification and dispersion from the point of view of information. 4422
  4418 If information is to be conserved, linearity must be achieved everywhere.
23-Mar-53 4420 Proof that messages that are heavily contaminated with noise are best ignored.
  4421 Necessary conditions for a system to have resting states that differ only at a few variables.
1-Apr-53 4423 Effect of magnification on behaviour.
2-Apr-53 4424 Invariants of a dynamic system with parameters.
2-Apr-53 4424 The Conditioned Reflex as a loss of power to transmit. 4430
  4425 Distinguish variety in design from variety during performance. Continued 4427 top, 4427, 4428, 4431
6-Apr-53 4428 A system can "know" by having the right values of variables or parameters. 4438
  4429 When a designer makes a machine of n states and a parameter-combinations, he puts in variety of a.n.log n This is its intrinsic content. 4463, 4704
  4430 Information that can come from a machine.
  4432 Trial and error in reaction to shock.
  4432 Information in printed English.
  4437 Riguet on binary relations. 4470, 4498, 4566, 4581, 4604, 4632
17-Apr-53 4439 Prediction and control are just forms of regulation.
17-Apr-53 4439 Wave as constraint; travelling immobility. 4440, 4943
20-Apr-53 4441 Way of behaving, constraint, thing, part-function.
20-Apr-53 4443 More on "constraint". 4553, 4564
21-Apr-53 4445 Computing entropy.
  4446 Shorthand has more disadvantages than advantages. List of symbols:- End of this volume and 5108
24-Apr-53 4447 Every material system is equivalent to a transducer and a noise-source. [deleted]
24-Apr-53 4448 One formulation covers "design" "input" and "noise". (Next section) 4449
27-Apr-53 4454 Information in a machine. 4701, 4847
28-Apr-53 4462 Outline of the theory of the Black Box. 4480
28-Apr-53 4465 What "designing" a machine means abstractly.
2-May-53 4469 The variation of the essential variables must be supplemented. 4482, 4581
  4470 A single machine contains many "informations", most of which do not interact with the others. Example 4577
2-May-53 4471 Joining absolute systems without metric. Example 4473, 4498, 4733
2-May-53 4472 Must every system drift to the condition of maximal internal separation? 4500, 4524
2-May-53 4472 Cap or intersection as selective operator.
2-May-53 4472 Unsolved problem. Solved 5009
2-May-53 4474 Anything that can have variety is really a set.
  4479 The relation "observer A cannot distinguish x from y"; homomorphism. 4501, 6254
2-May-53 4480 Are there "levels" of design? 4595
3-May-53 4481 The Black Box is a set.
3-May-53 4481 Randomisation as a way of passing a message that is no message.
3-May-53 4482 The whole cannot be at a resting state unless every part is are a resting state. 4508, 4581, Example 2916.7, Markov chain 4904
  4483 How the homeostat works. 4520, 4538, 4581, 4701
  4493 Partial knowledge; equivalent relation between machines. 4729, 4777, 5001
11-May-53 4494 More constraints means fewer possibilities but more discoverable patterns, 4504
11-May-53 4494 In set theory, remember that inequalities are likely to have cybernetic applications. 4503
13-May-53 4495 Set theory and its use.
13-May-53 4496 'Large' and 'small' machines.
13-May-53 4497 Logic and theory.
19-May-53 4498 Homomorphism in machines.
  4500 Joining machines.
21-Jun-53 4504 Observations on set theory.
11-Jul-53 4509 Principle of ultrastability stated more vigorously. Better still 4581
  4510 Ergodicity and loss of information.
13-Jul-53 4511 Tactics for getting DAMS better aligned.
17-Jul-53 4513 Machines are related to the algebraic laws of internal composition, as well as those of external.
  4519 Built-in structure in an adapting system implies that part of the solution has already been obtained. 4599, 4600
18-Jul-53 4521 Amount of selection and ultrastability. 4582.6, 4904
  4523 How chromosomes reproduce themselves. High survival power.
  4535 Habituation. 4559, 4596, 4609, 4762, 5512
22-Jul-53 4536 Formal proof that, if a set is stable, no state in it can lead ever to a state outside the set.
23-Jul-53 4537 Power for adaptation. (See next page) 4583
25-Jul-53 4539 Adaptation needs a transducer between the prime (statistical) mover and the useful result. 4583
25-Jul-53 4539 Markov processes in machines.
28-Jul-53 4545 Markoff process in machinery. 4671
28-Jul-53 4545 The human brain may not be optimal for inclusion in computer.
  4547 Trials within trials, or the admission of variation into sub-units of an ultrastable system.
  4549 Examples of how reducibility shortens time of search. 4552, 4563, 4650, 4948
31-Jul-53 4552 All problems can be reduced to a canonical form. 4560, 4585
1-Aug-53 4557 The method of models, for quicker searching. Review 4560-4575
3-Aug-53 4558 Isomorphism between machines.
3-Aug-53 4559 Distinguishability correspond to dependence.
4-Aug-53 4560 A Review on "Speed of Adaptation" with special reference to that of a Problem-Solving System. ... it is now possble to build a system, or machine, of more than human intelligence.
4-Aug-53 4560 Contents
§1 Introduction 4560
§2 The method of models 4562
§3 Constraints on the operands 4563
§4 Constraints on the transformation:
  (i) Reducibility
    (a) What is Reducibility? 4564
    (b) The effect of Reducibility 4567
  (ii) Continuity
    (a) What is Continuity?4568
    (b) The effect of Continuity 4569
§5 Selection by components 4570
§6 The Maximal Speed 4574
  4562 §2 The method of models
  4563 §3 Constraints on the operands A and B
  4564 §4 Constraints on the transformation:
(i) Reducibility
  (a) What is reducibility?
  4567 (b) The use of reducibility
  4568 (ii)Continuity
  (a) What is continuity?
  4569 (b) Value of continuity
  4570 §5 Selection by components
  4574 §6 The Maximal Speed of Adaptation
  4575 (1) A first estimate of how long a problem will take in the solving might be given by the product of the possibilities in its components, assuming independence.
(2) This is a bad estimator, being biassed. It is in fact an upper bound of the true value.
(3) By the use of models the process of search can often be hastened.
(4) Often the components are not independent, and only a portion of the product-space need be searched. Various factors (described) may have this effect.
(5) Selection by components may be possible. It reduces the time to its logarithm.
(6) There is a minimal time for the solution of a problem (or adaptation): it is the time that the fastest isomorphic system can get the answer out in binary notation. 4650, 4668
  4577 Poincaré on the study of functions.
7-Aug-53 4578 Two messages in a channel need not interact. 4641
8-Aug-53 4579 Emission of "cos2x + sin2x =1" randomly.
  4580 Two agents may select the same element, yet differ widely in their degrees of selection. 4583, 4598
8-Aug-53 4581 An even more rigorous statement of ultrastablity. 4882 4467 4508 4520
9-Aug-53 4582 Rigorous statement of ultrastablity. 4881, 4904, 5046
12-Aug-53 4584 Relation of essential variables to selection-amplifier. 4586
12-Aug-53 4587 What is 'problem solving'?
16-Aug-53 4589 Every real object is an element in an indefinitely large number of sets. Which sets are to be considered must first be defined.
18-Aug-53 4593 Neumann's theory of games translated into my theory of systems. 4650
19-Aug-53 4594 Stability checked.
21-Aug-53 4595 Review of the book. [Design for a Brain]
22-Aug-53 4596 'Equilibrium' refers to a state, 'stability' to the region around the state.
25-Aug-53 4597 Properties of metric-less system. 4623
26-Aug-53 4598 The fullest description of a 'stimulus' is still inadequate to define its content of information.
26-Aug-53 4599 In comparing an ultrastable (mechanical) solver with Man we must take care that they start with comparable amounts of prior knowledge.
28-Aug-53 4600 Ways of getting effective discriminative feedback are to be found specially, for each type of system, not as a general problem. 4613, 4641, 5548
28-Aug-53 4602 Control, and part-function, in terms of set theory. 4604
28-Aug-53 4603 Incentives in the ultrastable system.
28-Aug-53 4604 Practically all my concepts are non-metrical.
29-Aug-53 4605 Having several basins has nothing to do with being divisible into parts. Noticed again 5502
31-Aug-53 4606 Organisation of the German General Staff. 6534
  4607 Is the Darwinian system a specialised one? 4608, 4613
31-Aug-53 4608 How much of a field should be known?
31-Aug-53 4609 In Darwinian evolution; the part of essential variables is played by those parts whose disequilibrium leads to widespread disturbance around them.
  4612 Self locking and self-reproducing systems in the terms of set theory.
31-Aug-53 4613 Precise statement of the fact that instability is infectious.
31-Aug-53 4613 The general solution of the problem of the least discriminative feedback is - that there is no general solution. Every problem has its own optimum, and finding the optimum is a part of the problem. 4600, 5548
31-Aug-53 4613 Am still totally unable to write Darwinian ideas in any rigorous way, in spite of many motes ever since 4051.
1-Sep-53 4615 What Darwin really did do. 4618
1-Sep-53 4616 Darwin's actual theory.
1-Sep-53 4617 What does "endurance" mean?
1-Sep-53 4619 Darwin's method for the study of complex systems. 4655
1-Sep-53 4620 Darwin's theory and that of the multistable system are related by intersecting in a set of theorems that contains both.
1-Sep-53 4620 How to develop the theory of "knowing".
3-Sep-53 4622 How a machine transforms a set of representative points in its field.
4-Sep-53 4624 "Stability"defined. A "machine" is a stable sub-set. 4630, 4632, 4643, 4656, 4795
4-Sep-53 4624 Every set in a machine generates a stable set that contains it. 4630
  4627 Studying variety with the methods of the theory of sets.
  4629 Repetition of a well-defined stimulus simply creates a new, compound, operator, that has stable sets with new, interesting, properties. 4630, 4632
  4631 Stable sets of a product application. 4762
28-Sep-53 4633 "Basin" defined algebraically. Better 4743
  4634 Strategy. 4640
30-Sep-53 4640 The costing accountant and the strategy of control.
  4641 Mechanism for simultaneous adaptation. 4577, 5417
30-Sep-53 4642 "Maximising profits" as a "keeping within limits."
  4643 Self-locking in society.
12-Oct-53 4647 Theorems on transients. 4761
12-Oct-53 4647 System in which x chases α.
12-Oct-53 4648 Of what use is neurophysiology to me?
12-Oct-53 4648 Drugs of addiction.
19-Oct-53 4649 If the environment offers constraint, the cortex can profit.
  4652 Strategy of trial and error. 4797, 4822, 4844, 4947, 4941
23-Oct-53 4655 Box-diagrams are not precise.
23-Oct-53 4655 Evolution as habituation.
3-Nov-53 4657 Meaning of 'stability'. 4741, 4785, 4795
  4659 Only variation can force variation down - exact conditions necessary. 4662, 4674, 4750
  4661 All regulations are included in the Markov chain's progression to an absorbing state. [deleted] 4676, 4678, 4683, 4695, 4701
  4665 Entropies in regulation. 4666, 4722, 4971
5-Nov-53 4666 Entropy and information.
  4668 An organism cab control an environment of its own size (channel capacity), but not more.
5-Nov-53 4671 An error-controlling regulator cannot reduce the incoming variation to less than a half. But see 4688
6-Nov-53 4673 Markovian parameters to Markov chain. 4700
6-Nov-53 4673 Meaning of "output".
  4679 On regulation. 4709, 4795
8-Nov-53 4682 Regulation when several inputs disturb.
10-Nov-53 4687 Regulation in the homeostat's second order feedback. 4695, 4701, 4709
11-Nov-53 4690 Error-controlled regulation is possible only by blocking conduction.
  4694 In information, the point of view of the element is very different from that of the set.
16-Nov-53 4699 Progression to an absorbing state in a Markov chain and progression along a line of behaviour in a stable, continuous system are two extremes of a continuous scale. 4842
17-Nov-53 4701 Markov chains as component parts for building a machine. 4703, 4770
19-Nov-53 4703 If a designer is only partly responsible for the determination of a machine, the fraction (implied by "partly") can be given meaning only if there is no loss of variety in the transduction.
  4704 A determinate machine, with single-valued field, can be formed only by supplying variety of n log n bits. 4722
21-Nov-53 4708 Quality in design. 4725, 4733, 4788
23-Nov-53 4722 Regulations at various levels reduced to standard and common form. 4737, 4906
24-Nov-53 4727 The homeostat does not amplify. Contradicted 4792
  4728 How many environments can the cortex adapt to ? [deleted]
  4730 More homomorphisms quotient machines (4778) 4777
24-Nov-53 4732 A set of determinate machines do not give a Markov chain.
27-Nov-53 4737 Information going into a system to design two parts. 5006
2-Dec-53 4740 The unreliability of introspective evidence.
7-Dec-53 4749 Riguet's statement of "relational mechanics." 4751
9-Dec-53 4750 Regulation implies both activity of the regulator and inactivity of the essential variable.
9-Dec-53 4757 Coordinates and projections in relational form.
  4759 Riguet's definition of "dependance". 4813, 4992
12-Dec-53 4761 Riguet's "trajectory" is practically my "transient".
31-Dec-53 4765 More on habituation. 4917
  4773 Stochastic machines. 4847, 4876, 4868, 4904, 5097
  4775 Properties of tensor product.
7-Jan-54 4776 Equilibrium of Markov chain.
  4779 Quotient machines. 4937, 5001, 5165, 5148
28-Jan-54 4781 Observations on controlling a system that can learn.
  4782 Set theory in machines can dispense with the idea of "information". 4795
16-Feb-54 4787 "Survival in spite of disturbance" in the terms of set theory. 4790, 4795
19-Feb-54 4788 "Output to an input" is a relation of order, and may give a lattice.
  4789 Complex taps can be easily built by mere conjunction of many simple. 4792
19-Feb-54 4790 I am able to approach the subject of the origin of intelligence, i.e. regulation, from two points of view, but do not seem to be able to relate them.
  4791 Why regulation?
19-Feb-54 4792 The homeostat does amplify. 4794>
  4793 Designing a machine to build a machine. 4808 (top), 5070, 5072
22-Feb-54 4794 The limit of progressive regulation.
  4796 Many concepts include that of "reduction". 4880, 4950, 4963
26-Feb-54 4798 Strategy of trial and error. 4844, 4949
2-Mar-54 4801 Every machine on states M defies "machines" on states in Mn (n=1,2,...). Only in the latter is variety bound to fall. (Its "tensor powers") 4869
2-Mar-54 4801 "Transformation".
2-Mar-54 4809 Gain in regulation when the sequence has repetition. 4831, 5002, 5070
5-Mar-54 4810 Change of state and change of design.
5-Mar-54 4810 The "tracker" as regulator.
5-Mar-54 4811 Error controlled regulation.
5-Mar-54 4812 Levels in regulation.
12-Mar-54 4813 Learning is worth while only when the disturbance will be repeated.
17-Mar-54 4814 The diagram of immediate effects as a higher relation.
  4816 The circularity of reasoning about reasoning. 4835, 4897
29-Mar-54 4819 Slowing down a machine, and sleep.
29-Mar-54 4823 Getting the disruptive feedback from the distant environment. 4844, 4927
30-Mar-54 4830 Proving the existence of hidden variables.
30-Mar-54 4832 Discriminative feedback. 4834, 5345
31-Mar-54 4833 On attention, and vigilance.
2-Apr-54 4835 The "problem" of discriminative feedback must be shown to exist in the real environment.
  4839 Nature of relations and sets. 4897
7-Apr-54 4841 More on the Black Box. 4951
  4843 Hunt-and-stick is a more general form of stability. 4881, 5046
14-Apr-54 4845 Strategy of trial and distribution of probabilities. 4849
14-Apr-54 4845 Two ways of regarding "design".
15-Apr-54 4847 Law of Requisite Variety stated with respect to a rectangular table. Stated purely in terms of set theory 4850
22-Apr-54 4849 An input can be saturated i.e. has a capacity as a channel.
  4851 The Law of Requisite Variety in full rigours of set theory. 5002, 5047
23-Apr-54 4860 Machines, with inputs and outputs, treated wholly by mappings. All this is, in substance, identical with Riguet's form. 4867. Simpler 4876, 4991
  4861 Feeding a machine with input and output back into itself.
  4866 Adaptation in evolution.
28-Apr-54 4867 Quotations.
28-Apr-54 4868 "A machine" implies three sets and two mappings. 4871 Simpler 4876 Best 5097
  4870 A set of replicate machines.
28-Apr-54 4872 The machine of intermittent observation.
28-Apr-54 4873 Initial states may appear simply as a source of variety.
29-Apr-54 4874 Re-entrant chain of mappings. 4876
29-Apr-54 4876 What is a scientific "theory"? 4948
  4877 A "machine" implies two sets and a mapping; coupling requires an extra mapping. 4932, 4952, Formal statement 5097
27-May-54 4880 The amount of design in "keep moving".
  4881 There are two distinct reasons why a machine may be used in regulation. 5046
28-Apr-54 4883 "Independence" is a special case of "incomplete transmission of variety".
  4894 Why the uniselectors have many values. 5046
3-Jun-54 4895 Specifying the second-order feedback rigorously.
  4897 Church's theorem.
8-Jun-54 4899 Logic in the multistable system. 5305, 5313
8-Jun-54 4901 Speed is merely one of many demands that can made to qualify simple adaptation. 4964
8-Jun-54 4904 On identifying an optimum in a set.
10-Jun-54 4905 Equilibrium in coupled Markov systems.
  4913 All sorts of continuous and discontinuous systems put together to make all sorts of ultrastable systems.
12-Jun-54 4915 Bellman on 'stability'.
14-Jun-54 4918 Statistical laws in the Markov chain. 4919, 4946
23-Jun-54 4927 Relation of the physicist's "entropy" to my work.
  4928 Supplementary information and its mode of use.
5-Jul-54 4931 Evolution and psychology must study the basic question "what will in fact happen?" 5535
  4934 Isomorphism and equiformality. 4990, 5000
  4936 The theoretical structure of the theory of machines, according to Bourbaki. 4970, 5904, 5907
6-Jul-54 4938 Homomorphism returns.
28-Jul-54 4941 Closed sets of states in a black box. 4951, 4968, 4989
30-Jul-54 4942 Trials are good, for they bring information. 4945, 4948, 4965, 4963
  4944 A "thing" is a way of behaving.
4-Aug-54 4945 Proof of 4871
4-Aug-54 4946 Discriminative feedback. 4963
4-Aug-54 4946 Information repair.
5-Aug-54 4947 Letters as Markov chain.
17-Aug-54 4950 The strategy of adaptation. 4962, 4964, 4980
17-Aug-54 4951 The Black Box is built. [see photos: Description | Black Box | Details]
17-Aug-54 4952 On the accessibility of states. 4953, 4968
17-Aug-54 4953 The "partly observable machine with input." 4956
17-Aug-54 4956 What "examining a machine with input" means. 5055
22-Aug-54 4961 When a system is partly unobservable, the method of trying to restore absoluteness by taking earlier values into account is fundamentally second-rate; it will succeed only when the case is peculiarly favourable. 4979
22-Aug-54 4963 All necessary improvements to the basic ultrastable system can be had by the addition of further orders of feedback.
23-Aug-54 4964 More on the chess-playing team.
  4965 Efficiency of solving is adaptation at a higher level than solving.
  4967 Scales of measurement.
  4970 Science is interested chiefly in the case where the parameters and states are so related that every state is accessible at will. 4989
30-Aug-54 4971 "State of equilibrium" in the hierarchy or sets.
30-Aug-54 4971 Orthogonality of actions in regulation.
17-Sep-54 4972 We live by the incorporation of pieces that are already keepers-out of noise.
  4973 Living organisms surround themselves with invariants.
  4973 Example of an adequate channel. Pantagruel, l.iii,ch.xxix
22-Sep-54 4978 With a random transformation the variety tends to fall to two thirds at each step. Qualified 5158
27-Sep-54 4980 "Time" can be treated as a disturber of a machine, like an input.
27-Sep-54 4981 Research and the strategy of adaptation.
26-Sep-54 4982 "Integrating" and transformation.
26-Sep-54 4983 Nature of "invariance."
26-Sep-54 4984 Notes on "closure" of a transformation. 4989
26-Sep-54 4984 Getting from the discrete to the continuous.
  4987 Whether properties "emerge" or not depends on our knowledge of the parts.
  4987 Why information?
27-Sep-54 4988 "How to dichotomise" takes time to be learned.
30-Sep-54 4991 However many states are available, the experimenter confines himself to some set satisfying certain conditions.
5-Oct-54 4994 Algebraic form of "immediate effect".
7-Oct-54 4995 How to deduce the connexions from input to variable. 5055
  4996 "Connexion" depends on the operations brought to its study.
22-Oct-54 4999 An exact electromechanical analogy.
  5000 Isomorphism.
27-Oct-54 5001 Homomorphism.
28-Oct-54 5002 A problem.
2-Nov-54 5004 What is a machine? 5056
  5005 Game that is wholly arbitrary. 5024
  5010 Design of a machine part by part. 5474, 5072
26-Nov-54 5011 Example of triunique relation.
2-Dec-54 5012 Behaviour when the feedback can carry only one bit.
  5021 The relations between regulators are complex and hardly worth developing.
10-Dec-54 5023 Problems that are not wholly new. 5066
10-Dec-54 5023 A numerical illustration of continuity as a constant. 4569 5005 4597
16-Dec-54 5025 Example of the effect of continuity as a constraint. Caution: See 5054. 5636
  5026 Effects of channel capacity in joining two systems, only one of which is observed.
  5038 Flow of information during trials.
22-Dec-54 5042 The Turing machine.
  5045 A machine that makes itself. 5088
  5047 McCallum and Smith also use the method of veto. 5583
23-Dec-54 5048 Requisite variety stated algebraically. 5075
24-Dec-54 5050 The field, when memory is used, is not isomorphic with that found when all is observed.
  5054 Studying a system via one variable.
11-Jan-55 5055 (Comment on "continuity")
11-Jan-55 5056 Studying a system...
11-Jan-55 5057 "Machine" as constraint in a sequence. But see 5074
11-Jan-55 5061 Converting observed behaviour to specification of machine. 5063, 5081, 6071
11-Jan-55 5061 Beware! The "design" of a machine costs simply what is necessary to get it selected from what is available. There is no unique quantity "in" a machine. 5006
12-Jan-55 5062 The quatity of design in measured by the size of the set that is drawn from. 5070, 5071, 5072
12-Jan-55 5064 Algebra can operate directly with observed behaviour.
14-Jan-55 5065 Mnemonic for "everywhere defined" and "single valued".
14-Jan-55 5065 Metron and logon.
  5066 What is problem solving? I say it is finding an element in a set.
  5068 Problem solving.
15-Jan-55 5069 Another example of a self-locking system, this one harmful.
15-Jan-55 5071 Briefing a deputy calls for the same capacity as doing the job oneself. 5073
15-Jan-55 5071 Amount of design required for a machine to do a job.
15-Jan-55 5073 More on "the amount of design in a machine".
16-Jan-55 5074 Why build a regulator?
16-Jan-55 5075 A machine embodies a transformation and, in addition, may act repetitively.
16-Jan-55 5075 Two problems.
18-Jan-55 5076 Theory of the homeostat.
15-Feb-55 5077 Demonstration of selection-amplifier.
18-Jan-55 5080 Systems that interact finitely with their observer.
18-Jan-55 5082 The structure of a machine, derived from a protocol.
18-Feb-55 5084 Structure of machine in a protocol. 5170, 5192, 6071
21-Feb-55 5085 The problem of "simplifying" a machine.
8-Mar-55 5088 Godel's theorem as process.
17-Mar-55 5089 More on the self-reproducing system. 5261
1-May-55 5091 A strategy must be related to the actual constraints of a system.
  5093 Reducibility and channel capacity are independent. 5532
17-May-55 5094 Finding a maximising formula.
18-May-55 5099 Formally stated method of coupling by using the tensor product of Riguet.
  5104 Tensor method of coupling systems.
  5104 Tensor method of coupling systems.
  5108 List of shorthand symbols that may be found between pages 4416 and 4446, and in the Index.
1-Jul-55 5109 Review of Pringle.
  5111 The problem of the glass of milk.
2-Aug-55 5112 What is meant by "He does not know......."
1-Sep-55 5113 With systems in general, do not look for the law; each must be studied and taken as it is found. Over a set of systems a constraint may be found. 5114.7.
2-Sep-55 5114 Bridgman on operations.
  5116 There is no "law" to be found in systems much removed from the atomic level. 5142
7-Sep-55 5117 On causality. (Continued over)
9-Sep-55 5129 Concepts of cause, why, because etc related to Black Box theory.
12-Sep-55 5131 The simplifications obtained by cutting channels lie on a lattice. 5135
  5134 Why the organised and inter-connected can usually defeat the unorganised and individualistic.
13-Sep-55 5136 Quantity of organisation.
17-Sep-55 5144 Application of system theory to History.
21-Sep-55 5146 How can a machine express a binary relation? 5181
  5147 Law of Experience algebraically. 5155, 5209.7
  5152 Simplification by running together, or deleting, the elements of time. 5165, 5245
5-Oct-55 5153 "Loss of control" in set theory. 5155
5-Oct-55 5154 The conditioned reflex, and shedding of scatter by going to an equilibrium. 5249.1, 5277.8
  5159 Law of Experience, given rigorously. 5179
12-Oct-55 5160 Kershner and Wilcox' book.
17-Oct-55 5164 Variety in mathematical forms. (Continued 5167.6)
18-Oct-55 5166 Markovian machines simplify on to a lattice.
18-Oct-55 5167 Dichotomy versus trichotomy.
18-Oct-55 5169 Mathematical expressions have inputs and outputs.
18-Oct-55 5169 Black Box looks at itself and others.
20-Oct-55 5174 Algebraic form of "immediate effect". 6070
  5177 The use and limitations of the integral equation. 5192, 5210, 6036
21-Oct-55 5178 Must a person's private "map" be observable to all?
24-Oct-55 5180 Memory must fail if new information is forced in. 5205
  5184 Machine with input and binary relation.
  5186 "A can predict the behaviour of B" is equivalent to "A is isomorphic with B". 5193
27-Oct-55 5188 Quotations from Mach.
30-Oct-55 5189 The concept of "constraint" includes correspondence, mapping, relation, as special cases.
31-Oct-55 5190 Psychological and anatomical patterns will usually be different. Cf. Introduction to Cybernetics S.6/11
31-Oct-55 5191 Two meanings of "input".
  5195 Constraints in protocols. 5978
4-Nov-55 5209 Use of observations at times earlier than "immediately preceding." Qualified 5210.3 5228, 5236
  5210 Definition, and the law of experience. 5254
9-Nov-55 5213 In the absolute system, the use of earlier states may be inefficient. 5869
14-Nov-55 5217 Thoughts provoked by Savage.
14-Nov-55 5218 The mapping of the homomorphic machine.
  5220 The structure of the regulator. (Note that the inverse, [w-1], has appeared at last!)
14-Nov-55 5223 Must a constraint go on holiday in the future? 5273
15-Nov-55 5224 Example of message that depends on the set it came from. 6275
  5227 Ultrastability in Design and in Introduction reconciled.
21-Nov-55 5229 Real existence of "variety".
22-Nov-55 5230 Metastability.
  5234 Concept of the "distance" between two input states, or two designs. 5506, 6282
23-Nov-55 5235 Distance of movement.
5-Dec-55 5240 Why the scientist should relate the event to what is adjacant rather than distant.
  5241 "Complexity" is a relation between units and construct.
19-Dec-55 5243 Law of Requisite Variety as law for suppression of noise.
2-Jan-56 5244 A minute crack at the problem of consciousness. 5275
5-Feb-56 5245 The end of the hunt?
  5247 The machine, when observed only so far as the states of equilibrium it goes to. 5556
6-Feb-56 5248 What is a "variable"?
6-Feb-56 5249 Mathematical proof "in detail" means going through a sequence of states of equilibrium.
6-Feb-56 5250 Is there any way by which a person can communicate an infinite amount of information?
14-Feb-56 5252 "Consistency" in mathematics.
  5253 Personal note.
  5254 What is a "logical definition"?
24-Feb-56 5256 The structures of space as habituation. 5289, 5313
  5260 New machine to demonstrate statistical mechanisms. 5317, 5408, 5526
24-Feb-56 5261 On "imitation".
  5262 More "self-reproducing" systems. 5797
  5263 Pain educates mostly in childhood.
2-Mar-56 5265 A contribution to the theory of the distribution of basin size.
6-Mar-56 5267 Probability of getting a single basin. 5308
9-Mar-56 5270 Schizophrenia and noisiness.
  5272 Raiffa et al. describe maths as isomorphic with real systems. 5298, 6260
5-Apr-56 5275 "Will", and acting now so that certain things shall be. 6321
  5276 On consciousness.
14-Apr-56 5277 What good is "Design..."
29-Apr-56 5278 Movement between states of equilibrium.
29-Apr-56 5278 "Yes-no" is a language capable of explaining, or getting, all things, however complex.
29-Apr-56 5279 Program.
1-May-56 5280 Selection cannot proceed quickly, by dichotomising, in a class that is undefined.
16-May-56 5281 Example of a case in which information about the initial state gets lost.
17-May-56 5282 Science forswears direct knowledge in favor of the indirect.
21-May-56 5283 "Statistical machine" has two widely different meanings.
22-May-56 5286 Fast adaptation can be a manifestation of habituation. 5287.7, 5288, 5342
23-May-56 5287 How to sample equilibrium states.
31-May-56 5289 The fringe-variables of a system (in this world) are an unbounded set. 5292, 5330
  5291 Learning structure by habituation to a constraint. Appalling! Habituation is not to a constraint - the ideas have no relation. 5294.4, 5313.3
  5292 How to join motor (and sensory) nerves to a network of part-mechanisms. Now read 3420 and see how much I have advanced in five years!
7-Jun-56 5294 Adaptation always consists of one level working with a lower level as units.
  5295 In a statistical system, habituation must be used first, in order to provide the permanent entities among which alone trials are worth conducting.
  5296 Why random play should come before serious learning.
  5298 Finding a way of getting a matrix reducible.
  5299 What is a theory? Cf. Reprint 144
25-Jun-56 5301 Abstract machinery.
  5303 How to make a brain.
29-Jun-56 5304 The multi-stable system must have low interaction on the average. 5312
29-Jun-56 5304 On the pains of learning.
6-Aug-56 5307 Structure is a form of constraint. 5314, 5496
6-Aug-56 5307 To evoke a property, the designer vetoes its negation. 5316, 5331.5
21-Aug-56 5313 Cross connexions, immediate effects, random transformations, and memory.
24-Aug-56 5314 If structure is present in the (set of) inputs, it will turn up in the (set of) states induced by the law of Experience. 5437, 5322
24-Aug-56 5314 A reason why a chess-player will automatically tend to learn quick ways of winning.
14-Sep-56 5316 Fixing the step-mechanisms on the occurrence of 'success' adds little to the resources of an ultrstable system. 5331.5
  5319 How to chop up a field. 5408, 5524
20-Sep-56 5323 How does the child get "stucture" from the world around it? It can't keep it out!
24-Sep-56 5324 The "structure" developed by the child (as a result of structure in the world) need not copy the world's structure.
24-Sep-56 5324 I need not worry further about reversibility.
24-Sep-56 5327 Curie's principle is merely a special case of my decay of variety.
25-Sep-56 5329 "Looking one move ahead does not require special programming.
25-Sep-56 5331 On the size (duration) of a significant step. 5288
  5332 If punishments only are used, zero punishment is equivalent to reward.
  5333 Selection and elimination.
28-Sep-56 5337 There is no general rule for characterising the more efficient forms of corrective feedback. 5369.2, 5371, 5417, 5539
1-Oct-56 5339 Effect of computing a transformation sequentially.
2-Oct-56 5340 Train by situations so matched to the system's present ability that feedbacks of "right" or "wrong" are equally likely.
  5341 There is no general machine that can be specialised, only a class of individual machines. It is the class that can be broad or narrow. 5507
  5343 The ultrastable system has an intrinsic bias towards efficiency and quickness in learning.
  5344 Basic methods with complex systems.
  5355 What can be deduced from the accumulation of adaptations. 5360 Simpler: 5732
  5356 What is necessary for the accumulation of adaptations. 5410, 5540, 5592, 5601, 5617, 5632, 5746
13-Oct-56 5358 Dispersion demands redundancy. 5372, 5379
  5360 A system that attempts to correct multiple arcs will go to an equilibrium with a certain fraction of its arcs correct. If momentarily better than that fraction, it will drift back to it. 5410, 5415
18-Oct-56 5366 Relays can do everything I want, if suitably coupled.
18-Oct-56 5366 Inputs and outputs of a relay.
  5368 A system of variables each of which does not depend on its past can depend on the system's parts if it contains internal feedback. 5397.7 Example 5412
  5370 Discriminative feedback's optimal spread depends on the spread of constraints in the environment.
26-Oct-56 5371 Feedback in a dispersive system should be first wide-spread and then progressingly narrower. 5413
17-Nov-56 5374 How fast information decays when passed through a number of variables at random. 5381
  5375 If a system is affected, with feedback by another, each can be regarded as a transducer with separated input and output (= conceptual uncoupling). 5428
  5378 Environments that have to be adapted to fall into two very different classes: those that do, and those that do not, contain a teacher. 5382.6
  5380 Keeping things apart by giving them room to spread in is too wasteful. r things would require about r2 spaces.
21-Nov-56 5382 Probability of district balls getting into same cells. 5830
22-Nov-56 5383 Abstract form of a "teacher". 5430
1-Dec-56 5389 Time of adaptation can be cut down if more space is available. The distinct reactions should be sent to distinct places, any one reaction should not change its place during its training. 5410, 5415
1-Dec-56 5391 "Plastic" behaviour. by itself, specifies nothing about parts or their couplings. [deleted]
1-Dec-56 5391 "Having many small basins" does not give any information about parts or couplings.
  5394 Relation between amount of coupling and length of trajectory. 5399, 5411. Summary 5524
  5397 Layout necessary for a plastic transducer, of brief trajectory. 5421, 5476, 5522, 5631
  5398 Multiple equilibria, in the systems in a chain, give a transducer with memory.
  5401 Another approach again suggests that trajectories get very long if system gets large. 5407.5, 5479 Summary 5524
4-Dec-56 5407 Equilibria in part, in whole, and coupling. Rich coupling can create equilibria (and destroy them) 5447, 5983. Summary 5524
  5409 An indefinitely large system with half its states equilibrial, and no trajectory longer than one step. 5471.6, Opposite 5412, 5524
6-Dec-56 5411 A system that accumulates adaptations with appreciable success must use discrimination in its distribution of corrective feedback. 5415, 5421, 5440, 5610
  5412 Some systems with long cycles. No equilibrium 5455
7-Dec-56 5414 If active arcs have a non-transient trace, feedback can correct that which caused the bad reaction. 5629
  5418 If a system accumulates adaptations, it must have some way of getting the disruptive feedback fairly accurately to the appropriate step-mechanisms. 5440, 5606, 5655
  5421 Behaviour may be plastic in two senses: showing an effect or showing a copy. 5437
10-Dec-56 5422 The system that is both multiple and plastic. 5522, 5545, 5535, 5631
11-Dec-56 5423 Go for the quality of "survival" - all the rest shall be added unto you.
  5425 Arcs and genes. 5522 (Reprints 130, 131)
19-Dec-56 5426 Remember that an input may work by releasing, to the output, some sub-system within: - the jukebox.
  5430 A trajectory may be reducible (into parts that are unconditionally good or bad). 5462, 5532, 5537, 5573, 5675
  5436 Reducibility in a set of trajectories, 5441, 5528, 5537, 5626
27-Dec-56 5438 "Gaining structure" as "experience to a set of trajectories." 5552
  5439 Demonstrate the state of a system by giving a stimulus to a dominated system and see its trajectory. 5552
28-Dec-56 5440 Farley demonstrates a statistical machine that adapts.
  5444 The transformation on unanalysed states is completely general provided that... 5456, 5474, 5466
  5445 Constraints on parts and couplings show in the transformation on states. 5456, 5460 5466, 5474, 5524
14-Jan-57 5446 Anti-habituation may occur. 5490
14-Jan-57 5450 If all parts have a constant probability that a given state, for various conditions, is equilibrial*, the whole's probability that its (whole) state is equilibrial depends on the coupling. 5461 * And one arbitrary, coupling is used.
  5452 If all the parts have probability π of being in equilibrium, the whole's probability may be as high as π. (For this to happen, the coupling must be highly selected, for each part must, as it were, both give and take equilibrium without loss) 6019
  5455 If parts have most of their states equilibrial, and are many, the whole may [for a suitably selected coupling] have remarkably few equilibrial states; maybe none at all if π ≤ 1-(1/n). 5670, 5484, 5489. Summary 5524
  5458 Meaning of "coupling at random", so as to get a sample space. 5474, 5481.7, 5500. Summary 5524
  5460 If each variable goes equiprobably to its next value, and the couplings are equiprobable, then the transformations of the whole make each state of the whole go equiprobably to all states. The equiprobability does not follow if either variables' transformations or couplings are not equiprobable. [deleted]
  5464 Equilibria must be specially fostered; in the general random system they are vanishingly few. 5476, 5482, 5503. Summary 5524
15-Jan-57 5465 A game for the machine.
  5471 What sort of parts, how coupled, give the whole in which all transitions occur in all combinations? 5474, 5489, 5662, 5982. Summary 5524
  5472 A system as large as you please, with no trajectory exceeding three steps.
  5473 Mean length of trajectory when system has high probability of finding the next state equilibrial. 5479, 5504
15-Jan-57 5475 How the building of any whole from parts can be given complete generality: let each part's input range over all other part's states; and let the cells of the table be filled arbitrarily and independently. 5482, 5507, 5662
  5478 That a whole should have many states of equilibrium, given that designs of parts are not to be matched to parts, it is necessary and sufficient that each part have many states of equilirium. Summary 5524, 5489
18-Jan-57 5479 Making a whole of parts each with a high probability of equilibrium is sufficient to ensure short average length of trajectory (but not necessary). Example 5408
18-Jan-57 5480 The world that is is just those properties that are not relative to the observer.
  5481 Page 5407 clarified.
21-Jan-57 5485 If the parts have probability of equilibrium πi, and if the parts have all combinations of canonical representation, and if all cells in the same representation are filled independently, then the probability of a state of the whole being equilibrial is Πiπi. If joined so that all information is brought to each part, the probabilities are independent. 5505
  5486 If the parts have probability of πi of being in equilibrium, and if the parts vary fully in their canonical representation but the coupling are restricted, then the probabilities of two or more states being in equilibrium (in the whole) are no longer independent. Summary 5524
  5489 "Probability of equilibrium" summarised. [deleted]
  5491 Habituation.
  5493 Synthetic habituation.(Continued 5494.6)
  5494 Repeated samples with some sticking.
  5495 Synthetic display of habituation and its "inhibition".
28-Jan-57 5496 The use of a transformation repetitively in time is a constraint, so structure becomes apparent.
  5498 "Confluent" defined (as noun). 5512
1-Feb-57 5499 The theory of the determinate machine includes the practical aspects of the theory of the Markovian machine.
1-Feb-57 5502 Sample space of a whole made from parts by coupling, they having sample spaces of their own.
1-Feb-57 5503 One system may have many confluants, and many separated systems may have a single confluent
2-Feb-57 5506 The whole built from random parts, by random coupling, when each part has probability πi that its state is equilibrial, does not go (if not in equilibrium) equiprobably to all states but favours those "near" itself. Summary 5524
  5507 Refusal to give a machine (or state, or input-valve, or transformation, etc) a particular value corresponds to talking about a set of machines (or states, or input-values, or transformations, etc). The set has no associated probabilities, but can use the concept of "independence". 5666.7
4-Feb-57 5510 The system that is contained only to have high equilibrium in its parts.
5-Feb-57 5511 High probability of equilibrium in the parts cuts the whole up into (temporarily) isolated sub-systems. 5522
4-Feb-57 5522 Habituation and its relation to equilibrium.
  5523 The system that habituates must be a flat sheet. (But see 5632) 5545, 5631
  5523 of relations between equilibria in part and equilibria in whole. 5259 (See article for refs) 5317, 5510
12-Feb-57 5527 Relations between equilibria in parts and equilibria in whole collected from the last 130 pages. Review 5983 5667, 6019, 6025, 5436
  5530 Reducing major Good to minor goods. 5537, 5532, 5578, 5626
18-Feb-57 5533 Basic meanings of organisation, reducibility, conditionality. 5537, 5675, 5993
20-Feb-57 5534 Example of isomorphism in differential equation form.
  5535 The time-factor insists that genetic adaptations and cerebral-learned adaptations shall be done mostly in the piece-meal way. 5601, 5631
  5536 Where I am now. 5558
22-Feb-57 5538 From essential variables to Grand Outcome, via trials. 5573, 5642
23-Feb-57 5540 Feedback cannot be discriminating unless an adequate channel brings the necessary information; (but any particular channel may perhaps be supplementable) 5628.7, 5547, 5584
  5544 Systems with super-fast sub-components.
  5547 "Thinking things over" in a multistable system. Discriminative feedback requires mere opportunism. 5549, 5584, 5601
27-Feb-57 5549 No general principle can be sufficient guide when selection must be done; some actual channel is also necessary. 5585
2-Mar-57 5550 In all cases so far, all arcs are assumed to have some sign that they are, or have recently been, active, and the discriminative feedback hits only those with the sign. 5557, 5584, 5601, 5609, 5628
  5551 Unsolved problem. (Strachey's solution, 5559)
  5555 The "diffusion" of structure is a manifestation of a whole which is really a chain going to equilibrium.
  5556 More on the spread of "structure".
6-Mar-57 5557 Others are building machines with discriminative feedback. 5584
11-Mar-57 5558 Personal note.
20-Mar-57 5559 The optimal duration of memory.
20-Mar-57 5559 A minimal quality of memory is not definable.
25-Mar-57 5568 Identification by random criteria is (in the defined circumstances) practically as good as accurate dichotomy.
25-Mar-57 5569 Major strategies are determined at the genetic level, minor at the cerebral.
28-Mar-57 5570 How this works yields application to psychiatry. 5651
  5572 The distinction between aggression and non-aggression corresponds, respectively, to having or not having a regulator. 5694
2-Apr-57 5576 The "essential variables" to a machine with input are those other parameters to it whose change would alter its canonical representation.
  5578 "System" and "machine with input" are very different.
2-May-57 5579 Essential variables in Multistable System 5601, 5625, 5642
2-May-57 5581 General formulation of "the environment" for an artificial brain. 5522
6-May-57 5585 Solution in principle of the problem of discriminative feedback. 5590, 5594, 5601, 5608, 5631
6-May-57 5588 Any question about how something can be achieved is answered: a regulator is necessary; lacking it the achievement is impossible. 5601
13-May-57 5590 Serial or sequential adaptation is equivalent, in a sense, to semi-iterated simultaneous adaptation. 5593
  5591 General phenomena should be explained by proportionately general mechanisms.
13-May-57 5595 What is necessary for the accumulation of adaptations. 5601, 5608
18-May-57 5600 From iterated systems to the multistable. 5612
20-May-57 5605 What is necessary for fast adaptation by reducibility. Much modified 5608 5736
  5607 Random dispersion will not achieve a useful degree of reducibility. 5619
24-May-57 5613 When the set of disturbances is a product set of minor disturbances, each of which has its appropriate reaction unconditionally, accumulation is adaptation is readily obtained. Often, the set of disturbances must be defined explicitly.
  5614 There are two quite different "lengths of trajectory." Better "transient"
  5618 Conservation (or accumulation) of adaptations as deference against imperfect isolation, when the "leakage" occurs in slow discrete steps. 5620, 5746
27-May-57 5621 The multistable system re-viewed. 5733, 5735, 5746
27-May-57 5625 How big should an arc be? 5746
27-May-57 5626 Why have arcs that are dynamic systems?
  5628 Reducibility of the essential variables in set theory. 5631, 5642, 5652, 5675
28-May-57 5629 How good a synthetic brain can I make?
  5631 The principles of search are not altered if what we search for is a decision (about what to search for - at a lower level)
30-May-57 5634 One unit for adaptation (in Multistable System) may comprise many portions (arcs) in the cortex. 5653, 5746
30-May-57 5635 Optimal duration of trial; optimal time back to make disruptive feedback work. 5642
31-May-57 5636 Continuity as a restraint.
  5641 The natural duration of a trial is the time of transmission of information from step-mechanism round then organism and environment back to step mechanism What is implied by "trail."
  5643 Distinguish between Essential and Vital variables.
13-Jun-57 5650 Vital variable identified generally; what it is vital to; sub-goals. 5811
14-Jun-57 5656 Various ways in which senility may affect the primary function of adaptation.
  5661 The information given by the behaviour of a whole, may often be insufficient for unique characterisation of its parts or couplings. 5983
  5665 In the relating of properties of the whole to those of the parts, one case (described) is of central importance.
17-Jun-57 5667 The unspecified machine.
18-Jun-57 5671 The extreme cases of the relations between equilibria in parts and whole. 5983, 6025, 6019
18-Jun-57 5673 If the stimuli are not restricted, the terminal responses to Limn→∞TnD mark out the areas of the T- confluants.
  5674 Clearer statements of the theorem on habituation. 5687, 5702.4, 5707, 5730, 6088
24-Jun-57 5676 If variables can't communicate, any operator on them may have to be reducible.
  5677 When two operators act alternately they still each have power of veto over any proposed state of equilibrium. 5708
  5680 High equilibrium in the parts versus communication of activity between them.
  5685 The machine that jumps directly to the answer, by spotting a constraint, extrapolates. It can do this only after having had previous experience with other problems in the same class, and by having a regulator that selects the better extrapolation functions. 5728
11-Jul-57 5686 Complexities in integration and coordination may be shown adequately by some simple evidence of their success.
15-Jul-57 5689 Program for habituation. 6088
15-Jul-57 5689 Normal behaviour is loopy.
30-Jul-57 5692 The homeostat programmed.
30-Jul-57 5692 The dynamic cannot claim that the static is just a sub-case of it.
1-Aug-57 5693 Design for a Brain seems to have been successful.
  5696 What is meant by "force" in psychology.
9-Aug-57 5697 When a set is called for, refuse to answer the question: which of these elements is the "actual" one?
9-Aug-57 5698 Evidence that learned reactions are related to one another in a primarily random way, order appearing only when the environment selects or enforces it.
  5699 Example showing how adaptation must be measured against a defined class of problems.
9-Aug-57 5700 "Transfer of patterns" demands only a transfer of values.
10-Aug-57 5702 The structure that is necessary and sufficient if the whole's later behaviour is to be much dependent on its earlier experience. (Note that all this is equivalent to saying that the system has memory)
12-Aug-57 5703 In habituation I have shown that the operator does matter and the system does not (within broad limits).
  5707 Implications of "going to equilibrium."
16-Aug-57 5709 When the alternation of two stimuli to a machine reaches equilibrium, the two effects and the equilibrium are related. 5724, 5729
17-Aug-57 5711 Every absolute system defines a topology, the "confluential", over the set of states. This topology may be similar to some other topology, well known over same set.
17-Aug-57 5713 For general guidance, one can think of a "topology" as a more complex equivalence relation, allowing degrees of "equivalence."
  5714 The intermediate degree of the conditioned response being brought "towards" the unconditioned
19-Aug-57 5721 Basic theory of the conditioned reflex
  5722 Some experiments on my theory.
20-Aug-57 5726 Simultaneous presentation does not give conditioning. 5730, 5827, 5862
23-Aug-57 5727 A very new way of producing "conditioning".
  5728 Constraints are found by applying information-losing transformations and seeing whether they are still acceptable to the essential variables. 5756
24-Aug-57 5730 If two forcing operators alternate, they will lose their distinction while forcing.
  5731 Cycles under compound operators. 5734, 5893, 6088
  5733 Arcs are necessary because, for adaptation to progress cumulatively, stores are necessary to hold the information that came from the essential variables. 5746
  5736 The Multistable System of D.f.B. (Design for a Brain) is one whose corrective feedback has already been made discriminating. D.f.B. shows how a system will behave after discriminative feedback has been established in it. 5746, 5766.7
31-Aug-57 5739 How habituation will show in a multistable system of arcs.
31-Aug-57 5740 An arc may "see" only a certain few out of a sequence of stimuli; these few are then "adjacent" for that arc, and may have unexpected effect, e.g. habituation. 5746
31-Aug-57 5740 If a variable is forced to a value, perhaps it does not matter whether the forcing is "discreet" or via an ultrastable, vetoing feedback.
3-Sep-57 5743 Variety, uncertainty analysis, and information. 5794, 5820
13-Sep-57 5747 Basic functional necessities for an arc, or store.
14-Sep-57 5755 Any restriction on one part of a system is likely to show as "structure" in another part of it, Reducibility exemplifier.
19-Sep-57 5756 Axiom that the "typical member" identifies the sub-set and the constraint.
19-Sep-57 5759 Layout for accumulative adaptation. 5766.7, 5775
20-Sep-57 5760 Additive mechanisms in the brain. 5763, 5765.1, 5766.1, 5768
  5762 The problem of the moving critical states. 5778
20-Sep-57 5763 Psychiatric application of the system that adapts additively.
20-Sep-57 5764 Importance of information whose changes occur only at long intervals.
26-Sep-57 5765 Psychiatric application.
26-Sep-57 5765 Operational meaning of "correct translation".
26-Sep-57 5766 Mechanisms for memory may well vastly outnumber those for action
1-Oct-57 5767 Essential variables for adaptation by accumulation.
1-Oct-57 5768 Complexity of remembering old adaptations is independent of complexity within one adaptation.
3-Oct-57 5771 Serial adaptation, and flow to the step-mechanisms.
8-Oct-57 5774 My proof (that adaptation demands step-functions) demands in fact only that there must be entities having a step-function aspect. This aspect may be one that is by no means obvious in the real object. 5781.7
8-Oct-57 5776 Design of DAMS. (Corrected 5778) 5779
8-Oct-57 5777 I may now use design and regulation freely in building DAMS, provided I admit its introduction.
25-Oct-57 5778 Layout for DAMS, and for the system that accumulates adaptations.
28-Oct-57 5780 Under certain conditions, communication between arcs is necessary.
4-Nov-57 5781 So far I have used essential variables as little more than links determining how the environment affects the step-mechanism.
5-Nov-57 5782 My claim that step-functions are necessary, must be made conditional.
25-Nov-57 5784 Step-functions have done their job and may now retire.
  5788 Index [?] of degree of stability of a whole, and its behaviour. 5800
9-Jan-58 5794 Some systems are not to be understood, or controlled, by the amount of information that can be accepted in 1 man lifetime. 5810
11-Jan-58 5795 The symmetrical relation between transmitter and receiver, of McGill and Garner and Woodward, is: between two variables' variations a constraint has been perceived. 5820
23-Jan-58 5796 Present position of the machine for solving super-problems.
  5798 Survival of the fittest, demonstrated in a computer. 5801, 5828, 5961
11-Feb-58 5801 Shrinkage to equilibrium, and adaptation to the operator that produces the shrinkage, are equivalent. 5961
  5807 How fast does a system adapt to an operator? "Convergency".
17-Feb-58 5809 Spontaneous generation of brain in a computer. 5812, 5816.7, 5958
  5810 Another example of how a large, and irreducible, quantity of information may be necessary.
22-Feb-58 5812 A variable may be essential to an organism and yet outside of it.
24-Feb-58 5814 Abstract formulation of "survival" and "essential variable". 5828, 5963, 5984
3-Mar-58 5816 (1) A part, may be rich in stable subsets. (2) Death hits both organism and environment.
  5819 An operator may be thought of as "changing its properties" if it moves from one sub-set to another. 5844, 6109
  5823 McGill and Garner's uncertainty analysis applied to machines.
  5825 The D.I.E. (diagram of immediate effects) marks out a subset from the set of all transformations. 5982
25-Mar-58 5826 Habituation and the conditioned reflex as consequences of the law of experience.
  5827 All that a mechanism for the conditioned reflex needs is a clear bias.
27-Mar-58 5829 Survival of the fittest in random operations. 5961
28-Mar-58 5830 In the cortex, study only the unspecialised case.
  5833 Transmission of variety through a random network, Let the net be not a chain but broad.
8-Apr-58 5835 When the machine with input is determinate, the output-trajectory determined by a given input-trajectory is stable.
  5836 Demonstration of how, over any set, any subset can be marked off as having a "natural" grouping. Even bigger batch 5896, 6167
  5839 The trap under a two-valued variation at the input.
12-Apr-58 5845 The pattern in the confluents tends to copy the pattern in the input-transitions. Stochastic case: 5873, 5892
14-Apr-58 5849 Jennings' law of the resolution of physiological states. 5880, 6101, 6137
15-Apr-58 5851 There are complications before "in same confluent" means "moving towards".
15-Apr-58 5854 The homeostat's confluents.
  5957 Conditioning on the homeostat examined by the method of confluents. 5877
16-Apr-58 5858 Paradoxical predictions for conditioned reflexes.
16-Apr-58 5861 Simple, second-order, third order Conditioned Reflexes examined by the method of confluents. 6097
16-Apr-58 5861 The conditioned dog must have these relations.
  5865 Defeat of my attempt to uncover the "secret" of the conditioned reflex.
  5870 Restoring single-valuedness of prediction, when parts of a machine with active input are not observable, by taking its history into account. 6050, 6069
21-Apr-58 5871 Constraint in the environment will show (in certain conditions) in the organism's behaviour.
  5872 Examples of patterns that will spread into the nervous system. 5949
22-Apr-58 5875 Transfer of pattern when input and machine are stochastic.
24-Apr-58 5876 Fully joined systems must be known k steps back if k variables are unobservable.
  5881 Relation between adaptation and anticipation.
25-Apr-58 5885 "Conditioned" stability can readily be defined rigorously. 6091
25-Apr-58 5886 "Conditioned" inaccessibility can readily be defined rigorously.
  5887 A system may have different subsets conditionally stable when the input has different constraints. 6091
25-Apr-58 5888 Transfer of constraints from the world outside to that inside.
8-May-58 5889 A machine with input may correspond to an algebra.
9-May-58 5891 Statistical trends (in stochastic processes) are, to be evolving species, simply a method that may or may not be adapted for the job. Once adopted, they have the force of a law.
9-May-58 5893 How a relation is transmitted by an operator.
  5895 Patterns on the transitions at the input lead to isomorphic patterns on the transitions internally. 5900, 5905 [deleted].
  5899 Pattern recognising. 6167, 6305
  5902 If a sequence of impulsive stimuli is constrained to certain transitions, the transitions of the representative point between equilibria tends to an isomorphic pattern. 5905 [deleted].
12-May-58 5905 Present-day topology is obsessed by continuity, and is therefore of no use to me. (I must evidently develop my own theory of structure. This structure* was identified on 4934, in Bourbal's sense, and I have been developing it ever since, with "laws of experience" and such like. Restricted neither to continuity nor groups, nor numbers, nor algera, nor metric) 5949 * This structure was identified on 4934, in Bourbaki's sense, and I have been developing it ever since, with "laws of experience" and such like.
12-May-58 5905 Adaptation, and diffusion of structure may go on independently. [deleted]
13-May-58 5909 Program for developing the mathematical theory of machines.
17-May-58 5913 Rigorous form of what is implied by the operator "let it get to equilibrium before applying the next stimulus". 5994, 6084
19-May-58 5914 A new form of independence and the "proxy" relation.
  5916 Hilton's very wide definition of "isomorphism".
19-May-58 5922 "Isomorphism" as one of many relations that may hold between relations.
27-May-58 5928 The theory of super-relations and the laws of pattern.
28-May-58 5929 Do not confuse "patterns R are like patterns S", with "there is constraint in [RxS]. 6063
2-Jun-58 5941 The relationship S=ΦRΦ-1, studied from various angles. 5946
3-Jun-58 5948 Transition at input and transition between equilibria are related in the form S [subset] ΦRΦ-1. Not = , as given on 5893) 5949 [deleted]
3-Jun-58 5948 Algebraic form of "[T~'s] trajectories are not more than one step long".
4-Jun-58 5951 The constraint algebraically when a transition can only be to an "adjacent" state.
  5957 The set of stable sub-sets forms a lattice on which the representative point moves only downwards. (True both for determinate and stochastic transformations) 6091, 6093
24-Jun-58 5961 How to generate Life and Intelligence with probability 1
  5965 Intricate cleverness in an organism can be demonstrated only when the whole has been analysed into plenty of parts. 5985
25-Jun-58 5966 Spontaneous generation of life and intelligence in analogue form. 5967, 5984
  5968 The typical, or modal, element from EE will not provide a system showing the spontaneous generation of intelligence. 5984
  5969 A set may be expressed with full generality both by arbitrary labels and by any arbitrary product-set-form. The product set is fully general. Review 5978
  5971 We may see a whole with any set of components we like. Division of a whole into parts is relative, so far as labelling is concerned. Review 5977
  5973 Wholes are divisible into parts specifiable by the observer, arbitrarily. 5984
  5976 Any arbitrary system may allow the demonstration that it contains any arbitrarily selected part.
12-Jul-58 5984 A review of the relations between "whole" and "part". 6019, 6025
  5985 Abstractness can go too far. 'Adaptation' demands several parts.
17-Jul-58 5986 Cortex - not statistical but stochastic.
19-Jul-58 5990 Imposing a property on the set of input-trajectories will necessarily impose a property on the set of output-trajectories. 6063.4
  5991 "Constraint" is a relation between an Observer and a set.
  5992 Pidget on conception of space.
22-Jul-58 5995 Rigorous form of saying that behaviour is "organised". 6007, 6021
  6002 Review of Elsasser. 6046
24-Jul-58 6005 "How much information in a brain?" is best preceeded by consideration of "how much information in a flip-flop?" 6043.8, 6179.9
29-Jul-58 6007 Notes from Birkhoff's Hydrodynamics.
31-Jul-58 6011 Every theory has two informational aspects: its passive, when it is learnt or otherwise acquired; and its active, when it is used as transducer. The two qualities of information are not linked necessarily.
  6014 The notion of two machines being "similar", or even just "related", has been completely generalised.
1-Aug-58 6016 Relations between machines.
1-Aug-58 6018 DAMS was built by an ignoramus. 6025
  6019 Parts that have only one state of equilibrium (for each given input) may build a whole with a multiplicity of equilibria.
  6020 In DAMS, I went for the cutting-up; I should have gone for the equilibria. 6028
  6023 Sommerhoff's basic formulation given set theory. 6104
8-Aug-58 6024 Wiener suggests that maths is a dynamic process, that may end in a cycle.
8-Aug-58 6029 Effect of D.I.E. on maximal equilibria of whole - cuts make the maximal number fall.
11-Aug-58 6032 Eigen-theory generalised. 6109
13-Aug-58 6033 A physical system that is not completely analysable. 6065
30-Aug-58 6035 Algebraic property of the machine that transmits without loss of information.
  6039 Coding a function.
9-Sep-58 6042 Certain concepts about a machine demand a set, which can exist only in another machine. Such concepts can hardly be used by the machine if thinking about itself.
9-Sep-58 6042 Machine whose output is invariant for changes in the speed with which the input is sent in. There must be an intervening stage of memory.
22-Sep-58 6044 Number of atoms in the brain, and the maximal information it can store. 6179
  6045 Distinguish between the qualities, in the brain, of information and of memory.
  6049 Finding how much information there is in a brain.
  6057 "Memory capacity" is basically channel capacity between times in the same system. Any Black Box provides an infinite number of capacities. 6069
29-Sep-58 6058 Of all the !memory capacities", the maximal value may be of physical interest. 6179
  6059 Build devices for demonstration.
22-Oct-58 6060 Build small specialist machines, each devised to show one fact with perfect clarity.
  6062 Blitz-therapy.
13-Nov-58 6063 Two sorts of memory are identifiable. 6068
19-Nov-58 6067 Irreducible complexity.
18-Nov-58 6066 A proposition is "atomic" if its user does not propose to break it up.
18-Nov-58 6066 The brain may be like a digital computer in being error-free by going from equilibrium to equilibrium. 6126
19-Nov-58 6067 Simple "relations".
19-Nov-58 6068 To test whether memory really is permanent.
  6070 Effect of "memory" is studied by the usual method for studying effect, but the two variables are separated in time (as well, usually, as in space)
  6072 A DIE can be demonstrated rigorously in a machine with memory, and by the same basic operations as when there is no delay. Continued 6105
28-Nov-58 6073 Learning by pain is fundamentally simpler (demands less communication ) than learning by reward.
10-Jan-59 6074 The theory of machines may help with interpolation rather than with long range prediction. 6076
  6075 The physicists are not yet clear about what they mean by 'casual' and 'determinate'.
17-Jan-59 6078 The value of the new logic of mechanism can easily be over-rated.
  6082 Equilibria attract. 6267
  6083 The process of inscription is much weaker than I thought on 5844. Continued: 6092
  6085 Operation "go to your basin". 6267
21-Jan-59 6088 Habituation with cycles allowed. 6108
  6090 A general method for solving problems in combination dynamics. 6108, 6349, 6334
  6091 Closure under a sequence imposes little restriction on the closures at intermediate stages.
23-Jan-59 6098 "Inscription" goes. How a pattern of equilibria is related to the pattern of transitions at the input. 6143
  6103 Final conclusions (to date!) about my explanation of Jennings' law. 6347, 6137, 6108, 6143, 6127, 6128, 6269
14-Feb-59 6104 Another way of writing Sommerhoff's directive correlation. 6105, 6284
14-Feb-59 6104 Are isomorphisms denser around equilibrium?
25-Feb-59 6105 Isolating a pure concept is like isolating a pure element.
  6107 Berge's book shows me I must develop my combinatorial dynamics myself.
16-Mar-59 6110 Restriction of an operator to a selected domain may make evident a property that is otherwise inconspicuous. 6137, 6350
  6111 Quantum mechanics is moulded chiefly by specific atomic peculiarities, not by general epistemological principles. 6179, 6303
2-Jun-59 6116 Oscillating systems, when coupled, do not necessarily pull together in frequency.
13-Jun-59 6117 When a simplification is permissible. 6148, Better: 6254
13-Jun-59 6117 Today I can say I have solved the problem I set out to solve on 7 May 1928 [31 years prior]. I asked, roughly, whence came the patterning properties of the nervous system. The answer is now clear...
  6118 ... As the selection gets more intense, and the closed set smaller, so does the relation show more intensely. But also, so does it become more degenerate, until finally, at a state of equilibrium, the degeneracy is complete. Then all - disturbances and responses - meet at zero. The adaptation is perfect, intelligence infallible, all in Nirvana. The final statement.
25-Jun-59 6119 General, abstract, nature of "induction",
21-Aug-59 6120 Threshold combines lots of equilibria with continuity.
  6123 Possible function for the "functionless" parts of the mid-brain.
  6123 The "size" of a system had no unique meaning.
15-Sep-59 6125 Isomorphism, homomorphism and now protomorphism. 6150, 6260
18-Sep-59 6127 The environment goes much from equilibrium to equilibrium, constant on route but noisy in timing. The brain, appropriately, also goes much from equilibrium to equilibrium.
  6128 Any part of the brain that behaves, with a characteristic pattern will tend to send that pattern to other parts. 6137, 6143, 6248
19-Oct-59 6131 How the amines may come in.
  6133 Rapid adaptation in an irreducible whole implies many equilibria in the parts.
  6136 Simultaneous forcing of two variables may give a slight tendency to association. 6140, 6197
14-Dec-59 6137 Closure under a sequence, and a property of one operator, implies a corresponding property on the other operators. 6143, 6269
18-Dec-59 6140 A more general type of "forcing" operator". 6269, 6247, 6312, 6322
  6141 Razran's review reviewed. 6269
18-Dec-59 6142 Set theory: model or language?
  6146 Given a machine, an input restricted to certain transitions, and a subset closed under all sequences (words) restricted to such transitions, to find the properties of the pattern of transitions at the output. 6152
  6147 The outcome of an infinitely long input can be predicted from a finite number of steps.
15-Jan-60 6150 Measuring how much a machine has been simplified.
4-Feb-60 6151 'Relations' between patterns.
5-Feb-60 6157 Input pattern of transition showing as output pattern.
5-Feb-60 6157 Nearness in time encourages similarity in response.
19-Feb-60 6158 ... no regulator can be more effective than the state-determined system.
23-Feb-60 6160 No regulator (other things being equal) can give performance better than the machine with input.
3-Mar-60 6162 Meaning of H(A)=0.
11-Apr-60 6165 Example of the coordination that exists at a state of equilibrium. 6350
13-Apr-60 6167 When there is no information about the problems that recur, accumulation demands that the activations are small and that the "chance" method be used. 6227
  6169 What are grouped together as "equivalent" must be specified; information is required. 6181, 6222, 6305
  6173 When a particular equivalence relation is to be specified, the variety to be suppressed is of the order of |n. 6182
  6177 The concept of feedback being positive or negative is usefully simple only when the system is continuous. 6184 [Goes in small steps - Riguet 6184]
12-May-60 6179 Solution of the linear difference equation.
3-Aug-60 6181 More on self-reproduction.
5-Aug-60 6184 Selfridge's Pandemonium and pattern recognition. 6222
10-Aug-60 6185 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".
10-Aug-60 6187 The "general purpose" computer of today is in fact extremely specialised.
  6189 The general purpose computer, to become a really general machine must simply become a table-searcher.
21-Aug-60 6192 Rubin and Sitgreaves' results summarised. 6199
22-Aug-60 6193 I must demonstrate, some day, that a heap of manure has as high an organisation as a man.
2-Sep-60 6194 In a lot of ways a system cannot, strictly, be "self-.....ing". 6566
6-Sep-60 6197 Independence of probabilities of equilibrium demands that all loops of connexion be long. 6199, 6333
19-Sep-60 6198 Can two fields be very different if both have lots of equilibria? 6248
  6206 Properties of the polystable system. 6243, 6248, 6342, 6363
  6207 Estes finds learning to go in jumps. 6542
16-Oct-60 6222 Zato-coding.
  6224 Pattern-recognising after coding. 6260, 6346
  6226 Form all mappings, and you are performing all pattern-recognitions. 6346
  6228 Adaptation to the recurrent situation demands step-mechanisms with a multiplicity of channels.
30-Oct-60 6233 What properties of a brain are specialisation to terrestrial life and what are good absolutely? 6404
13-Nov-60 6242 We study "machines" that depend on their immediately preceding states because experience has shown them to be very common in the world around us. 6246
  6243 I must write a text book on the Theory of Equilibrium. 6350
  6245 Why systems prefer small responses. 6248, 6250
19-Nov-60 6247 Only restricted types of trajectory or process are suitable for cybernetic studies.
23-Nov-60 6249 "Association" clarified further. 6269
  6250 Sketch of a theory that two coupled systems, in going to equilibrium, tend to prefer regions in their phase-spaces that are topologically similar.
24-Nov-60 6251 At equilibrium, with suitable metric, the responses have a bias towards smallness.
  6257 Machine Σ may be simplified by equivalence Relation [formula] 6260
  6259 Campbell won't allow "genius". 6289
4-Dec-60 6262 [SRS-1] is the "shadow" of R when "projected" by S. It can be inverted back to R if and only if [S-1S=Δ]. 6265
  6264 Immediate effect is a reality-shadow reaction.
  6265 A machine is a "shadow" of simple progression.
16-Dec-60 6266 Meaning of [formula]
17-Dec-60 6271 A better statement of the equilibrium theory of the Conditioned Reflex and Jennings' law. 6295, 6312, 6323, 6333, 6338, 6347
  6273 Theory of Conditioned Reflex and Jennings' law without equilibria under each operator. 6316, 6338
  6276 Review of Suppes' book.
8-Jan-61 6283 There is no difficulty in getting from a structure of mere clubbing to a full topology.
16-Jan-61 6284 Extension of homomorphism.
17-Jan-61 6288 Directive correlation quite simply. 6297
  6289 Specifying the "worst" brain.
2-Feb-61 6290 The genius searches. 6335, 6339, 6430, 6570
2-Feb-61 6291 Unsolved problem: must systems grow in a way that is grossly self limiting in organisational possibilities?
  6292 The Hamiltonian is a constraint on the field, therefore uninteresting.
  6293 The Hamiltonian is not for me. 6321
12-Feb-61 6295 Energy flow is neither maximal nor minimal at equilibrium; it is just irrelevant. 6321, 6345, 6350, 6365
23-Feb-61 6296 If a set is diminished, any set tied to it by any relation will be diminished.
  6297 Getting from simple equilibrium to directive correlation. 6350
4-Mar-61 6298 What a species can do, it can recognise.
4-Mar-61 6301 So we have exemplified the fact that laws that are functions of their place of action, will develop different adaptations in different places. 6350
18-Mar-61 6302 A species that needs its competitors. 6350, 6355
  6305 The dynamics of the wave-function is that of a state-determined system.
24-Mar-61 6306 Pattern recognition is arbitrary. 6346
2-Apr-61 6307 The "anatomical" body is only one way of identifying the boundary of a system.
  6310 What "isolated" means. 6349
1-Apr-61 6311 Natural systems, observation, and experiment.
  6314 Five properties necessary for the conditioned reflex. [deleted]
  6315 New layout for the conditioned reflex. [deleted]
  6317 More on Conditioned Reflex 6323, 6347
15-Apr-61 6320 I read the riddle of [Pavlov's] page 197. 6338
  6321 Clear example of how a Newtonian system, with no convergence by Liouville, may show strong convergence if seen by a simpler observer. 6627
16-Apr-61 6322 "Forcing" does not imply "one confluent."
  6325 Final (?) statement of the lae of anticipation. 6334, 6342, 6347
  6331 Mechanical layout for showing law of anticipation. 6333, 6334, 6342, 6347, 6352
  6332 To show anticipation. 6334
22-Apr-61 6334 Mixing network, one way.
4-May-61 6335 "Transmission" of selection among the components of equilibria. 6347, 6350
11-May-61 6337 In a process of search, knowing the goal, and especially of intermediate goals, can cut the time fabulously.
  6339 Dickens says eloquence comes from thinking about the subject.
  6341 Information when two inputs try to get through one output.
  6344 Construction to get many compact confluents. 6347, 6362.9
25-Jun-61 6345 Convergence to equilibrium in Markov chain.
27-Jun-61 6346 Pattern recognition is arbitrary.
  6349 Theory of anticipation. 6352, 6374, 6389
  6351 Equilibria and their properties. 6373, 6389
1-Jul-61 6352 The elementary conditioned reflex processes only about 2 bits of information, and needs a mechanism of only that capacity. 6363
  6354 Notes on: Finding stored information. 6362
  6357 Example of natural selection and evolution in a computer. 6358
  6359 Survival of the fittest in a computer.
  6361 Survival of the fittest in a computer.
29-Jul-61 6362 For economy, the brain must store memories at the site of use. 6383
14-Sep-61 6364 How to make a multistable system.
15-Sep-61 6366 The physicist's equilibrium at zero free-energy and the biologist's homeostasis.
17-Sep-61 6369 A game of chess shows three "organisations" simultaneously. One goes down, one up, and one does not change. 6379
27-Nov-61 6370 The great difference between teaching by pain and teaching by pleasure. 6550
27-Nov-61 6370 To feel sympathy is to have no assurance that the other entity is really feeling. 6384
  6371 It is often forgotten that planning must have a goal. 6401
29-Dec-61 6373 The polystable system tends automatically to find and to use the constraints.
9-Jan-62 6374 To show anticipation, the operations must be such as lead to a unique state; by what route, whether quickly or slowly, are irrelevant 6389
  6375 How a Markov chain shows in Uncertainty Analysis of the triples.
9-Jan-62 6376 How many parts produce this trajectory?
  6377 Proof of previous note.
  6380 Organisation and redundancy should be defined, in set theory, as [RR-1'R].
26-Feb-62 6381 [RR-1'R≠0] is a sensitive test for the existence of constraint, but [RR-1'R] does not equal it.
13-Mar-62 6382 On the subjective. 6384, 6427
1-Apr-62 6383 Memory held on constraints.
  6385 A machine can transmit only ......what?
  6386 When [x'=Φ(x)], no convergence anywhere implies div Φ=0 everywhere.
  6388 Examples of ideas that demand the pre-existence of other ideas.
  6393 Theorem on anticipation. 6394
21-Jul-62 6396 The hard core of "habituation", rigorously.
21-Jul-62 6396 Two random mappings in succession do not give a random mapping. Nor one used twice, similarly.
22-Jul-62 6399 The unit that develops anticipation must be tiny.
1-Sep-62 6401 Specialising the anticipation, may properly go into μ. 6457, 6588
12-Nov-62 6404 The designer (or planner) must select among the equilibria.
  6406 Every faculty is good or bad according to the environment.
  6409 The number of circuits traceable round n fully joint parts increases as |n (approx). 6426
27-Jan-63 6417 The theoretical unit is simply a mixer.
  6418 To build any machine, only a mixer is sufficient.
  6420 The Pitts-McCulloch neuron from my atom.
  6423 Stability of a mixed net of Ashby atoms.
  6426 How big numbers arrive. 6438
  6428 Some peculiarities of the "self" relationship.
10-Jun-63 6429 Some problems become non-trivial only when much detailed specification is added.
  6432 Shannon to Sommerhoff.
  6435 How two functions f and g must be related if they transmit the value x independently of the value of y. [DIAGRAM]
  6435 Some "geniuses" are just the people who happen to be right. 6570
28-Jul-63 6437 "Thing" and auto-correlation.
  6439 The topologies on n points number about exp(n2). (Size No. 7 on 6424) 6454
5-Aug-63 6442 Review of Waddington's "Nature of life".
  6443 Algebraic form of "the behaviour doesn't depend on variables Z".
6-Aug-63 6445 "Remembering" as hallucination.
6-Aug-63 6446 Example of how too much memory can be disadvantageous.
16-Aug-63 6450 Some details about binary relations from B. Russell.
  6453 Logical dynamics. 6455
27-Aug-63 6454 Example of how a topology is learned.
  6456 A memory of a pattern does not have to be stored anywhere.
19-Nov-63 6460 Proofs the orders of size.
  6461 Indefinitely long memory in simple machine. 6470
7-Jan-64 6464 A practical way of getting fairly long trajectories with all ending in states of equilibrium. 6485 says joins need not be invariant in time.
  6465 The start of Relation and Constraint Analysis. 6467, 6473, 6476
10-Aug-64 6475 Much in "Computers and Thought" is relevant to cylindrance.
12-Sep-64 6477 In the system that is not richly joined, the cylindrance of the set of initial and terminal states tends to increase exponentially with time. 6485, 6549
17-Sep-64 6479 Examples of low cylindrance in everyday life.
  6483 Movement of Amoeba: parts and whole. 6703
21-Sep-64 6484 Contractile molecules in an Amoeba can readily get coordinated for movement. 6789
  6488 If every unit has only k inputs, but may move the k around over all the variables, the cylindrance in the 2n-space X'x X is restricted to k + 1. 6493
  6489 If the inputs are changed infinitely fast, the restriction on cylindrance holds, but no trajectory can be found. 6491
  6490 Simpler proof that seeing k keeps cylindrance, in the 2n space, down to k.
  6492 "Interaction" corresponds to the last elements removed as Cp-1R shrinks to R.
7-Nov-64 6495 A set may increase in cylindrance if a variable is ignored. 6522 Generalised to n dimensions: 6531 Footnote 6502
7-Nov-64 6496 Meaning of "meaning".
8-Nov-64 6498 If the distinction between two values of a variable is lost (and the relation re-formed by union, i.e. + and 0 counts as +), then cylindrance may increase. 6504
8-Nov-64 6502 Effect on cylindrance of adding new values to variables (values that did not occur before in R)
18-Nov-64 6504 Cutting out a slice cannot make cylindrance rise.
22-Nov-64 6506 Effect on cylindrance of an equivalence relation when the sections combine by intersection.
25-Nov-64 6509 If only g variables vary, the cylindrance cannot exceed g. 6509 (foot)
  6512 Rigorous proof that a set with t points cannot exceed t in cylindrance.
  6515 Theorem.
5-Dec-64 6518 When they are cylindrance-one sets, composition does not raise the cylindrance. 6519
5-Dec-64 6518 Combining sets to form their product does not raise cylindrance. 6824
  6523 Composition (or elimination) will not raise cylindrance unless the implied projection raises it. And a proof that projection can raise it. 6826
  6525 Section will not raise cylindrance unless the implied projection raises it. And a proof that section can raise it.
  6527 Proof of: As base, so cylinder. Better: 6825 Example of 6494
23-Dec-64 6528 Cylindrance is a generalisation of reducibility.
24-Dec-64 6529 Defeated. Not this time - see page 6531
24-Dec-64 6530 There is no obvious relation between cylindrance and stability.
7-Jan-65 6533 Example showing how projection may jump the cylindrance up from 2 to any given number. Another example 6829
7-Jan-65 6533 The theory of the determinate dynamic system leads naturally to set theory and cylindrance.
  6534 The man who understands.
  6539 Goodwin's results are magnificent, and rigorous; but dangerously specialised.
  6542 Estes on the permanence of many traces.
16-Apr-65 6544 All the maths we know has low cylindrance. 6551
16-Apr-65 6546 Any selection of 1 from more than 101000...(47 zeros)...0 is physically impossible.
  6548 How information-quality can explode when complicated at the sensory side. 6549
14-Jun-65 6549 Length of sequence increases the uncertainty exponentially.
21-Jul-65 6550 Learning by pleasure is sophisticated.
  6551 Almost all the operations used in proving theorems do not raise cylindrance.
  6553 Simpler proof of Lemma.
25-Oct-65 6558 Extracts from Huxley.
  6559 p-dimensional projections may not be allowed arbitrarily (if n>2)
15-Nov-65 6561 A relation can always be found that has projections including, or not including, in arbitrary fashion, those of a given point.
  6563 The idea of a system reporting on its own behaviour is better replaced by some much simpler equivalent.
  6566 A mathematical virus.
  6568 Reduction of high cylindrance to low; examples. 6611
4-Apr-66 6572 Every subset (of a product set) implies a quantity of internal transmission of information.
  6574 A woeful special case in transmission. 6579 Solved again 7006!
7-Apr-66 6577 Analyses of data or relations (Fourier, of variance, into partial correlations, etc) are of use only if the first few terms collect all that is significant. 6615
  6578 Transforming sets of low cylindrance to a "simpler form". 6679