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 425 over the period 19411972. 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 
4May39  0586  Nirvanophilia is identical with stable equilibrium. 
20Jun39  0588  A great idea... organisation must spread from the environment inwards. 
4Jan41  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. 
4Jan41  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}/dx_{k}" is given. (3) The Question "Does x_{i} depend on x_{k}" is meaningless. (4) New form of matrix test for dominance is given. (5) Definitions given of (a) x_{i}t curve depends on x^{0}_{k}, (b) x_{i}t curve is independant of x^{0}_{k}, (c) x_{i} dominates x_{k}, (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.  
22Jul41  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). 
22Jul41  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. 
22Jul41  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? 
24Jul41  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. 
24Jul41  0970  Our substitutions deal quite adequately with the idea of the free energy available to the brain and body  by ignoring it. 
24Jul41  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. 
25Jul41  0972  If, from a given system, we remove knowledge of a variable, we must introduce probability to replace it. (But see next paragraph) 
25Jul41  0974  If initial conditions are unknown we must replace them with probability. 
25Jul41  0976  The idea is suggested that the old memories, as organisations, may be present implicitly rather than explicitly. 
27Jul41  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. 
27Jul41  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 ypoint in yspace 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.  
13Aug41  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 stepfunction 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  "Stepfunction" 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 stepfunction of the time. The effect in a field of a stepfunction 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 stepfunctions to this new value" and not a surface as suggested on 898.  
22Aug41  1009  (1) Brain activity will sometimes conduct an animal, with great ingenuity, to its death. (2) Survival is a byproduct of brain activity. 
22Aug41  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. 
22Aug41  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.  
28Aug41  1020  All stepfunctions can be expressed as a linear function of one basic stepfunction, stp (x), "stepx", here defined. (Not true) 
1022  The behaviour of breaksurfaces.  
28Aug41  1023  Another example of the conclusion of 1006. 
28Aug41  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. 
29Aug41  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 stepfunctions. It confirms the theorum of 1021. The existence of "false neutral points" is noted.  
3Sep41  1038  A much better statement is given of the idea of varying patterns of dominance etc in a system. 
3Sep41  1038  "Break" does not involve "irreversibility". 
1041  In the specification of a system with stepfunctions present, the latter cannot be specified by differential equation form. It seems that our equations for the system must be in form { dx_{i}/dt = f_{i}(x;y), y'_{i} = a_{i}+b_{i}stp{V_{i}(x;y)} } or { x_{i} = F_{i}(x^{0};y;t), y'_{i} = a_{i}+b_{i}stp{V_{i}(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.  
15Sep41  1044  The Vsurface of a stepfunction cannot have a free edge. 
15Sep41  1045  Substitutions may, perhaps, define an infinite continuous group. 
1046  "Simplicity", "wholeness", etc are perhaps clarified by the discussion above.  
26Sep41  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. 
29Sep41  1051  Differential equations with stepfunctions 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)  
29Sep41  1055  Examples are given in ordinary machinery of "change of organisation" and "break". Both are rare. 
2Oct41  1056  Our definition of "dominance" of 960 is correct. See 1077 for a fuller survey. 
4Oct41  1057  The idea of a system, like the brain, altering its own organisation necessarily implies the presence of stepfunctions and breaks. 
24Oct41  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. 
18Nov41  1061  It is shown conclusively that "isomorphism" does not necessarily imply "group". 
19Nov41  1062  Some examples are given showing how a statement may be quite true about the whole and yet quite untrue of all the parts. 
2Dec41  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.  
1Dec41  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.  
8Mar42  1074  Actual equations are constructed giving the theoretical views of the nervous system in mathematical form. (See 1092) 
8Mar42  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". 
22Mar42  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)  
25Apr42  1095  "Breaksurfaces" 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.  
15May42  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. 
18May42  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. 
4Jun42  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. 
7Jun42  1106  A variable may add further breaksurfaces 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.  
8Jun42  1111  A red letter day. A problem in the application to the brain is solved. 
1114  If a machine with variables x has breakvariables h with Vsurfaces 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 Vregion. 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 xmachine changing its organisation again until it has found a new equilibrium, with the x's still inside the Vregion. O.K., O.K!  
1118  A list of examples of equilibrium in biology.  
9Jul42  1122  If two environments keep occurring, a system will break till it finds an organisation making it stable to both. 
9Jul42  1123  "Reaction" is divided into "response" and "variation". 
9Jul42  1123  The intrinsic form of a substitution might prove interesting. 
16Jul42  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. 
16Jul42  1127  After all these years I conclude that "vectors" are not what I want. 
1132  Some musings on bicycle riding.  
6Sep42  1134  Preliminary discussion of a machine falling, temporarily, into parts. 
2Oct42  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. 
14Oct42  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.  
31Oct42  1141  n breaks provide 2^{n} 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.  
31Oct42  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)  
19Nov42  1155  A review of Jennings' book. 
20Nov42  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) 
22Nov42  1157  A refinement of the definition of "organisation". 
22Nov42  1157  "Memory" equals change of organisation. 
22Nov42  1158  "Adapted" behaviour equals the behaviour of any system around a point of normal equilibrium. (1148) 
24Nov42  1159  All my theory explains the "trial and error" method in terms of nonliving 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.  
28Nov42  1176  A clarification of the concept of a "breaksurface". 
28Nov42  1176  The conditioned reflex is not clear yet. 
28Nov42  1177  A field can be explored easily, but breaksurfaces are destroyed by their discovery. This may involve curious philosophical properties. 
1180  Dynamic systems are, in general, fundamentally irreversible.  
1Feb43  1181  The concept of "break" does not need that of "irreversibility". 
8Feb43  1182  Theory has been submitted for publication for the third time. 
1187  The concept of "a reflex" is translated into my organisational terminology.  
20Feb43  1189  A dominating system can control the position of breaksurfaces of a second system. 
1198  It has been shown that a representative point, staying within a region bounded by a layer of breaksurfaces, 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.  
25Feb43  1201  "Adaptation" is more properly divided into: the adapted state after this has been reached, and the process of finding this state. 
8Apr43  1209  We study how adaptation can increase qualitatively, and are led to define and examine "partfunction" and "partsurface". (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)  
15Apr43  1219  A property of stepfunctions. 
18Apr43  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 nonadaptation; 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.  
4Jun43  1259  We have a right to expect that normal equilibrium will be commoner than other sorts 
9Jun43  1265  Partfunctions and stepfunctions should be defined as special types of path in a field. 
1267  Whittaker defines "equilibrium" and also a "neutral cycle".  
16Jun43  1282  We have got a grip of "partfunction", finding that it depends simply on zero values of dx_{i}/dt. 
30Jun43  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.  
20Jul43  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. 
21Jul43  1298  We may not write arbitrary functions in the solutions x_{i}=F_{i}(x^{o};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.  
23Jul43  1304  A review of Carrel's "Man, the unknown". 
24Jul43  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 x_{i}=F_{i}(x^{o};t). (Assembling a machine gives us the [x^{o}_{i}=f_{i}(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.  
27Jul43  1318  "Stepfunction" 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.  
1Aug43  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.  
1Aug43  1327  The nonzero 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!)  
7Aug43  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 n_{1}, variables dominating n_{2} will in 1p^{n2} cases get equilibrium by getting it in the n_{1} and then in the n_{2}, while in p^{n2} cases it will get the whole simultaneously, the latter proportion being vanishingly small. Experiment will therefore demonstrate the equilibrium appearing in stages.  
9Aug43  1359  An unsolved problem in organisation. (Now see 1420) 
11Aug43  1367  If a complete system has n variables and r parameters [x^{}_{i}=f_{i}(x;λ)], then the λ's can, from given starting point, control the movement of the xpoint within an rdimensional space which moves with time through the nspace, but the λ's cannot control the movement of the rspace. (Now see 1376) 
11Aug43  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.  
13Aug43  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!  
16Aug43  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.  
19Aug43  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). 
20Aug43  1396  A proof, with modern technique, of the old problem, showing that two stable machines can be joined to form an unstable one. 
21Aug43  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 chainfashion is reexamined. 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.  
23Aug43  1409  Contrary to p.____ [0599], the concept of equilibrium does not depend on a circuit. 
23Aug43  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 coordinatetime 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.  
31Aug43  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. 
4Sep43  1424  It is shown that the "hourglass" 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 coordinatetime pairs, the particular path is fixed.  
1427  Notes from Eisenhart. (Ref. 476)  
11Sep43  1431  Six definitions of a "complete" system are given and are all proved equivalent. 
14Sep43  1433  Some references to amoeboid activity in nerve cells. 
1435  The brain is an equilibriumtrap. And if the equilibrium can only occur on certain conditions then the brain will trap those conditions too! 1487.  
29Sep43  1439  Stabilising some variables almost certainly stabilises those other variables connected with them. 
30Sep43  1441  More notes on the "hourglass" case. 
1Oct43  1442  A definition of transient and permanent equilibria. 
1443  The projections of a path, and the solutions x_{i}=F_{i}(x^{o},t) are two forms of the same thing.  
4Oct43  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. 
5Oct43  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.  
6Oct43  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. 
6Oct43  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 F_{i} contains (or not) x^{o}_{i}  
8Oct43  1470  A simple practical example of the "hourglass" 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.  
15Oct43  1476  The shift is calculated, of a neutral point as a result of small changes in parameters. 
15Oct43  1477  How to use my theoretical discovery for practical purposes. "Organisers, Ltd". "You want the best organisation, we have them." 
15Oct43  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 selfcontradiction. It is analogous to "magnifying". 4930 
19Oct43  1494  A superb theorem, much more general than that of 1113, and much more precise. It includes the other theorem as a subcase. 
20Oct43  1497  A test, and example, for stability or instability of a neutral cycle. 
21Oct43  1498  Reasons for changing the form of the index. 
23Oct43  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. 
23Oct43  1503  "Stepfunction" 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.  
26Oct43  1512  1506 is confirmed, that a change of variables does not generally affect the applicability of the theorem of 1493. 
27Oct43  1515  Variables cannot be exchanged for derivatives when the conditions of 1493 are to hold. 
28Oct43  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 hourglass 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.  
6Nov43  1524  James stating that a machine cannot vary its behaviour. 
8Nov43  1525  Levy supports my view that knowledge of a real dynamic system is purely empirical. 
8Nov43  1525  Notes from Bradley's book. 
9Nov43  1526  The problem of the "distributor" solved, in essence. 
1529  A few notes on the important question of exposition.  
3Dec43  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.  
11Dec43  1535  Fisher's book. 
22Dec43  1538  A first attempt at a theory of selective operators. 
1Jan44  1540  An "instant" system is defined. A noninstant 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.  
11Jan44  1548  The elementary ideas on systems and their behaviour is thoroughly tidied up and clarified. 
1553  The properties of noncomplete systems are described.  
1554  An attempt to find the effect on the field of permanent zeros in the first Jacobian matrix.  
11Jan44  1555  Two problems for the future are noted. 
12Jan44  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.  
22Jan44  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.  
2Feb44  1573  Theorem B is rejected. 
2Feb44  1573  A field. 
2Feb44  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 stepfunction of the time. (The change defines the stepfunction).  
18Feb44  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.  
19Feb44  1582  Observation provides x_{i}=F_{i}(x^{o};t), the derivative form is  er  derived; method given. 
27Feb44  1585  An attempt at the analytical expression of a partfunction. 
27Feb44  1586  The least possible join of two absolute systems is that they should share a common stepfunction. 
27Feb44  1587  Convenient equations in the technique of joining and separating parts and wholes. 
27Feb44  1588  A symbolic way of writing stepfunctions. 
27Feb44  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. 
28Feb44  1589  An actual example of "distribution". 
29Feb44  1591  The mere presence of partfunctions 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.  
5Mar44  1593  "Equilibrium" is an invariant. It belongs only to an absolute system. 
8Mar44  1594  If reactions are to adapt independently, the breaks must be restricted to the regions of partfunctions. 
18Mar44  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 "partfunctions", "activated" and "activationregion". It is shown that activations are localised, that different paths may cause different variables to become activated, and that a partfunction can cause a break only when activated.  
8Apr44  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 x_{ρ} to a we shall eventually get, and keep, a field which stabilises x_{ρ} at, or near, a.  
19Apr44  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) 
19Apr44  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. 
19Apr44  1626  The layering of the cerebral cortex may be explained as required for wide distribution. 
24Apr44  1627  A note on exposition. 
28Apr44  1628  "Disturbance" and "ingressive" are defined. 
30Apr44  1629  Collected notes and references on "invariance". 
1635  A proof is given that: If a random displacement y_{1} , y_{2} , ... , y_{n} with probability distribution df=Φ(y_{1} , ... , y_{n}) dy_{1} ... dy_{n} is added to a point at X_{1}, ..., X_{n} then the probability that it (i.e. X_{1}+y_{1} , ... , X_{n}+y_{n}) should still be within a space V is maximal if, and only if, X_{1} ... X_{n} satisfy the equation (8). (See next note).  
2May44  1637  If a field (provided by a commutive system with breaksurfaces) has maximal probability of not breaking after random disturbance, then it is of normal equilibrium and the paths must meet at the point X_{1} ... X_{n} (defined in the previous note). 
5May44  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. 
5May44  1639  Disturbances must usually be applied to a system at a slower order of time than its reactions. 
10May44  1646  
1657  K_{1} and K_{2} are defined, also "terminal", "simple" and "displacement". If the fields provided by random h values have K_{1} and K_{2} values distributed as Φ(K_{1} , K_{2}), then the terminal fields have values distributed as A.K_{1}Φ(K_{1} , K_{2}). If the terminal fields are displaced from time to time the terminal fields develope distribution B.(K_{1}/(1K_{2})).Φ(K_{1} , K_{2}). (Graph 1698) (Corollary 1705)  
19May44  1659  Any number of unstable systems joined must be unstable. 
31May44  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). 
31May44  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.  
9Jun44  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.  
10Jun44  1673  A proof is given that the commutive process must increase the mean of K_{1}. 
15Jun44  1675  If K_{1} and K_{2} are uncorrelated, then disturbances give fields with K_{2} always increased. 
15Jun44  1679  Proof that a nonactivated variable, in contact only with other nonactivated 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 partfunctions present. [But see 1748]  
22Jun44  1692  A test of independence both necessary and sufficient, is deduced from x_{i}=e^{tX}x^{o}_{i}. Although the rigour of application to arbitary functions is doubtful, it leads to the same results as the previous test. 
1695  A proof that nonactivated variables cannot transmit effects. (Much better proof 1921)  
24Jun44  1698  Much human behaviour is reaction to an internal environment: anxiety. (Cf. 1877) 
25Jun44  1700  A graph of the multiplying factor K_{1}/(1K_{2}). (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 K_{2} after disturbance is given in terms of the original distribution and the means of K_{1} at each K_{2}value.  
19Jul44  1708  An example of two reactions, each quite adaptive, which are in unstable equilibrium if joined. 
21Jul44  1710  Some details contributed by Carroll. 
22Jul44  1715  For K_{2} among the terminal fields to be 1, i.e. for the fields to be immune to disturbance, it is necessary and sufficient either that K_{2}=1 in the original fields or, if K_{2}≠1, that Φ(K_{1} K_{2}), for some value of K_{1} other than K_{1}=0 should have, at K_{2}=1, a pole of order ≥1. The most interesting corollary is that if any fields in Φ have K_{2}=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.  
30Jul44  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.  
2Aug44  1725  In an absolute system (variables x_{1} ... x_{K} ... x_{n}) of fixed organisation [x^{~}_{i} = f_{i}(x)], that a subsystem (variables x_{1} ... x_{K}) should itself be absolute (the other variables x_{K+1} ... x_{n} being given all random starting points in the testing) it is necessary and sufficient that f_{1} ... f_{K} should not change for any or all changes of x_{K+1} ... x_{n}. 
3Aug44  1729  A proof that stepfunctions are necessary, as well as sufficient, to get changes of organisation of a subsystem in an absolute system. 
11Aug44  1731  Pavlov says that adaptation and survival equals equilibrium. 
14Aug44  1734  James describes the facts of adaptation = equilibrium without calling it such. 
19Aug44  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.  
5Sep44  1740  Two notes from a book. 
19Sep44  1744  A note on exposition. 
20Sep44  1745  Another example of selection leading automatically to adaptation. 
1746  An outline of quantum theory.  
28Oct44  1801  Two points on applications to society. 
1Nov44  1803  Note on exposition. 
2Nov44  1804  The ordinary pendulum is not stable if we are referring to both position and velocity 
3Nov44  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.  
5Nov44  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) 
11Nov44  1811  A detailed nonlinear use. 
18Nov44  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.  
9Dec44  1827  Another actual absolute system. 
9Dec44  1829  Equation of the plane which contains n consecutive points. 
18Dec44  1836  Review of Spencer, with useful quotations. 
1839  Independence over two regions.  
22Dec44  1840  Several parts, all unstable, can form a stable whole. (Simple example 2044) 
7Jan45  1844  Routh's test for stability. (Ready for use, 1862) 
12Jan45  1846  The probability of stability is in general unsolvable, but certain special cases might be attacked again later. (Continued 1868) 
19Jan45  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.  
22Jan45  1853  Some suggestions for a word to mean "survivalvalue". Note on selective operators. 
1856  A machine that learns.  
22Jan45  1857  Partfunction is now redefined. 
2Feb45  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 survivalprobability when all the neutral points are in the same place. (See next note) (see 1942) 
5Feb45  1862  It is to be remembered that Fisher's book was highly successful though no formal proofs are given anywhere. 
7Feb45  1864  Routh's test for stability given in immediately usable form. 
9Feb45  1867  The relations of independences and activations of partfunctions. 
1870  There is good reason to assume that the chance of stable equilibrium will often fall off as (1/2)^{n}.  
12Feb45  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) 
18Feb45  1877  Sex activity by my theory must result in a lowering of impulsedensity. 
18Feb45  1879  Two adaptations may be better than two independent adaptations. 
19Feb45  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.  
20Feb45  1893  "Dominant and recessive" applied to a distributive system. 
28Feb45  1895  A dynamic system must definitely either proceed to equilibrium or to infinity. 
10Mar45  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 hourglass 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. stepfunctions). [* Now called 'essential', not 'main'.]  
27Mar45  1909  Usable extracts from Sherrington's "Life's unfolding". 
3Apr45  1916  Extract of Schrödinger. 
1919  For the world to be suitable to be adapted to, it must contain a large proportion of partfunctions.  
21Apr45  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.  
6May45  1926  "Break" is better "saltus". 
6May45  1928  Quotation from Wells. Note on the basic meaning of "organisation". 
9May45  1934  Simple, workedout examples for exposition. 
11May45  1936  Distributive system vs. Genetic analogue. 
11May45  1941  A further list of correspondences between genetic and neuronic adaptation. 
12May45  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 
28May45  1946  So far I have discovered five basic operators and their variants. 
17Jun45  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.  
3Jul45  1967  Some points after reading all my back notes. 
4Jul45  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)  
26Jul45  1980  Handling partfunctions. 
26Jul45  1983  Explanation of the simple conditioned reflex. "Traffic" Principle. (2240, 4596) 
26Jul45  1984  "Signals" and Jennings' "Law of the resolution of physiological states" are now explained. 
28Jul45  1986  An improvement on the theorem about what is necessary in a multistable system. 
30Jul45  1988  For independence test, we must find ∑_{ρ=1..n1}[f]^{ρ}. The old method of Lim_{ρ→∞}[f]^{ρ} is rejected. See 2054 
1Aug45  1991  It is decided that a 1st Jacobian matrix (J.M.) cannot be accepted as physically real unless, for each i, not all a_{ii} , a_{iσ} a_{σi} , ... are zero. This is necessary and sufficient that the 2nd J.M. has all maindiagonal elements nonzero 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 nth power. This last power adds any missing diagonal terms. See 2056 
5Aug45  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. 
5Aug45  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.  
13Sep45  2007  Modern proof of the basic theorem of the multistable system. 
13Sep45  2011  Elementary rigorous properties of the multistable system, and of partfunctions. 
13Sep45  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) 
17Sep45  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.  
7Oct45  2019  On play. Also on reactions which look complete and turn out to be simple. 
23Feb46  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.  
24May46  2031  Noninstant systems, those with delay, may easily be converted to complete and instant by including derivatives. 
5Jun46  2034  Details about values, for reference. 
5Jun46  2035  If A dominates B, and B dominates C, in one complete system, then A must dominate C. 
7Jun46  2036  The case of the top shoot of a tree dominating the growth of lateral shoots fits into my formulation of "dominance" quite naturally. 
22Jun46  2040  Clarification of the position when dependence itself depends on other variables. 
2043  An overall theorem on the stabilities of joined systems.  
6Jun46  2051  Extracts from Masserman. 
15Jun46  2053  A simple example of the substitution equation of a complete system, suitable as an elementary exercise. 
4Aug46  2056  An improved statement of the main theorems on independence. 
2059  Answer to "how general is the field of linear equations [x'=Ax] ?"  
3Sep46  2062  By dealing with averages of many ultrastable systems we arrive at a new order or level of phenomena. 
14Oct46  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.  
19Nov46  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. 
25Nov46  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.  
21Dec46  2090  Electromechanical 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].  
31Dec46  2100  A theoretical study of a Unit devised, and part built, by myself. (Further, 2161, 2182) 
31Dec46  2102  Details for setting the machine of 2094 to correspond to assigned set of coefficients in [x'=Ax]. 
1Jan47  2103  Importance of echo impulses. 
2104  To demonstrate importance of echo impulses  
9Jan47  2107  Practical notes for use when converting known systems to differential equations in absolute form. 
14Jan47  2113  Notes the effect of altering the general speed of reaction of one variable. 
15Jan47  2114  Example of stability in the nonlinear case. 
15Jan47  2117  Equations of a simple dynamic system. 
22Jan47  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 nonlinear differential equations.  
26Jan47  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.  
10Feb47  2144  A study of dynamic systems which are themselves processes, like the Bunsen burner. 
10Feb47  2145  A new way in which one absolute system can be derived from another. 
11Feb47  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. 
13Feb47  2152  Equations tying the variables in the systems of chemical dynamics. 
15Feb47  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)  
22Mar47  2165  Chemical dynamics and thermodynamics. 
26Mar47  2169  Instability and threshold in chemical dynamics with catalysts. 
20Apr47  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!)  
26Apr47  2180  A number of interesting points from Richardson's book. 
3May47  2181  The various "constancies" of the body, so carefully maintained (homeostasis), are also separations and independencies. This needs further investigation. (See 2314) 
14May47  2183  A workable unit has actually been made (second system, other was 2094). (Improved, 2432) 
14May47  2187  Extracts from book. 
19May47  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.  
23Jun47  2212  The formulation of "signal", "symbol", "association" given vaguely on 786 is confirmed and given more precision. 
20Jul47  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.  
21Jul47  2227  Independence by delay. (See below) (Another example 2229) 
2231  The mathematical core of "association". (Example next page)  
25Jul47  2235  An attempted explanation of "association" on an actual experiment. 
27Jul47  2238  Some elementary observations on the organismenvironment relation. 
28Jul47  2239  A stimulus is many stimuli. 
29Jul47  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. 
2Aug47  2242  It is dangerous for an ultrastable system to move. (4596) 
7Sep47  2245  The multistable reserve. 
17Sep47  2246  A clear example of my concept of "independence". 
17Sep47  2247  Neurosis as instability. 
2263  A linear dynamic system can be forced to beat at any frequency.  
30Oct47  2270  A good example of the principle of the differential equation and its integration suitable for nonmathematicians. (See also 2278) 
2Nov47  2271  In the exposition of scientific matter, style is even more important than usual. 
5Nov47  2274  Notes the relations between my dynamic theory and the methods used in electrical circuit theory. 
5Nov47  2276  Neuronic patterns are always breaking up and being laid down. The new ones are formed in relation to those persisting. 
6Nov47  2277  A theory of G.P.I. [general paralysis of the insane] delusions. 
8Nov47  2279  Two variations on the theme of 2269. 
10Nov47  2280  Every vestige of claim and boast must be eliminated, being replaced by equivalent facts, or dropped. 
11Nov47  2282  Quotations. 
14Nov47  2284  Two points in exposition. 
16Nov47  2287  Exposition. 
18Nov47  2288  Exposition. 
2291  Interaction in the multistable system.  
4Dec47  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. 
10Dec47  2302  Examples of schizophrenics being displaced further from homeostasis by chemical stimuli. And a note of an objection. 
16Dec47  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."  
21Dec47  2311  Null, step, and partfunctions are, by definition, already in equilibrium and adjustment is needed only for full functions. 
21Dec47  2313  "Joining" two machines is essentially a break and rebuild. Nullfunction theory is fitted. 
2315  Homeostasis is ultimately produced by the genepattern, and it protects the genepattern from the dangers of the world because the constancy means independence.  
24Dec47  2316  Feedback. 
28Dec47  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.  
1Jan48  2324  Memory is not necessarily good. Some examples to the contrary. 
1Jan48  2326  If a stable set is to be found soon, the average number of partfunctions activated should not exceed 610 
2327  A proof, modernised from 1724, about an absolute system within an absolute system.  
3Jan48  2328  Absolute system defined more exactly in group form. 
10Jan48  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.  
12Jan48  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.  
19Jan48  2395  Matrix representation of partfunctions. 
2397  Correction to independence tests.  
3Feb48  2399  Quotation on the CNS betraying its blindness. 
7Feb48  2400  Richter believes the basic drives are homeostatic. 
8Feb48  2401  In large systems the intrinsic stabilities of the units may become less important while the effect of joinings become dominant. 
26Feb48  2422  Quotation of echo impulses which seem to be absent but are shown present. 
29Feb48  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) 
3Mar48  2431  Full equations and approximations of the machine. (see below). 
13Mar48  2433  Reporting progress in the machine. 2435 
2434  Social example of instability.  
20Mar48  2440  Method for investigating friction coefficients in my machine. (2432) 
24Mar48  2442  How well does the machine's actual behavior correspond with the settings? (see also 2448, 2452) 
28Mar48  2443  Memory and multistability. 
2444  Trying to make a system give assigned roots.  
14Apr48  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)  
14Apr48  2451  In a multistable system with multiple subsystems, the number of stable subsystems rises exponentially with the time towards its limit. 
23Apr48  2457  Two much stability gives rigidity and loss of control over other systems stability has an optimum. (Generalised in next two sections). 
24Apr48  2460  The fault of too much stability proved more generally. Over stability just means slavery. 
2461  Multistable system point.  
5May48  2466  Equations [x'=f(x)] and x=F(x^{o};t) when n→∞. 
6May48  2469  Definition and test for two patterns of initial displacement, differently sited to be equal. 4148 
10May48  2485  One factor in multistable systems tend to decrease interaction when two lines are activated simultaneously. 
10May48  2486  Concept of a "stimulus". 
14May48  2490  The conditioned reflex and association possibly solved. 
2491  The diagram of immediate effects must conform to the type of experiment.  
16May48  2497  When nullfunctions 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  
17May48  2507  Whenever possible, postulate many independent ultrastable systems rather than one multistable system. 
21May48  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)  
3Jun48  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.  
19Jul48  2527  Theorem on f's and F's invariant under transformation Φ. 
2528  Biographical note.  
20Jul48  2530  Systems of (almost) maximal stability (and see below) 
27Jul48  2531  Systems of maximal stability. 
16Aug48  2538  My theory explains why nerve cells cannot regenerate. 
3539  Neurofibrils exist.  
23Aug48  2541  One part of an ultrastable system can act as "trainer" to another part. 
23Aug48  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.  
14Jun49  2583  A system of stepfunctions reaches a resting state or cycle instantaneously 
14Jun49  2584  Define the parts and predict the behavior of the whole, not vice versa. 
14Jun49  2585  Any absolute system can be regarded as built of parts. 
14Jun49  2585  Constancies are conserved when parts are joined or separated. 
17Jun49  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 partfunctions.  
2597  Response of linear system to an input when its response to a stepfunction 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)  
13Jul49  2605  Nyquist's criterion is merely a convenience. Routh is fundamental 
15Jul49  2606  Transfer function of a single variable. 
16Jul49  2608  Oscillation necessarily implies feedback. 
2613  Habituation to a moving stimulus, prediction, and the conditioned reflex.  
18Jul49  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)  
20Sep49  2623  Stability of a chaincircuit of variables. (See also 2604) 
20Sep49  2624  Inaugural meeting of the Ratio Club at the National Hospital for Nervous Diseases. 
29Sep49  2627  Systems with high selectivity must have long dieaway by cybernetic necessity. 
2Oct49  2628  Memory in the dogs of the "Tinder Box". 
2Oct49  2634  The multistable system much clarified. 
3Oct49  2635  Goalseeking behavior does not necessarily imply feedback. (Continued, 2643) 
2638  Granit on causalgia.  
5Oct49  2641  The main properties of the multistable system are proved necessary. 
2642  Canonical equations from the transfer function.  
2645  Goalseeking behavior does not necessarily imply feedback. (Continued, 2650, 2654)  
10Oct49  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 
10Oct49  2649  Memories may perhaps float. 4155 
2651  Strong goalseeking usually needs a servomechanism. (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.  
21Nov49  2669  If one or more variables are unobserved, a cycle of parametervalues 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.  
22Nov49  2674  The conditioned reflex cannot be explained this way. 
22Nov49  2676  A parameter can be localised in action by partfunctions. 
22Nov49  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 subsystems. 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 partfunctions when a single parameter causes activations by its alternation.  
6Dec49  2686  A theorem on localised absoluteness. 
6Dec49  2688  A second stimulation can not only break a field but can save it. 
6Dec49  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.  
7Dec49  2694  Note on the previous note. 
7Dec49  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)  
12Dec49  2700  A possible mechanism for conditioned reflexes of the second order. 
12Dec49  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.  
19Dec49  2710  A system for relating stimuli given to arcs activated. 
31Dec49  2714  The effects of selection on the distribution of a statistic. 
31Dec49  2716  Numerical example of the solution of [x'=Ax] by x=e^{tA}x^{0}. 
2718  Example of equations solved by Laplace transformations.  
2722  An enumeration of the possible types of organisation. Summarised 2736  
21Jan50  2725  In a given absolute system, if n1 variables follow a given line of behaviour and the initial state of the nth is given, then the behaviour of the nth 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.  
28Jan50  2737  The ways of organising classified and tabulated. 
1Feb50  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  
8Feb50  2754  Examples of simple substitutions. 
2755  On the nature of 'mind'. (An application 2790)  
10Feb50  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.  
28Feb50  2770  Emperical tests of the chance of stability collected to date. 
2772  Chance of stability. 3050  
4Mar50  2773  Wholes whose stability differs entirely from those of the parts. 
2776  Joining unstable systems to form a stable one.  
13Apr50  2787  Genetic inheritance as information. (See 2806) 
13Apr50  2787  Dictionary definitions: Absolute, Behaviour, Break, Critical. 
2788  Dictionary definitions: Disperse, Essential, Field, Independence, Interaction, Iterate, Parameter, Regular.  
17Apr50  2789  Dictionary definitions: Representative, Stability, State, System, Variable. 
23Apr50  2792  Discovering a scientific law is like an animal getting one reactionsystem 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)  
26Apr50  2796  The meaning of 'several' environments. (Amplified on 2801) 
28Apr50  2801  Groups and learning. 
28Apr50  2806  Examples of environments that can be divided into subenvironments. 
2815  A list of actions in which some object has to be avoided.  
6May50  2816  Some items of information theory. 
19May50  2820  Information theory. 
21May50  2824  Example of pattern and group. 
24May50  2825  A stochastic process and information. 
25May50  2828  What a mammal does to an environment that cannot be adapted to. 
2830  Social systems that can change their own parameters.  
26May50  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.  
5Jun50  2848  How to 'prove' a theory of the conditioned reflex. 
2854  Extracts from Hebb's book.  
2858  A paper to be returned to later.  
10Jun50  2859  Conditioned reflex without cortex. 
10Jun50  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)  
10Jun50  2862  A process, in natural selection, that cannot reach a steady state but moves like the Flying Dutchman. 
11Jun50  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.  
14Jun50  2887  Correspondence of primative animal to machine, and object recognition. 
15Jun50  2888  Social cybernetics. 2898 
2889  Partenvironment relation in the Multistable System. 4193  
20Jun50  2890  Example of multistable system. 
28Jun50  2896  Comments on the books. Examples of partfunctions. 
2900  The new point of view.  
2904  Axiomatic basis of the canonical equations, preliminary.  
9Jul50  2907  I have little to learn from what is known of ecological systems. 
9Jul50  2914  Canonical equations of a regular system. See 2922 
16Jul50  2921  Defining and testing an absolute system. 
2925  On the canonical equations of a regular system  
2930  Some collected notes on pattern or classrecognition, and invariants.  
2933  A simple form of motor equivalent. (See 2939)  
18Jul50  2936  'Twostage' ultrastability. 
2949  Essay on 'motor equivalents.' See also 2989.  
25Jul50  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 stepfunctions selectively.  
21Aug50  2978  Behaviour of systems of partfunctions. 
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.  
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)  
3Oct50  2999  Serial training in the machine. (See 3004) 
3000  Note on the 'principle of continuity'.  
3Oct50  3001  A display for the new machine. 
3002  A simple and well known example of a system of partfunctions.  
24Oct50  3005  Serial learning. 
3007  Canonical equations of the homeostat.  
29Oct50  3013  Facts on learning. 
29Oct50  3013  Absolute system conserves information. 
30Oct50  3019  Multistable system gives partly additive responses. A reaction pattern can be 'strengthened' by noisy variation of parameters. 4155 
31Oct50  3021  A better meaning for 'difficulty of finding stability.' 
3025  n partfunctions of which k are active at any one time is as easy to stabilise as k, not n, fullfunctions.  
3027  A multistable system adapting to several environments.  
7Nov50  3031  Necessary and sufficient conditions that a first adaptation should be still present after a second has taken place. 
12Nov50  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 stepfunctions...  
23Dec50  3041  Systems of partfunctions automatically provide stepfunction. (N.B. This need further investigation and more rigorous formulation). 
25Dec50  3043  Mark 13 DAMS works. 
26Dec50  3044  Stability in the system 'number of neons lit'. 
27Dec50  3048  Joining 'at random'. 
27Dec50  3051  Stability of systems whose units always tend to some function of the variables. 
27Dec50  3054  The equations of DAMS. (Effect of neon, next page) Example next page. 
27Dec50  3054  Control of DAMS' stability. 
3058  Essential variables may work by 'habituation'. (Review 3280)  
29Dec50  3059  A simple mode of action of the essential variables. 3382, 4526 
3062  Partfunctions will divide the whole more effectively if the permanent connections are few.  
16Jan51  3070  Wiener says cycles will be common in DAMS; I say they will be few. 4892, 5461, 5472 
20Jan51  3075  Setup necessary, in brain and DAMS, for serial learning. (3087, 3141) 
3080  Functional knowledge obtainable when only some of the variables are observable. 3716  
28Jan51  3082  Wiener's opinion on the 'absolute' system. 
3085  The Markoff process. Cf. 3223  
3086  Stability of system of Markoff chains.  
28Jan51  3088  Relation of essential variables to system of partfunctions. 
29Jan51  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 byproduct.  
5Feb51  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  
12Feb51  3115  Psychological facts to be explained by DAMS. 
3116  A partfunction's 'degree of constancy.'  
3118  Variables 'sticking' does not necessarily cause a bias.  
14Feb51  3119  No excuse is necessary to suppose that partfunctions are constant only at certain values. Perhaps the concept of 3200 may be usable. 
14Feb51  3120  In an absolute system one variable knows nothing of another variable's constancy. 
3123  Infinite systems of stable parts.  
19Feb51  3127  How a variable's distribution changes after an internal dt. 
19Feb51  3129  Steady states in an infinite system. 
23Feb51  3132  I am now ready to account for learning by 'pleasure'. 
23Feb51  3133  In a linear system with all variables distributed, the means of the variables behave the same as the variables would if undisturbed. 
25Feb51  3137  In an absolute system independent distributions don't stay independent. 
27Feb51  3138  'Delay' in a machine is only behaviour of zero amplitude. 
27Feb51  3139  In a system of partfunctions there are no 'parts' only distributed activations. 
3142  To get cumulative adaptation, the environment must be traversed by a variety of paths. (4546, 4215)  
6Mar51  3143  Conditions affect, in the long run, only the stable patterns. 
10Mar51  3146  On the chance that a disturbance should alter the resting state of some part. (3272) 
14Mar51  3148  A system of partfunctions may be easier to change if it is built in stages of assembly. 
3151  Darwinian mechanisms are to be developed by Darwinian process.  
19Mar51  3163  Switches that see a Markoff process only through themselves: consequent bias in their settings. (Theory in metricless 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 log_{2} ρ + log_{2} σ cannot be exceeded whatever part has been chosen.  
3173  Information in an absolute system always falls to log_{2} 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)  
6Apr51  3193  Information in machines. 
6Apr51  3200  Shannon and I. 
6Apr51  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) 
7Apr51  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)  
7Apr51  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 log_{2}[(a^{a} b^{b})/(a+b)^{a+b}].  
9Apr51  3210  We cannot measure information by finding contributions from subensembles and adding. (Another example 3249) 
10Apr51  3212  An absolute machine can never gain more information than is put into it. 
10Apr51  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)  
11Apr51  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)  
13Apr51  3224  Canonical equations of the densities in state of a system disturbed by an information source. (See 3227) 
13Apr51  3226  Another measure of information applicable to a machine. 
13Apr51  3228  When driven by a steady statistical source, the information in a machine does not tend to a minimum. 
13Apr51  3230  States that lock accumulate all the members of the ensemble. 3233, 3291, 4524 
14Apr51  3234  Information when a stochastic parameter changes infrequently. 
3235  Ways of losing information. 3274  
16Apr51  3237  Wiring pattern of DAMS. 
3240  Conditions that a machine shall have the maximal number of resting states. This can be specified further...  
19Apr51  3241  Maximal number of resting states. (3308) 
3242  Information when A drives B.  
3244  The inverse of the canonical equations.  
23Apr51  3245  An experiment stops when the exchange of information has reached equilibrium. (3248, 3254, 3691) 
25Apr51  3247  Independence does not in general cause loss of information. (3274) 
25Apr51  3249  Entropies in the parts do not sum to that of the whole. Entropy of a part may equal that of the whole. 
25Apr51  3250  Information and experiment. 
25Apr51  3253  
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  
1May51  3279  Results collected from the last hundred pages (since 3164) on the subject 'Information in absolute systems.' 3297 3500 
2May51  3280  New layout for DAMS, and an unsolved problem. 
2May51  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... 
4May51  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 stepfunction change.  
3301  Information in machines.  
9May51  3303  The continuous system can gain information though absolute. 
9May51  3303  As soon as a subsystem is isolated it starts losing information. 
23May51  3307  Dispersion. 
23May51  3312  How many resting states has DAMS? (Continued 3319) 
3314  Resting states in DAMS will be few. (Continued 3319)  
28May51  3316  Pneumatic controllers. 
3318  Measuring how much one variable affect another. The partfunction 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}=K_{i}{Φ_{i}(x_{1},...,*,...,x_{n})x_{i})}. (3) The variables in the parentheses (above) are the 'inputs' to the part, and Φ_{i} is the 'output'. (x_{i} merely follows Φ_{i}). (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 phasespace then the surfaces must waggle within it, and also across it. (3325 top). 

3347  (Continued) (7) If Φ_{i} tends to a form resembling ρ_{i} parallel planes (3334), then the number of resting states (stable and unstable) tends to Πρ_{i}. (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  
13Jun51  3351  Modifying a stable field. 
13Jun51  3353  Ways of altering a system's sensitiveness to disturbance. 
13Jun51  3354  Effect of richness of joining on the number of stable resting states. 
13Jun51  3356  The nervous system should not have internal feedbacks (unless for special reasons) But see 3396. Confirm 3425, 3521 
3359  Information and adaptation. 3521  
18Jun51  3360  How many nerve calls has an earthworm? 
3365  Conditions that one system may control another in detail.  
18Jun51  3366  Control in systems of Constant Intrinsic Stability. 
3367  My machines are not ergodic.  
19Jun51  3377  Information going through a transducer. 
21Jun51  3381  Solution of the paradox of 3379. 
5Jul51  3382  The essential variables must be able to send much information into the rest of the system. 3500 
6Jul51  3386  Designing an essential variable that works by emitting noise. 3521. 
9Jul51  3387  DAMS needs a complex environment, but a simple trainingschedule. 
11Jul51  3390  My work is the 'chemistry' of machines. Progress in it will be largely empirical. Review 4141 
12Jul51  3392  That a set of stepfunctions should provide many resting states it is necessary that they should be uncorrelated. This can be achieved by many crossconnexions. 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.  
13Jul51  3395  Of the resting states, the number stable can be anything from none to all. 
13Jul51  3398  A system joined in a circuit is likely to have very few resting states. Confirmed 3426 but see 3571. 
13Jul51  3398  To retain information in DAMS Mark 13, use output 3 and either of 1 or 2 in all cases. 
16Jul51  3399  Thinking of the machine as having a finite number of states is the fundamentally sound method. 
16Jul51  3400  How to integrate step by step when parts have outputs. 4498 shows how it should be done. 
16Jul51  3402  Further data on what is required for many resting states. 
17Jul51  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.  
26Jul51  3410  Design of a part and the number of resting states. 
3415  My standardised vocabulary, collected. (Standard symbols, 2004)  
30Jul51  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 
1Aug51  3418  Law of the Invariance of Distribution. 
8Aug51  3422  How to stop partfunctions from destroying information. 5291.9 
10Aug51  3425  The conclusion is, then, that for many resting states we must have plenty of independence. 
10Aug51  3426  Historical note. 
3427  Complex wholes are unstudiable. 3474, 3496, 3513  
11Aug51  3428  Information in DAMS. 
3430  Value of a determinant.  
25Aug51  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.  
8Sep51  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.  
12Sep51  3460  Let DAMS keep moving. 
12Sep51  3462  Society. 
3463  How DAMS can be made neurotic. (See next section) (See 3480)  
12Sep51  3465  Neurosis by conflict must use up a system's resources of stepfunctions. 
14Sep51  3474  The question 'what is a 'statistical' machine?' answered. 
14Sep51  3475  What makes a complex machine 'statistical'? Review 4141 
14Sep51  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.  
22Sep51  3479  DAMS should tend to avoid activating variables with widespread effects. 4155 
3481  On neurosis.  
23Sep51  3483  A more practical form of environment for DAMS. 
24Sep51  3486  Details of the Essential Variables. 
3487  How long should an arc be? 3511, 3514, 3557  
25Sep51  3489  Partfunctions are apt to lead to many useless neutral equilibria. 3491  No they are acceptable; 3495 
25Sep51  3490  Variable of constant intrinsic stability as partfunction. (See also below) 
25Sep51  3493  Equilibria in systems of partfunctions. (See below) 
26Sep51  3495  Types of equilibria in DAMS. Conclusion: Neutral equilibria, with esential variables within limits, are acceptable. 
26Sep51  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.  
27Sep51  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?  
15Oct51  3509  History of DAMS. 
15Oct51  3509  Sex and the Multistable System 
3513  Testing DAMS. 4511  
21Oct51  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'.  
29Oct51  3522  Index to Essential Variables since 3289. 3582 
29Oct51  3522  Reduction of all variables to a common form is of no importance. 
3526  Fundamental theorem that the nervous system must contain stepfunctions.  
3Nov51  3530  Fully developed form of the 'mechanical brain'; design for a chessplaying 'machine'.4563 
5Nov51  3531  The brain should have some stepfunctions 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  
12Nov51  3538  Fixed qualities in a system. 
3545  The neon in DAMS as absolute system.  
18Nov51  3547  Some statistical systems. Review 4141 
3552  Joining at random and by subsystems.  
3554  We think dynamically, not logically.  
21Nov51  3558  How to join DAMS. 
21Nov51  3561  Joining up Essential Variables, Environment, and network. Review 3582 
22Nov51  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.  
27Nov51  3580  Processes for elementary study. 
26Nov51  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  
30Nov51  3596  A clearer statement about the Essential Variable. 
3598  A glance at the theory of games. 4589  
3602  Getting dispersion. 3870  
1Dec51  3603  How the cortex perhaps gets selective disruption of wrong arcs. 3825, 4600, 4831 
1Dec51  3606  Long lines of behaviour in phasespace often appear in the living world as circulating between organism and environment. 3645, 3760 
7Dec51  3608  Statistical mechanics. 
7Dec51  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 informationamplifiers. (3616)  
8Dec51  3616  Details of chessplaying. 
11Dec51  3628  Properties of an informationamplifier. 4155 
11Dec51  3629  The elimination of wrong moves at chess may eliminate too much. 
12Dec51  3630  Random transformations. 
12Dec51  3631  How instinct is activated. 
3632  Random transformation in taste. 3665  
3637  Calculations on dispersion.  
17Dec51  3642  The chance that inactivity will stop an effect getting into the rest of the machine. 
22Dec51  3643  Environment reducible to orthogonal subsystems. Also 3648 
29Dec51  3644  Innate mechanisms must be studied for their organisational properties. 
2Jan52  3645  Three ideas. 
7Jan52  3647  Functional levels may be topologically rearranged within organism and environment. 
8Jan52  3649  Example of an environment. 
8Jan52  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)  
17Jan52  3661  Information in the field and in the equations of an absolute system is S log S. 3695 
17Jan52  3661  The homeostat's amplification factor is less than x1, but I was the first to point this out. 
20Jan52  3662  Again the necessity for achieving success by stages. 
3663  Approximate estimate of the amount of design put into the homeostat.  
20Jan52  3664  How many uniselectors the homeostat should have. 3743 
3665  Example of a random transducer. 3667  
3666  Chess strategy.  
25Jan52  3670  Chess player's manual. 4569 
25Jan52  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  
31Jan52  3685  When there is more than one source, how many entropies are calculable? 
3687  Information from multiple sources.  
31Jan52  3688  Definition of 'memory'. 3810 
3692  Experimenter and system. 3697, 3725  
3Feb52  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 
3Feb52  3698  Even the experimenter must be regarded as an ensemble. 3709 
4Feb52  3700  To compute information, members having the same field must be kept together. 
3703  Chess strategy. 4590, 4651  
3705  Every parameterchange allows (or forces) the information in an ensemble to drop to a new lower level. Same applies to δimpulse 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.  
9Feb52  3710  The concept of 'cause' implies more than one line of behaviour. 5118 
9Feb52  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  
27Feb52  3720  Two unstable systems joined to give a stable. 
3Mar52  3723  More examples of mathematics as a study of real dynamic possibilities. 3729 
12Mar52  3729  'Knowing' means 'controlling', which means 'keeping invariant'. Review 4348, 4294 
28Mar52  3730  More illustrations that maths is based on physical, empirical knowledge. 3926 
28Mar52  3730  Real 'dialreadings'. 
28Mar52  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?  
28Mar52  3738  Wallace's Mazesolving Computer. 
3741  Shannon's mechanical brains.  
3743  Information in the homeostat.  
2Apr52  3744  Information in the homeostat. 
3752  Searching, random and systematic.  
3753  Qualification to 3746.  
3760  The division by partfunctions is not objective. Transformation can destroy partfunctions. 3767, 3799  
8Apr52  3761  Details of dispersion. 
3763  Addendum to the definition of the primary operation. Corrected 3894  
9Apr52  3766  A misunderstanding about partfunctions. 3868 
10Apr52  3772  Rank of the differential matrix, and nullfunctions. 
3775  Partfunction 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 observersystem relation is symmetrical; so we can calculate 'information' over an ensemble of observers  
3May52  3789  Information, rank, equations. 3799 
5May52  3792  On the operation that brings the representative point to a particular initial state. 3846, 4628 
6May52  3794  Convergence of lines as invariance. 
6May52  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.  
10May52  3806  Transmission of information through a chain of absolute systems. 
11May52  3808  Homogeneity implies group statistical regularity implies group. 3849 
12May52  3809  Examples testing dependence of F on x^{o}. 
3814  (1) What is meant by 'memory'. (2) Memory does not require feedback. 3840  
13May52  3815  Memory as conjugate behaviour. 
13May52  3815  Habituation implies memory. 3842 
17May52  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  
22May52  3837  What is essential in the homeostat. 3841, 3856, 4161 
23May52  3840  On habituation. 3842, 3856, 3865, 4524 
3841  Memory implies that stepfunctions 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  
25May52  3852  Only an observer with dispersion can take advantage of a system's absoluteness. 
3853  Exploring a machine.  
28May52  3854  Detail of 3844. 
28May52  3855  Change full to stepfunctions for resting states. 
29May52  3856  Other things being equal, the system with more stepfunctions will have more resting states. 
31May52  3859  The importance of the age of thing. Review 4155 
1Jun52  3860  The catchment areas define a partition. 
4Jun52  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.  
11Jun52  3866  The reactive condition is the more probable, from which the system may diverge under habituation. 
3867  The channel from stepfunction to observer must be broad if the observer is to see variety of behaviour.  
12Jun52  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  
17Jun52  3876  Stability of a circuit of levels. Another interesting system... 
3880  Behaviour of the 'clover' system.  
3882  Feedback can occur along a single channel.  
21Jun52  3891  An incomplete solution of the problem of the probability of stability. 
22Jun52  3892  A variable 'is' whatever a particular system, perhaps ourselves, sees it as. (But see 4000) and 3896, 
22Jun52  3893  "interacts with" is an equivalence relation. 
22Jun52  3894  A likely mechanism for the conditioned reflex. 3897 
23Jun52  3896  The primary operation, and testing absoluteness. 
23Jun52  3899  More on the Conditioned Reflex 
24Jun52  3901  A hybrid stepfullfunction. By 4000 it is in (2), a full function. 
26Jun52  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 complexvariable 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  
28Jun52  3927  All maths should be expressible in terms of dynamic systems. 
30Jun52  3928  Topology of absolute system. 
3929  'Stability' must be restated in terms of information. 3963, 3980, 3975  
30Jun52  3931  The disturbances of most interest are those that are infinitesimal and the system becomes linear. 
1Jul52  3932  Selfreproducing arcs are of very great importance, for good or evil. Review 4154 
2Jul52  3935  A derivation of the partitionfunction. 
2Jul52  3937  Administering a determinate impulse to an ensemble can only cause its information to fall. 3954 
2Jul52  3939  Unsolved problem. 3959, 3962 
3943  Examples showing how 'adaptation' means 'destroying information'. 4133, 4155, 4159, 4167  
3Jul52  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  
4Jul52  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 stepfunctions!  
7Jul52  3968  Ultrastability can act without a metric. 3986 
8Jul52  3979  How to get many resting states (argued without a metric). 
9Jul52  3984  My concepts divided into the topological and the metrical. 4026 
10Jul52  3985  The concept of 'state' does not require number or metric. 
3990  Ultrastability proved at last! Worked out example 3967 Obsolete! 4232  
14Jul52  3993  'Stepfunctions' topologically. 4000, 4005, 4602 
15Jul52  3994  Why do our brains take so much notice of a stepfunction? 4233 
21Jul52  3995  'Absoluteness' is relative to an observer. 4031, 4043. 
3997  Residue classes in behaviour.  
27Jul52  3999  A chemical dynamic system. 
27Jul52  4002  A more rigorous definition of full, part, step, and null functions. Try it on 3900, 4604 
24Jul52  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.  
1Aug52  4005  Note on the subjective. 
3Aug52  4011  Lewin's Topological Psychology. 4026 
6Aug52  4012  Absolute systems. Q.E.D. 
6Aug52  4015  On memory and schizophrenia. 
6Aug52  4015  For progressive adaptation the essential variables must be multiple. 4167 
6Aug52  4015  On infinitesimal disturbances. 
6Aug52  4017  Examples of systems with part functions. 
6Aug52  4018  Two independent 'complexities' in the 'complex system'. 4167, 4189 
4019  Importance of a system's history. 4041, 4048, 4302  
21Aug52  4021  Interaction between adaptations. 
21Aug52  4021  My solution includes all solutions. 
8Aug52  4022  S.8/2 should be reworded. 
10Aug52  4025  'Coarsening' an absolute system. 4041, 4475, 4919 
12Aug52  4026  Field as vector. 
12Aug52  4026  Meaning of 'topological'. 
12Aug52  4029  Quotations 
13Aug52  4030  The absolute system does not imply a group. 4033 
14Aug52  4031  An absolute system is a selected projection of the worldlines. 4038, 4043, 4292 
15Aug52  4032  The homeostat's equations. 
15Aug52  4033  Being a oneparameter group is not sufficient to ensure absoluteness. 
15Aug52  4034  I formally reject the concept of 'group'. 
15Aug52  4035  The 'group property' without groups. 
15Aug52  4037  Abstract, and objective form of 'selection'. Review: 4137. 4099, 4229 
4038  Nonmetrical definition of 'stability'.  
4038  Why not two, or more, representative points? 4121  
16Aug52  4041  Every regular system can be made to yield an absolute system. 4042, 4302 
4042  A regular system is practically an absolute system.  
18Aug52  4043  Nature of absoluteness. 4292, 4306 
18Aug52  4046  The joining of machines can be represented without a metric. 4332, 4471 
19Aug52  4047  Continuity of transformation. 
19Aug52  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  
22Aug52  4053  Essential variables. 4161 
22Aug52  4054  In exposition, use nonlearning systems as examples of organisational facts. 
22Aug52  4054  Arcs breed. ? 4151, 4065 
30Aug52  4057  The field of the selflocking system. 4065, 4155 
4059  The 'ordinary' and the 'statistical' machine differ only in the proportions allotted to the directly functioning part and the parameteradjusting, servomechanistic part. 4061  
4060  More examples of the stable and unstable. 4062, 4070, 4074  
4061  Example of 'stability' missused. Further examples 4062, 4070  
4062  Economic systems vary in their amounts of stabilising machinery.  
1Sep52  4063  The organism that 'knows' a line of behaviour is better if it knows the adjustment lines as well. Answered 4608 
3Sep52  4066  Musings on evolution and the cortex. Review: 4155, 4071 
4069  The basis of both the multistable and the evolving system is the selflocking system (and its superior, the selfreproducing). 4071, 4099, 4153, 4166, 4201, 4229  
4070  Learning that have to adapt to a fixed (reflex) mechanism.  
4070  Meteorological dynamics. 4072  
6Sep52  4072  Selfreproducing 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.  
7Sep52  4076  Random transformations. 
4079  The multistable system may have no trend if wrongly devised. 4080.0, 4175, 4201  
12Sep52  4080  Multiple faults in a machine. 4613, 4195, 4201 
4081  A possible cause of psychosis.  
4083  Waismann's book.  
12Sep52  4084  Example for localisation. 
4085  Absolute systems within absolute systems. (Continued 4113)  
4087  More on evolution. 4610, Review 4201, 4155, 4099  
13Sep52  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.  
17Sep52  4097  How many primary operations are required to establish the diagram of immediate effects? 
17Sep52  4098  To study an absolute system of σ states, σ elementary operations are necessary, and they yield σ log σ of information. 4112 
17Sep52  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.  
21Sep52  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 
21Sep52  4112  Two points about dreams and the cortex. 
23Sep52  4113  The difficulty of 'delay' is identical with the 'difficulty' of having too few variables. 
23Sep52  4117  Absolute systems in absolute systems. 4119, 4145 
23Sep52  4119  Tests for absoluteness. 
4120  Absolute systems within absolute systems. 4145  
24Sep52  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 stepfunctions. 4158, 4161, 4238  
29Sep52  4136  Destruction of information. 4164, 4166. Review 4151, 4385 
29Sep52  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 stepfunctions.  
4165  The adapting system  generalised, (next section). 4166, 4225  
4Oct52  4171  (1) The homeostat is a selfregulator 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 controlflow relations. 4179, 4282, 4285 
4177  Darwinian adaptation, and the multistable systems. 4197, 4201  
4178  Psychiatry of the informationblock.  
6Oct52  4181  The selflocking system will also often be internally selflocking. 4229 
4182  For rapid and successful adaptation in the Multistable System, δ, α,η and ζ must, as channels, have large capacities.  
10Oct52  4183  Origin of depression. 
10Oct52  4183  The regenerative abnormality as selflocking system. 4229 
11Oct52  4185  Genes and memory. 4206 
4186  The essence of intelligence is selection. 4285  
4187  Chaos first becomes worth studying when a constancy appears.  
13Oct52  4189  Lashley on learning. 
16Oct52  4193  More observations on discriminative feedback. (Foot of this page) 4201 4613 
16Oct52  4193  Sufficient to ensure high probability of'. 
16Oct52  4195  Discriminative feedback. 4225, 4514, 4613, 4831 
16Oct52  4196  Discriminative feedback. 4216, 4201 
17Oct52  4197  Trial and error by model has advantages, if the system can achieve it. 
4201  Various ideas on Darwinian and multistable evolution.  
23Oct52  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  
22Nov52  4224  The necessity for selecting variables. 
23Nov52  4227  The multistable system as merely one of many. 
23Nov52  4228  Definition of system 'independent' of a parameter. 
4232  Precise conditions under which a system is selflocking. 4242, 4275  
4232  Better proof of ultrastability.  
4233  We take 'things' invariants, and nullfunctions 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.  
28Nov52  4239  The field of [DIAGRAM] 
29Nov52  4241  Darwinian and multistable systems. 4425, 4655 
1Dec52  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 
2Dec52  4245  The diagram is more general than it looks. 
2Dec52  4245  Getting information from a system. 
4257  On the time taken by a large system to get adapted. 4264, 4515, 4560  
3Dec52  4260  Building an exceptionally unintelligent machine. 
3Dec52  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.  
7Dec52  4267  Precise instructions for commercial organisation. 4269, 4273 
7Dec52  4267  Is the power of abstraction the same as the power of developing an hysterical blindness? 
8Dec52  4269  Play is an investment of surplus adaptation. 4271 (13), 4425 
4272  Explicit instructions for commercial or social organisation. 4273  
14Dec52  4275  Building a society for chessplaying. 
15Dec52  4276  A better way of stating my 'limit' theorems, and 'trend' theorems. 
4278  Power and I.Q. have many similar properties. 4285  
14Dec52  4280  Appearance of a superclever machine. 
14Dec52  4281  'Noise' when an Ultrastable System is built of Ultrastable Systems. 
18Dec52  4282  By serial adaptation, time falls to its logarithm. 
21Dec52  4283  The entropies of the variationamplifier. 4285 
4284  Multiple, competing, essential variables lead to the same problem, whether occurring in one person or scattered among many. 4289  
22Dec52  4289  A selectionamplifier, in the multiplying sense, is not wanted; but a selectionsupplementer 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  
24Dec52  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  
27Dec52  4302  Effectiveness of parameters with finite substitution. Applied 4414 
28Dec52  4303  Examples of states that include history. 
28Dec52  4303  Knowledge must be tested by control. 4438 
4305  Oneoneone relation between parameter and transition. 4396  
30Dec52  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  
30Dec52  4311  Scientific knowledge is knowledge of a transformation. 4344, 4454 
4315  'Variety' in systems.  
4316  'Variety' in systems. See page 4327  
14Jan53  4373  Variety in state accumulates. 
14Jan53  4374  Uniform activity in the parameters drives down variety in state. 
14Jan53  4375  Longterm memories. 
14Jan53  4376  On basins. 
20Jan53  4377  'Delay' need not be rejected as a basic concept. 
1Feb53  4380  Note on Darwinism. 
1Feb53  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  
9Feb53  4384  The αrhythm. 
12Feb53  4385  Speed of adaptation can be achieved only by trials and comparisons. 
4387  Regulation (destruction of information) requires extra information. Continuous form 4395, 4658  
17Feb53  4388  Lack of variety and stepfunction are equivalent. 4439, 4440 
18Feb53  4389  Apparent inertia in adaptation. 
4392  'Transient' translated into nonmetric terms. 4644 (vol.18)  
19Feb53  4393  Gödel's coding. Theorem 5086 
19Feb53  4393  Digital and analogue. 
26Feb53  4394  Quotation showing gross ignorance of the principles of organisation, by one who should know better. 
4395  Two functions combining to an invariant. 4658  
27Feb53  4401  The absolute system as coder and decoder. Extended 4414, 4461 
4410  Limiting basin when determinate machine is affected occasionally by impulseoperate. 4524, 5512  
1Mar53  4411  Proof of theorem 
1Mar53  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.  
23Mar53  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.  
1Apr53  4423  Effect of magnification on behaviour. 
2Apr53  4424  Invariants of a dynamic system with parameters. 
2Apr53  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  
6Apr53  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 parametercombinations, 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  
17Apr53  4439  Prediction and control are just forms of regulation. 
17Apr53  4439  Wave as constraint; travelling immobility. 4440, 4943 
20Apr53  4441  Way of behaving, constraint, thing, partfunction. 
20Apr53  4443  More on "constraint". 4553, 4564 
21Apr53  4445  Computing entropy. 
4446  Shorthand has more disadvantages than advantages. List of symbols: End of this volume and 5108  
24Apr53  4447  
24Apr53  4448  One formulation covers "design" "input" and "noise". (Next section) 4449 
27Apr53  4454  Information in a machine. 4701, 4847 
28Apr53  4462  Outline of the theory of the Black Box. 4480 
28Apr53  4465  What "designing" a machine means abstractly. 
2May53  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  
2May53  4471  Joining absolute systems without metric. Example 4473, 4498, 4733 
2May53  4472  Must every system drift to the condition of maximal internal separation? 4500, 4524 
2May53  4472  Cap or intersection as selective operator. 
2May53  4472  Unsolved problem. Solved 5009 
2May53  4474  Anything that can have variety is really a set. 
4479  The relation "observer A cannot distinguish x from y"; homomorphism. 4501, 6254  
2May53  4480  Are there "levels" of design? 4595 
3May53  4481  The Black Box is a set. 
3May53  4481  Randomisation as a way of passing a message that is no message. 
3May53  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  
11May53  4494  More constraints means fewer possibilities but more discoverable patterns, 4504 
11May53  4494  In set theory, remember that inequalities are likely to have cybernetic applications. 4503 
13May53  4495  Set theory and its use. 
13May53  4496  'Large' and 'small' machines. 
13May53  4497  Logic and theory. 
19May53  4498  Homomorphism in machines. 
4500  Joining machines.  
21Jun53  4504  Observations on set theory. 
11Jul53  4509  Principle of ultrastability stated more vigorously. Better still 4581 
4510  Ergodicity and loss of information.  
13Jul53  4511  Tactics for getting DAMS better aligned. 
17Jul53  4513  Machines are related to the algebraic laws of internal composition, as well as those of external. 
4519  Builtin structure in an adapting system implies that part of the solution has already been obtained. 4599, 4600  
18Jul53  4521  Amount of selection and ultrastability. 4582.6, 4904 
4523  How chromosomes reproduce themselves. High survival power.  
4535  Habituation. 4559, 4596, 4609, 4762, 5512  
22Jul53  4536  Formal proof that, if a set is stable, no state in it can lead ever to a state outside the set. 
23Jul53  4537  Power for adaptation. (See next page) 4583 
25Jul53  4539  Adaptation needs a transducer between the prime (statistical) mover and the useful result. 4583 
25Jul53  4539  Markov processes in machines. 
28Jul53  4545  Markoff process in machinery. 4671 
28Jul53  4545  The human brain may not be optimal for inclusion in computer. 
4547  Trials within trials, or the admission of variation into subunits of an ultrastable system.  
4549  Examples of how reducibility shortens time of search. 4552, 4563, 4650, 4948  
31Jul53  4552  All problems can be reduced to a canonical form. 4560, 4585 
1Aug53  4557  The method of models, for quicker searching. Review 45604575 
3Aug53  4558  Isomorphism between machines. 
3Aug53  4559  Distinguishability correspond to dependence. 
4Aug53  4560  A Review on "Speed of Adaptation" with special reference to that of a ProblemSolving System. ... it is now possble to build a system, or machine, of more than human intelligence. 
4Aug53  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 productspace 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.  
7Aug53  4578  Two messages in a channel need not interact. 4641 
8Aug53  4579  Emission of "cos^{2}x + sin^{2}x =1" randomly. 
4580  Two agents may select the same element, yet differ widely in their degrees of selection. 4583, 4598  
8Aug53  4581  An even more rigorous statement of ultrastablity. 4882 4467 4508 4520 
9Aug53  4582  Rigorous statement of ultrastablity. 4881, 4904, 5046 
12Aug53  4584  Relation of essential variables to selectionamplifier. 4586 
12Aug53  4587  What is 'problem solving'? 
16Aug53  4589  Every real object is an element in an indefinitely large number of sets. Which sets are to be considered must first be defined. 
18Aug53  4593  Neumann's theory of games translated into my theory of systems. 4650 
19Aug53  4594  Stability checked. 
21Aug53  4595  Review of the book. [Design for a Brain] 
22Aug53  4596  'Equilibrium' refers to a state, 'stability' to the region around the state. 
25Aug53  4597  Properties of metricless system. 4623 
26Aug53  4598  The fullest description of a 'stimulus' is still inadequate to define its content of information. 
26Aug53  4599  In comparing an ultrastable (mechanical) solver with Man we must take care that they start with comparable amounts of prior knowledge. 
28Aug53  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 
28Aug53  4602  Control, and partfunction, in terms of set theory. 4604 
28Aug53  4603  Incentives in the ultrastable system. 
28Aug53  4604  Practically all my concepts are nonmetrical. 
29Aug53  4605  Having several basins has nothing to do with being divisible into parts. Noticed again 5502 
31Aug53  4606  Organisation of the German General Staff. 6534 
4607  Is the Darwinian system a specialised one? 4608, 4613  
31Aug53  4608  How much of a field should be known? 
31Aug53  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 selfreproducing systems in the terms of set theory.  
31Aug53  4613  Precise statement of the fact that instability is infectious. 
31Aug53  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 
31Aug53  4613  Am still totally unable to write Darwinian ideas in any rigorous way, in spite of many motes ever since 4051. 
1Sep53  4615  What Darwin really did do. 4618 
1Sep53  4616  Darwin's actual theory. 
1Sep53  4617  What does "endurance" mean? 
1Sep53  4619  Darwin's method for the study of complex systems. 4655 
1Sep53  4620  Darwin's theory and that of the multistable system are related by intersecting in a set of theorems that contains both. 
1Sep53  4620  How to develop the theory of "knowing". 
3Sep53  4622  How a machine transforms a set of representative points in its field. 
4Sep53  4624  "Stability"defined. A "machine" is a stable subset. 4630, 4632, 4643, 4656, 4795 
4Sep53  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 welldefined 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  
28Sep53  4633  "Basin" defined algebraically. Better 4743 
4634  Strategy. 4640  
30Sep53  4640  The costing accountant and the strategy of control. 
4641  Mechanism for simultaneous adaptation. 4577, 5417  
30Sep53  4642  "Maximising profits" as a "keeping within limits." 
4643  Selflocking in society.  
12Oct53  4647  Theorems on transients. 4761 
12Oct53  4647  System in which x chases α. 
12Oct53  4648  Of what use is neurophysiology to me? 
12Oct53  4648  Drugs of addiction. 
19Oct53  4649  If the environment offers constraint, the cortex can profit. 
4652  Strategy of trial and error. 4797, 4822, 4844, 4947, 4941  
23Oct53  4655  Boxdiagrams are not precise. 
23Oct53  4655  Evolution as habituation. 
3Nov53  4657  Meaning of 'stability'. 4741, 4785, 4795 
4659  Only variation can force variation down  exact conditions necessary. 4662, 4674, 4750  
4661  
4665  Entropies in regulation. 4666, 4722, 4971  
5Nov53  4666  Entropy and information. 
4668  An organism cab control an environment of its own size (channel capacity), but not more.  
5Nov53  4671  An errorcontrolling regulator cannot reduce the incoming variation to less than a half. But see 4688 
6Nov53  4673  Markovian parameters to Markov chain. 4700 
6Nov53  4673  Meaning of "output". 
4679  On regulation. 4709, 4795  
8Nov53  4682  Regulation when several inputs disturb. 
10Nov53  4687  Regulation in the homeostat's second order feedback. 4695, 4701, 4709 
11Nov53  4690  Errorcontrolled 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.  
16Nov53  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 
17Nov53  4701  Markov chains as component parts for building a machine. 4703, 4770 
19Nov53  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 singlevalued field, can be formed only by supplying variety of n log n bits. 4722  
21Nov53  4708  Quality in design. 4725, 4733, 4788 
23Nov53  4722  Regulations at various levels reduced to standard and common form. 4737, 4906 
24Nov53  4727  The homeostat does not amplify. Contradicted 4792 
4728  
4730  More 

24Nov53  4732  A set of determinate machines do not give a Markov chain. 
27Nov53  4737  Information going into a system to design two parts. 5006 
2Dec53  4740  The unreliability of introspective evidence. 
7Dec53  4749  Riguet's statement of "relational mechanics." 4751 
9Dec53  4750  Regulation implies both activity of the regulator and inactivity of the essential variable. 
9Dec53  4757  Coordinates and projections in relational form. 
4759  Riguet's definition of "dependance". 4813, 4992  
12Dec53  4761  Riguet's "trajectory" is practically my "transient". 
31Dec53  4765  More on habituation. 4917 
4773  Stochastic machines. 4847, 4876, 4868, 4904, 5097  
4775  Properties of tensor product.  
7Jan54  4776  Equilibrium of Markov chain. 
4779  Quotient machines. 4937, 5001, 5165, 5148  
28Jan54  4781  Observations on controlling a system that can learn. 
4782  Set theory in machines can dispense with the idea of "information". 4795  
16Feb54  4787  "Survival in spite of disturbance" in the terms of set theory. 4790, 4795 
19Feb54  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  
19Feb54  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?  
19Feb54  4792  The homeostat does amplify. 4794> 
4793  Designing a machine to build a machine. 4808 (top), 5070, 5072  
22Feb54  4794  The limit of progressive regulation. 
4796  Many concepts include that of "reduction". 4880, 4950, 4963  
26Feb54  4798  Strategy of trial and error. 4844, 4949 
2Mar54  4801  Every machine on states M defies "machines" on states in M^{n} (n=1,2,...). Only in the latter is variety bound to fall. (Its "tensor powers") 4869 
2Mar54  4801  "Transformation". 
2Mar54  4809  Gain in regulation when the sequence has repetition. 4831, 5002, 5070 
5Mar54  4810  Change of state and change of design. 
5Mar54  4810  The "tracker" as regulator. 
5Mar54  4811  Error controlled regulation. 
5Mar54  4812  Levels in regulation. 
12Mar54  4813  Learning is worth while only when the disturbance will be repeated. 
17Mar54  4814  The diagram of immediate effects as a higher relation. 
4816  The circularity of reasoning about reasoning. 4835, 4897  
29Mar54  4819  Slowing down a machine, and sleep. 
29Mar54  4823  Getting the disruptive feedback from the distant environment. 4844, 4927 
30Mar54  4830  Proving the existence of hidden variables. 
30Mar54  4832  Discriminative feedback. 4834, 5345 
31Mar54  4833  On attention, and vigilance. 
2Apr54  4835  The "problem" of discriminative feedback must be shown to exist in the real environment. 
4839  Nature of relations and sets. 4897  
7Apr54  4841  More on the Black Box. 4951 
4843  Huntandstick is a more general form of stability. 4881, 5046  
14Apr54  4845  Strategy of trial and distribution of probabilities. 4849 
14Apr54  4845  Two ways of regarding "design". 
15Apr54  4847  Law of Requisite Variety stated with respect to a rectangular table. Stated purely in terms of set theory 4850 
22Apr54  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  
23Apr54  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.  
28Apr54  4867  Quotations. 
28Apr54  4868  "A machine" implies three sets and two mappings. 4871 Simpler 4876 Best 5097 
4870  A set of replicate machines.  
28Apr54  4872  The machine of intermittent observation. 
28Apr54  4873  Initial states may appear simply as a source of variety. 
29Apr54  4874  Reentrant chain of mappings. 4876 
29Apr54  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  
27May54  4880  The amount of design in "keep moving". 
4881  There are two distinct reasons why a machine may be used in regulation. 5046  
28Apr54  4883  "Independence" is a special case of "incomplete transmission of variety". 
4894  Why the uniselectors have many values. 5046  
3Jun54  4895  Specifying the secondorder feedback rigorously. 
4897  Church's theorem.  
8Jun54  4899  Logic in the multistable system. 5305, 5313 
8Jun54  4901  Speed is merely one of many demands that can made to qualify simple adaptation. 4964 
8Jun54  4904  On identifying an optimum in a set. 
10Jun54  4905  Equilibrium in coupled Markov systems. 
4913  All sorts of continuous and discontinuous systems put together to make all sorts of ultrastable systems.  
12Jun54  4915  Bellman on 'stability'. 
14Jun54  4918  Statistical laws in the Markov chain. 4919, 4946 
23Jun54  4927  Relation of the physicist's "entropy" to my work. 
4928  Supplementary information and its mode of use.  
5Jul54  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  
6Jul54  4938  Homomorphism returns. 
28Jul54  4941  Closed sets of states in a black box. 4951, 4968, 4989 
30Jul54  4942  Trials are good, for they bring information. 4945, 4948, 4965, 4963 
4944  A "thing" is a way of behaving.  
4Aug54  4945  Proof of 4871 
4Aug54  4946  Discriminative feedback. 4963 
4Aug54  4946  Information repair. 
5Aug54  4947  Letters as Markov chain. 
17Aug54  4950  The strategy of adaptation. 4962, 4964, 4980 
17Aug54  4951  The Black Box is built. [see photos: Description  Black Box  Details] 
17Aug54  4952  On the accessibility of states. 4953, 4968 
17Aug54  4953  The "partly observable machine with input." 4956 
17Aug54  4956  What "examining a machine with input" means. 5055 
22Aug54  4961  When a system is partly unobservable, the method of trying to restore absoluteness by taking earlier values into account is fundamentally secondrate; it will succeed only when the case is peculiarly favourable. 4979 
22Aug54  4963  All necessary improvements to the basic ultrastable system can be had by the addition of further orders of feedback. 
23Aug54  4964  More on the chessplaying 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  
30Aug54  4971  "State of equilibrium" in the hierarchy or sets. 
30Aug54  4971  Orthogonality of actions in regulation. 
17Sep54  4972  We live by the incorporation of pieces that are already keepersout of noise. 
4973  Living organisms surround themselves with invariants.  
4973  Example of an adequate channel. Pantagruel, l.iii,ch.xxix  
22Sep54  4978  With a random transformation the variety tends to fall to two thirds at each step. Qualified 5158 
27Sep54  4980  "Time" can be treated as a disturber of a machine, like an input. 
27Sep54  4981  Research and the strategy of adaptation. 
26Sep54  4982  "Integrating" and transformation. 
26Sep54  4983  Nature of "invariance." 
26Sep54  4984  Notes on "closure" of a transformation. 4989 
26Sep54  4984  Getting from the discrete to the continuous. 
4987  Whether properties "emerge" or not depends on our knowledge of the parts.  
4987  Why information?  
27Sep54  4988  "How to dichotomise" takes time to be learned. 
30Sep54  4991  However many states are available, the experimenter confines himself to some set satisfying certain conditions. 
5Oct54  4994  Algebraic form of "immediate effect". 
7Oct54  4995  How to deduce the connexions from input to variable. 5055 
4996  "Connexion" depends on the operations brought to its study.  
22Oct54  4999  An exact electromechanical analogy. 
5000  Isomorphism.  
27Oct54  5001  Homomorphism. 
28Oct54  5002  A problem. 
2Nov54  5004  What is a machine? 5056 
5005  Game that is wholly arbitrary. 5024  
5010  Design of a machine part by part. 5474, 5072  
26Nov54  5011  Example of triunique relation. 
2Dec54  5012  Behaviour when the feedback can carry only one bit. 
5021  The relations between regulators are complex and hardly worth developing.  
10Dec54  5023  Problems that are not wholly new. 5066 
10Dec54  5023  A numerical illustration of continuity as a constant. 4569 5005 4597 
16Dec54  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.  
22Dec54  5042  The Turing machine. 
5045  A machine that makes itself. 5088  
5047  McCallum and Smith also use the method of veto. 5583  
23Dec54  5048  Requisite variety stated algebraically. 5075 
24Dec54  5050  The field, when memory is used, is not isomorphic with that found when all is observed. 
5054  Studying a system via one variable.  
11Jan55  5055  (Comment on "continuity") 
11Jan55  5056  Studying a system... 
11Jan55  5057  "Machine" as constraint in a sequence. But see 5074 
11Jan55  5061  Converting observed behaviour to specification of machine. 5063, 5081, 6071 
11Jan55  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 
12Jan55  5062  The quatity of design in measured by the size of the set that is drawn from. 5070, 5071, 5072 
12Jan55  5064  Algebra can operate directly with observed behaviour. 
14Jan55  5065  Mnemonic for "everywhere defined" and "single valued". 
14Jan55  5065  Metron and logon. 
5066  What is problem solving? I say it is finding an element in a set.  
5068  Problem solving.  
15Jan55  5069  Another example of a selflocking system, this one harmful. 
15Jan55  5071  Briefing a deputy calls for the same capacity as doing the job oneself. 5073 
15Jan55  5071  Amount of design required for a machine to do a job. 
15Jan55  5073  More on "the amount of design in a machine". 
16Jan55  5074  Why build a regulator? 
16Jan55  5075  A machine embodies a transformation and, in addition, may act repetitively. 
16Jan55  5075  Two problems. 
18Jan55  5076  Theory of the homeostat. 
15Feb55  5077  Demonstration of selectionamplifier. 
18Jan55  5080  Systems that interact finitely with their observer. 
18Jan55  5082  The structure of a machine, derived from a protocol. 
18Feb55  5084  Structure of machine in a protocol. 5170, 5192, 6071 
21Feb55  5085  The problem of "simplifying" a machine. 
8Mar55  5088  Godel's theorem as process. 
17Mar55  5089  More on the selfreproducing system. 5261 
1May55  5091  A strategy must be related to the actual constraints of a system. 
5093  Reducibility and channel capacity are independent. 5532  
17May55  5094  Finding a maximising formula. 
18May55  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.  
1Jul55  5109  Review of Pringle. 
5111  The problem of the glass of milk.  
2Aug55  5112  What is meant by "He does not know......." 
1Sep55  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. 
2Sep55  5114  Bridgman on operations. 
5116  There is no "law" to be found in systems much removed from the atomic level. 5142  
7Sep55  5117  On causality. (Continued over) 
9Sep55  5129  Concepts of cause, why, because etc related to Black Box theory. 
12Sep55  5131  The simplifications obtained by cutting channels lie on a lattice. 5135 
5134  Why the organised and interconnected can usually defeat the unorganised and individualistic.  
13Sep55  5136  Quantity of organisation. 
17Sep55  5144  Application of system theory to History. 
21Sep55  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  
5Oct55  5153  "Loss of control" in set theory. 5155 
5Oct55  5154  The conditioned reflex, and shedding of scatter by going to an equilibrium. 5249.1, 5277.8 
5159  Law of Experience, given rigorously. 5179  
12Oct55  5160  Kershner and Wilcox' book. 
17Oct55  5164  Variety in mathematical forms. (Continued 5167.6) 
18Oct55  5166  Markovian machines simplify on to a lattice. 
18Oct55  5167  Dichotomy versus trichotomy. 
18Oct55  5169  Mathematical expressions have inputs and outputs. 
18Oct55  5169  Black Box looks at itself and others. 
20Oct55  5174  Algebraic form of "immediate effect". 6070 
5177  The use and limitations of the integral equation. 5192, 5210, 6036  
21Oct55  5178  Must a person's private "map" be observable to all? 
24Oct55  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  
27Oct55  5188  Quotations from Mach. 
30Oct55  5189  The concept of "constraint" includes correspondence, mapping, relation, as special cases. 
31Oct55  5190  Psychological and anatomical patterns will usually be different. Cf. Introduction to Cybernetics S.6/11 
31Oct55  5191  Two meanings of "input". 
5195  Constraints in protocols. 5978  
4Nov55  5209  Use of observations at times earlier than "immediately preceding." Qualified 5210.3 5228, 5236 
5210  Definition, and the law of experience. 5254  
9Nov55  5213  In the absolute system, the use of earlier states may be inefficient. 5869 
14Nov55  5217  Thoughts provoked by Savage. 
14Nov55  5218  The mapping of the homomorphic machine. 
5220  The structure of the regulator. (Note that the inverse, [w^{1}], has appeared at last!)  
14Nov55  5223  Must a constraint go on holiday in the future? 5273 
15Nov55  5224  Example of message that depends on the set it came from. 6275 
5227  Ultrastability in Design and in Introduction reconciled.  
21Nov55  5229  Real existence of "variety". 
22Nov55  5230  Metastability. 
5234  Concept of the "distance" between two input states, or two designs. 5506, 6282  
23Nov55  5235  Distance of movement. 
5Dec55  5240  Why the scientist should relate the event to what is adjacant rather than distant. 
5241  "Complexity" is a relation between units and construct.  
19Dec55  5243  Law of Requisite Variety as law for suppression of noise. 
2Jan56  5244  A minute crack at the problem of consciousness. 5275 
5Feb56  5245  The end of the hunt? 
5247  The machine, when observed only so far as the states of equilibrium it goes to. 5556  
6Feb56  5248  What is a "variable"? 
6Feb56  5249  Mathematical proof "in detail" means going through a sequence of states of equilibrium. 
6Feb56  5250  Is there any way by which a person can communicate an infinite amount of information? 
14Feb56  5252  "Consistency" in mathematics. 
5253  Personal note.  
5254  What is a "logical definition"?  
24Feb56  5256  The structures of space as habituation. 5289, 5313 
5260  New machine to demonstrate statistical mechanisms. 5317, 5408, 5526  
24Feb56  5261  On "imitation". 
5262  More "selfreproducing" systems. 5797  
5263  Pain educates mostly in childhood.  
2Mar56  5265  A contribution to the theory of the distribution of basin size. 
6Mar56  5267  Probability of getting a single basin. 5308 
9Mar56  5270  Schizophrenia and noisiness. 
5272  Raiffa et al. describe maths as isomorphic with real systems. 5298, 6260  
5Apr56  5275  "Will", and acting now so that certain things shall be. 6321 
5276  On consciousness.  
14Apr56  5277  What good is "Design..." 
29Apr56  5278  Movement between states of equilibrium. 
29Apr56  5278  "Yesno" is a language capable of explaining, or getting, all things, however complex. 
29Apr56  5279  Program. 
1May56  5280  Selection cannot proceed quickly, by dichotomising, in a class that is undefined. 
16May56  5281  Example of a case in which information about the initial state gets lost. 
17May56  5282  Science forswears direct knowledge in favor of the indirect. 
21May56  5283  "Statistical machine" has two widely different meanings. 
22May56  5286  Fast adaptation can be a manifestation of habituation. 5287.7, 5288, 5342 
23May56  5287  How to sample equilibrium states. 
31May56  5289  The fringevariables 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 partmechanisms. Now read 3420 and see how much I have advanced in five years!  
7Jun56  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  
25Jun56  5301  Abstract machinery. 
5303  How to make a brain.  
29Jun56  5304  The multistable system must have low interaction on the average. 5312 
29Jun56  5304  On the pains of learning. 
6Aug56  5307  Structure is a form of constraint. 5314, 5496 
6Aug56  5307  To evoke a property, the designer vetoes its negation. 5316, 5331.5 
21Aug56  5313  Cross connexions, immediate effects, random transformations, and memory. 
24Aug56  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 
24Aug56  5314  A reason why a chessplayer will automatically tend to learn quick ways of winning. 
14Sep56  5316  Fixing the stepmechanisms 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  
20Sep56  5323  How does the child get "stucture" from the world around it? It can't keep it out! 
24Sep56  5324  The "structure" developed by the child (as a result of structure in the world) need not copy the world's structure. 
24Sep56  5324  I need not worry further about reversibility. 
24Sep56  5327  Curie's principle is merely a special case of my decay of variety. 
25Sep56  5329  "Looking one move ahead does not require special programming. 
25Sep56  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.  
28Sep56  5337  There is no general rule for characterising the more efficient forms of corrective feedback. 5369.2, 5371, 5417, 5539 
1Oct56  5339  Effect of computing a transformation sequentially. 
2Oct56  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  
13Oct56  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  
18Oct56  5366  Relays can do everything I want, if suitably coupled. 
18Oct56  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.  
26Oct56  5371  Feedback in a dispersive system should be first widespread and then progressingly narrower. 5413 
17Nov56  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 r^{2} spaces.  
21Nov56  5382  Probability of district balls getting into same cells. 5830 
22Nov56  5383  Abstract form of a "teacher". 5430 
1Dec56  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 
1Dec56  5391  "Plastic" behaviour. 
1Dec56  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  
4Dec56  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  
6Dec56  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  
7Dec56  5414  If active arcs have a nontransient 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 stepmechanisms. 5440, 5606, 5655  
5421  Behaviour may be plastic in two senses: showing an effect or showing a copy. 5437  
10Dec56  5422  The system that is both multiple and plastic. 5522, 5545, 5535, 5631 
11Dec56  5423  Go for the quality of "survival"  all the rest shall be added unto you. 
5425  Arcs and genes. 5522 (Reprints 130, 131)  
19Dec56  5426  Remember that an input may work by releasing, to the output, some subsystem 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  
27Dec56  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  
28Dec56  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  
14Jan57  5446  Antihabituation may occur. 5490 
14Jan57  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  
5464  Equilibria must be specially fostered; in the general random system they are vanishingly few. 5476, 5482, 5503. Summary 5524  
15Jan57  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  
15Jan57  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  
18Jan57  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 
18Jan57  5480  The world that is is just those properties that are not relative to the observer. 
5481  Page 5407 clarified.  
21Jan57  5485  If the parts have probability of equilibrium π_{i}, 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 Π_{i}π_{i}. If joined so that all information is brought to each part, the probabilities are independent. 5505 
5486  If the parts have probability of π_{i} 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  " 

5491  Habituation.  
5493  Synthetic habituation.(Continued 5494.6)  
5494  Repeated samples with some sticking.  
5495  Synthetic display of habituation and its "inhibition".  
28Jan57  5496  The use of a transformation repetitively in time is a constraint, so structure becomes apparent. 
5498  "Confluent" defined (as noun). 5512  
1Feb57  5499  The theory of the determinate machine includes the practical aspects of the theory of the Markovian machine. 
1Feb57  5502  Sample space of a whole made from parts by coupling, they having sample spaces of their own. 
1Feb57  5503  One system may have many confluants, and many separated systems may have a single confluent 
2Feb57  5506  The whole built from random parts, by random coupling, when each part has probability π_{i} 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 inputvalve, or transformation, etc) a particular value corresponds to talking about a set of machines (or states, or inputvalues, or transformations, etc). The set has no associated probabilities, but can use the concept of "independence". 5666.7  
4Feb57  5510  The system that is contained only to have high equilibrium in its parts. 
5Feb57  5511  High probability of equilibrium in the parts cuts the whole up into (temporarily) isolated subsystems. 5522 
4Feb57  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  
12Feb57  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  
18Feb57  5533  Basic meanings of organisation, reducibility, conditionality. 5537, 5675, 5993 
20Feb57  5534  Example of isomorphism in differential equation form. 
5535  The timefactor insists that genetic adaptations and cerebrallearned adaptations shall be done mostly in the piecemeal way. 5601, 5631  
5536  Where I am now. 5558  
22Feb57  5538  From essential variables to Grand Outcome, via trials. 5573, 5642 
23Feb57  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 superfast subcomponents.  
5547  "Thinking things over" in a multistable system. Discriminative feedback requires mere opportunism. 5549, 5584, 5601  
27Feb57  5549  No general principle can be sufficient guide when selection must be done; some actual channel is also necessary. 5585 
2Mar57  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".  
6Mar57  5557  Others are building machines with discriminative feedback. 5584 
11Mar57  5558  Personal note. 
20Mar57  5559  The optimal duration of memory. 
20Mar57  5559  A minimal quality of memory is not definable. 
25Mar57  5568  Identification by random criteria is (in the defined circumstances) practically as good as accurate dichotomy. 
25Mar57  5569  Major strategies are determined at the genetic level, minor at the cerebral. 
28Mar57  5570  How this works yields application to psychiatry. 5651 
5572  The distinction between aggression and nonaggression corresponds, respectively, to having or not having a regulator. 5694  
2Apr57  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.  
2May57  5579  Essential variables in Multistable System 5601, 5625, 5642 
2May57  5581  General formulation of "the environment" for an artificial brain. 5522 
6May57  5585  Solution in principle of the problem of discriminative feedback. 5590, 5594, 5601, 5608, 5631 
6May57  5588  Any question about how something can be achieved is answered: a regulator is necessary; lacking it the achievement is impossible. 5601 
13May57  5590  Serial or sequential adaptation is equivalent, in a sense, to semiiterated simultaneous adaptation. 5593 
5591  General phenomena should be explained by proportionately general mechanisms.  
13May57  5595  What is necessary for the accumulation of adaptations. 5601, 5608 
18May57  5600  From iterated systems to the multistable. 5612 
20May57  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  
24May57  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  
27May57  5621  The multistable system reviewed. 5733, 5735, 5746 
27May57  5625  How big should an arc be? 5746 
27May57  5626  Why have arcs that are dynamic systems? 
5628  Reducibility of the essential variables in set theory. 5631, 5642, 5652, 5675  
28May57  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)  
30May57  5634  One unit for adaptation (in Multistable System) may comprise many portions (arcs) in the cortex. 5653, 5746 
30May57  5635  Optimal duration of trial; optimal time back to make disruptive feedback work. 5642 
31May57  5636  Continuity as a restraint. 
5641  The natural duration of a trial is the time of transmission of information from stepmechanism round then organism and environment back to step mechanism What is implied by "trail."  
5643  Distinguish between Essential and Vital variables.  
13Jun57  5650  Vital variable identified generally; what it is vital to; subgoals. 5811 
14Jun57  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.  
17Jun57  5667  The unspecified machine. 
18Jun57  5671  The extreme cases of the relations between equilibria in parts and whole. 5983, 6025, 6019 
18Jun57  5673  If the stimuli are not restricted, the terminal responses to Lim_{n→∞}T^{n}D mark out the areas of the T confluants. 
5674  Clearer statements of the theorem on habituation. 5687, 5702.4, 5707, 5730, 6088  
24Jun57  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  
11Jul57  5686  Complexities in integration and coordination may be shown adequately by some simple evidence of their success. 
15Jul57  5689  Program for habituation. 6088 
15Jul57  5689  Normal behaviour is loopy. 
30Jul57  5692  The homeostat programmed. 
30Jul57  5692  The dynamic cannot claim that the static is just a subcase of it. 
1Aug57  5693  Design for a Brain seems to have been successful. 
5696  What is meant by "force" in psychology.  
9Aug57  5697  When a set is called for, refuse to answer the question: which of these elements is the "actual" one? 
9Aug57  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.  
9Aug57  5700  "Transfer of patterns" demands only a transfer of values. 
10Aug57  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) 
12Aug57  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."  
16Aug57  5709  When the alternation of two stimuli to a machine reaches equilibrium, the two effects and the equilibrium are related. 5724, 5729 
17Aug57  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. 
17Aug57  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  
19Aug57  5721  Basic theory of the conditioned reflex 
5722  Some experiments on my theory.  
20Aug57  5726  Simultaneous presentation does not give conditioning. 5730, 5827, 5862 
23Aug57  5727  A very new way of producing "conditioning". 
5728  Constraints are found by applying informationlosing transformations and seeing whether they are still acceptable to the essential variables. 5756  
24Aug57  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  
31Aug57  5739  How habituation will show in a multistable system of arcs. 
31Aug57  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 
31Aug57  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. 
3Sep57  5743  Variety, uncertainty analysis, and information. 5794, 5820 
13Sep57  5747  Basic functional necessities for an arc, or store. 
14Sep57  5755  Any restriction on one part of a system is likely to show as "structure" in another part of it, Reducibility exemplifier. 
19Sep57  5756  Axiom that the "typical member" identifies the subset and the constraint. 
19Sep57  5759  Layout for accumulative adaptation. 5766.7, 5775 
20Sep57  5760  Additive mechanisms in the brain. 5763, 5765.1, 5766.1, 5768 
5762  The problem of the moving critical states. 5778  
20Sep57  5763  Psychiatric application of the system that adapts additively. 
20Sep57  5764  Importance of information whose changes occur only at long intervals. 
26Sep57  5765  Psychiatric application. 
26Sep57  5765  Operational meaning of "correct translation". 
26Sep57  5766  Mechanisms for memory may well vastly outnumber those for action 
1Oct57  5767  Essential variables for adaptation by accumulation. 
1Oct57  5768  Complexity of remembering old adaptations is independent of complexity within one adaptation. 
3Oct57  5771  Serial adaptation, and flow to the stepmechanisms. 
8Oct57  5774  My proof (that adaptation demands stepfunctions) demands in fact only that there must be entities having a stepfunction aspect. This aspect may be one that is by no means obvious in the real object. 5781.7 
8Oct57  5776  Design of DAMS. (Corrected 5778) 5779 
8Oct57  5777  I may now use design and regulation freely in building DAMS, provided I admit its introduction. 
25Oct57  5778  Layout for DAMS, and for the system that accumulates adaptations. 
28Oct57  5780  Under certain conditions, communication between arcs is necessary. 
4Nov57  5781  So far I have used essential variables as little more than links determining how the environment affects the stepmechanism. 
5Nov57  5782  My claim that stepfunctions are necessary, must be made conditional. 
25Nov57  5784  Stepfunctions have done their job and may now retire. 
5788  Index [?] of degree of stability of a whole, and its behaviour. 5800  
9Jan58  5794  Some systems are not to be understood, or controlled, by the amount of information that can be accepted in 1 man lifetime. 5810 
11Jan58  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 
23Jan58  5796  Present position of the machine for solving superproblems. 
5798  Survival of the fittest, demonstrated in a computer. 5801, 5828, 5961  
11Feb58  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".  
17Feb58  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.  
22Feb58  5812  A variable may be essential to an organism and yet outside of it. 
24Feb58  5814  Abstract formulation of "survival" and "essential variable". 5828, 5963, 5984 
3Mar58  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 subset 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  
25Mar58  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.  
27Mar58  5829  Survival of the fittest in random operations. 5961 
28Mar58  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.  
8Apr58  5835  When the machine with input is determinate, the outputtrajectory determined by a given inputtrajectory 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 twovalued variation at the input.  
12Apr58  5845  The pattern in the confluents tends to copy the pattern in the inputtransitions. Stochastic case: 5873, 5892 
14Apr58  5849  Jennings' law of the resolution of physiological states. 5880, 6101, 6137 
15Apr58  5851  There are complications before "in same confluent" means "moving towards". 
15Apr58  5854  The homeostat's confluents. 
5957  Conditioning on the homeostat examined by the method of confluents. 5877  
16Apr58  5858  Paradoxical predictions for conditioned reflexes. 
16Apr58  5861  Simple, secondorder, third order Conditioned Reflexes examined by the method of confluents. 6097 
16Apr58  5861  The conditioned dog must have these relations. 
5865  Defeat of my attempt to uncover the "secret" of the conditioned reflex.  
5870  Restoring singlevaluedness of prediction, when parts of a machine with active input are not observable, by taking its history into account. 6050, 6069  
21Apr58  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  
22Apr58  5875  Transfer of pattern when input and machine are stochastic. 
24Apr58  5876  Fully joined systems must be known k steps back if k variables are unobservable. 
5881  Relation between adaptation and anticipation.  
25Apr58  5885  "Conditioned" stability can readily be defined rigorously. 6091 
25Apr58  5886  "Conditioned" inaccessibility can readily be defined rigorously. 
5887  A system may have different subsets conditionally stable when the input has different constraints. 6091  
25Apr58  5888  Transfer of constraints from the world outside to that inside. 
8May58  5889  A machine with input may correspond to an algebra. 
9May58  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. 
9May58  5893  How a relation is transmitted by an operator. 
5895  
5899  Pattern recognising. 6167, 6305  
5902  
12May58  5905  Presentday 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. 
12May58  5905  
13May58  5909  Program for developing the mathematical theory of machines. 
17May58  5913  Rigorous form of what is implied by the operator "let it get to equilibrium before applying the next stimulus". 5994, 6084 
19May58  5914  A new form of independence and the "proxy" relation. 
5916  Hilton's very wide definition of "isomorphism".  
19May58  5922  "Isomorphism" as one of many relations that may hold between relations. 
27May58  5928  The theory of superrelations and the laws of pattern. 
28May58  5929  Do not confuse "patterns R are like patterns S", with "there is constraint in [RxS]. 6063 
2Jun58  5941  The relationship S=ΦRΦ^{1}, studied from various angles. 5946 
3Jun58  5948  
3Jun58  5948  Algebraic form of "[T^{~}'s] trajectories are not more than one step long". 
4Jun58  5951  The constraint algebraically when a transition can only be to an "adjacent" state. 
5957  The set of stable subsets forms a lattice on which the representative point moves only downwards. (True both for determinate and stochastic transformations) 6091, 6093  
24Jun58  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  
25Jun58  5966  Spontaneous generation of life and intelligence in analogue form. 5967, 5984 
5968  The typical, or modal, element from E^{E} 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 productsetform. 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.  
12Jul58  5984  A review of the relations between "whole" and "part". 6019, 6025 
5985  Abstractness can go too far. 'Adaptation' demands several parts.  
17Jul58  5986  Cortex  not statistical but stochastic. 
19Jul58  5990  Imposing a property on the set of inputtrajectories will necessarily impose a property on the set of outputtrajectories. 6063.4 
5991  "Constraint" is a relation between an Observer and a set.  
5992  Pidget on conception of space.  
22Jul58  5995  Rigorous form of saying that behaviour is "organised". 6007, 6021 
6002  Review of Elsasser. 6046  
24Jul58  6005  "How much information in a brain?" is best preceeded by consideration of "how much information in a flipflop?" 6043.8, 6179.9 
29Jul58  6007  Notes from Birkhoff's Hydrodynamics. 
31Jul58  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.  
1Aug58  6016  Relations between machines. 
1Aug58  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 cuttingup; I should have gone for the equilibria. 6028  
6023  Sommerhoff's basic formulation given set theory. 6104  
8Aug58  6024  Wiener suggests that maths is a dynamic process, that may end in a cycle. 
8Aug58  6029  Effect of D.I.E. on maximal equilibria of whole  cuts make the maximal number fall. 
11Aug58  6032  Eigentheory generalised. 6109 
13Aug58  6033  A physical system that is not completely analysable. 6065 
30Aug58  6035  Algebraic property of the machine that transmits without loss of information. 
6039  Coding a function.  
9Sep58  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. 
9Sep58  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. 
22Sep58  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  
29Sep58  6058  Of all the !memory capacities", the maximal value may be of physical interest. 6179 
6059  Build devices for demonstration.  
22Oct58  6060  Build small specialist machines, each devised to show one fact with perfect clarity. 
6062  Blitztherapy.  
13Nov58  6063  Two sorts of memory are identifiable. 6068 
19Nov58  6067  Irreducible complexity. 
18Nov58  6066  A proposition is "atomic" if its user does not propose to break it up. 
18Nov58  6066  The brain may be like a digital computer in being errorfree by going from equilibrium to equilibrium. 6126 
19Nov58  6067  Simple "relations". 
19Nov58  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  
28Nov58  6073  Learning by pain is fundamentally simpler (demands less communication ) than learning by reward. 
10Jan59  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'.  
17Jan59  6078  The value of the new logic of mechanism can easily be overrated. 
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  
21Jan59  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.  
23Jan59  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  
14Feb59  6104  Another way of writing Sommerhoff's directive correlation. 6105, 6284 
14Feb59  6104  Are isomorphisms denser around equilibrium? 
25Feb59  6105  Isolating a pure concept is like isolating a pure element. 
6107  Berge's book shows me I must develop my combinatorial dynamics myself.  
16Mar59  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  
2Jun59  6116  Oscillating systems, when coupled, do not necessarily pull together in frequency. 
13Jun59  6117  When a simplification is permissible. 6148, Better: 6254 
13Jun59  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.  
25Jun59  6119  General, abstract, nature of "induction", 
21Aug59  6120  Threshold combines lots of equilibria with continuity. 
6123  Possible function for the "functionless" parts of the midbrain.  
6123  The "size" of a system had no unique meaning.  
15Sep59  6125  Isomorphism, homomorphism and now protomorphism. 6150, 6260 
18Sep59  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  
19Oct59  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  
14Dec59  6137  Closure under a sequence, and a property of one operator, implies a corresponding property on the other operators. 6143, 6269 
18Dec59  6140  A more general type of "forcing" operator". 6269, 6247, 6312, 6322 
6141  Razran's review reviewed. 6269  
18Dec59  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.  
15Jan60  6150  Measuring how much a machine has been simplified. 
4Feb60  6151  'Relations' between patterns. 
5Feb60  6157  Input pattern of transition showing as output pattern. 
5Feb60  6157  Nearness in time encourages similarity in response. 
19Feb60  6158  ... no regulator can be more effective than the statedetermined system. 
23Feb60  6160  No regulator (other things being equal) can give performance better than the machine with input. 
3Mar60  6162  Meaning of H(A)=0. 
11Apr60  6165  Example of the coordination that exists at a state of equilibrium. 6350 
13Apr60  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]  
12May60  6179  Solution of the linear difference equation. 
3Aug60  6181  More on selfreproduction. 
5Aug60  6184  Selfridge's Pandemonium and pattern recognition. 6222 
10Aug60  6185  I should reread my Notes, Vol. 5 or so onwards, reading "lots of stepfunctions" as the more general "lots of equilibria", and lots of stepsurfaces" as "lots of boundaries of confluents". 
10Aug60  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 tablesearcher.  
21Aug60  6192  Rubin and Sitgreaves' results summarised. 6199 
22Aug60  6193  I must demonstrate, some day, that a heap of manure has as high an organisation as a man. 
2Sep60  6194  In a lot of ways a system cannot, strictly, be "self.....ing". 6566 
6Sep60  6197  Independence of probabilities of equilibrium demands that all loops of connexion be long. 6199, 6333 
19Sep60  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  
16Oct60  6222  Zatocoding. 
6224  Patternrecognising after coding. 6260, 6346  
6226  Form all mappings, and you are performing all patternrecognitions. 6346  
6228  Adaptation to the recurrent situation demands stepmechanisms with a multiplicity of channels.  
30Oct60  6233  What properties of a brain are specialisation to terrestrial life and what are good absolutely? 6404 
13Nov60  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  
19Nov60  6247  Only restricted types of trajectory or process are suitable for cybernetic studies. 
23Nov60  6249  "Association" clarified further. 6269 
6250  Sketch of a theory that two coupled systems, in going to equilibrium, tend to prefer regions in their phasespaces that are topologically similar.  
24Nov60  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  
4Dec60  6262  [SRS^{1}] is the "shadow" of R when "projected" by S. It can be inverted back to R if and only if [S^{1}S=Δ]. 6265 
6264  Immediate effect is a realityshadow reaction.  
6265  A machine is a "shadow" of simple progression.  
16Dec60  6266  Meaning of [formula] 
17Dec60  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.  
8Jan61  6283  There is no difficulty in getting from a structure of mere clubbing to a full topology. 
16Jan61  6284  Extension of homomorphism. 
17Jan61  6288  Directive correlation quite simply. 6297 
6289  Specifying the "worst" brain.  
2Feb61  6290  The genius searches. 6335, 6339, 6430, 6570 
2Feb61  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  
12Feb61  6295  Energy flow is neither maximal nor minimal at equilibrium; it is just irrelevant. 6321, 6345, 6350, 6365 
23Feb61  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  
4Mar61  6298  What a species can do, it can recognise. 
4Mar61  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 
18Mar61  6302  A species that needs its competitors. 6350, 6355 
6305  The dynamics of the wavefunction is that of a statedetermined system.  
24Mar61  6306  Pattern recognition is arbitrary. 6346 
2Apr61  6307  The "anatomical" body is only one way of identifying the boundary of a system. 
6310  What "isolated" means. 6349  
1Apr61  6311  Natural systems, observation, and experiment. 
6314  
6315  
6317  More on Conditioned Reflex 6323, 6347  
15Apr61  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  
16Apr61  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  
22Apr61  6334  Mixing network, one way. 
4May61  6335  "Transmission" of selection among the components of equilibria. 6347, 6350 
11May61  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  
25Jun61  6345  Convergence to equilibrium in Markov chain. 
27Jun61  6346  Pattern recognition is arbitrary. 
6349  Theory of anticipation. 6352, 6374, 6389  
6351  Equilibria and their properties. 6373, 6389  
1Jul61  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.  
29Jul61  6362  For economy, the brain must store memories at the site of use. 6383 
14Sep61  6364  How to make a multistable system. 
15Sep61  6366  The physicist's equilibrium at zero freeenergy and the biologist's homeostasis. 
17Sep61  6369  A game of chess shows three "organisations" simultaneously. One goes down, one up, and one does not change. 6379 
27Nov61  6370  The great difference between teaching by pain and teaching by pleasure. 6550 
27Nov61  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  
29Dec61  6373  The polystable system tends automatically to find and to use the constraints. 
9Jan62  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.  
9Jan62  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].  
26Feb62  6381  [RR_{1}'R≠0] is a sensitive test for the existence of constraint, but [RR_{1}'R] does not equal it. 
13Mar62  6382  On the subjective. 6384, 6427 
1Apr62  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 preexistence of other ideas.  
6393  Theorem on anticipation. 6394  
21Jul62  6396  The hard core of "habituation", rigorously. 
21Jul62  6396  Two random mappings in succession do not give a random mapping. Nor one used twice, similarly. 
22Jul62  6399  The unit that develops anticipation must be tiny. 
1Sep62  6401  Specialising the anticipation, may properly go into μ. 6457, 6588 
12Nov62  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  
27Jan63  6417  The theoretical unit is simply a mixer. 
6418  To build any machine, only a mixer is sufficient.  
6420  The PittsMcCulloch 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.  
10Jun63  6429  Some problems become nontrivial only when much detailed specification is added. 
6432  Sannon 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  
28Jul63  6437  "Thing" and autocorrelation. 
6439  The topologies on n points number about exp(n^{2}). (Size No. 7 on 6424) 6454  
5Aug63  6442  Review of Waddington's "Nature of life". 
6443  Algebraic form of "the behaviour doesn't depend on variables Z".  
6Aug63  6445  "Remembering" as hallucination. 
6Aug63  6446  Example of how too much memory can be disadvantageous. 
16Aug63  6450  Some details about binary relations from B. Russell. 
6453  Logical dynamics. 6455  
27Aug63  6454  Example of how a topology is learned. 
6456  A memory of a pattern does not have to be stored anywhere.  
19Nov63  6460  Proofs the orders of size. 
6461  Indefinitely long memory in simple machine. 6470  
7Jan64  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 

10Aug64  6475  Much in "Computers and Thought" is relevant to cylindrance. 
12Sep64  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 
17Sep64  6479  Examples of low cylindrance in everyday life. 
6483  Movement of Amoeba: parts and whole. 6703  
21Sep64  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 2nspace 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 C_{p1}R shrinks to R.  
7Nov64  6495  A set may increase in cylindrance if a variable is ignored. 6522 Generalised to n dimensions: 6531 Footnote 6502 
7Nov64  6496  Meaning of "meaning". 
8Nov64  6498  If the distinction between two values of a variable is lost (and the relation reformed by union, i.e. + and 0 counts as +), then cylindrance may increase. 6504 
8Nov64  6502  Effect on cylindrance of adding new values to variables (values that did not occur before in R) 
18Nov64  6504  Cutting out a slice cannot make cylindrance rise. 
22Nov64  6506  Effect on cylindrance of an equivalence relation when the sections combine by intersection. 
25Nov64  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.  
5Dec64  6518  When they are cylindranceone sets, composition does not raise the cylindrance. 6519 
5Dec64  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  
23Dec64  6528  Cylindrance is a generalisation of reducibility. 
24Dec64  6529  Defeated. Not this time  see page 6531 
24Dec64  6530  There is no obvious relation between cylindrance and stability. 
7Jan65  6533  Example showing how projection may jump the cylindrance up from 2 to any given number. Another example 6829 
7Jan65  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.  
16Apr65  6544  All the maths we know has low cylindrance. 6551 
16Apr65  6546  Any selection of 1 from more than 10^{1000...(47 zeros)...0} is physically impossible. 
6548  How informationquality can explode when complicated at the sensory side. 