In July 1941 Ross decided to end his journal entries with a summary:
The following table lists and links to all of the summaries, covering volumes 4-25 over the period 1941-1972. Text that is in [square brackets] was either an editorial comment, difficult to read, impossible to type, or a case where Ross used square brackets himself! Because the summaries appear at the end of sections, when you use the link to jump to the page where the summary is, you generally have to flip back a few pages to find the start of the section. The dates listed are often actually associated with a following journal entry on the same page as the summary.
Date | Page | Summary |
4-May-39 | 0586 | Nirvanophilia is identical with stable equilibrium. |
20-Jun-39 | 0588 | A great idea... organisation must spread from the environment inwards. |
4-Jan-41 | 0858 | Had my severe illness here. Was it febrile reaction to enormous cortical readjustment? I don't know. But it felt as if I had "swallowed a rainbow". And the next page contains the essential discovery. |
4-Jan-41 | 0859 | A new idea. Suppose the cortex is a 'representation' of the environment, i.e. corresponding to events in the periphery (stimuli, reactions) there are events in the cortex. Nothing new in this idea. But suppose that the cortex is more 'sensitive', so that if the periphery is being driven out of its range of stability the corresponding variable in the cortex will break first, i.e. get outside its range of stability, and thus switch to another portion of the field (817), and change partially to another organisation. |
0960 | (1) It is impossible to say how much one variable depends on another. (2) The meaning of "dx'i/dxk" is given. (3) The Question "Does xi depend on xk" is meaningless. (4) New form of matrix test for dominance is given. (5) Definitions given of (a) xi-t curve depends on x0k, (b) xi-t curve is independant of x0k, (c) xi dominates xk, (d) "parameter". | |
0960 | I have decided in future to end the Sections with a Summary. It may perhaps force rather more tidiness into the ideas and will be useful for reference. | |
22-Jul-41 | 0963 | Three methods are given for exploring a system of equations like 957 (top) in order to find parameters, and dominances using basically the method of 958 (top). |
22-Jul-41 | 0966 | If a field should alter its organisation, and particularly its dominances and independences, reversibly when a variable exceeds a given value, we may either look on it in this way, or (preferably) we may set up new and more comprehensive field equations treating it as one constant organisation. But see 1038 for a much improved statement. |
22-Jul-41 | 0967 | After a lot of breaking and final reaching of a neutral point, if we test it by displacing it a little and ask 'will it be stable' the answer is that if it is stable O.K., and if it is no longer stable, we've broken it. So who cares? |
24-Jul-41 | 0969 | The use of diagrams like those of 940, 946, 967 are permissible only if they represent (a) immediate dependencies as given by the substitutions and subject to its restrictions, or (b) as completed diagrams (961) to represent final dominances etc, but not as both haphazardly. Completed diagrams may be used to typify an organisation (contrary to 928). Also an addendum to the method of 962. |
24-Jul-41 | 0970 | Our substitutions deal quite adequately with the idea of the free energy available to the brain and body - by ignoring it. |
24-Jul-41 | 0971 | A higher level must usually change more slowly than a lower level, in order that the lower level may be given time to catch its neutral point. |
25-Jul-41 | 0972 | If, from a given system, we remove knowledge of a variable, we must introduce probability to replace it. (But see next paragraph) |
25-Jul-41 | 0974 | If initial conditions are unknown we must replace them with probability. |
25-Jul-41 | 0976 | The idea is suggested that the old memories, as organisations, may be present implicitly rather than explicitly. |
27-Jul-41 | 0978 | The lower animals, at any rate, with their environment may be much simplified for our purpose by noting that one animal may be considered to be split into several, or many, parts, each of which has its own environment. So animal and environment = several machines, not one. |
27-Jul-41 | 0982 | We have discussed the situation: p's dominate x's, and x's dominate y's. Under these conditions we can get a stability of organisation. Also we can get y-point in y-space moving twice through the same point in different directions. If the x's react rapidly they will tend to disappear functionally. A succession of such gives transmission through a series of organisations. If one level has only a few, or a single, variable this introduces an essential simplicity into all subsequent levels. A large organisation may be 'simple' because it depends on only one or a few parameters. |
0983 | Details are given showing that it is possible to explore, experimentally, a given field or organisation. To do this parameters are necessary, and it may be necessary to introduce new ones not mentioned before. | |
0985 | An organisation with n variables and m parameters has two separate complexities. Subject to conditions, m describes the number of coordinates in the space in which the neutral point moves, when m=n we have a 'transative' state. | |
0987 | A (better) restatement of the theorem of 680. | |
0989 | Mathematical definition and test is given for 'neutral point' and 'neutral cycle' when the substitution is given as a differentil equation. (Actual example next paragraph). | |
0990 | An example of neutral cycle in a differential equation is given. | |
13-Aug-41 | 0995 | A break may be treated as a mere incident in the development (in time) of one machine. Also one machine may be considered as split into two parts with a break between if one of the variables is a step-function of the time (see next paragraph). A break is a change of organisation. Changes of organisation have two causes: (1) Due to conditions outside the machine, which are arbitary parameter changes, and are my doing. (2) Due to conditions inside the machine - a break if we ignore the cause. |
1004 | "Step-function" is defined. An analytic formula given for one. If a function in a substitution is a step function of the variables, the corresponding variable in the solved equations is a step-function of the time. The effect in a field of a step-function is discussed, The essential conditions for a break are a cloud of dots, each of which has a number associated with it saying "change one of the step-functions to this new value" and not a surface as suggested on 898. | |
22-Aug-41 | 1009 | (1) Brain activity will sometimes conduct an animal, with great ingenuity, to its death. (2) Survival is a by-product of brain activity. |
22-Aug-41 | 1009 | It is agreed, with 928, that a reversible system is of no interest from our point of view and does not exist in nature anyway. |
22-Aug-41 | 1010 | We show how to calculate the shift of a neutral point for a small change of parameter when the substitution is given as differential equations, (if finite substitution 927) (if several parameters, 1023) |
1016 | The general principle of "pressures", that difference means movement, suggests a method of combining sustitutions, or stimuli, to form a "product". If the number of parameters is greater than the number of variables, this product exists always, and powers are associative. The inverse in not unique. But the whole suggests a way in which groups might get in. | |
1018 | In general, after a break has occurred due to the x- point touching a break point, not only the field changes but also the break points. | |
28-Aug-41 | 1020 | All step-functions can be expressed as a linear function of one basic step-function, stp (x), "step-x", here defined. (Not true) |
1022 | The behaviour of break-surfaces. | |
28-Aug-41 | 1023 | Another example of the conclusion of 1006. |
28-Aug-41 | 1024 | Equations are given for determining the shift in a neutral point if several parameters are altered a little. The change in each coordinate is a linear function of the changes of parameters. |
29-Aug-41 | 1026 | A carefully calculated field is given, with four neutral points. Useful for experimenting. (Others are on 817, 828, 839, 885, 941, 990, 1021) |
1028 | An example is given, in all detail, of a substitution with two step-functions. It confirms the theorum of 1021. The existence of "false neutral points" is noted. | |
3-Sep-41 | 1038 | A much better statement is given of the idea of varying patterns of dominance etc in a system. |
3-Sep-41 | 1038 | "Break" does not involve "irreversibility". |
1041 | In the specification of a system with step-functions present, the latter cannot be specified by differential equation form. It seems that our equations for the system must be in form { dxi/dt = fi(x;y), y'i = ai+bistp{Vi(x;y)} } or { xi = Fi(x0;y;t), y'i = ai+bistp{Vi(x;y)} }. And as these define the future behaviour of the x's, and as in any case they can usually be solved only numerically, we might as well leave them in this state. (Compare 1048) (Better 1086) | |
1043 | Later we shall have to show how we can break down the minute rigidity of our dynamic systems, where the minutest change has to be put in and may lead to something profoundly different. Suggested way of doing it. | |
15-Sep-41 | 1044 | The V-surface of a step-function cannot have a free edge. |
15-Sep-41 | 1045 | Substitutions may, perhaps, define an infinite continuous group. |
1046 | "Simplicity", "wholeness", etc are perhaps clarified by the discussion above. | |
26-Sep-41 | 1047 | The idea that "orderliness" or "intelligence" spreads like crystallisation is probably covered more correctly by the more precise idea that it is "reaching neutral point and stopping still" which spreads along a chain of dominance. |
29-Sep-41 | 1051 | Differential equations with step-functions are fundamentally unsolvable. |
1053 | The concept of "breaks" by itself is not sufficient to cause any emergence of adaptation or intelligence. Brain, i.e. a machine of particular type, is necessary. (See 1063) | |
29-Sep-41 | 1055 | Examples are given in ordinary machinery of "change of organisation" and "break". Both are rare. |
2-Oct-41 | 1056 | Our definition of "dominance" of 960 is correct. See 1077 for a fuller survey. |
4-Oct-41 | 1057 | The idea of a system, like the brain, altering its own organisation necessarily implies the presence of step-functions and breaks. |
24-Oct-41 | 1059 | One stage in our long journey is finished and solved: the 'exact' case, i.e. an organisation where we are given full and exact information about every little detail. |
18-Nov-41 | 1061 | It is shown conclusively that "isomorphism" does not necessarily imply "group". |
19-Nov-41 | 1062 | Some examples are given showing how a statement may be quite true about the whole and yet quite untrue of all the parts. |
2-Dec-41 | 1064 | Although a general system has no tendency to survival by adaptive behaviour, yet a "brain" has. Details are given. (see 1068) |
1065 | A definition of 'organisation' is given which covers both dynamic, machine, organisations, and static, pattern ones. | |
1-Dec-41 | 1066 | An "organisation", by the definition of the previous page, need not be a group. |
1067 | Formulae are given in the special case where one variable always moves towards some function of the other variables. | |
8-Mar-42 | 1074 | Actual equations are constructed giving the theoretical views of the nervous system in mathematical form. (See 1092) |
8-Mar-42 | 1077 | A discussion is given of the meaning of the "change of organisation" (if any) which occurs when a system settles at a new neutral point without change of the field. i.e. a variable, without change of field, going outside the "range of stability" of one neutral point. A complete clarification is given, together with its relation to my previous ideas of "breaks". |
22-Mar-42 | 1083 | The question of "dominance" is still further clarified. I define "immediate", "distant" and "ultimate" dependance. Also "completed matrix of an organisation". "Dominance" (two equivalent definitions). "Parameter" is defined as "dominant and constant". It is proved that if a dominates b, and b dominates c, then a dominates c. |
1086 | A method is given for changing the abrupt h'=... method of defining a break to an equivalent dh/dt method. This puts the whole system into ordinary differential equation form. The equations are in "normal" form. | |
1090 | An example of a break is given in substitution form, like 991. | |
1092 | "Equilibrium" means not moving out of a given region. (But see 1143) | |
25-Apr-42 | 1095 | "Break-surfaces" are examined and some properties noted. |
1098 | A statement is given of the theorem that a multilayer of break surfaces "encourages" the representative point to stay in that region. | |
15-May-42 | 1099 | It might be suggested that with a million neurons the chance of getting them all properly adjusted is negligibly small. The answer is that there is usually no such thing as the right solution. We count as suitable any organisation whatsoever so long as it gets the equilibrium where we want it. |
18-May-42 | 1100 | After studying the fixed points in a dynamic world (i.e. neutral points) I presume the next step would be to take a lot of neutral points and set them moving. |
4-Jun-42 | 1102 | A layer of break surfaces keeps within bounds not only the variables concerned, but any other variable which is a direct function of them. |
7-Jun-42 | 1106 | A variable may add further break-surfaces for its further protection by deputising, i.e. by controlling another variable so that the latter breaks if the first goes too far. And this leads to the important observation that it does not matter where or why a break occurs as long as it occurs. From my point of view, all that is wanted is some change of organisation and it doesn't matter how or why it is done. Any change is as good as any other change. |
1109 | We discover how to join and unjoin two machines. Also we notice that if a machine is at a neutral point it is possible, under restricted conditions, to separate and rejoin without disturbing the state of equilibrium. | |
8-Jun-42 | 1111 | A red letter day. A problem in the application to the brain is solved. |
1114 | If a machine with variables x has break-variables h with V-surfaces which surround an x region, and if we join this to any machine y, then the presence of the h's and the V's will tend to keep the x's within the V-region. And when the machine has settled to equilibrium, disconnecting the machine y and putting on another one, z (or changing parameters R) merely starts the x-machine changing its organisation again until it has found a new equilibrium, with the x's still inside the V-region. O.K., O.K! | |
1118 | A list of examples of equilibrium in biology. | |
9-Jul-42 | 1122 | If two environments keep occurring, a system will break till it finds an organisation making it stable to both. |
9-Jul-42 | 1123 | "Reaction" is divided into "response" and "variation". |
9-Jul-42 | 1123 | The intrinsic form of a substitution might prove interesting. |
16-Jul-42 | 1127 | It is concluded that if a whole is to be (almost) separated into two parts, the variables concerned at the "join" must be (almost) constant. Delay is not an important factor. |
16-Jul-42 | 1127 | After all these years I conclude that "vectors" are not what I want. |
1132 | Some musings on bicycle riding. | |
6-Sep-42 | 1134 | Preliminary discussion of a machine falling, temporarily, into parts. |
2-Oct-42 | 1135 | We want to get adaptation on a scale, so that we can show that systems, under certain conditions, will move from lesser to greater adaptation. |
14-Oct-42 | 1136 | A statement of my present emotional position. |
1140 | If an organisation stops at a field which is only partly stable this does not really matter; for if the danger of breaking is large, it will soon break and try new fields, while if the danger is small then there is little to worry about. | |
31-Oct-42 | 1141 | n breaks provide 2n organisations. To give 10 different organisations every second throughout a man's life we need only 35 breaks! |
1142 | Does the acquisition of a new reaction upset all the older one's as demanded by my theory? The answer seems to be "yes" but it may in some cases be of zero extent. | |
31-Oct-42 | 1143 | Each single environment is a (hyper) complex number. |
1148 | The definition of "equilibrium" is taken up from 1092, and made much more precise. It is concluded that it belongs to a path A special type of common occurrence is defined and given the name of "normal" equilibrium. | |
1153 | (1) Changing coordinates in two machines is apt to make one of them. (2) Changing to normal coordinates splits a machine into independent parts. (Cf. 3868) | |
19-Nov-42 | 1155 | A review of Jennings' book. |
20-Nov-42 | 1156 | The "constants" i.e. variables whose changes make observed behaviour may themselves be activities composed of other variables. And these "constants" whose changes make.... This needs specifying from the organisational point of view. (See 1193) |
22-Nov-42 | 1157 | A refinement of the definition of "organisation". |
22-Nov-42 | 1157 | "Memory" equals change of organisation. |
22-Nov-42 | 1158 | "Adapted" behaviour equals the behaviour of any system around a point of normal equilibrium. (1148) |
24-Nov-42 | 1159 | All my theory explains the "trial and error" method in terms of non-living matter. All that, but nothing more. |
1160 | Courant's definition of equilibrium. On closer reading, as R and ρ may be small to any degree, it appears that Courant's definition does not allow finite cycles like that of 1144. | |
1174 | The sheets give the mathematical theory up to about Oct '42; but, of cource, not at all completely. | |
28-Nov-42 | 1176 | A clarification of the concept of a "break-surface". |
28-Nov-42 | 1176 | The conditioned reflex is not clear yet. |
28-Nov-42 | 1177 | A field can be explored easily, but break-surfaces are destroyed by their discovery. This may involve curious philosophical properties. |
1180 | Dynamic systems are, in general, fundamentally irreversible. | |
1-Feb-43 | 1181 | The concept of "break" does not need that of "irreversibility". |
8-Feb-43 | 1182 | Theory has been submitted for publication for the third time. |
1187 | The concept of "a reflex" is translated into my organisational terminology. | |
20-Feb-43 | 1189 | A dominating system can control the position of break-surfaces of a second system. |
1198 | It has been shown that a representative point, staying within a region bounded by a layer of break-surfaces, can act as a "variable" in a substitution composed of n such points provided the representative points move with a velocity of a higher "order" than that of the substitution. "Order" is defined and explained. The ordinary substitution can be considered as the limit of this type. | |
1200 | A discussion of a simple reflex along my lines. | |
25-Feb-43 | 1201 | "Adaptation" is more properly divided into: the adapted state after this has been reached, and the process of finding this state. |
8-Apr-43 | 1209 | We study how adaptation can increase qualitatively, and are led to define and examine "part-function" and "part-surface". (Continued 1219) |
1217 | The number of possible ways of organising n variables is at last answered. It is of the order of |n | |
1218 | An interesting elementary substitution is described. It demonstrates paths going to infinity and neutral cycles. (Better 3776) | |
15-Apr-43 | 1219 | A property of step-functions. |
18-Apr-43 | 1226 | A method is described by which a machine can show increasing adaptation, by one part after another getting into equilibrium. A clear explanation of "threshold" and "summation" in the Central Nervous System follows. It is concluded that between a sense organ and the adaptive part a "distributor" must occur. 5345 |
1233 | An attempt is made to classify and exhaust the causes of non-adaptation; but it seems that non- adaptation must be taken as fundamental, adaptation occuring only if there is some special reason for it. | |
1244 | Arrangement and collected materials for my book. | |
1247 | Discusses the application of the concept of the "invariant" of a substitution. | |
1254 | Notes on adaptation to "internal" environment; and an example of how a set of adaptations can collapse. | |
1257 | Huxley's book reviewed, and proof that a holistic set must be altered by infinitesimal steps. | |
4-Jun-43 | 1259 | We have a right to expect that normal equilibrium will be commoner than other sorts |
9-Jun-43 | 1265 | Part-functions and step-functions should be defined as special types of path in a field. |
1267 | Whittaker defines "equilibrium" and also a "neutral cycle". | |
16-Jun-43 | 1282 | We have got a grip of "part-function", finding that it depends simply on zero values of dxi/dt. |
30-Jun-43 | 1283 | Some points from a book. |
1292 | A description is given of relations between differential equations and solutions when certain variables are not present in some of the equations. Two matrices |f| and |F| are defined. Particularly it is shown that the "independence" test of p applies to either. | |
1295 | A view of Levy's book. He specifically notices that breaks are an essential feature of matter and not a trivial one. | |
20-Jul-43 | 1297 | The concept of "dominance" involves an inverted way of looking at things, and is better replaced by the same variables being "independent of the others" in a system. |
21-Jul-43 | 1298 | We may not write arbitrary functions in the solutions xi=Fi(xo;t), for the f's are to be free from t. This means that there are restrictions on the F's, and it is shown that suitable F's will satisfy certain equations. (Cf. 1315)(and 1341) |
1299 | Definition of the First and Second Jacobian matrices of a dynamic system, with a note that "completion" applies to the Second and not the First. | |
23-Jul-43 | 1304 | A review of Carrel's "Man, the unknown". |
24-Jul-43 | 1306 | The concept of "parameter" should be replaced, (except in simple cases), by the idea of a variable having some special properties, These are given. The fundamental is [x-k=0]. (But see 1324) |
1316 | Exploring the interaction of a given set of variables means finding the F's in xi=Fi(xo;t). (Assembling a machine gives us the [xoi=fi(x)] equations). By the independence test on the Second Jacobian Matrix applied in one stroke we eliminate what is not wanted. That its behaviour is reproducible is equivalent to the requirement that t is explicitly absent from the f's. This restricts possible F's. An equation is given which they must satisfy. It is proved that under these conditions the F's are always completed. | |
27-Jul-43 | 1318 | "Step-function" in practice is not usually so restricted as on 1279. |
1320 | At last an exact meaning can be given to the idea of whether one variable does, or does not, affect another. It can only be tested when the complete system containing the affected one is obtained. A set, independant of the others, contained in a complete set, must itself be complete. | |
1321 | Nil. | |
1323 | A definition of a complete system, and some elementary properties. | |
1-Aug-43 | 1324 | Parameters which are regarded as constant "variables" thereby lose some freedom, perhaps too much sometimes. |
1326 | A single permanent zero in [f] introduces a slight, permanent restriction in the field. | |
1-Aug-43 | 1327 | The non-zero elements in [f] correspond, in a sense, to dendrons. |
1334 | The chance that n variables should all independently be in equilibrium is discussed and this gives an estimate of the time required to reach equilibrium. The fastest method of getting equilibrium will be the one found in practice, for the system selects the fastest. And this suggests that the brain will automatically manifest an "analysing" tendency. | |
1340 | The environment (probably) consists of many small complete systems contained in larger complete systems, etc slow time changes upsetting all. Two more ways of graduating adaptation are noted. The dynamic form of "whole" and "part" is clarified. | |
1344 | The solutions of a complete system form a finite continuous group of order one. | |
1346 | Notes from Bieberbach on finite continuous groups. | |
1350 | Variables changing at different orders of velocity hardly interact. A study of interaction must therefore assume the variables are of the same order of velocity (Now turn to 1474!) | |
7-Aug-43 | 1353 | The relations of "complete sets which contain complete sets which ..." can be shown accurately by an isomorphic diagram. |
1357 | Assuming each variable has a fixed chance of getting equilibrium, it is shown that a system of n1, variables dominating n2 will in 1-pn2 cases get equilibrium by getting it in the n1 and then in the n2, while in pn2 cases it will get the whole simultaneously, the latter proportion being vanishingly small. Experiment will therefore demonstrate the equilibrium appearing in stages. | |
9-Aug-43 | 1359 | An unsolved problem in organisation. (Now see 1420) |
11-Aug-43 | 1367 | If a complete system has n variables and r parameters [x-i=fi(x;λ)], then the λ's can, from given starting point, control the movement of the x-point within an r-dimensional space which moves with time through the n-space, but the λ's cannot control the movement of the r-space. (Now see 1376) |
11-Aug-43 | 1370 | A Permanent zero in the 1st. Jacobian Matrix, i.e. incomplete joining, means that a sudden change of the variables does not immediately alter the path as projected on to the other variable's axis. (Continued 1372) |
1371 | The 1st Jacobian Matrix (1) cannot be filled in arbitrarily (2) does not accurately specify a dynamic system. | |
1373 | If each break (a) depends only on one variable, (b) affects, or appears in only that variables' f, then each variable will become stabilised almost independently of the others. Under these conditions the time taken by n is of the order of log n. | |
13-Aug-43 | 1376 | As first approximation, the "largest of a sample of n" tends to increase as log n. |
1377 | If r parameters controlling a complete system are arbitrarily under our control, then we can, by controlling the parameters, force an arbitrarily selected set of r variables to behave as we chose. The detailed control can, so to speak, be transmitted through the many other variables without any loss of control! | |
16-Aug-43 | 1378 | Note from Eddington. |
1389 | The problem of several complete systems joining into an interacting system without losing (entirely) their completeness is discussed and partially solved. | |
19-Aug-43 | 1392 | The solutions are given of the problems of: Given the f's (or the F's), to find the F's (or the f's). |
20-Aug-43 | 1396 | A proof, with modern technique, of the old problem, showing that two stable machines can be joined to form an unstable one. |
21-Aug-43 | 1400 | A test to see whether a neutral point is stable or unstable. (Test for neutral cycle, 1494) |
1407 | The old case of several variables affecting one another chain-fashion is re-examined. It is shown that if an "increase" leads back to a "decrease" the system will be stable, though probably with oscillations (of decreasing amplitude). If it leads to an "increase" the system may still be stable. | |
23-Aug-43 | 1409 | Contrary to p.____ [0599], the concept of equilibrium does not depend on a circuit. |
23-Aug-43 | 1410 | Definition of an "almost" complete system. |
1414 | If the study of a complete system of n variables is restricted to some of the variables only, the others being hidden, the behaviour of the visible variables can be predicted correctly when we know any n coordinate-time combinations. A machine may appear to show imagination. (Restated 1424) | |
1416 | The (real) environment may be absolutely anything. But we can devise theoretical systems to which a given brain could and would adapt, and we then examine the real world to see if such sorts exist. | |
31-Aug-43 | 1420 | The idea of a "constraint" added to a dynamic system may have meaning with Newtonian dynamics but it has no general meaning. And the idea of thereby losing a "degree of freedom" is also of restricted applicability. |
4-Sep-43 | 1424 | It is shown that the "hour-glass" type of organisation will differ little from others in its properties of adaptation. |
1425 | If, in a system of n variables complete or not, we are given n coordinate-time pairs, the particular path is fixed. | |
1427 | Notes from Eisenhart. (Ref. 476) | |
11-Sep-43 | 1431 | Six definitions of a "complete" system are given and are all proved equivalent. |
14-Sep-43 | 1433 | Some references to amoeboid activity in nerve cells. |
1435 | The brain is an equilibrium-trap. And if the equilibrium can only occur on certain conditions then the brain will trap those conditions too! 1487. | |
29-Sep-43 | 1439 | Stabilising some variables almost certainly stabilises those other variables connected with them. |
30-Sep-43 | 1441 | More notes on the "hour-glass" case. |
1-Oct-43 | 1442 | A definition of transient and permanent equilibria. |
1443 | The projections of a path, and the solutions xi=Fi(xo,t) are two forms of the same thing. | |
4-Oct-43 | 1447 | Outline for a book. 1) Introduction 2) Theory of dynamic systems 3) Equilibrium 4) Change of organisation 5) Breaks (up to the theorem on layers) 6) Further developments. |
5-Oct-43 | 1462 | Complete systems containing complete systems etc, is the same as a chain of dominances. |
1464 | Of the methods available for solving my differential equations, some apply generally, and some only to complete systems. | |
6-Oct-43 | 1466 | It is believed that the theorems relating zeros in [f] and [F] to each other is still valid if the system is not complete. |
6-Oct-43 | 1467 | It is proved that, if they are complete systems, then if A dominates B and B C, then A dominates C. |
1468 | It seems best to define whether one variable "affects" another as whether Fi contains (or not) xoi | |
8-Oct-43 | 1470 | A simple practical example of the "hour-glass" type of organisation. |
1473 | An actual numerical example showing that a path can be fixed by using later values of a few observable variables. | |
1475 | Orders of velocity make complete systems. | |
15-Oct-43 | 1476 | The shift is calculated, of a neutral point as a result of small changes in parameters. |
15-Oct-43 | 1477 | How to use my theoretical discovery for practical purposes. "Organisers, Ltd". "You want the best organisation, we have them." |
15-Oct-43 | 1480 | The idea of "adaptation" is one which we bring to the data: it does not exist in the facts themselves. Any attempt to treat it as a reality leads to self-contradiction. It is analogous to "magnifying". 4930 |
19-Oct-43 | 1494 | A superb theorem, much more general than that of 1113, and much more precise. It includes the other theorem as a sub-case. |
20-Oct-43 | 1497 | A test, and example, for stability or instability of a neutral cycle. |
21-Oct-43 | 1498 | Reasons for changing the form of the index. |
23-Oct-43 | 1503 | In a complete system variables may be changed for derivatives and the system is still complete. In this way reference to particular variables may be avoided without spoiling the completeness. |
23-Oct-43 | 1503 | "Step-function" is an official word in general use. |
1506 | The theorem of 1493 is unaltered by any change of variables. The essential equilibrium facts of a field are unaltered by change of variables. (Further tested 1512) | |
1511 | The equations of a dynamic system with layers of break surfaces given in completely continuous form, suitable for general analytic studies. | |
26-Oct-43 | 1512 | 1506 is confirmed, that a change of variables does not generally affect the applicability of the theorem of 1493. |
27-Oct-43 | 1515 | Variables cannot be exchanged for derivatives when the conditions of 1493 are to hold. |
28-Oct-43 | 1516 | The substitution of derivatives for variables is apt to lead to troubles due to multiple values, and must be used with caution. |
1519 | In the hour-glass type of organisation substitute variables will be set up, as required by the theorem of 1493. They are found to be just a different way of looking at the variables! | |
1522 | The theorem of 1493 is easily extendible to the case where there are a number of parameters altering arbitrarily from time to time. In this case we get a set of organisations as limit. | |
6-Nov-43 | 1524 | James stating that a machine cannot vary its behaviour. |
8-Nov-43 | 1525 | Levy supports my view that knowledge of a real dynamic system is purely empirical. |
8-Nov-43 | 1525 | Notes from Bradley's book. |
9-Nov-43 | 1526 | The problem of the "distributor" solved, in essence. |
1529 | A few notes on the important question of exposition. | |
3-Dec-43 | 1531 | The presence of "velocity" or "inertia" effects in an artificial nervous system merely means that the "environment" is rather more complicated than it would appear to be. |
1532 | Some details about getting a system of my type started. | |
11-Dec-43 | 1535 | Fisher's book. |
22-Dec-43 | 1538 | A first attempt at a theory of selective operators. |
1-Jan-44 | 1540 | An "instant" system is defined. A non-instant system must be part of an instant and complete system, and can be made instant by adding differences, or derivatives as extra variables. (Better proof, 2031) |
1541 | Two notes on exposition. | |
11-Jan-44 | 1548 | The elementary ideas on systems and their behaviour is thoroughly tidied up and clarified. |
1553 | The properties of non-complete systems are described. | |
1554 | An attempt to find the effect on the field of permanent zeros in the first Jacobian matrix. | |
11-Jan-44 | 1555 | Two problems for the future are noted. |
12-Jan-44 | 1561 | A very precise statement of my basic theorems. (but see 1564) |
1562 | A proof that finite continuous groups have differential equations not containing t explicitly. | |
22-Jan-44 | 1564 | The word "absolute" seems better than the "complete" already used. |
1570 | A very economical proof of the main elementary theorems by defining and using "commutive" systems. "Restricted" equilibrium is defined. | |
1571 | A useful approximation for finding p and P. | |
1572 | The smallest value of p ever likely to be used is estimated. Also a common value. | |
2-Feb-44 | 1573 | Theorem B is rejected. |
2-Feb-44 | 1573 | A field. |
2-Feb-44 | 1574 | The study of the graduation of adaptation seems to be essentially empirical and unsystematic. |
1576 | It is shown that a "spontaneous change of organisation" implies the presence of a step-function of the time. (The change defines the step-function). | |
18-Feb-44 | 1578 | Absoluteness is not altered by separating or joining machines. |
1581 | In an absolute system, knowing the behaviour of the parts (and the method of assembly) specifies the behaviour of the whole; and vice versa. | |
19-Feb-44 | 1582 | Observation provides xi=Fi(xo;t), the derivative form is - er - derived; method given. |
27-Feb-44 | 1585 | An attempt at the analytical expression of a part-function. |
27-Feb-44 | 1586 | The least possible join of two absolute systems is that they should share a common step-function. |
27-Feb-44 | 1587 | Convenient equations in the technique of joining and separating parts and wholes. |
27-Feb-44 | 1588 | A symbolic way of writing step-functions. |
27-Feb-44 | 1588 | The whole question of the graduation of adaptaation (or equilibrium) must be realised to be really an attempt to increase the probability of the whole being adapted. It is only part of the general problem of altering the probabilities. |
28-Feb-44 | 1589 | An actual example of "distribution". |
29-Feb-44 | 1591 | The mere presence of part-functions in a system allows variables to be active in some reactions and inert in others. |
1592 | In a commutive system with many part functions, distribution will occur, because it is more probable. | |
5-Mar-44 | 1593 | "Equilibrium" is an invariant. It belongs only to an absolute system. |
8-Mar-44 | 1594 | If reactions are to adapt independently, the breaks must be restricted to the regions of part-functions. |
18-Mar-44 | 1596 | A better proof that chance of equilibrium, other things being equal, falls off as e-kn. This means nothing, for p means nothing definite. |
1598 | Definitions are given of "part-functions", "activated" and "activation-region". It is shown that activations are localised, that different paths may cause different variables to become activated, and that a part-function can cause a break only when activated. | |
8-Apr-44 | 1602 | Two or more [variables] which are always stable apart may be unstable when joined. (Inverse, 1658) (Note 1665) |
1613 | The principle of Le Chatelier is examined in detail and given exact mathematical form. It appears that it is an emperical peculiarity of the equi;ibria of physical chemistry and is in no way general to all equilibria. | |
1617 | It is sometimes possible to fix the value of some variables in a machine. Details are given of the process of adding another machine to act as "stabiliser" to a variable. | |
1620 | In a commutive system, if we keep returning xρ to a we shall eventually get, and keep, a field which stabilises xρ at, or near, a. | |
19-Apr-44 | 1622 | The conditioned reflex is an elementary property of a commutive system when a variable is repeatedly forced to take a given value. (Much improved 1981) |
19-Apr-44 | 1625 | The probability that a system should have an equilibrium cannot be deduced from the probabilities of the parts being in equilibrium. The case where they combine as a product is likely to be common and important but it must be introduced as a specific postulate. |
19-Apr-44 | 1626 | The layering of the cerebral cortex may be explained as required for wide distribution. |
24-Apr-44 | 1627 | A note on exposition. |
28-Apr-44 | 1628 | "Disturbance" and "ingressive" are defined. |
30-Apr-44 | 1629 | Collected notes and references on "invariance". |
1635 | A proof is given that: If a random displacement y1 , y2 , ... , yn with probability distribution df=Φ(y1 , ... , yn) dy1 ... dyn is added to a point at X1, ..., Xn then the probability that it (i.e. X1+y1 , ... , Xn+yn) should still be within a space V is maximal if, and only if, X1 ... Xn satisfy the equation (8). (See next note). | |
2-May-44 | 1637 | If a field (provided by a commutive system with break-surfaces) has maximal probability of not breaking after random disturbance, then it is of normal equilibrium and the paths must meet at the point X1 ... Xn (defined in the previous note). |
5-May-44 | 1638 | Equilibrial features are not the only ones in a field which persist after change of coordinates. Thus, the meeting of two paths is also invariant. |
5-May-44 | 1639 | Disturbances must usually be applied to a system at a slower order of time than its reactions. |
10-May-44 | 1646 | |
1657 | K1 and K2 are defined, also "terminal", "simple" and "displacement". If the fields provided by random h values have K1 and K2 values distributed as Φ(K1 , K2), then the terminal fields have values distributed as A.K1Φ(K1 , K2). If the terminal fields are displaced from time to time the terminal fields develope distribution B.(K1/(1-K2)).Φ(K1 , K2). (Graph 1698) (Corollary 1705) | |
19-May-44 | 1659 | Any number of unstable systems joined must be unstable. |
31-May-44 | 1664 | A dynamic organisation has, as a whole, the extra properties (over those possessed by the parts): that the Neutral Points can be restricted to sets; that a field may be stable though some of the units unstable; that the field has a neutral cycle. (There may be more). |
31-May-44 | 1665 | Two machines may form a whole which is stable if they were joined one way, and unstable if joined the other. |
1666 | Two stable machines may be unstable when joined if either contains more than one variable. | |
9-Jun-44 | 1668 | A review of Craik's book. And a statement of the present position, re publishing, of my theory. |
1671 | An attempt to handle the similarity of machine to machine. "Equiformal" defined. | |
10-Jun-44 | 1673 | A proof is given that the commutive process must increase the mean of K1. |
15-Jun-44 | 1675 | If K1 and K2 are uncorrelated, then disturbances give fields with K2 always increased. |
15-Jun-44 | 1679 | Proof that a non-activated variable, in contact only with other non-activated variables, cannot become activated. |
1684 | A "distributive" system is defined. Three theorems are given, including one showing rigorously how adaptation can proceed by parts in such a system. | |
1689 | I am unable at present to get a satisfactorily rigorous test for independence when there are part-functions present. [But see 1748] | |
22-Jun-44 | 1692 | A test of independence both necessary and sufficient, is deduced from xi=etXxoi. Although the rigour of application to arbitary functions is doubtful, it leads to the same results as the previous test. |
1695 | A proof that non-activated variables cannot transmit effects. (Much better proof 1921) | |
24-Jun-44 | 1698 | Much human behaviour is reaction to an internal environment: anxiety. (Cf. 1877) |
25-Jun-44 | 1700 | A graph of the multiplying factor K1/(1-K2). (Another aspect, 1705) |
1704 | With linear equations, control of the coefficient of one variable is enough to enable us to put the roots and the neutral point where we like. | |
1707 | The distribution of K2 after disturbance is given in terms of the original distribution and the means of K1 at each K2-value. | |
19-Jul-44 | 1708 | An example of two reactions, each quite adaptive, which are in unstable equilibrium if joined. |
21-Jul-44 | 1710 | Some details contributed by Carroll. |
22-Jul-44 | 1715 | For K2 among the terminal fields to be 1, i.e. for the fields to be immune to disturbance, it is necessary and sufficient either that K2=1 in the original fields or, if K2≠1, that Φ(K1 K2), for some value of K1 other than K1=0 should have, at K2=1, a pole of order ≥1. The most interesting corollary is that if any fields in Φ have K2=1, then these monopolise the terminal fields. |
1717 | It must be carefully remembered that the physicist always tries to use knowledge from every source about a given dynamic system while I am rigorously confined to studying systems by observing only their behaviour. | |
30-Jul-44 | 1720 | The possibility of giving some of the variables a fixed value and letting others vary is functionally identical with taking the machine to pieces. |
1721 | Some other people's quotations on equilibrium. | |
1723 | Extracts from a book. | |
2-Aug-44 | 1725 | In an absolute system (variables x1 ... xK ... xn) of fixed organisation [x~i = fi(x)], that a subsystem (variables x1 ... xK) should itself be absolute (the other variables xK+1 ... xn being given all random starting points in the testing) it is necessary and sufficient that f1 ... fK should not change for any or all changes of xK+1 ... xn. |
3-Aug-44 | 1729 | A proof that step-functions are necessary, as well as sufficient, to get changes of organisation of a subsystem in an absolute system. |
11-Aug-44 | 1731 | Pavlov says that adaptation and survival equals equilibrium. |
14-Aug-44 | 1734 | James describes the facts of adaptation = equilibrium without calling it such. |
19-Aug-44 | 1736 | Quotations demonstrating field experiments clearly as examples of my type of system. |
1739 | Known examples in physics of my type of absolute system, one of which shows dominance. | |
5-Sep-44 | 1740 | Two notes from a book. |
19-Sep-44 | 1744 | A note on exposition. |
20-Sep-44 | 1745 | Another example of selection leading automatically to adaptation. |
1746 | An outline of quantum theory. | |
28-Oct-44 | 1801 | Two points on applications to society. |
1-Nov-44 | 1803 | Note on exposition. |
2-Nov-44 | 1804 | The ordinary pendulum is not stable if we are referring to both position and velocity |
3-Nov-44 | 1805 | Useful quotations. |
1806 | There is no limit to the number of variables which have to be fixed to get an isolated or absolute system. | |
5-Nov-44 | 1810 | Notes on effect of fixing an economic variable. This may make a stable system unstable. Spur of joined machines. (see 1910) and (1995 bottom) |
11-Nov-44 | 1811 | A detailed non-linear use. |
18-Nov-44 | 1813 | Effect on a field of fixing a variable. |
1822 | (Under conditions) two linear systems are equiformal if and only if they have the same characteristic equation. | |
1826 | Examples of a system tending to restore previous constants. | |
9-Dec-44 | 1827 | Another actual absolute system. |
9-Dec-44 | 1829 | Equation of the plane which contains n consecutive points. |
18-Dec-44 | 1836 | Review of Spencer, with useful quotations. |
1839 | Independence over two regions. | |
22-Dec-44 | 1840 | Several parts, all unstable, can form a stable whole. (Simple example 2044) |
7-Jan-45 | 1844 | Routh's test for stability. (Ready for use, 1862) |
12-Jan-45 | 1846 | The probability of stability is in general unsolvable, but certain special cases might be attacked again later. (Continued 1868) |
19-Jan-45 | 1848 | Some facts which any organisation must stabilise. |
1849 | Stability, and not mere fixity, is needed in society, even if only to deal with small errors. | |
1851 | Unstable equilibrium in a society. | |
22-Jan-45 | 1853 | Some suggestions for a word to mean "survival-value". Note on selective operators. |
1856 | A machine that learns. | |
22-Jan-45 | 1857 | Part-function is now redefined. |
2-Feb-45 | 1860 | If there are many commutive systems sometimes affecting one another, and a parameter taking several values affects one of them, the fields in that one resulting have maximal survival-probability when all the neutral points are in the same place. (See next note) (see 1942) |
5-Feb-45 | 1862 | It is to be remembered that Fisher's book was highly successful though no formal proofs are given anywhere. |
7-Feb-45 | 1864 | Routh's test for stability given in immediately usable form. |
9-Feb-45 | 1867 | The relations of independences and activations of part-functions. |
1870 | There is good reason to assume that the chance of stable equilibrium will often fall off as (1/2)n. | |
12-Feb-45 | 1875 | For a system to get adapted by parts, it is proved necessary that most of the features of a distributive must be present; i.e. there is no other way. (Improved, 1985) |
18-Feb-45 | 1877 | Sex activity by my theory must result in a lowering of impulse-density. |
18-Feb-45 | 1879 | Two adaptations may be better than two independent adaptations. |
19-Feb-45 | 1880 | In future, I hope to effect an improvement in literary style. |
1888 | Mendelian theory vs. Distributive theory. | |
1892 | Mendelian and neuronic adaptations compared and contrasted. | |
20-Feb-45 | 1893 | "Dominant and recessive" applied to a distributive system. |
28-Feb-45 | 1895 | A dynamic system must definitely either proceed to equilibrium or to infinity. |
10-Mar-45 | 1900 | It seems that, if A dominates B, no examination of B's behaviour can reveal the organisation of A. To "examine" B means that the observer forms an hour-glass system with it. |
1905 | In forming a big organisation the process must be (1) to list the main* variables, (2) to attempt stability by the same number of completely independent commutive systems, (3) with variables which refuse to get stable, add small joins, letting them be few in number and simple in type (i.e. step-functions). [* Now called 'essential', not 'main'.] | |
27-Mar-45 | 1909 | Usable extracts from Sherrington's "Life's unfolding". |
3-Apr-45 | 1916 | Extract of Schrödinger. |
1919 | For the world to be suitable to be adapted to, it must contain a large proportion of part-functions. | |
21-Apr-45 | 1922 | Inactive variables cannot transmit effects, either from other variables or from bounds. (Converse 1977) |
1924 | Masserman on what happens when an animal meets a deliberately chaotic environment. | |
6-May-45 | 1926 | "Break" is better "saltus". |
6-May-45 | 1928 | Quotation from Wells. Note on the basic meaning of "organisation". |
9-May-45 | 1934 | Simple, worked-out examples for exposition. |
11-May-45 | 1936 | Distributive system vs. Genetic analogue. |
11-May-45 | 1941 | A further list of correspondences between genetic and neuronic adaptation. |
12-May-45 | 1943 | In a distributive system, if from time to time certain variables are constrained to certain values, the variables will tend to become in equilibrium at those values. (Better 2015) Also 1981, 2011, 2012 |
28-May-45 | 1946 | So far I have discovered five basic operators and their variants. |
17-Jun-45 | 1947 | The peculiarities of a system (may) impose "drifts" on the field, to which any path must conform. |
1953 | Exposition. | |
1959 | Points on exposition. | |
1966 | My misunderstandings, taken from my own notes, which must be well explained lest they become the reader's, too. | |
3-Jul-45 | 1967 | Some points after reading all my back notes. |
4-Jul-45 | 1968 | A very practical note on nomenclature in exposition. (Continued next note) |
1972 | New nomenclature and slogans. | |
1975 | Better to think of constancy than activation; and of separation rather than distribution. The idea of a "movement dying out" is shown due to the fact that a common region of constancy is a resting region. | |
1978 | A theorem that if a variable, properly joined to others, does not transmit an effect it must be constant (or possibly, changing uniformly). (Converse of 1921) | |
26-Jul-45 | 1980 | Handling part-functions. |
26-Jul-45 | 1983 | Explanation of the simple conditioned reflex. "Traffic" Principle. (2240, 4596) |
26-Jul-45 | 1984 | "Signals" and Jennings' "Law of the resolution of physiological states" are now explained. |
28-Jul-45 | 1986 | An improvement on the theorem about what is necessary in a multistable system. |
30-Jul-45 | 1988 | For independence test, we must find ∑ρ=1..n-1[f]ρ. The old method of Limρ→∞[f]ρ is rejected. See 2054 |
1-Aug-45 | 1991 | It is decided that a 1st Jacobian matrix (J.M.) cannot be accepted as physically real unless, for each i, not all aii , aiσ aσi , ... are zero. This is necessary and sufficient that the 2nd J.M. has all main-diagonal elements non-zero and this is the simplest test for it. It follows that a more correct form of the relation is ∑1..n[f]ρ=[F], the sum including the n-th power. This last power adds any missing diagonal terms. See 2056 |
5-Aug-45 | 1994 | A clarification of interaction where one reaction uses another. "Dominance" is really a negative concept. Ultrastability is not enough, we must have multistability. A "helping" B, and B "using" A are really the same thing. |
5-Aug-45 | 1995 | More extended tests of the chance of stability. |
1996 | Empirical study of the effect of fixing variables in stable systems. | |
2000 | Multistable system defined in new form. Theorem in modern form proves possibility of adaptation by parts. | |
2002 | A very crude estimate of the chance, in a multistable system, of getting an adaptation without upsetting previously established adaptations. It suggests the great importance of low activations and the gross disturbance which might follow even a small increase in it. 5416 | |
2004 | Standard symbols: General mathematical, complete systems, and for general repeated use. | |
13-Sep-45 | 2007 | Modern proof of the basic theorem of the multistable system. |
13-Sep-45 | 2011 | Elementary rigorous properties of the multistable system, and of part-functions. |
13-Sep-45 | 2011 | When bounds in a multistable system are altering, a line's chance of destruction is proportional to the number of variables it activates, and therefore also to its length. (See next note) |
17-Sep-45 | 2014 | In a multistable system, with bounds changing at random, shorter lines have greater survival. Under parameter change, resting states have maximal endurance if they coalesce. Hence Habituation. (See below) |
2016 | A more rigorous statement and proof of the theorem that repeated constraints on a multistable system lead to the system becoming stable at that state. | |
7-Oct-45 | 2019 | On play. Also on reactions which look complete and turn out to be simple. |
23-Feb-46 | 2024 | Some calculated lines of behaviour of a pendulum from different starting configurations and with various parameter values. |
2027 | As working hypothesis it is assumed that "coordination" always means "arranging things so that we get (1) stability (2) where we want it. | |
24-May-46 | 2031 | Non-instant systems, those with delay, may easily be converted to complete and instant by including derivatives. |
5-Jun-46 | 2034 | Details about values, for reference. |
5-Jun-46 | 2035 | If A dominates B, and B dominates C, in one complete system, then A must dominate C. |
7-Jun-46 | 2036 | The case of the top shoot of a tree dominating the growth of lateral shoots fits into my formulation of "dominance" quite naturally. |
22-Jun-46 | 2040 | Clarification of the position when dependence itself depends on other variables. |
2043 | An over-all theorem on the stabilities of joined systems. | |
6-Jun-46 | 2051 | Extracts from Masserman. |
15-Jun-46 | 2053 | A simple example of the substitution equation of a complete system, suitable as an elementary exercise. |
4-Aug-46 | 2056 | An improved statement of the main theorems on independence. |
2059 | Answer to "how general is the field of linear equations [x'=Ax] ?" | |
3-Sep-46 | 2062 | By dealing with averages of many ultrastable systems we arrive at a new order or level of phenomena. |
14-Oct-46 | 2065 | An important, though imprecise observation on requirements for a solution of the conditioned reflex problem. |
2066 | Detailed example showing the roots moving with change of one coefficient in [x'=Ax] | |
2070 | Notes on one parameter groups. | |
19-Nov-46 | 2072 | Effect on latent roots of adding constant to main diagonal, how to move all latent roots to right or left, and a new test for stability. |
25-Nov-46 | 2080 | Principles and details for a machine to be absolute, show ultrastability, etc. (see 2095, 2161, 2182 etc) |
2081 | Experiment. | |
2083 | Simple units with output a linear function of the inputs are sufficiently general provided we can control also their general speed of working. | |
2085 | I suspect that any change in timing of a reaction really means learning a new reaction, i.e. new arcs developed. | |
21-Dec-46 | 2090 | Electro-mechanical equiformality. |
2091 | The important thing is to push to the limit and then make this a new starting point. | |
2093 | Latent roots of [2x2 matrix: 0 I a 0]. | |
31-Dec-46 | 2100 | A theoretical study of a Unit devised, and part built, by myself. (Further, 2161, 2182) |
31-Dec-46 | 2102 | Details for setting the machine of 2094 to correspond to assigned set of coefficients in [x'=Ax]. |
1-Jan-47 | 2103 | Importance of echo impulses. |
2104 | To demonstrate importance of echo impulses | |
9-Jan-47 | 2107 | Practical notes for use when converting known systems to differential equations in absolute form. |
14-Jan-47 | 2113 | Notes the effect of altering the general speed of reaction of one variable. |
15-Jan-47 | 2114 | Example of stability in the non-linear case. |
15-Jan-47 | 2117 | Equations of a simple dynamic system. |
22-Jan-47 | 2122 | The dynamic system which controls the pH of the blood exhibited in my form, as illustration. |
2124 | A method of getting an approximate solution to non-linear differential equations. | |
26-Jan-47 | 2126 | A physical example of the principle that when a change needs a rare combination to make it possible, it will usually occur by some other way, in stages. (Cf. 2329) |
2131 | The dynamics of chemical systems. | |
10-Feb-47 | 2144 | A study of dynamic systems which are themselves processes, like the Bunsen burner. |
10-Feb-47 | 2145 | A new way in which one absolute system can be derived from another. |
11-Feb-47 | 2147 | In the study of enzyme systems and chemical dynamics, the equations of 2130 are the ultimate foundation: they are the bricks out of which further knowledge is to be built. |
13-Feb-47 | 2152 | Equations tying the variables in the systems of chemical dynamics. |
15-Feb-47 | 2158 | Principles for the experimental study of the dynamics of chemical systems. |
2159 | Example of coordination and training as equilibrium in a dynamic system. | |
2162 | Further practical details for making a unit. (See 2182) | |
22-Mar-47 | 2165 | Chemical dynamics and thermodynamics. |
26-Mar-47 | 2169 | Instability and threshold in chemical dynamics with catalysts. |
20-Apr-47 | 2174 | The Adams- Bashforth method for numerical integration of ant simultaneous ordinary differential equations. |
2175 | Exposition. Clear ideas can be transmitted to a listener who does not know the argument by language only simple and direct. (What a sentence!) | |
26-Apr-47 | 2180 | A number of interesting points from Richardson's book. |
3-May-47 | 2181 | The various "constancies" of the body, so carefully maintained (homeostasis), are also separations and independencies. This needs further investigation. (See 2314) |
14-May-47 | 2183 | A workable unit has actually been made (second system, other was 2094). (Improved, 2432) |
14-May-47 | 2187 | Extracts from book. |
19-May-47 | 2189 | Coordination and keeping within limits. |
2194 | Pavlov and the conditioned reflex seems to make little contact with my work, chiefly because he allows the dog no interaction with the environment. | |
2199 | Review of "The wisdom of the body." | |
2209 | Experiments in learning compared with my theory. | |
23-Jun-47 | 2212 | The formulation of "signal", "symbol", "association" given vaguely on 786 is confirmed and given more precision. |
20-Jul-47 | 2218 | Clarification of "stimulus" and some collected types. (See 2486) |
2221 | Look out for linkages in experimental dynamic systems. There are often much closer linkages in the structure of the experiment than seems at first sight. Several parameter often turn out to be one parameter. | |
21-Jul-47 | 2227 | Independence by delay. (See below) (Another example 2229) |
2231 | The mathematical core of "association". (Example next page) | |
25-Jul-47 | 2235 | An attempted explanation of "association" on an actual experiment. |
27-Jul-47 | 2238 | Some elementary observations on the organism-environment relation. |
28-Jul-47 | 2239 | A stimulus is many stimuli. |
29-Jul-47 | 2241 | If a variable of an ultrastable system is repeatedly forced to take a particular value arbitrarily, then the resting state tends to develop with the variable at that value. |
2-Aug-47 | 2242 | It is dangerous for an ultrastable system to move. (4596) |
7-Sep-47 | 2245 | The multistable reserve. |
17-Sep-47 | 2246 | A clear example of my concept of "independence". |
17-Sep-47 | 2247 | Neurosis as instability. |
2263 | A linear dynamic system can be forced to beat at any frequency. | |
30-Oct-47 | 2270 | A good example of the principle of the differential equation and its integration suitable for non-mathematicians. (See also 2278) |
2-Nov-47 | 2271 | In the exposition of scientific matter, style is even more important than usual. |
5-Nov-47 | 2274 | Notes the relations between my dynamic theory and the methods used in electrical circuit theory. |
5-Nov-47 | 2276 | Neuronic patterns are always breaking up and being laid down. The new ones are formed in relation to those persisting. |
6-Nov-47 | 2277 | A theory of G.P.I. [general paralysis of the insane] delusions. |
8-Nov-47 | 2279 | Two variations on the theme of 2269. |
10-Nov-47 | 2280 | Every vestige of claim and boast must be eliminated, being replaced by equivalent facts, or dropped. |
11-Nov-47 | 2282 | Quotations. |
14-Nov-47 | 2284 | Two points in exposition. |
16-Nov-47 | 2287 | Exposition. |
18-Nov-47 | 2288 | Exposition. |
2291 | Interaction in the multistable system. | |
4-Dec-47 | 2299 | The effects on stability of the intrinsic stabilities of the units forming the whole. If, as is usual, these are all stable, there tends to be an extra stabilising effect on the whole. |
10-Dec-47 | 2302 | Examples of schizophrenics being displaced further from homeostasis by chemical stimuli. And a note of an objection. |
16-Dec-47 | 2305 | An "intelligent" machine must adjust more parameters than have been specified in its design. It is not clear whether my machine passes this test. (Cf. 2315) |
2307 | Some very simple "variables" do not change, i.e. [x'=0]. These are what used to be called "parameters." | |
21-Dec-47 | 2311 | Null-, step-, and part-functions are, by definition, already in equilibrium and adjustment is needed only for full functions. |
21-Dec-47 | 2313 | "Joining" two machines is essentially a break and rebuild. Null-function theory is fitted. |
2315 | Homeostasis is ultimately produced by the gene-pattern, and it protects the gene-pattern from the dangers of the world because the constancy means independence. | |
24-Dec-47 | 2316 | Feedback. |
28-Dec-47 | 2321 | Circuit theory in its relation to my absolute systems and stability; feedback in particular. |
2322 | The production of the new compounds of behavior is only interaction and has nothing to do with Intelligence. | |
1-Jan-48 | 2324 | Memory is not necessarily good. Some examples to the contrary. |
1-Jan-48 | 2326 | If a stable set is to be found soon, the average number of part-functions activated should not exceed 6-10 |
2327 | A proof, modernised from 1724, about an absolute system within an absolute system. | |
3-Jan-48 | 2328 | Absolute system defined more exactly in group form. |
10-Jan-48 | 2330 | Numerical example showing how much faster it is to adapt by parts instead of simultaneously |
2331 | Chemical proof that fast reactions prevail over slow. | |
12-Jan-48 | 2334 | The clock recording time must go uniformly though there are special cases where this could be modified. |
2394 | Joining units never adds to the system's stability unless they want to "borrow" stability. | |
19-Jan-48 | 2395 | Matrix representation of part-functions. |
2397 | Correction to independence tests. | |
3-Feb-48 | 2399 | Quotation on the CNS betraying its blindness. |
7-Feb-48 | 2400 | Richter believes the basic drives are homeostatic. |
8-Feb-48 | 2401 | In large systems the intrinsic stabilities of the units may become less important while the effect of joinings become dominant. |
26-Feb-48 | 2422 | Quotation of echo impulses which seem to be absent but are shown present. |
29-Feb-48 | 2424 | Making one unit more stable intrinsically may make the whole system less stable or actually unstable. Worked out example. (Fuller discussion 2454, 2458, 2463) |
3-Mar-48 | 2431 | Full equations and approximations of the machine. (see below). |
13-Mar-48 | 2433 | Reporting progress in the machine. 2435 |
2434 | Social example of instability. | |
20-Mar-48 | 2440 | Method for investigating friction coefficients in my machine. (2432) |
24-Mar-48 | 2442 | How well does the machine's actual behavior correspond with the settings? (see also 2448, 2452) |
28-Mar-48 | 2443 | Memory and multistability. |
2444 | Trying to make a system give assigned roots. | |
14-Apr-48 | 2447 | If there are no feedbacks, a linear dynamic system cannot develope steady oscillations, but more general systems can. |
2449 | Relations between stability of the machine and its supposed stability of setting. j→∞ is sufficient to make the behavior tend to the theoretical form. (see 2452) | |
14-Apr-48 | 2451 | In a multistable system with multiple subsystems, the number of stable subsystems rises exponentially with the time towards its limit. |
23-Apr-48 | 2457 | Two much stability gives rigidity and loss of control over other systems stability has an optimum. (Generalised in next two sections). |
24-Apr-48 | 2460 | The fault of too much stability proved more generally. Over stability just means slavery. |
2461 | Multistable system point. | |
5-May-48 | 2466 | Equations [x'=f(x)] and x=F(xo;t) when n→∞. |
6-May-48 | 2469 | Definition and test for two patterns of initial displacement, differently sited to be equal. 4148 |
10-May-48 | 2485 | One factor in multistable systems tend to decrease interaction when two lines are activated simultaneously. |
10-May-48 | 2486 | Concept of a "stimulus". |
14-May-48 | 2490 | The conditioned reflex and association possibly solved. |
2491 | The diagram of immediate effects must conform to the type of experiment. | |
16-May-48 | 2497 | When null-functions are present we can get absolute systems by either including them or excluding them. |
2498 | On "fixing" and "releasing" a variable. | |
2504 | The ultrastable system shows a tendency to stabilize a variable at a value to which it is repeatedly forced. Cf. 2690 | |
17-May-48 | 2507 | Whenever possible, postulate many independent ultrastable systems rather than one multistable system. |
21-May-48 | 2510 | Yet another attempt at the conditioned reflex and association. Cf. 2691 |
2512 | The concept of "negative feedback" is just too simple to be worth anything. (See also 2524) | |
3-Jun-48 | 2523 | The ACE, if the operator knows the trick, can imitate the homeostat. |
2524 | This concept of negative feedback is most unsuitable as a fundamental concept. | |
19-Jul-48 | 2527 | Theorem on f's and F's invariant under transformation Φ. |
2528 | Biographical note. | |
20-Jul-48 | 2530 | Systems of (almost) maximal stability (and see below) |
27-Jul-48 | 2531 | Systems of maximal stability. |
16-Aug-48 | 2538 | My theory explains why nerve cells cannot regenerate. |
3539 | Neurofibrils exist. | |
23-Aug-48 | 2541 | One part of an ultrastable system can act as "trainer" to another part. |
23-Aug-48 | 2542 | A snag in the multistable system, which must be answered. (see 2647) |
2547 | Exposition. | |
2551 | In general, if a series of related compound stimuli evoke a series of patterns of activations, we can expect a priori no particular relation between the patterns of activations. Any special relation found to exist must be due to some special arrangement in the machine. | |
2554 | On "memory" in society. | |
2566 | Ideas for new homeostat. (continued 2568) | |
2581 | Constancy is by no means necessary for independence. The latter can be obtained even with gross fluctuation provided it is forced. | |
14-Jun-49 | 2583 | A system of step-functions reaches a resting state or cycle instantaneously |
14-Jun-49 | 2584 | Define the parts and predict the behavior of the whole, not vice versa. |
14-Jun-49 | 2585 | Any absolute system can be regarded as built of parts. |
14-Jun-49 | 2585 | Constancies are conserved when parts are joined or separated. |
17-Jun-49 | 2586 | Fields may, and should, be thought of as bounded and finite in extent. |
2595 | Discussion of the stability of a system formed by joining an infinite number of part-functions. | |
2597 | Response of linear system to an input when its response to a step-function is known. | |
2600 | Solution of linear differential equations by Laplace transforms. | |
2603 | Transfer functions and my equations. | |
2604 | Stability of a chain with feedback. (See also 2621) | |
13-Jul-49 | 2605 | Nyquist's criterion is merely a convenience. Routh is fundamental |
15-Jul-49 | 2606 | Transfer function of a single variable. |
16-Jul-49 | 2608 | Oscillation necessarily implies feedback. |
2613 | Habituation to a moving stimulus, prediction, and the conditioned reflex. | |
18-Jul-49 | 2615 | A mechanism for conditioned reflex. Made: 16 Aug '49. |
2616 | Evidence that neurons learn and then "fix". | |
2617 | An extremely simple example of feedback modifying behavior. (See 2729) | |
2620 | Properties of the relaxation oscillator. | |
2622 | Weiner's example (2604) amplified. (See next section) | |
20-Sep-49 | 2623 | Stability of a chain-circuit of variables. (See also 2604) |
20-Sep-49 | 2624 | Inaugural meeting of the Ratio Club at the National Hospital for Nervous Diseases. |
29-Sep-49 | 2627 | Systems with high selectivity must have long dieaway by cybernetic necessity. |
2-Oct-49 | 2628 | Memory in the dogs of the "Tinder Box". |
2-Oct-49 | 2634 | The multistable system much clarified. |
3-Oct-49 | 2635 | Goal-seeking behavior does not necessarily imply feedback. (Continued, 2643) |
2638 | Granit on causalgia. | |
5-Oct-49 | 2641 | The main properties of the multistable system are proved necessary. |
2642 | Canonical equations from the transfer function. | |
2645 | Goal-seeking behavior does not necessarily imply feedback. (Continued, 2650, 2654) | |
10-Oct-49 | 2648 | The problem of 2541 ─ that with replicated arcs there is no longer individual correction of the wrong ones ─ may be solved statistically if the brain uses combinations obtained by sampling. 4216 |
10-Oct-49 | 2649 | Memories may perhaps float. 4155 |
2651 | Strong goal-seeking usually needs a servo-mechanism. (Continued 2654) | |
2656 | If a part is to behave with more stability than it has intrinsically, then feedback is necessary. | |
2658 | Meditations on a new statistical mechanics. | |
2667 | Machine for Boole's logic. | |
21-Nov-49 | 2669 | If one or more variables are unobserved, a cycle of parameter-values need not elicit a cycle of observed values. |
2670 | An essential feature of the development of the conditional reflex is that an independence changes to dependence. | |
22-Nov-49 | 2674 | The conditioned reflex cannot be explained this way. |
22-Nov-49 | 2676 | A parameter can be localised in action by part-functions. |
22-Nov-49 | 2677 | If the observer tries to control a variable he may be forming part of the whole system. |
2678 | A "stimulus"is one of a pair of initial states. | |
2679 | If systems are joined by dominance, the latent roots are unmoved. | |
2680 | Two possible ways of proving feedback between two sub-systems. Feedback is also proved present if we can find in A a single frequency not found in A + B. | |
2684 | Some properties of a system of part-functions when a single parameter causes activations by its alternation. | |
6-Dec-49 | 2686 | A theorem on localised absoluteness. |
6-Dec-49 | 2688 | A second stimulation can not only break a field but can save it. |
6-Dec-49 | 2690 | Briefly, an adapted system cannot be broken by forcing it to do what it was going to do anyway. This idea only restates what was said 18 months ago on 2503! |
2693 | The conditioned reflex again! Yet another mechanism! This time in iterated ultrastable systems. 4596. No! Just the same old one rediscovered yet again. | |
7-Dec-49 | 2694 | Note on the previous note. |
7-Dec-49 | 2696 | The two ways of getting a conditioned reflex are almost identical. |
2698 | Better definition of a system which shows extinction of its conditioned reflex. (Continued over) | |
12-Dec-49 | 2700 | A possible mechanism for conditioned reflexes of the second order. |
12-Dec-49 | 2701 | A slight tendency within the nervous system can easily be magnified to a maximal change in the effectors. |
2703 | We must distinguish in a conditioned reflex experiment between the pattern represented by the experimenter's controls and the pattern of what arrives at the cortex. | |
2704 | Example of preceeding section. | |
19-Dec-49 | 2710 | A system for relating stimuli given to arcs activated. |
31-Dec-49 | 2714 | The effects of selection on the distribution of a statistic. |
31-Dec-49 | 2716 | Numerical example of the solution of [x'=Ax] by x=etAx0. |
2718 | Example of equations solved by Laplace transformations. | |
2722 | An enumeration of the possible types of organisation. Summarised 2736 | |
21-Jan-50 | 2725 | In a given absolute system, if n-1 variables follow a given line of behaviour and the initial state of the n-th is given, then the behaviour of the n-th is also determined. 5051 |
2727 | Predicting behaviour of unobservable variables. (Continued 2732) | |
2731 | Binary counters. | |
2734 | A new way of getting information about unobservable variables in an absolute system. 5051 | |
2736 | Examples. | |
28-Jan-50 | 2737 | The ways of organising classified and tabulated. |
1-Feb-50 | 2741 | Proof of an entry in the previous section. |
2746 | Organisation of a civil service. 2888, 2828, 4245 | |
2753 | A conditioned reflex demonstrated on the homeostat. 2762, 5708, 5855 | |
8-Feb-50 | 2754 | Examples of simple substitutions. |
2755 | On the nature of 'mind'. (An application 2790) | |
10-Feb-50 | 2761 | Effect of diverting a variable from its path. |
2766 | Conditioned reflex in ultrastable system regarded as change of resting state. 2855, 5855, 6745 | |
2768 | Fundamental theory of relays and Boole's algebra. | |
28-Feb-50 | 2770 | Emperical tests of the chance of stability collected to date. |
2772 | Chance of stability. 3050 | |
4-Mar-50 | 2773 | Wholes whose stability differs entirely from those of the parts. |
2776 | Joining unstable systems to form a stable one. | |
13-Apr-50 | 2787 | Genetic inheritance as information. (See 2806) |
13-Apr-50 | 2787 | Dictionary definitions: Absolute, Behaviour, Break, Critical. |
2788 | Dictionary definitions: Disperse, Essential, Field, Independence, Interaction, Iterate, Parameter, Regular. | |
17-Apr-50 | 2789 | Dictionary definitions: Representative, Stability, State, System, Variable. |
23-Apr-50 | 2792 | Discovering a scientific law is like an animal getting one reaction-system adapted to more than one environment. (Summary 2797) |
2793 | A set of numerical values can be, in variables, an operand, and in parameters, an operator. (See next section) | |
26-Apr-50 | 2796 | The meaning of 'several' environments. (Amplified on 2801) |
28-Apr-50 | 2801 | Groups and learning. |
28-Apr-50 | 2806 | Examples of environments that can be divided into sub-environments. |
2815 | A list of actions in which some object has to be avoided. | |
6-May-50 | 2816 | Some items of information theory. |
19-May-50 | 2820 | Information theory. |
21-May-50 | 2824 | Example of pattern and group. |
24-May-50 | 2825 | A stochastic process and information. |
25-May-50 | 2828 | What a mammal does to an environment that cannot be adapted to. |
2830 | Social systems that can change their own parameters. | |
26-May-50 | 2831 | Allbutt on a type of man. |
2833 | Description of a child lacking a sense of pain and often injured. | |
2842 | Solution of Harlow's problem. | |
2847 | Modern psychology and my theory. | |
5-Jun-50 | 2848 | How to 'prove' a theory of the conditioned reflex. |
2854 | Extracts from Hebb's book. | |
2858 | A paper to be returned to later. | |
10-Jun-50 | 2859 | Conditioned reflex without cortex. |
10-Jun-50 | 2860 | Razran's article. |
2861 | A stimulus contains, in addition to its obvious content, derived and integrated components. (Not so much the stimulus contains them as that it will affect the nervous system as if it did) This is the principle: the 'stimulus' contains everything the nervous system can transform it into. Futile, therefore, is it to worry much about the exact details of the presentation. (Continued 2878) | |
10-Jun-50 | 2862 | A process, in natural selection, that cannot reach a steady state but moves like the Flying Dutchman. |
11-Jun-50 | 2877 | An empirical test on 30 cases of whether my definition of dependence agrees with what is understood by 'causation'. 5118, 3679, 3709 |
2880 | A 'stimulus' is not what it seems to be. It is all that happens between the experimenter and the depths of the subject's brain. 2896 | |
2884 | A popular misunderstanding of what 'mechanistic' means. | |
14-Jun-50 | 2887 | Correspondence of primative animal to machine, and object recognition. |
15-Jun-50 | 2888 | Social cybernetics. 2898 |
2889 | Part-environment relation in the Multistable System. 4193 | |
20-Jun-50 | 2890 | Example of multistable system. |
28-Jun-50 | 2896 | Comments on the books. Examples of part-functions. |
2900 | The new point of view. | |
2904 | Axiomatic basis of the canonical equations, preliminary. | |
9-Jul-50 | 2907 | I have little to learn from what is known of ecological systems. |
9-Jul-50 | 2914 | Canonical equations of a regular system. See 2922 |
16-Jul-50 | 2921 | Defining and testing an absolute system. |
2925 | On the canonical equations of a regular system | |
2930 | Some collected notes on pattern or class-recognition, and invariants. | |
2933 | A simple form of motor equivalent. (See 2939) | |
18-Jul-50 | 2936 | 'Two-stage' ultrastability. |
2949 | Essay on 'motor equivalents.' See also 2989. | |
25-Jul-50 | 2951 | A new principle for a new machine. |
2952 | Law relating the lingering of the representative point with the density of critical states. | |
2954 | Elementary features of my new machine. (See 2955) (changed to 3042) | |
2974 | Multistable systems, essential variables, dispersion, how to alter step-functions selectively. | |
21-Aug-50 | 2978 | Behaviour of systems of part-functions. |
2980 | Intrinsic stability: general, and of my new machine. | |
2983 | The equations of the new machine, (See next page) Confirmed 2990 | |
2984 | Chance in my machine that n active variables are stable. | |
2986 | Intrinsic stability of brain and my new machine. 4154 | |
2989 | Sensory (dispersive) cortex must contain no learning mechanisms. | |
30-Sep-50 | 2991 | Canonical equations of systems composed of units each of which tries to make itself (its dial value) some function of the others. (3200) |
2992 | The system that does not generate information is identical with an absolute system. 3032 | |
2993 | Redundancy and information. | |
2996 | For training, essential variables are not necessary. (See 3003) | |
3-Oct-50 | 2999 | Serial training in the machine. (See 3004) |
3000 | Note on the 'principle of continuity'. | |
3-Oct-50 | 3001 | A display for the new machine. |
3002 | A simple and well known example of a system of part-functions. | |
24-Oct-50 | 3005 | Serial learning. |
3007 | Canonical equations of the homeostat. | |
29-Oct-50 | 3013 | Facts on learning. |
29-Oct-50 | 3013 | Absolute system conserves information. |
30-Oct-50 | 3019 | Multistable system gives partly additive responses. A reaction pattern can be 'strengthened' by noisy variation of parameters. 4155 |
31-Oct-50 | 3021 | A better meaning for 'difficulty of finding stability.' |
3025 | n part-functions of which k are active at any one time is as easy to stabilise as k, not n, full-functions. | |
3027 | A multistable system adapting to several environments. | |
7-Nov-50 | 3031 | Necessary and sufficient conditions that a first adaptation should be still present after a second has taken place. |
12-Nov-50 | 3034 | The noiseless transducer is the absolute system.(Continued 3164) |
3035 | Theorem on absolute systems. Continued next page. | |
3037 | Theorem on absolute systems. Here is the theorem in its final form for proving step-functions... | |
23-Dec-50 | 3041 | Systems of part-functions automatically provide step-function. (N.B. This need further investigation and more rigorous formulation). |
25-Dec-50 | 3043 | Mark 13 DAMS works. |
26-Dec-50 | 3044 | Stability in the system 'number of neons lit'. |
27-Dec-50 | 3048 | Joining 'at random'. |
27-Dec-50 | 3051 | Stability of systems whose units always tend to some function of the variables. |
27-Dec-50 | 3054 | The equations of DAMS. (Effect of neon, next page) Example next page. |
27-Dec-50 | 3054 | Control of DAMS' stability. |
3058 | Essential variables may work by 'habituation'. (Review 3280) | |
29-Dec-50 | 3059 | A simple mode of action of the essential variables. 3382, 4526 |
3062 | Part-functions will divide the whole more effectively if the permanent connections are few. | |
16-Jan-51 | 3070 | Wiener says cycles will be common in DAMS; I say they will be few. 4892, 5461, 5472 |
20-Jan-51 | 3075 | Set-up necessary, in brain and DAMS, for serial learning. (3087, 3141) |
3080 | Functional knowledge obtainable when only some of the variables are observable. 3716 | |
28-Jan-51 | 3082 | Wiener's opinion on the 'absolute' system. |
3085 | The Markoff process. Cf. 3223 | |
3086 | Stability of system of Markoff chains. | |
28-Jan-51 | 3088 | Relation of essential variables to system of part-functions. |
29-Jan-51 | 3090 | There should be many essential variables, allowing patterns to endure in proportion to their suitability, and averaging of the behaviours. |
3091 | The elementary conditioned reflex does not need essential variables. Corollary: It is thus a by-product. | |
5-Feb-51 | 3093 | The probability of stability. |
3094 | If the f in the canonical equation behaves as a Markoff chain, the variable's behaviour is - Brownian movement with drift. | |
3095 | Stochastic differential equations. | |
3099 | Systems that are partly stochastic. | |
3105 | The basic equations of statistical mechanics (Continued 3134) | |
3109 | Probability of stability in an infinite machine. (3121) | |
3110 | Two things necessary if an infinite system is to be stable. (Cf. 3200) | |
3110 | Reactions to delay are difficult. (3138) | |
3112 | Animals react to more things than the experimenter thinks he is supplying. 4597 | |
12-Feb-51 | 3115 | Psychological facts to be explained by DAMS. |
3116 | A part-function's 'degree of constancy.' | |
3118 | Variables 'sticking' does not necessarily cause a bias. | |
14-Feb-51 | 3119 | No excuse is necessary to suppose that part-functions are constant only at certain values. Perhaps the concept of 3200 may be usable. |
14-Feb-51 | 3120 | In an absolute system one variable knows nothing of another variable's constancy. |
3123 | Infinite systems of stable parts. | |
19-Feb-51 | 3127 | How a variable's distribution changes after an internal dt. |
19-Feb-51 | 3129 | Steady states in an infinite system. |
23-Feb-51 | 3132 | I am now ready to account for learning by 'pleasure'. |
23-Feb-51 | 3133 | In a linear system with all variables distributed, the means of the variables behave the same as the variables would if undisturbed. |
25-Feb-51 | 3137 | In an absolute system independent distributions don't stay independent. |
27-Feb-51 | 3138 | 'Delay' in a machine is only behaviour of zero amplitude. |
27-Feb-51 | 3139 | In a system of part-functions there are no 'parts' only distributed activations. |
3142 | To get cumulative adaptation, the environment must be traversed by a variety of paths. (4546, 4215) | |
6-Mar-51 | 3143 | Conditions affect, in the long run, only the stable patterns. |
10-Mar-51 | 3146 | On the chance that a disturbance should alter the resting state of some part. (3272) |
14-Mar-51 | 3148 | A system of part-functions may be easier to change if it is built in stages of assembly. |
3151 | Darwinian mechanisms are to be developed by Darwinian process. | |
19-Mar-51 | 3163 | Switches that see a Markoff process only through themselves: consequent bias in their settings. (Theory in metric-less states, 4527) |
3170 | In an absolute system formed by the junction of independent parts, if a particular part can take one of ρ initial states and can show σ lines of behaviour from each initial state, then the quantity of information log2 ρ + log2 σ cannot be exceeded whatever part has been chosen. | |
3173 | Information in an absolute system always falls to log2 η* (3176) where η is the number of the system's stable states and cycles. *Allowance should be made for the fact that the resting states are not equally probable. | |
3176 | Information in a machine. The catchment area of a resting state. | |
3177 | Information in a conjoined system. 3274 | |
3181 | Example and proof of Shannon's Theorem 7 | |
3189 | Networks for DAMS. (Cf. 3237) (Further example 3306) | |
6-Apr-51 | 3193 | Information in machines. |
6-Apr-51 | 3200 | Shannon and I. |
6-Apr-51 | 3201 | A variable of constant intrinsic stability and one that always moves towards some function of its neighbours' states are identical. (Cf. 3110) (Behaviour 3134, 3239) |
7-Apr-51 | 3203 | Passing information from parameter into machine. The previous theorem can be improved. Here is a better statement... |
3205 | Accurate statement of the amount of information that can be put into a machine by arbitrary interference. (3275) | |
7-Apr-51 | 3206 | A physical example of habituation. |
3207 | In the field of an absolute system, every convergent junction acts as a sink for information. | |
3209 | Maximal loss at a convergent point in a field. Table of log2[(aa bb)/(a+b)a+b]. | |
9-Apr-51 | 3210 | We cannot measure information by finding contributions from sub-ensembles and adding. (Another example 3249) |
10-Apr-51 | 3212 | An absolute machine can never gain more information than is put into it. |
10-Apr-51 | 3214 | When a parameter affects a machine, the gain in information is stationary (and a maximum) if the parameter's values are distributed independently of the machine's. |
3216 | Passage of information as machine dominates machine. (See 3298, 3218, 3275) | |
11-Apr-51 | 3220 | (Stated at the front - on 3218): If a machine is driven by an absolute system, the duration of coupling makes no difference to the amount of information received. |
3222 | An information source controlling an otherwise absolute system raises it to a definite information content at which it is in stable equilibrium. (3086) (Canonical equations next page) | |
13-Apr-51 | 3224 | Canonical equations of the densities in state of a system disturbed by an information source. (See 3227) |
13-Apr-51 | 3226 | Another measure of information applicable to a machine. |
13-Apr-51 | 3228 | When driven by a steady statistical source, the information in a machine does not tend to a minimum. |
13-Apr-51 | 3230 | States that lock accumulate all the members of the ensemble. 3233, 3291, 4524 |
14-Apr-51 | 3234 | Information when a stochastic parameter changes infrequently. |
3235 | Ways of losing information. 3274 | |
16-Apr-51 | 3237 | Wiring pattern of DAMS. |
3240 | Conditions that a machine shall have the maximal number of resting states. This can be specified further... | |
19-Apr-51 | 3241 | Maximal number of resting states. (3308) |
3242 | Information when A drives B. | |
3244 | The inverse of the canonical equations. | |
23-Apr-51 | 3245 | An experiment stops when the exchange of information has reached equilibrium. (3248, 3254, 3691) |
25-Apr-51 | 3247 | Independence does not in general cause loss of information. (3274) |
25-Apr-51 | 3249 | Entropies in the parts do not sum to that of the whole. Entropy of a part may equal that of the whole. |
25-Apr-51 | 3250 | Information and experiment. |
25-Apr-51 | 3253 | |
3263 | Information and the experimenting on dynamic systems. | |
3266 | This then is the maximal information obtainable in an absolute system of σ states by starting it at a state selected arbitrarily and then observing how it's behaviour goes from state to state. | |
3270 | Information always decreases, step by step, as an unknown line of behaviour unfolds. | |
3271 | Uncertainty about the details within a line of behaviour is independent of whether that line, or some other, will occur. 3274 | |
1-May-51 | 3279 | Results collected from the last hundred pages (since 3164) on the subject 'Information in absolute systems.' 3297 3500 |
2-May-51 | 3280 | New layout for DAMS, and an unsolved problem. |
2-May-51 | 3280 | I have just reviewed the notes on the pages mentioned (2955, 2996, 3001, 3003, 3014, 3026, 3028, 3056, 3059, 3071, 3082, 3087, 3115, 3138, 3140, 3149 and the previous note), all dealing with the relations between environment, essential variables, and the 'red mass' of 2957, once the essential variables have been specialised and separated. Here are my conclusions... |
4-May-51 | 3290 | A review of essential variables. (3484, 3521) |
3294 | Equations of density in phase of systems that tend to stick at certain states. 4153 | |
3297 | The longer the line of behaviour, the higher the chance of step-function change. | |
3301 | Information in machines. | |
9-May-51 | 3303 | The continuous system can gain information though absolute. |
9-May-51 | 3303 | As soon as a sub-system is isolated it starts losing information. |
23-May-51 | 3307 | Dispersion. |
23-May-51 | 3312 | How many resting states has DAMS? (Continued 3319) |
3314 | Resting states in DAMS will be few. (Continued 3319) | |
28-May-51 | 3316 | Pneumatic controllers. |
3318 | Measuring how much one variable affect another. The part-function as a limit. | |
3325 | Designing parts for a system with many resting states. (3333) | |
3333 | How to find the distribution of values in a system of many parts. | |
3346 | (1) I ignore resting cycles here, as they will probably be rare. (2) I treat only of parts of constant intrinsic stability with equations of form x-i=Ki{Φi(x1,...,*,...,xn)-xi)}. (3) The variables in the parentheses (above) are the 'inputs' to the part, and Φi is the 'output'. (xi merely follows Φi). (3323) (4) Just solving f(X)=0 is of little use, for an unknown, and large, number of roots may be complex. The total number of roots, real and complex, is the product of the degrees of the several f's regarded as polynomials (3308) (5) To get the real distinct resting states, find geometrically the real intersections of the surfaces, f(X)=0. (6) Figure of 3322 shows that, if we want to get our resting states into a certain region of phase-space then the surfaces must waggle within it, and also across it. (3325 top). |
|
3347 | (Continued) (7) If Φi tends to a form resembling ρi parallel planes (3334), then the number of resting states (stable and unstable) tends to Πρi. (3336) (8) (3340: a method, of little importance, for getting the sets of planes all orthogonal. (9) (3342: what happens when all parts are identical. (Not the case with DAMS) (10) To get the maximal number of resting states within a given region: (a) construct each part so that the output consists of many parallel planes, (b) join them so that the sets of planes are orthogonal. (12) If the number of resting states is increased, we can expect the number of stable states to be increased in about the same proportion. (3345) |
|
3348 | How many resting states has a system assembled from parts of known properties? Also 3496 | |
13-Jun-51 | 3351 | Modifying a stable field. |
13-Jun-51 | 3353 | Ways of altering a system's sensitiveness to disturbance. |
13-Jun-51 | 3354 | Effect of richness of joining on the number of stable resting states. |
13-Jun-51 | 3356 | The nervous system should not have internal feedbacks (unless for special reasons) But see 3396. Confirm 3425, 3521 |
3359 | Information and adaptation. 3521 | |
18-Jun-51 | 3360 | How many nerve calls has an earthworm? |
3365 | Conditions that one system may control another in detail. | |
18-Jun-51 | 3366 | Control in systems of Constant Intrinsic Stability. |
3367 | My machines are not ergodic. | |
19-Jun-51 | 3377 | Information going through a transducer. |
21-Jun-51 | 3381 | Solution of the paradox of 3379. |
5-Jul-51 | 3382 | The essential variables must be able to send much information into the rest of the system. 3500 |
6-Jul-51 | 3386 | Designing an essential variable that works by emitting noise. 3521. |
9-Jul-51 | 3387 | DAMS needs a complex environment, but a simple training-schedule. |
11-Jul-51 | 3390 | My work is the 'chemistry' of machines. Progress in it will be largely empirical. Review 4141 |
12-Jul-51 | 3392 | That a set of step-functions should provide many resting states it is necessary that they should be uncorrelated. This can be achieved by many cross-connexions. 3521 |
3393 | If the number of resting states is increased by some change of design, take care that the number stable is not actually reduced. | |
13-Jul-51 | 3395 | Of the resting states, the number stable can be anything from none to all. |
13-Jul-51 | 3398 | A system joined in a circuit is likely to have very few resting states. Confirmed 3426 but see 3571. |
13-Jul-51 | 3398 | To retain information in DAMS Mark 13, use output 3 and either of 1 or 2 in all cases. |
16-Jul-51 | 3399 | Thinking of the machine as having a finite number of states is the fundamentally sound method. |
16-Jul-51 | 3400 | How to integrate step by step when parts have outputs. 4498 shows how it should be done. |
16-Jul-51 | 3402 | Further data on what is required for many resting states. |
17-Jul-51 | 3405 | A machine's tendency to destroy or conserve information (as uncertainty of state) depends slightly on certain necessary factors in the parts but depends more on the holistic factor of assembly. |
3407 | Two similar parts that will give many stable resting states. | |
26-Jul-51 | 3410 | Design of a part and the number of resting states. |
3415 | My standardised vocabulary, collected. (Standard symbols, 2004) | |
30-Jul-51 | 3417 | With a new and complex system there are no 'usual' values for the parameters, and this increases the difficulty of getting to know it. 3514 |
1-Aug-51 | 3418 | Law of the Invariance of Distribution. |
8-Aug-51 | 3422 | How to stop part-functions from destroying information. 5291.9 |
10-Aug-51 | 3425 | The conclusion is, then, that for many resting states we must have plenty of independence. |
10-Aug-51 | 3426 | Historical note. |
3427 | Complex wholes are unstudiable. 3474, 3496, 3513 | |
11-Aug-51 | 3428 | Information in DAMS. |
3430 | Value of a determinant. | |
25-Aug-51 | 3434 | The latent roots of a system formed as a circular chain of levels. Cf. 3573 |
3437 | A multistable system tends to lose reactivity, which will often be restored by applying some strong, but unrelated, stimulus, at the cost of some forgetting. ? Action of E.C.T. (Corollary 3464). ? Explanation of 'induction'. 3656, 4628, 4524. | |
3450 | Ninety quotations. | |
8-Sep-51 | 3452 | In the cortex the relentless necessity for survival may lead to some interesting consequences. (See 3454) (Review, 4155) |
3457 | The art of war - in the cortex. Review 4155, 4589 | |
3459 | The animal reacts to all its surroundings. Retroactive inhibition and the theory of interaction in a Multistable System. | |
12-Sep-51 | 3460 | Let DAMS keep moving. |
12-Sep-51 | 3462 | Society. |
3463 | How DAMS can be made neurotic. (See next section) (See 3480) | |
12-Sep-51 | 3465 | Neurosis by conflict must use up a system's resources of step-functions. |
14-Sep-51 | 3474 | The question 'what is a 'statistical' machine?' answered. |
14-Sep-51 | 3475 | What makes a complex machine 'statistical'? Review 4141 |
14-Sep-51 | 3477 | How does a statistical machine work? |
3478 | DAMS should demonstrate that it can manage the statistics of its environment as well as the exact details. | |
22-Sep-51 | 3479 | DAMS should tend to avoid activating variables with widespread effects. 4155 |
3481 | On neurosis. | |
23-Sep-51 | 3483 | A more practical form of environment for DAMS. |
24-Sep-51 | 3486 | Details of the Essential Variables. |
3487 | How long should an arc be? 3511, 3514, 3557 | |
25-Sep-51 | 3489 | Part-functions are apt to lead to many useless neutral equilibria. 3491 - No they are acceptable; 3495 |
25-Sep-51 | 3490 | Variable of constant intrinsic stability as part-function. (See also below) |
25-Sep-51 | 3493 | Equilibria in systems of part-functions. (See below) |
26-Sep-51 | 3495 | Types of equilibria in DAMS. Conclusion: Neutral equilibria, with esential variables within limits, are acceptable. |
26-Sep-51 | 3496 | How to study a complex system. |
3498 | For a small disturbance, the effects everywhere tend to be proportional to the size of the disturbance. | |
27-Sep-51 | 3500 | If the environment is E the brain must become -E-1 4294 |
3501 | Two new types of information in the multistable system. 3521 | |
3503 | Haldane's book. | |
3503 | Example of dispersion. | |
3505 | How many resting states has DAMS? | |
15-Oct-51 | 3509 | History of DAMS. |
15-Oct-51 | 3509 | Sex and the Multistable System |
3513 | Testing DAMS. 4511 | |
21-Oct-51 | 3515 | Designing DAMS. |
3516 | More complexity means more essential variables, which then have all to be satisfied. | |
3517 | Improvement by the purely empirical is as old as industry. | |
3521 | How to arrange DAMS. DAMS can react to a 'signal' or 'symbol'. | |
29-Oct-51 | 3522 | Index to Essential Variables since 3289. 3582 |
29-Oct-51 | 3522 | Reduction of all variables to a common form is of no importance. |
3526 | Fundamental theorem that the nervous system must contain step-functions. | |
3-Nov-51 | 3530 | Fully developed form of the 'mechanical brain'; design for a chess-playing 'machine'.4563 |
5-Nov-51 | 3531 | The brain should have some step-functions almost inaccessible to the environment. |
3535 | Definition of a system's 'intelligence' at a resting state. | |
3537 | Anatomical features gives quick success but lose generality. (Next page) 4563 | |
12-Nov-51 | 3538 | Fixed qualities in a system. |
3545 | The neon in DAMS as absolute system. | |
18-Nov-51 | 3547 | Some statistical systems. Review 4141 |
3552 | Joining at random and by sub-systems. | |
3554 | We think dynamically, not logically. | |
21-Nov-51 | 3558 | How to join DAMS. |
21-Nov-51 | 3561 | Joining up Essential Variables, Environment, and network. Review 3582 |
22-Nov-51 | 3563 | Representation of a typical environment. |
3570 | The number of circuits that passes through each valve in DAMS is large. | |
3578 | Proof that circuits of levels that include a one- variable level arc easy to stabilise. | |
27-Nov-51 | 3580 | Processes for elementary study. |
26-Nov-51 | 3581 | Infinitesimal displacements activate a unique set of variables. (3599) |
3594 | How essential variables, environment, and network are to be arranged in organism and DAMS. 3603, 3825, 4600, 4613 - there is no general solution, 4832, 5737 | |
30-Nov-51 | 3596 | A clearer statement about the Essential Variable. |
3598 | A glance at the theory of games. 4589 | |
3602 | Getting dispersion. 3870 | |
1-Dec-51 | 3603 | How the cortex perhaps gets selective disruption of wrong arcs. 3825, 4600, 4831 |
1-Dec-51 | 3606 | Long lines of behaviour in phase-space often appear in the living world as circulating between organism and environment. 3645, 3760 |
7-Dec-51 | 3608 | Statistical mechanics. |
7-Dec-51 | 3610 | 'Positive' cleverness may be really only what is left after the elimination of nonsense. 4578 5307.3 (See 3629) |
3614 | Evolution and the homeostat are information-amplifiers. (3616) | |
8-Dec-51 | 3616 | Details of chess-playing. |
11-Dec-51 | 3628 | Properties of an information-amplifier. 4155 |
11-Dec-51 | 3629 | The elimination of wrong moves at chess may eliminate too much. |
12-Dec-51 | 3630 | Random transformations. |
12-Dec-51 | 3631 | How instinct is activated. |
3632 | Random transformation in taste. 3665 | |
3637 | Calculations on dispersion. | |
17-Dec-51 | 3642 | The chance that inactivity will stop an effect getting into the rest of the machine. |
22-Dec-51 | 3643 | Environment reducible to orthogonal subsystems. Also 3648 |
29-Dec-51 | 3644 | Innate mechanisms must be studied for their organisational properties. |
2-Jan-52 | 3645 | Three ideas. |
7-Jan-52 | 3647 | Functional levels may be topologically re-arranged within organism and environment. |
8-Jan-52 | 3649 | Example of an environment. |
8-Jan-52 | 3654 | Cybernetics and the psychoses. 3673 |
3655 | The mechanism underlying paranoia. | |
3657 | The number of resting states that a machine can display to an observer depends on the information that the observer can get into the machine. (Next page) | |
17-Jan-52 | 3661 | Information in the field and in the equations of an absolute system is S log S. 3695 |
17-Jan-52 | 3661 | The homeostat's amplification factor is less than x1, but I was the first to point this out. |
20-Jan-52 | 3662 | Again the necessity for achieving success by stages. |
3663 | Approximate estimate of the amount of design put into the homeostat. | |
20-Jan-52 | 3664 | How many uniselectors the homeostat should have. 3743 |
3665 | Example of a random transducer. 3667 | |
3666 | Chess strategy. | |
25-Jan-52 | 3670 | Chess player's manual. 4569 |
25-Jan-52 | 3670 | Amount of design in the homeostat. |
3672 | Possible reason why psychoses are rare in children. Cf. 3650 | |
3674 | Isolating a system. | |
3684 | Extracts from Sommerhoff. 3709, 3715 | |
31-Jan-52 | 3685 | When there is more than one source, how many entropies are calculable? |
3687 | Information from multiple sources. | |
31-Jan-52 | 3688 | Definition of 'memory'. 3810 |
3692 | Experimenter and system. 3697, 3725 | |
3-Feb-52 | 3696 | A function that measures information but is free from the concept of probability. Its basis is the 'partition'. Compare Neumann and Morgenstern 67. 5027 |
3-Feb-52 | 3698 | Even the experimenter must be regarded as an ensemble. 3709 |
4-Feb-52 | 3700 | To compute information, members having the same field must be kept together. |
3703 | Chess strategy. 4590, 4651 | |
3705 | Every parameter-change allows (or forces) the information in an ensemble to drop to a new lower level. Same applies to δ-impulse 3936. | |
3706 | Habituation, and adding information to an ensemble. 3774 | |
3707 | The effect of the initial state decays with time if some parametric input is active. 3954 | |
3708 | Decay of information in an ensemble. | |
9-Feb-52 | 3710 | The concept of 'cause' implies more than one line of behaviour. 5118 |
9-Feb-52 | 3710 | Today's tip: Cleverness, by Selection out of Thermal Noise, |
3715 | Mathematical knowledge is knowledge of how to control a certain environmental, physical, system. 3721, 3725, 3729 | |
3717 | Transformation of a linear absolute system. | |
3719 | Replacing variables by derivatives. 3723, 4296, 5202 | |
27-Feb-52 | 3720 | Two unstable systems joined to give a stable. |
3-Mar-52 | 3723 | More examples of mathematics as a study of real dynamic possibilities. 3729 |
12-Mar-52 | 3729 | 'Knowing' means 'controlling', which means 'keeping invariant'. Review 4348, 4294 |
28-Mar-52 | 3730 | More illustrations that maths is based on physical, empirical knowledge. 3926 |
28-Mar-52 | 3730 | Real 'dial-readings'. |
28-Mar-52 | 3730 | Itinerary in the States: London, New York, Chicago. |
3731 | Itinerary in the States: Warren McCulloch. John Bowman at Mellon Institute, Pittsburgh. Koskoff. New York. Boston. MIT: [Lethrin ?], Walter Pitts, Norbert Wiener, Aitkins, Marvin Minsky, Mary Brazier. | |
3732 | Itinerary in the States: Boston: Society for the Unity of Science. New York, Warren McCulloch, New England, 9th Macy Conference, Mrs Metzger (Ruth McCulloch's mother). Cambridge, Walter Pits, Norbert Wiener, Bell Laboratories, New Jersey, Claude Shannon | |
3733 | Itinerary in the States: Richard Wallace, Philadelphia. Washngton, Mina Rees, Seymour Kety. New york, London. | |
3736 | To make, or not to make, a calculating machine? | |
28-Mar-52 | 3738 | Wallace's Maze-solving Computer. |
3741 | Shannon's mechanical brains. | |
3743 | Information in the homeostat. | |
2-Apr-52 | 3744 | Information in the homeostat. |
3752 | Searching, random and systematic. | |
3753 | Qualification to 3746. | |
3760 | The division by part-functions is not objective. Transformation can destroy part-functions. 3767, 3799 | |
8-Apr-52 | 3761 | Details of dispersion. |
3763 | Addendum to the definition of the primary operation. Corrected 3894 | |
9-Apr-52 | 3766 | A misunderstanding about part-functions. 3868 |
10-Apr-52 | 3772 | Rank of the differential matrix, and null-functions. |
3775 | Part-function were introduced to cause retention of information. 3799 | |
3776 | Example of a canonical equation of nullity 2. 3799 | |
3784 | Rank, information, effective parameters. 3780, 3799, 3788 | |
3785 | Determination of initial states. 3789, 3847 | |
3787 | Field + field, and determinate changes of parameter. | |
3787 | The observer-system relation is symmetrical; so we can calculate 'information' over an ensemble of observers | |
3-May-52 | 3789 | Information, rank, equations. 3799 |
5-May-52 | 3792 | On the operation that brings the representative point to a particular initial state. 3846, 4628 |
6-May-52 | 3794 | Convergence of lines as invariance. |
6-May-52 | 3797 | An absolute system cannot give to another absolute system that it dominates more information than the first one contains. 3797 |
3799 | Rank, and control effected by parameters. 3800, 3802, 4301 | |
3801 | Channel capacity in a machine. | |
10-May-52 | 3806 | Transmission of information through a chain of absolute systems. |
11-May-52 | 3808 | Homogeneity implies group statistical regularity implies group. 3849 |
12-May-52 | 3809 | Examples testing dependence of F on xo. |
3814 | (1) What is meant by 'memory'. (2) Memory does not require feedback. 3840 | |
13-May-52 | 3815 | Memory as conjugate behaviour. |
13-May-52 | 3815 | Habituation implies memory. 3842 |
17-May-52 | 3824 | Habituation. 3837, 3842, 3856, 4526 |
3829 | How the Essential Variables must act to be selective. 5549, 5415, 4169, 4831, 5345 | |
3831 | Variables in the brain should be driven actively by the environment. | |
3832 | Odd notes. | |
3835 | A better view of the homeostat. 3837 | |
22-May-52 | 3837 | What is essential in the homeostat. 3841, 3856, 4161 |
23-May-52 | 3840 | On habituation. 3842, 3856, 3865, 4524 |
3841 | Memory implies that step-functions exist and that the system contains more than one resting state. 'Memory' is 'change of resting state'. Example 3833, 3856, 3842, 3900. Multiple resting states are necessary: they are also sufficient if we observe them through a system U, which can be the observer! | |
3845 | Habituation and memory. 3865, 4524 | |
25-May-52 | 3852 | Only an observer with dispersion can take advantage of a system's absoluteness. |
3853 | Exploring a machine. | |
28-May-52 | 3854 | Detail of 3844. |
28-May-52 | 3855 | Change full to step-functions for resting states. |
29-May-52 | 3856 | Other things being equal, the system with more step-functions will have more resting states. |
31-May-52 | 3859 | The importance of the age of thing. Review 4155 |
1-Jun-52 | 3860 | The catchment areas define a partition. |
4-Jun-52 | 3861 | Definition of 'stability'. |
3862 | Return of parameter to a previous value can cause further loss of information. 3863, 3954, 4057, 4074, 4373 | |
3864 | A fluctuating parameter tends to lesser the number of resting states. | |
11-Jun-52 | 3866 | The reactive condition is the more probable, from which the system may diverge under habituation. |
3867 | The channel from step-function to observer must be broad if the observer is to see variety of behaviour. | |
12-Jun-52 | 3869 | Every system can be transformed to [y~1=1, y~2=...=y~n=0] Cf. 1151 |
3871 | All control is based on the infinitesimal. 3930, 4015 | |
17-Jun-52 | 3876 | Stability of a circuit of levels. Another interesting system... |
3880 | Behaviour of the 'clover' system. | |
3882 | Feedback can occur along a single channel. | |
21-Jun-52 | 3891 | An incomplete solution of the problem of the probability of stability. |
22-Jun-52 | 3892 | A variable 'is' whatever a particular system, perhaps ourselves, sees it as. (But see 4000) and 3896, |
22-Jun-52 | 3893 | "interacts with" is an equivalence relation. |
22-Jun-52 | 3894 | A likely mechanism for the conditioned reflex. 3897 |
23-Jun-52 | 3896 | The primary operation, and testing absoluteness. |
23-Jun-52 | 3899 | More on the Conditioned Reflex |
24-Jun-52 | 3901 | A hybrid step-full-function. By 4000 it is in (2), a full function. |
26-Jun-52 | 3914 | n complex variables are equivalent to 2n real variables. Complex 'machinery'. |
3916 | n arcs can control n complex variables. | |
3918 | Resting states and latent roots of complex-variable systems. | |
3919 | Volterra's book. | |
3923 | Arcs that are simple as complex variables do not stay so as real variables. | |
3925 | In the brain, part often talks to part via the environment. 5424 | |
28-Jun-52 | 3927 | All maths should be expressible in terms of dynamic systems. |
30-Jun-52 | 3928 | Topology of absolute system. |
3929 | 'Stability' must be re-stated in terms of information. 3963, 3980, 3975 | |
30-Jun-52 | 3931 | The disturbances of most interest are those that are infinitesimal and the system becomes linear. |
1-Jul-52 | 3932 | Self-reproducing arcs are of very great importance, for good or evil. Review 4154 |
2-Jul-52 | 3935 | A derivation of the partition-function. |
2-Jul-52 | 3937 | Administering a determinate impulse to an ensemble can only cause its information to fall. 3954 |
2-Jul-52 | 3939 | Unsolved problem. 3959, 3962 |
3943 | Examples showing how 'adaptation' means 'destroying information'. 4133, 4155, 4159, 4167 | |
3-Jul-52 | 3950 | Partition and lattice. |
3951 | Partitions in absolute ensembles. | |
3953 | Fault in book, to be corrected. Yes. 3966, 3986 | |
3953 | Partitions in absolute ensembles. 3997 | |
4-Jul-52 | 3959 | Input makes for uniformity. 4048, 4122 |
3960 | A quite different way of defining and handling the absolute system. 3962, 4019. Review, 4338 | |
3965 | States and metric give field. | |
3965 | Ultrastability does not need step-functions! | |
7-Jul-52 | 3968 | Ultrastability can act without a metric. 3986 |
8-Jul-52 | 3979 | How to get many resting states (argued without a metric). |
9-Jul-52 | 3984 | My concepts divided into the topological and the metrical. 4026 |
10-Jul-52 | 3985 | The concept of 'state' does not require number or metric. |
3990 | Ultrastability proved at last! Worked out example 3967 Obsolete! 4232 | |
14-Jul-52 | 3993 | 'Step-functions' topologically. 4000, 4005, 4602 |
15-Jul-52 | 3994 | Why do our brains take so much notice of a step-function? 4233 |
21-Jul-52 | 3995 | 'Absoluteness' is relative to an observer. 4031, 4043. |
3997 | Residue classes in behaviour. | |
27-Jul-52 | 3999 | A chemical dynamic system. |
27-Jul-52 | 4002 | A more rigorous definition of full, part, step, and null functions. Try it on 3900, 4604 |
24-Jul-52 | 4003 | Joining parts to form a whole. |
4004 | Change of direction. | |
4004 | Examples of a single artificial absolute system. 4486 if some states become indistinguishable. | |
1-Aug-52 | 4005 | Note on the subjective. |
3-Aug-52 | 4011 | Lewin's Topological Psychology. 4026 |
6-Aug-52 | 4012 | Absolute systems. Q.E.D. |
6-Aug-52 | 4012 | Panta rhei - Heraclitus [~everything flows] |
6-Aug-52 | 4015 | On memory and schizophrenia. |
6-Aug-52 | 4015 | For progressive adaptation the essential variables must be multiple. 4167 |
6-Aug-52 | 4015 | On infinitesimal disturbances. |
6-Aug-52 | 4017 | Examples of systems with part functions. |
6-Aug-52 | 4018 | Two independent 'complexities' in the 'complex system'. 4167, 4189 |
4019 | Importance of a system's history. 4041, 4048, 4302 | |
21-Aug-52 | 4021 | Interaction between adaptations. |
21-Aug-52 | 4021 | My solution includes all solutions. |
8-Aug-52 | 4022 | S.8/2 should be re-worded. |
10-Aug-52 | 4025 | 'Coarsening' an absolute system. 4041, 4475, 4919 |
12-Aug-52 | 4026 | Field as vector. |
12-Aug-52 | 4026 | Meaning of 'topological'. |
12-Aug-52 | 4029 | Quotations |
13-Aug-52 | 4030 | The absolute system does not imply a group. 4033 |
14-Aug-52 | 4031 | An absolute system is a selected projection of the world-lines. 4038, 4043, 4292 |
15-Aug-52 | 4032 | The homeostat's equations. |
15-Aug-52 | 4033 | Being a one-parameter group is not sufficient to ensure absoluteness. |
15-Aug-52 | 4034 | I formally reject the concept of 'group'. |
15-Aug-52 | 4035 | The 'group property' without groups. |
15-Aug-52 | 4037 | Abstract, and objective form of 'selection'. Review: 4137. 4099, 4229 |
4038 | Non-metrical definition of 'stability'. | |
4038 | Why not two, or more, representative points? 4121 | |
16-Aug-52 | 4041 | Every regular system can be made to yield an absolute system. 4042, 4302 |
4042 | A regular system is practically an absolute system. | |
18-Aug-52 | 4043 | Nature of absoluteness. 4292, 4306 |
18-Aug-52 | 4046 | The joining of machines can be represented without a metric. 4332, 4471 |
19-Aug-52 | 4047 | Continuity of transformation. |
19-Aug-52 | 4050 | 'Observing' a system means letting the regularity of the system's behaviour lessen the scatter in the ensemble of experimenters. 4122, 4296, Review 4348 |
4052 | If a system is very large and its lines of behaviour very long, the 'later' ends of the lines must differ from the 'earlier' in some 'Darwinian' way. (Note on 4055) 4099, Review 4141, 4201 | |
22-Aug-52 | 4053 | Essential variables. 4161 |
22-Aug-52 | 4054 | In exposition, use non-learning systems as examples of organisational facts. |
22-Aug-52 | 4054 | Arcs breed. ? 4151, 4065 |
30-Aug-52 | 4057 | The field of the self-locking system. 4065, 4155 |
4059 | The 'ordinary' and the 'statistical' machine differ only in the proportions allotted to the directly functioning part and the parameter-adjusting, servo-mechanistic part. 4061 | |
4060 | More examples of the stable and unstable. 4062, 4070, 4074 | |
4061 | Example of 'stability' miss-used. Further examples 4062, 4070 | |
4062 | Economic systems vary in their amounts of stabilising machinery. | |
1-Sep-52 | 4063 | The organism that 'knows' a line of behaviour is better if it knows the adjustment lines as well. Answered 4608 |
3-Sep-52 | 4066 | Musings on evolution and the cortex. Review: 4155, 4071 |
4069 | The basis of both the multistable and the evolving system is the self-locking system (and its superior, the self-reproducing). 4071, 4099, 4153, 4166, 4201, 4229 | |
4070 | Learning that have to adapt to a fixed (reflex) mechanism. | |
4070 | Meteorological dynamics. 4072 | |
6-Sep-52 | 4072 | Self-reproducing systems. 4086, 4099, 4154 |
4073 | Complex systems can also be regular. | |
4075 | "Design for a Brain" must use methods of proof that correspond to what I hold are the natural, physiological, methods. | |
7-Sep-52 | 4076 | Random transformations. |
4079 | The multistable system may have no trend if wrongly devised. 4080.0, 4175, 4201 | |
12-Sep-52 | 4080 | Multiple faults in a machine. 4613, 4195, 4201 |
4081 | A possible cause of psychosis. | |
4083 | Waismann's book. | |
12-Sep-52 | 4084 | Example for localisation. |
4085 | Absolute systems within absolute systems. (Continued 4113) | |
4087 | More on evolution. 4610, Review 4201, 4155, 4099 | |
13-Sep-52 | 4088 | In discussion, force every question to be converted to an acceptable form before answering. |
4090 | Judge the difficulty of "Design for a Brain" by the comprehension shown by the average worker in EEG. Adjust the difficulty so that almost all such workers show comprehension. | |
4094 | Entropy etc. | |
4096 | The demonstration of feedback requires three primary operations. | |
17-Sep-52 | 4097 | How many primary operations are required to establish the diagram of immediate effects? |
17-Sep-52 | 4098 | To study an absolute system of σ states, σ elementary operations are necessary, and they yield σ log σ of information. 4112 |
17-Sep-52 | 4098 | Compare 'adaptation' in the multistable system with 'adaptation' in evolution. (My aim is to show them as identical). 4086, 4071, 4064, 4056, 4036 Reviews: 4136, 4201 |
4101 | What is a 'thing' in my type of concepts? | |
4105 | A 'thing', therefore, can be said to exist in an absolute system when the observer's parametric control is insufficient for the exploration of all initial states, so that the states have to be tested in blocks. | |
4106 | A 'thing' corresponds to a constraint. 4233, 4439, 4388, 4440, 4943 | |
4106 | A 'thing' means redundancy. Example 4187 | |
4111 | We can now consider the 'isolation' that exists when a system is not surrounded by the absolute constancies previously postulated but by variables that, though not constant, are statistically constant. | |
21-Sep-52 | 4112 | (a) Adaptations in multistable system and in Darwinian system compared
(b) What is a 'thing'? (c) What is 'reproduction'? 4522 (d) A system is in a sense 'isolated' if the disturbances are statistically constant. Review 4137 |
21-Sep-52 | 4112 | Two points about dreams and the cortex. |
23-Sep-52 | 4113 | The difficulty of 'delay' is identical with the 'difficulty' of having too few variables. |
23-Sep-52 | 4117 | Absolute systems in absolute systems. 4119, 4145 |
23-Sep-52 | 4119 | Tests for absoluteness. |
4120 | Absolute systems within absolute systems. 4145 | |
24-Sep-52 | 4122 | The representative point may be divided into parts, as the whole system is thought of in parts. |
4123 | More on information. 4133 | |
4132 | On the necessity for step-functions. 4158, 4161, 4238 | |
29-Sep-52 | 4136 | Destruction of information. 4164, 4166. Review 4151, 4385 |
29-Sep-52 | 4136 | Monograph on Evolution. |
4137 | Part 1: Selection. | |
4141 | Part 2: The study of very large systems. | |
4151 | Part 3: The properties of Φ(q) | |
4155 | Evolutionary processes. 4172. Review 4201, 4790 Part 1: Selection. 4137. Part 2: The study of very large systems. 4141. Part 3: The properties of Φ(q) 4151 |
|
4156 | Runaway and information. 4303 | |
1-Oct-52 | 4157 | Exposition of 'Design' |
4160 | Adaptation of essential variables, (next page) 4163 | |
4162 | Adaptation without step-functions. | |
4165 | The adapting system - generalised, (next section). 4166, 4225 | |
4-Oct-52 | 4171 | (1) The homeostat is a self-regulator that uses information instead of power, but has the usual amplifier - with - negative - feedback. (2) The environment should be divided into (a) affected by the organism, (b) independent of the organism. (3) These give the fundamental control-flow relations. 4179, 4282, 4285 |
4177 | Darwinian adaptation, and the multistable systems. 4197, 4201 | |
4178 | Psychiatry of the information-block. | |
6-Oct-52 | 4181 | The self-locking system will also often be internally self-locking. 4229 |
4182 | For rapid and successful adaptation in the Multistable System, δ, α,η and ζ must, as channels, have large capacities. | |
10-Oct-52 | 4183 | Origin of depression. |
10-Oct-52 | 4183 | The regenerative abnormality as self-locking system. 4229 |
11-Oct-52 | 4185 | Genes and memory. 4206 |
4186 | The essence of intelligence is selection. 4285 | |
4187 | Chaos first becomes worth studying when a constancy appears. | |
13-Oct-52 | 4189 | Lashley on learning. |
16-Oct-52 | 4193 | More observations on discriminative feedback. (Foot of this page) 4201 4613 |
16-Oct-52 | 4193 | Sufficient to ensure high probability of'. |
16-Oct-52 | 4195 | Discriminative feedback. 4225, 4514, 4613, 4831 |
16-Oct-52 | 4196 | Discriminative feedback. 4216, 4201 |
17-Oct-52 | 4197 | Trial and error by model has advantages, if the system can achieve it. |
4201 | Various ideas on Darwinian and multistable evolution. | |
23-Oct-52 | 4207 | Review of the relation of Darwinian to multistable system. 4216, 4239 |
4210 | The conditioned reflex. 4424 | |
4215 | Assume that the number of essential variables is large and given, and is much the same for all species. 4225 | |
4215 | Feedback through the environment. | |
4222 | Discriminative selection in poultry. 4233, 4239 | |
4222 | The 'essential variable' of a watch that is to undergo trial for the Kew 'A' certificate. | |
4223 | Maths is not logical. 4539 | |
22-Nov-52 | 4224 | The necessity for selecting variables. |
23-Nov-52 | 4227 | The multistable system as merely one of many. |
23-Nov-52 | 4228 | Definition of system 'independent' of a parameter. |
4232 | Precise conditions under which a system is self-locking. 4242, 4275 | |
4232 | Better proof of ultrastability. | |
4233 | We take 'things' invariants, and null-functions as fundamental because we must. 4146.2, 4235.9, 4943 | |
4235 | With 'state' as fundamental, canonical equations exist and parts can be joined, by parameters. 4604 | |
4235 | With 'state' as fundamental, 'independence' can be defined. | |
28-Nov-52 | 4239 | The field of [DIAGRAM] |
29-Nov-52 | 4241 | Darwinian and multistable systems. 4425, 4655 |
1-Dec-52 | 4244 | How to get the time of adaptation to be reduced by the machine automatically. (Also) An ad hoc design is equivalent to a feedback loop with selection amplifier. 4246 |
2-Dec-52 | 4245 | The diagram is more general than it looks. |
2-Dec-52 | 4245 | Getting information from a system. |
4257 | On the time taken by a large system to get adapted. 4264, 4515, 4560 | |
3-Dec-52 | 4260 | Building an exceptionally un-intelligent machine. |
3-Dec-52 | 4261 | Building a machine to display its powers of self adjustment. |
4262 | Orders or levels of essential variables. | |
4263 | Levels in social organisations and in the multistable system. | |
7-Dec-52 | 4267 | Precise instructions for commercial organisation. 4269, 4273 |
7-Dec-52 | 4267 | Is the power of abstraction the same as the power of developing an hysterical blindness? |
8-Dec-52 | 4269 | Play is an investment of surplus adaptation. 4271 (13), 4425 |
4272 | Explicit instructions for commercial or social organisation. 4273 | |
14-Dec-52 | 4275 | Building a society for chess-playing. |
15-Dec-52 | 4276 | A better way of stating my 'limit' theorems, and 'trend' theorems. |
4278 | Power and I.Q. have many similar properties. 4285 | |
14-Dec-52 | 4280 | Appearance of a super-clever machine. |
14-Dec-52 | 4281 | 'Noise' when an Ultrastable System is built of Ultrastable Systems. |
18-Dec-52 | 4282 | By serial adaptation, time falls to its logarithm. |
21-Dec-52 | 4283 | The entropies of the variation-amplifier. 4285 |
4284 | Multiple, competing, essential variables lead to the same problem, whether occurring in one person or scattered among many. 4289 | |
22-Dec-52 | 4289 | A selection-amplifier, in the multiplying sense, is not wanted; but a selection-supplementer is. 4520 |
4290 | Therapeutic possibilities. | |
4291 | Converting [x~=Ax] to x'=A'x | |
4295 | What 'knowing' a system means. Contrast 4315. 4429, 4438. Better stated in transitions 4305 | |
24-Dec-52 | 4298 | Differences, at a finite time later, can replace variables. 4301, 5206 |
4300 | Shannon's theory in its relation to the theory of the absolute system. 4312, 4396. Review 4345 | |
27-Dec-52 | 4302 | Effectiveness of parameters with finite substitution. Applied 4414 |
28-Dec-52 | 4303 | Examples of states that include history. |
28-Dec-52 | 4303 | Knowledge must be tested by control. 4438 |
4305 | One-one-one relation between parameter and transition. 4396 | |
30-Dec-52 | 4307 | My theory must become more circular, showing how an ultrastable brain is bound to work via the absolute system, etc. 4814 |
4310 | Entropy with two outputs, and the transmission of information from system to system. 4312, 4429 | |
30-Dec-52 | 4311 | Scientific knowledge is knowledge of a transformation. 4344, 4454 |
4315 | 'Variety' in systems. | |
4316 | 'Variety' in systems. See page 4327 | |
14-Jan-53 | 4373 | Variety in state accumulates. |
14-Jan-53 | 4374 | Uniform activity in the parameters drives down variety in state. |
14-Jan-53 | 4375 | Long-term memories. |
14-Jan-53 | 4376 | On basins. |
20-Jan-53 | 4377 | 'Delay' need not be rejected as a basic concept. |
1-Feb-53 | 4380 | Note on Darwinism. |
1-Feb-53 | 4380 | 'Experiment' = 'competition'. 4384 |
4383 | There is a maximal speed at which evolution or adaptation can proceed. The best one can do is to get near the maximum. 4384 | |
9-Feb-53 | 4384 | The α-rhythm. |
12-Feb-53 | 4385 | Speed of adaptation can be achieved only by trials and comparisons. |
4387 | Regulation (destruction of information) requires extra information. Continuous form 4395, 4658 | |
17-Feb-53 | 4388 | Lack of variety and step-function are equivalent. 4439, 4440 |
18-Feb-53 | 4389 | Apparent inertia in adaptation. |
4392 | 'Transient' translated into non-metric terms. 4644 (vol.18) | |
19-Feb-53 | 4393 | Gödel's coding. Theorem 5086 |
19-Feb-53 | 4393 | Digital and analogue. |
26-Feb-53 | 4394 | Quotation showing gross ignorance of the principles of organisation, by one who should know better. |
4395 | Two functions combining to an invariant. 4658 | |
27-Feb-53 | 4401 | The absolute system as coder and decoder. Extended 4414, 4461 |
4410 | Limiting basin when determinate machine is affected occasionally by impulse-operate. 4524, 5512 | |
1-Mar-53 | 4411 | Proof of theorem |
1-Mar-53 | 4411 | When many related theorems are possible, pick on one and prove it quite rigorously; the exact details will then show the exact effect of each proposed variation. |
4412 | (An addendum) | |
4416 | Canonical equations of the decoder. | |
4418 | Magnification and dispersion from the point of view of information. 4422 | |
4418 | If information is to be conserved, linearity must be achieved everywhere. | |
23-Mar-53 | 4420 | Proof that messages that are heavily contaminated with noise are best ignored. |
4421 | Necessary conditions for a system to have resting states that differ only at a few variables. | |
1-Apr-53 | 4423 | Effect of magnification on behaviour. |
2-Apr-53 | 4424 | Invariants of a dynamic system with parameters. |
2-Apr-53 | 4424 | The Conditioned Reflex as a loss of power to transmit. 4430 |
4425 | Distinguish variety in design from variety during performance. Continued 4427 top, 4427, 4428, 4431 | |
6-Apr-53 | 4428 | A system can "know" by having the right values of variables or parameters. 4438 |
4429 | When a designer makes a machine of n states and a parameter-combinations, he puts in variety of a.n.log n This is its intrinsic content. 4463, 4704 | |
4430 | Information that can come from a machine. | |
4432 | Trial and error in reaction to shock. | |
4432 | Information in printed English. | |
4437 | Riguet on binary relations. 4470, 4498, 4566, 4581, 4604, 4632 | |
17-Apr-53 | 4439 | Prediction and control are just forms of regulation. |
17-Apr-53 | 4439 | Wave as constraint; travelling immobility. 4440, 4943 |
20-Apr-53 | 4441 | Way of behaving, constraint, thing, part-function. |
20-Apr-53 | 4443 | More on "constraint". 4553, 4564 |
21-Apr-53 | 4445 | Computing entropy. |
4446 | Shorthand has more disadvantages than advantages. List of symbols:- End of this volume and 5108 | |
24-Apr-53 | 4447 | |
24-Apr-53 | 4448 | One formulation covers "design" "input" and "noise". (Next section) 4449 |
27-Apr-53 | 4454 | Information in a machine. 4701, 4847 |
28-Apr-53 | 4462 | Outline of the theory of the Black Box. 4480 |
28-Apr-53 | 4465 | What "designing" a machine means abstractly. |
2-May-53 | 4469 | The variation of the essential variables must be supplemented. 4482, 4581 |
4470 | A single machine contains many "informations", most of which do not interact with the others. Example 4577 | |
2-May-53 | 4471 | Joining absolute systems without metric. Example 4473, 4498, 4733 |
2-May-53 | 4472 | Must every system drift to the condition of maximal internal separation? 4500, 4524 |
2-May-53 | 4472 | Cap or intersection as selective operator. |
2-May-53 | 4472 | Unsolved problem. Solved 5009 |
2-May-53 | 4474 | Anything that can have variety is really a set. |
4479 | The relation "observer A cannot distinguish x from y"; homomorphism. 4501, 6254 | |
2-May-53 | 4480 | Are there "levels" of design? 4595 |
3-May-53 | 4481 | The Black Box is a set. |
3-May-53 | 4481 | Randomisation as a way of passing a message that is no message. |
3-May-53 | 4482 | The whole cannot be at a resting state unless every part is are a resting state. 4508, 4581, Example 2916.7, Markov chain 4904 |
4483 | How the homeostat works. 4520, 4538, 4581, 4701 | |
4493 | Partial knowledge; equivalent relation between machines. 4729, 4777, 5001 | |
11-May-53 | 4494 | More constraints means fewer possibilities but more discoverable patterns, 4504 |
11-May-53 | 4494 | In set theory, remember that inequalities are likely to have cybernetic applications. 4503 |
13-May-53 | 4495 | Set theory and its use. |
13-May-53 | 4496 | 'Large' and 'small' machines. |
13-May-53 | 4497 | Logic and theory. |
19-May-53 | 4498 | Homomorphism in machines. |
4500 | Joining machines. | |
21-Jun-53 | 4504 | Observations on set theory. |
11-Jul-53 | 4509 | Principle of ultrastability stated more vigorously. Better still 4581 |
4510 | Ergodicity and loss of information. | |
13-Jul-53 | 4511 | Tactics for getting DAMS better aligned. |
17-Jul-53 | 4513 | Machines are related to the algebraic laws of internal composition, as well as those of external. |
4519 | Built-in structure in an adapting system implies that part of the solution has already been obtained. 4599, 4600 | |
18-Jul-53 | 4521 | Amount of selection and ultrastability. 4582.6, 4904 |
4523 | How chromosomes reproduce themselves. High survival power. | |
4535 | Habituation. 4559, 4596, 4609, 4762, 5512 | |
22-Jul-53 | 4536 | Formal proof that, if a set is stable, no state in it can lead ever to a state outside the set. |
23-Jul-53 | 4537 | Power for adaptation. (See next page) 4583 |
25-Jul-53 | 4539 | Adaptation needs a transducer between the prime (statistical) mover and the useful result. 4583 |
25-Jul-53 | 4539 | Markov processes in machines. |
28-Jul-53 | 4545 | Markoff process in machinery. 4671 |
28-Jul-53 | 4545 | The human brain may not be optimal for inclusion in computer. |
4547 | Trials within trials, or the admission of variation into sub-units of an ultrastable system. | |
4549 | Examples of how reducibility shortens time of search. 4552, 4563, 4650, 4948 | |
31-Jul-53 | 4552 | All problems can be reduced to a canonical form. 4560, 4585 |
1-Aug-53 | 4557 | The method of models, for quicker searching. Review 4560-4575 |
3-Aug-53 | 4558 | Isomorphism between machines. |
3-Aug-53 | 4559 | Distinguishability correspond to dependence. |
4-Aug-53 | 4560 | A Review on "Speed of Adaptation" with special reference to that of a Problem-Solving System. ... it is now possble to build a system, or machine, of more than human intelligence. |
4-Aug-53 | 4560 | Contents
§1 Introduction 4560 §2 The method of models 4562 §3 Constraints on the operands 4563 §4 Constraints on the transformation: (i) Reducibility (a) What is Reducibility? 4564 (b) The effect of Reducibility 4567 (ii) Continuity (a) What is Continuity?4568 (b) The effect of Continuity 4569 §5 Selection by components 4570 §6 The Maximal Speed 4574 |
4562 | §2 The method of models | |
4563 | §3 Constraints on the operands A and B | |
4564 | §4 Constraints on the transformation:
(i) Reducibility (a) What is reducibility? |
|
4567 | (b) The use of reducibility | |
4568 | (ii)Continuity
(a) What is continuity? |
|
4569 | (b) Value of continuity | |
4570 | §5 Selection by components | |
4574 | §6 The Maximal Speed of Adaptation | |
4575 | (1) A first estimate of how long a problem will take in the solving might be given
by the product of the possibilities in its components, assuming independence. (2) This is a bad estimator, being biassed. It is in fact an upper bound of the true value. (3) By the use of models the process of search can often be hastened. (4) Often the components are not independent, and only a portion of the product-space need be searched. Various factors (described) may have this effect. (5) Selection by components may be possible. It reduces the time to its logarithm. (6) There is a minimal time for the solution of a problem (or adaptation): it is the time that the fastest isomorphic system can get the answer out in binary notation. 4650, 4668 |
|
4577 | Poincaré on the study of functions. | |
7-Aug-53 | 4578 | Two messages in a channel need not interact. 4641 |
8-Aug-53 | 4579 | Emission of "cos2x + sin2x =1" randomly. |
4580 | Two agents may select the same element, yet differ widely in their degrees of selection. 4583, 4598 | |
8-Aug-53 | 4581 | An even more rigorous statement of ultrastablity. 4882 4467 4508 4520 |
9-Aug-53 | 4582 | Rigorous statement of ultrastablity. 4881, 4904, 5046 |
12-Aug-53 | 4584 | Relation of essential variables to selection-amplifier. 4586 |
12-Aug-53 | 4587 | What is 'problem solving'? |
16-Aug-53 | 4589 | Every real object is an element in an indefinitely large number of sets. Which sets are to be considered must first be defined. |
18-Aug-53 | 4593 | Neumann's theory of games translated into my theory of systems. 4650 |
19-Aug-53 | 4594 | Stability checked. |
21-Aug-53 | 4595 | Review of the book. [Design for a Brain] |
22-Aug-53 | 4596 | 'Equilibrium' refers to a state, 'stability' to the region around the state. |
25-Aug-53 | 4597 | Properties of metric-less system. 4623 |
26-Aug-53 | 4598 | The fullest description of a 'stimulus' is still inadequate to define its content of information. |
26-Aug-53 | 4599 | In comparing an ultrastable (mechanical) solver with Man we must take care that they start with comparable amounts of prior knowledge. |
28-Aug-53 | 4600 | Ways of getting effective discriminative feedback are to be found specially, for each type of system, not as a general problem. 4613, 4641, 5548 |
28-Aug-53 | 4602 | Control, and part-function, in terms of set theory. 4604 |
28-Aug-53 | 4603 | Incentives in the ultrastable system. |
28-Aug-53 | 4604 | Practically all my concepts are non-metrical. |
29-Aug-53 | 4605 | Having several basins has nothing to do with being divisible into parts. Noticed again 5502 |
31-Aug-53 | 4606 | Organisation of the German General Staff. 6534 |
4607 | Is the Darwinian system a specialised one? 4608, 4613 | |
31-Aug-53 | 4608 | How much of a field should be known? |
31-Aug-53 | 4609 | In Darwinian evolution; the part of essential variables is played by those parts whose disequilibrium leads to widespread disturbance around them. |
4612 | Self locking and self-reproducing systems in the terms of set theory. | |
31-Aug-53 | 4613 | Precise statement of the fact that instability is infectious. |
31-Aug-53 | 4613 | The general solution of the problem of the least discriminative feedback is - that there is no general solution. Every problem has its own optimum, and finding the optimum is a part of the problem. 4600, 5548 |
31-Aug-53 | 4613 | Am still totally unable to write Darwinian ideas in any rigorous way, in spite of many motes ever since 4051. |
1-Sep-53 | 4615 | What Darwin really did do. 4618 |
1-Sep-53 | 4616 | Darwin's actual theory. |
1-Sep-53 | 4617 | What does "endurance" mean? |
1-Sep-53 | 4619 | Darwin's method for the study of complex systems. 4655 |
1-Sep-53 | 4620 | Darwin's theory and that of the multistable system are related by intersecting in a set of theorems that contains both. |
1-Sep-53 | 4620 | How to develop the theory of "knowing". |
3-Sep-53 | 4622 | How a machine transforms a set of representative points in its field. |
4-Sep-53 | 4624 | "Stability"defined. A "machine" is a stable sub-set. 4630, 4632, 4643, 4656, 4795 |
4-Sep-53 | 4624 | Every set in a machine generates a stable set that contains it. 4630 |
4627 | Studying variety with the methods of the theory of sets. | |
4629 | Repetition of a well-defined stimulus simply creates a new, compound, operator, that has stable sets with new, interesting, properties. 4630, 4632 | |
4631 | Stable sets of a product application. 4762 | |
28-Sep-53 | 4633 | "Basin" defined algebraically. Better 4743 |
4634 | Strategy. 4640 | |
30-Sep-53 | 4640 | The costing accountant and the strategy of control. |
4641 | Mechanism for simultaneous adaptation. 4577, 5417 | |
30-Sep-53 | 4642 | "Maximising profits" as a "keeping within limits." |
4643 | Self-locking in society. | |
12-Oct-53 | 4647 | Theorems on transients. 4761 |
12-Oct-53 | 4647 | System in which x chases α. |
12-Oct-53 | 4648 | Of what use is neurophysiology to me? |
12-Oct-53 | 4648 | Drugs of addiction. |
19-Oct-53 | 4649 | If the environment offers constraint, the cortex can profit. |
4652 | Strategy of trial and error. 4797, 4822, 4844, 4947, 4941 | |
23-Oct-53 | 4655 | Box-diagrams are not precise. |
23-Oct-53 | 4655 | Evolution as habituation. |
3-Nov-53 | 4657 | Meaning of 'stability'. 4741, 4785, 4795 |
4659 | Only variation can force variation down - exact conditions necessary. 4662, 4674, 4750 | |
4661 | ||
4665 | Entropies in regulation. 4666, 4722, 4971 | |
5-Nov-53 | 4666 | Entropy and information. |
4668 | An organism cab control an environment of its own size (channel capacity), but not more. | |
5-Nov-53 | 4671 | An error-controlling regulator cannot reduce the incoming variation to less than a half. But see 4688 |
6-Nov-53 | 4673 | Markovian parameters to Markov chain. 4700 |
6-Nov-53 | 4673 | Meaning of "output". |
4679 | On regulation. 4709, 4795 | |
8-Nov-53 | 4682 | Regulation when several inputs disturb. |
10-Nov-53 | 4687 | Regulation in the homeostat's second order feedback. 4695, 4701, 4709 |
11-Nov-53 | 4690 | Error-controlled regulation is possible only by blocking conduction. |
4694 | In information, the point of view of the element is very different from that of the set. | |
16-Nov-53 | 4699 | Progression to an absorbing state in a Markov chain and progression along a line of behaviour in a stable, continuous system are two extremes of a continuous scale. 4842 |
17-Nov-53 | 4701 | Markov chains as component parts for building a machine. 4703, 4770 |
19-Nov-53 | 4703 | If a designer is only partly responsible for the determination of a machine, the fraction (implied by "partly") can be given meaning only if there is no loss of variety in the transduction. |
4704 | A determinate machine, with single-valued field, can be formed only by supplying variety of n log n bits. 4722 | |
21-Nov-53 | 4708 | Quality in design. 4725, 4733, 4788 |
23-Nov-53 | 4722 | Regulations at various levels reduced to standard and common form. 4737, 4906 |
24-Nov-53 | 4727 | The homeostat does not amplify. Contradicted 4792 |
4728 | ||
4730 | More |
|
24-Nov-53 | 4732 | A set of determinate machines do not give a Markov chain. |
27-Nov-53 | 4737 | Information going into a system to design two parts. 5006 |
2-Dec-53 | 4740 | The unreliability of introspective evidence. |
7-Dec-53 | 4749 | Riguet's statement of "relational mechanics." 4751 |
9-Dec-53 | 4750 | Regulation implies both activity of the regulator and inactivity of the essential variable. |
9-Dec-53 | 4757 | Coordinates and projections in relational form. |
4759 | Riguet's definition of "dependance". 4813, 4992 | |
12-Dec-53 | 4761 | Riguet's "trajectory" is practically my "transient". |
31-Dec-53 | 4765 | More on habituation. 4917 |
4773 | Stochastic machines. 4847, 4876, 4868, 4904, 5097 | |
4775 | Properties of tensor product. | |
7-Jan-54 | 4776 | Equilibrium of Markov chain. |
4779 | Quotient machines. 4937, 5001, 5165, 5148 | |
28-Jan-54 | 4781 | Observations on controlling a system that can learn. |
4782 | Set theory in machines can dispense with the idea of "information". 4795 | |
16-Feb-54 | 4787 | "Survival in spite of disturbance" in the terms of set theory. 4790, 4795 |
19-Feb-54 | 4788 | "Output to an input" is a relation of order, and may give a lattice. |
4789 | Complex taps can be easily built by mere conjunction of many simple. 4792 | |
19-Feb-54 | 4790 | I am able to approach the subject of the origin of intelligence, i.e. regulation, from two points of view, but do not seem to be able to relate them. |
4791 | Why regulation? | |
19-Feb-54 | 4792 | The homeostat does amplify. 4794> |
4793 | Designing a machine to build a machine. 4808 (top), 5070, 5072 | |
22-Feb-54 | 4794 | The limit of progressive regulation. |
4796 | Many concepts include that of "reduction". 4880, 4950, 4963 | |
26-Feb-54 | 4798 | Strategy of trial and error. 4844, 4949 |
2-Mar-54 | 4801 | Every machine on states M defies "machines" on states in Mn (n=1,2,...). Only in the latter is variety bound to fall. (Its "tensor powers") 4869 |
2-Mar-54 | 4801 | "Transformation". |
2-Mar-54 | 4809 | Gain in regulation when the sequence has repetition. 4831, 5002, 5070 |
5-Mar-54 | 4810 | Change of state and change of design. |
5-Mar-54 | 4810 | The "tracker" as regulator. |
5-Mar-54 | 4811 | Error controlled regulation. |
5-Mar-54 | 4812 | Levels in regulation. |
12-Mar-54 | 4813 | Learning is worth while only when the disturbance will be repeated. |
17-Mar-54 | 4814 | The diagram of immediate effects as a higher relation. |
4816 | The circularity of reasoning about reasoning. 4835, 4897 | |
29-Mar-54 | 4819 | Slowing down a machine, and sleep. |
29-Mar-54 | 4823 | Getting the disruptive feedback from the distant environment. 4844, 4927 |
30-Mar-54 | 4830 | Proving the existence of hidden variables. |
30-Mar-54 | 4832 | Discriminative feedback. 4834, 5345 |
31-Mar-54 | 4833 | On attention, and vigilance. |
2-Apr-54 | 4835 | The "problem" of discriminative feedback must be shown to exist in the real environment. |
4839 | Nature of relations and sets. 4897 | |
7-Apr-54 | 4841 | More on the Black Box. 4951 |
4843 | Hunt-and-stick is a more general form of stability. 4881, 5046 | |
14-Apr-54 | 4845 | Strategy of trial and distribution of probabilities. 4849 |
14-Apr-54 | 4845 | Two ways of regarding "design". |
15-Apr-54 | 4847 | Law of Requisite Variety stated with respect to a rectangular table. Stated purely in terms of set theory 4850 |
22-Apr-54 | 4849 | An input can be saturated i.e. has a capacity as a channel. |
4851 | The Law of Requisite Variety in full rigours of set theory. 5002, 5047 | |
23-Apr-54 | 4860 | Machines, with inputs and outputs, treated wholly by mappings. All this is, in substance, identical with Riguet's form. 4867. Simpler 4876, 4991 |
4861 | Feeding a machine with input and output back into itself. | |
4866 | Adaptation in evolution. | |
28-Apr-54 | 4867 | Quotations. |
28-Apr-54 | 4868 | "A machine" implies three sets and two mappings. 4871 Simpler 4876 Best 5097 |
4870 | A set of replicate machines. | |
28-Apr-54 | 4872 | The machine of intermittent observation. |
28-Apr-54 | 4873 | Initial states may appear simply as a source of variety. |
29-Apr-54 | 4874 | Re-entrant chain of mappings. 4876 |
29-Apr-54 | 4876 | What is a scientific "theory"? 4948 |
4877 | A "machine" implies two sets and a mapping; coupling requires an extra mapping. 4932, 4952, Formal statement 5097 | |
27-May-54 | 4880 | The amount of design in "keep moving". |
4881 | There are two distinct reasons why a machine may be used in regulation. 5046 | |
28-Apr-54 | 4883 | "Independence" is a special case of "incomplete transmission of variety". |
4894 | Why the uniselectors have many values. 5046 | |
3-Jun-54 | 4895 | Specifying the second-order feedback rigorously. |
4897 | Church's theorem. | |
8-Jun-54 | 4899 | Logic in the multistable system. 5305, 5313 |
8-Jun-54 | 4901 | Speed is merely one of many demands that can made to qualify simple adaptation. 4964 |
8-Jun-54 | 4904 | On identifying an optimum in a set. |
10-Jun-54 | 4905 | Equilibrium in coupled Markov systems. |
4913 | All sorts of continuous and discontinuous systems put together to make all sorts of ultrastable systems. | |
12-Jun-54 | 4915 | Bellman on 'stability'. |
14-Jun-54 | 4918 | Statistical laws in the Markov chain. 4919, 4946 |
23-Jun-54 | 4927 | Relation of the physicist's "entropy" to my work. |
4928 | Supplementary information and its mode of use. | |
5-Jul-54 | 4931 | Evolution and psychology must study the basic question "what will in fact happen?" 5535 |
4934 | Isomorphism and equiformality. 4990, 5000 | |
4936 | The theoretical structure of the theory of machines, according to Bourbaki. 4970, 5904, 5907 | |
6-Jul-54 | 4938 | Homomorphism returns. |
28-Jul-54 | 4941 | Closed sets of states in a black box. 4951, 4968, 4989 |
30-Jul-54 | 4942 | Trials are good, for they bring information. 4945, 4948, 4965, 4963 |
4944 | A "thing" is a way of behaving. | |
4-Aug-54 | 4945 | Proof of 4871 |
4-Aug-54 | 4946 | Discriminative feedback. 4963 |
4-Aug-54 | 4946 | Information repair. |
5-Aug-54 | 4947 | Letters as Markov chain. |
17-Aug-54 | 4950 | The strategy of adaptation. 4962, 4964, 4980 |
17-Aug-54 | 4951 | The Black Box is built. [see photos: Description | Black Box | Details] |
17-Aug-54 | 4952 | On the accessibility of states. 4953, 4968 |
17-Aug-54 | 4953 | The "partly observable machine with input." 4956 |
17-Aug-54 | 4956 | What "examining a machine with input" means. 5055 |
22-Aug-54 | 4961 | When a system is partly unobservable, the method of trying to restore absoluteness by taking earlier values into account is fundamentally second-rate; it will succeed only when the case is peculiarly favourable. 4979 |
22-Aug-54 | 4963 | All necessary improvements to the basic ultrastable system can be had by the addition of further orders of feedback. |
23-Aug-54 | 4964 | More on the chess-playing team. |
4965 | Efficiency of solving is adaptation at a higher level than solving. | |
4967 | Scales of measurement. | |
4970 | Science is interested chiefly in the case where the parameters and states are so related that every state is accessible at will. 4989 | |
30-Aug-54 | 4971 | "State of equilibrium" in the hierarchy or sets. |
30-Aug-54 | 4971 | Orthogonality of actions in regulation. |
17-Sep-54 | 4972 | We live by the incorporation of pieces that are already keepers-out of noise. |
4973 | Living organisms surround themselves with invariants. | |
4973 | Example of an adequate channel. Pantagruel, l.iii,ch.xxix | |
22-Sep-54 | 4978 | With a random transformation the variety tends to fall to two thirds at each step. Qualified 5158 |
27-Sep-54 | 4980 | "Time" can be treated as a disturber of a machine, like an input. |
27-Sep-54 | 4981 | Research and the strategy of adaptation. |
26-Sep-54 | 4982 | "Integrating" and transformation. |
26-Sep-54 | 4983 | Nature of "invariance." |
26-Sep-54 | 4984 | Notes on "closure" of a transformation. 4989 |
26-Sep-54 | 4984 | Getting from the discrete to the continuous. |
4987 | Whether properties "emerge" or not depends on our knowledge of the parts. | |
4987 | Why information? | |
27-Sep-54 | 4988 | "How to dichotomise" takes time to be learned. |
30-Sep-54 | 4991 | However many states are available, the experimenter confines himself to some set satisfying certain conditions. |
5-Oct-54 | 4994 | Algebraic form of "immediate effect". |
7-Oct-54 | 4995 | How to deduce the connexions from input to variable. 5055 |
4996 | "Connexion" depends on the operations brought to its study. | |
22-Oct-54 | 4999 | An exact electromechanical analogy. |
5000 | Isomorphism. | |
27-Oct-54 | 5001 | Homomorphism. |
28-Oct-54 | 5002 | A problem. |
2-Nov-54 | 5004 | What is a machine? 5056 |
5005 | Game that is wholly arbitrary. 5024 | |
5010 | Design of a machine part by part. 5474, 5072 | |
26-Nov-54 | 5011 | Example of triunique relation. |
2-Dec-54 | 5012 | Behaviour when the feedback can carry only one bit. |
5021 | The relations between regulators are complex and hardly worth developing. | |
10-Dec-54 | 5023 | Problems that are not wholly new. 5066 |
10-Dec-54 | 5023 | A numerical illustration of continuity as a constant. 4569 5005 4597 |
16-Dec-54 | 5025 | Example of the effect of continuity as a constraint. Caution: See 5054. 5636 |
5026 | Effects of channel capacity in joining two systems, only one of which is observed. | |
5038 | Flow of information during trials. | |
22-Dec-54 | 5042 | The Turing machine. |
5045 | A machine that makes itself. 5088 | |
5047 | McCallum and Smith also use the method of veto. 5583 | |
23-Dec-54 | 5048 | Requisite variety stated algebraically. 5075 |
24-Dec-54 | 5050 | The field, when memory is used, is not isomorphic with that found when all is observed. |
5054 | Studying a system via one variable. | |
11-Jan-55 | 5055 | (Comment on "continuity") |
11-Jan-55 | 5056 | Studying a system... |
11-Jan-55 | 5057 | "Machine" as constraint in a sequence. But see 5074 |
11-Jan-55 | 5061 | Converting observed behaviour to specification of machine. 5063, 5081, 6071 |
11-Jan-55 | 5061 | Beware! The "design" of a machine costs simply what is necessary to get it selected from what is available. There is no unique quantity "in" a machine. 5006 |
12-Jan-55 | 5062 | The quatity of design in measured by the size of the set that is drawn from. 5070, 5071, 5072 |
12-Jan-55 | 5064 | Algebra can operate directly with observed behaviour. |
14-Jan-55 | 5065 | Mnemonic for "everywhere defined" and "single valued". |
14-Jan-55 | 5065 | Metron and logon. |
5066 | What is problem solving? I say it is finding an element in a set. | |
5068 | Problem solving. | |
15-Jan-55 | 5069 | Another example of a self-locking system, this one harmful. |
15-Jan-55 | 5071 | Briefing a deputy calls for the same capacity as doing the job oneself. 5073 |
15-Jan-55 | 5071 | Amount of design required for a machine to do a job. |
15-Jan-55 | 5073 | More on "the amount of design in a machine". |
16-Jan-55 | 5074 | Why build a regulator? |
16-Jan-55 | 5075 | A machine embodies a transformation and, in addition, may act repetitively. |
16-Jan-55 | 5075 | Two problems. |
18-Jan-55 | 5076 | Theory of the homeostat. |
15-Feb-55 | 5077 | Demonstration of selection-amplifier. |
18-Jan-55 | 5080 | Systems that interact finitely with their observer. |
18-Jan-55 | 5082 | The structure of a machine, derived from a protocol. |
18-Feb-55 | 5084 | Structure of machine in a protocol. 5170, 5192, 6071 |
21-Feb-55 | 5085 | The problem of "simplifying" a machine. |
8-Mar-55 | 5088 | Godel's theorem as process. |
17-Mar-55 | 5089 | More on the self-reproducing system. 5261 |
1-May-55 | 5091 | A strategy must be related to the actual constraints of a system. |
5093 | Reducibility and channel capacity are independent. 5532 | |
17-May-55 | 5094 | Finding a maximising formula. |
18-May-55 | 5099 | Formally stated method of coupling by using the tensor product of Riguet. |
5104 | Tensor method of coupling systems. | |
5104 | Tensor method of coupling systems. | |
5108 | List of shorthand symbols that may be found between pages 4416 and 4446, and in the Index. | |
1-Jul-55 | 5109 | Review of Pringle. |
5111 | The problem of the glass of milk. | |
2-Aug-55 | 5112 | What is meant by "He does not know......." |
1-Sep-55 | 5113 | With systems in general, do not look for the law; each must be studied and taken as it is found. Over a set of systems a constraint may be found. 5114.7. |
2-Sep-55 | 5114 | Bridgman on operations. |
5116 | There is no "law" to be found in systems much removed from the atomic level. 5142 | |
7-Sep-55 | 5117 | On causality. (Continued over) |
9-Sep-55 | 5129 | Concepts of cause, why, because etc related to Black Box theory. |
12-Sep-55 | 5131 | The simplifications obtained by cutting channels lie on a lattice. 5135 |
5134 | Why the organised and inter-connected can usually defeat the unorganised and individualistic. | |
13-Sep-55 | 5136 | Quantity of organisation. |
17-Sep-55 | 5144 | Application of system theory to History. |
21-Sep-55 | 5146 | How can a machine express a binary relation? 5181 |
5147 | Law of Experience algebraically. 5155, 5209.7 | |
5152 | Simplification by running together, or deleting, the elements of time. 5165, 5245 | |
5-Oct-55 | 5153 | "Loss of control" in set theory. 5155 |
5-Oct-55 | 5154 | The conditioned reflex, and shedding of scatter by going to an equilibrium. 5249.1, 5277.8 |
5159 | Law of Experience, given rigorously. 5179 | |
12-Oct-55 | 5160 | Kershner and Wilcox' book. |
17-Oct-55 | 5164 | Variety in mathematical forms. (Continued 5167.6) |
18-Oct-55 | 5166 | Markovian machines simplify on to a lattice. |
18-Oct-55 | 5167 | Dichotomy versus trichotomy. |
18-Oct-55 | 5169 | Mathematical expressions have inputs and outputs. |
18-Oct-55 | 5169 | Black Box looks at itself and others. |
20-Oct-55 | 5174 | Algebraic form of "immediate effect". 6070 |
5177 | The use and limitations of the integral equation. 5192, 5210, 6036 | |
21-Oct-55 | 5178 | Must a person's private "map" be observable to all? |
24-Oct-55 | 5180 | Memory must fail if new information is forced in. 5205 |
5184 | Machine with input and binary relation. | |
5186 | "A can predict the behaviour of B" is equivalent to "A is isomorphic with B". 5193 | |
27-Oct-55 | 5188 | Quotations from Mach. |
30-Oct-55 | 5189 | The concept of "constraint" includes correspondence, mapping, relation, as special cases. |
31-Oct-55 | 5190 | Psychological and anatomical patterns will usually be different. Cf. Introduction to Cybernetics S.6/11 |
31-Oct-55 | 5191 | Two meanings of "input". |
5195 | Constraints in protocols. 5978 | |
4-Nov-55 | 5209 | Use of observations at times earlier than "immediately preceding." Qualified 5210.3 5228, 5236 |
5210 | Definition, and the law of experience. 5254 | |
9-Nov-55 | 5213 | In the absolute system, the use of earlier states may be inefficient. 5869 |
14-Nov-55 | 5217 | Thoughts provoked by Savage. |
14-Nov-55 | 5218 | The mapping of the homomorphic machine. |
5220 | The structure of the regulator. (Note that the inverse, [w-1], has appeared at last!) | |
14-Nov-55 | 5223 | Must a constraint go on holiday in the future? 5273 |
15-Nov-55 | 5224 | Example of message that depends on the set it came from. 6275 |
5227 | Ultrastability in Design and in Introduction reconciled. | |
21-Nov-55 | 5229 | Real existence of "variety". |
22-Nov-55 | 5230 | Metastability. |
5234 | Concept of the "distance" between two input states, or two designs. 5506, 6282 | |
23-Nov-55 | 5235 | Distance of movement. |
5-Dec-55 | 5240 | Why the scientist should relate the event to what is adjacant rather than distant. |
5241 | "Complexity" is a relation between units and construct. | |
19-Dec-55 | 5243 | Law of Requisite Variety as law for suppression of noise. |
2-Jan-56 | 5244 | A minute crack at the problem of consciousness. 5275 |
5-Feb-56 | 5245 | The end of the hunt? |
5247 | The machine, when observed only so far as the states of equilibrium it goes to. 5556 | |
6-Feb-56 | 5248 | What is a "variable"? |
6-Feb-56 | 5249 | Mathematical proof "in detail" means going through a sequence of states of equilibrium. |
6-Feb-56 | 5250 | Is there any way by which a person can communicate an infinite amount of information? |
14-Feb-56 | 5252 | "Consistency" in mathematics. |
5253 | Personal note. | |
5254 | What is a "logical definition"? | |
24-Feb-56 | 5256 | The structures of space as habituation. 5289, 5313 |
5260 | New machine to demonstrate statistical mechanisms. 5317, 5408, 5526 | |
24-Feb-56 | 5261 | On "imitation". |
5262 | More "self-reproducing" systems. 5797 | |
5263 | Pain educates mostly in childhood. | |
2-Mar-56 | 5265 | A contribution to the theory of the distribution of basin size. |
6-Mar-56 | 5267 | Probability of getting a single basin. 5308 |
9-Mar-56 | 5270 | Schizophrenia and noisiness. |
5272 | Raiffa et al. describe maths as isomorphic with real systems. 5298, 6260 | |
5-Apr-56 | 5275 | "Will", and acting now so that certain things shall be. 6321 |
5276 | On consciousness. | |
14-Apr-56 | 5277 | What good is "Design..." |
29-Apr-56 | 5278 | Movement between states of equilibrium. |
29-Apr-56 | 5278 | "Yes-no" is a language capable of explaining, or getting, all things, however complex. |
29-Apr-56 | 5279 | Program. |
1-May-56 | 5280 | Selection cannot proceed quickly, by dichotomising, in a class that is undefined. |
16-May-56 | 5281 | Example of a case in which information about the initial state gets lost. |
17-May-56 | 5282 | Science forswears direct knowledge in favor of the indirect. |
21-May-56 | 5283 | "Statistical machine" has two widely different meanings. |
22-May-56 | 5286 | Fast adaptation can be a manifestation of habituation. 5287.7, 5288, 5342 |
23-May-56 | 5287 | How to sample equilibrium states. |
31-May-56 | 5289 | The fringe-variables of a system (in this world) are an unbounded set. 5292, 5330 |
5291 | Learning structure by habituation to a constraint. Appalling! Habituation is not to a constraint - the ideas have no relation. 5294.4, 5313.3 | |
5292 | How to join motor (and sensory) nerves to a network of part-mechanisms. Now read 3420 and see how much I have advanced in five years! | |
7-Jun-56 | 5294 | Adaptation always consists of one level working with a lower level as units. |
5295 | In a statistical system, habituation must be used first, in order to provide the permanent entities among which alone trials are worth conducting. | |
5296 | Why random play should come before serious learning. | |
5298 | Finding a way of getting a matrix reducible. | |
5299 | What is a theory? Cf. Reprint 144 | |
25-Jun-56 | 5301 | Abstract machinery. |
5303 | How to make a brain. | |
29-Jun-56 | 5304 | The multi-stable system must have low interaction on the average. 5312 |
29-Jun-56 | 5304 | On the pains of learning. |
6-Aug-56 | 5307 | Structure is a form of constraint. 5314, 5496 |
6-Aug-56 | 5307 | To evoke a property, the designer vetoes its negation. 5316, 5331.5 |
21-Aug-56 | 5313 | Cross connexions, immediate effects, random transformations, and memory. |
24-Aug-56 | 5314 | If structure is present in the (set of) inputs, it will turn up in the (set of) states induced by the law of Experience. 5437, 5322 |
24-Aug-56 | 5314 | A reason why a chess-player will automatically tend to learn quick ways of winning. |
14-Sep-56 | 5316 | Fixing the step-mechanisms on the occurrence of 'success' adds little to the resources of an ultrstable system. 5331.5 |
5319 | How to chop up a field. 5408, 5524 | |
20-Sep-56 | 5323 | How does the child get "stucture" from the world around it? It can't keep it out! |
24-Sep-56 | 5324 | The "structure" developed by the child (as a result of structure in the world) need not copy the world's structure. |
24-Sep-56 | 5324 | I need not worry further about reversibility. |
24-Sep-56 | 5327 | Curie's principle is merely a special case of my decay of variety. |
25-Sep-56 | 5329 | "Looking one move ahead does not require special programming. |
25-Sep-56 | 5331 | On the size (duration) of a significant step. 5288 |
5332 | If punishments only are used, zero punishment is equivalent to reward. | |
5333 | Selection and elimination. | |
28-Sep-56 | 5337 | There is no general rule for characterising the more efficient forms of corrective feedback. 5369.2, 5371, 5417, 5539 |
1-Oct-56 | 5339 | Effect of computing a transformation sequentially. |
2-Oct-56 | 5340 | Train by situations so matched to the system's present ability that feedbacks of "right" or "wrong" are equally likely. |
5341 | There is no general machine that can be specialised, only a class of individual machines. It is the class that can be broad or narrow. 5507 | |
5343 | The ultrastable system has an intrinsic bias towards efficiency and quickness in learning. | |
5344 | Basic methods with complex systems. | |
5355 | What can be deduced from the accumulation of adaptations. 5360 Simpler: 5732 | |
5356 | What is necessary for the accumulation of adaptations. 5410, 5540, 5592, 5601, 5617, 5632, 5746 | |
13-Oct-56 | 5358 | Dispersion demands redundancy. 5372, 5379 |
5360 | A system that attempts to correct multiple arcs will go to an equilibrium with a certain fraction of its arcs correct. If momentarily better than that fraction, it will drift back to it. 5410, 5415 | |
18-Oct-56 | 5366 | Relays can do everything I want, if suitably coupled. |
18-Oct-56 | 5366 | Inputs and outputs of a relay. |
5368 | A system of variables each of which does not depend on its past can depend on the system's parts if it contains internal feedback. 5397.7 Example 5412 | |
5370 | Discriminative feedback's optimal spread depends on the spread of constraints in the environment. | |
26-Oct-56 | 5371 | Feedback in a dispersive system should be first wide-spread and then progressingly narrower. 5413 |
17-Nov-56 | 5374 | How fast information decays when passed through a number of variables at random. 5381 |
5375 | If a system is affected, with feedback by another, each can be regarded as a transducer with separated input and output (= conceptual uncoupling). 5428 | |
5378 | Environments that have to be adapted to fall into two very different classes: those that do, and those that do not, contain a teacher. 5382.6 | |
5380 | Keeping things apart by giving them room to spread in is too wasteful. r things would require about r2 spaces. | |
21-Nov-56 | 5382 | Probability of district balls getting into same cells. 5830 |
22-Nov-56 | 5383 | Abstract form of a "teacher". 5430 |
1-Dec-56 | 5389 | Time of adaptation can be cut down if more space is available. The distinct reactions should be sent to distinct places, any one reaction should not change its place during its training. 5410, 5415 |
1-Dec-56 | 5391 | "Plastic" behaviour. |
1-Dec-56 | 5391 | "Having many small basins" does not give any information about parts or couplings. |
5394 | Relation between amount of coupling and length of trajectory. 5399, 5411. Summary 5524 | |
5397 | Layout necessary for a plastic transducer, of brief trajectory. 5421, 5476, 5522, 5631 | |
5398 | Multiple equilibria, in the systems in a chain, give a transducer with memory. | |
5401 | Another approach again suggests that trajectories get very long if system gets large. 5407.5, 5479 Summary 5524 | |
4-Dec-56 | 5407 | Equilibria in part, in whole, and coupling. Rich coupling can create equilibria (and destroy them) 5447, 5983. Summary 5524 |
5409 | An indefinitely large system with half its states equilibrial, and no trajectory longer than one step. 5471.6, Opposite 5412, 5524 | |
6-Dec-56 | 5411 | A system that accumulates adaptations with appreciable success must use discrimination in its distribution of corrective feedback. 5415, 5421, 5440, 5610 |
5412 | Some systems with long cycles. No equilibrium 5455 | |
7-Dec-56 | 5414 | If active arcs have a non-transient trace, feedback can correct that which caused the bad reaction. 5629 |
5418 | If a system accumulates adaptations, it must have some way of getting the disruptive feedback fairly accurately to the appropriate step-mechanisms. 5440, 5606, 5655 | |
5421 | Behaviour may be plastic in two senses: showing an effect or showing a copy. 5437 | |
10-Dec-56 | 5422 | The system that is both multiple and plastic. 5522, 5545, 5535, 5631 |
11-Dec-56 | 5423 | Go for the quality of "survival" - all the rest shall be added unto you. |
5425 | Arcs and genes. 5522 (Reprints 130, 131) | |
19-Dec-56 | 5426 | Remember that an input may work by releasing, to the output, some sub-system within: - the jukebox. |
5430 | A trajectory may be reducible (into parts that are unconditionally good or bad). 5462, 5532, 5537, 5573, 5675 | |
5436 | Reducibility in a set of trajectories, 5441, 5528, 5537, 5626 | |
27-Dec-56 | 5438 | "Gaining structure" as "experience to a set of trajectories." 5552 |
5439 | Demonstrate the state of a system by giving a stimulus to a dominated system and see its trajectory. 5552 | |
28-Dec-56 | 5440 | Farley demonstrates a statistical machine that adapts. |
5444 | The transformation on unanalysed states is completely general provided that... 5456, 5474, 5466 | |
5445 | Constraints on parts and couplings show in the transformation on states. 5456, 5460 5466, 5474, 5524 | |
14-Jan-57 | 5446 | Anti-habituation may occur. 5490 |
14-Jan-57 | 5450 | If all parts have a constant probability that a given state, for various conditions, is equilibrial*, the whole's probability that its (whole) state is equilibrial depends on the coupling. 5461 * And one arbitrary, coupling is used. |
5452 | If all the parts have probability π of being in equilibrium, the whole's probability may be as high as π. (For this to happen, the coupling must be highly selected, for each part must, as it were, both give and take equilibrium without loss) 6019 | |
5455 | If parts have most of their states equilibrial, and are many, the whole may [for a suitably selected coupling] have remarkably few equilibrial states; maybe none at all if π ≤ 1-(1/n). 5670, 5484, 5489. Summary 5524 | |
5458 | Meaning of "coupling at random", so as to get a sample space. 5474, 5481.7, 5500. Summary 5524 | |
5460 | ||
5464 | Equilibria must be specially fostered; in the general random system they are vanishingly few. 5476, 5482, 5503. Summary 5524 | |
15-Jan-57 | 5465 | A game for the machine. |
5471 | What sort of parts, how coupled, give the whole in which all transitions occur in all combinations? 5474, 5489, 5662, 5982. Summary 5524 | |
5472 | A system as large as you please, with no trajectory exceeding three steps. | |
5473 | Mean length of trajectory when system has high probability of finding the next state equilibrial. 5479, 5504 | |
15-Jan-57 | 5475 | How the building of any whole from parts can be given complete generality: let each part's input range over all other part's states; and let the cells of the table be filled arbitrarily and independently. 5482, 5507, 5662 |
5478 | That a whole should have many states of equilibrium, given that designs of parts are not to be matched to parts, it is necessary and sufficient that each part have many states of equilirium. Summary 5524, 5489 | |
18-Jan-57 | 5479 | Making a whole of parts each with a high probability of equilibrium is sufficient to ensure short average length of trajectory (but not necessary). Example 5408 |
18-Jan-57 | 5480 | The world that is is just those properties that are not relative to the observer. |
5481 | Page 5407 clarified. | |
21-Jan-57 | 5485 | If the parts have probability of equilibrium πi, and if the parts have all combinations of canonical representation, and if all cells in the same representation are filled independently, then the probability of a state of the whole being equilibrial is Πiπi. If joined so that all information is brought to each part, the probabilities are independent. 5505 |
5486 | If the parts have probability of πi of being in equilibrium, and if the parts vary fully in their canonical representation but the coupling are restricted, then the probabilities of two or more states being in equilibrium (in the whole) are no longer independent. Summary 5524 | |
5489 | " |
|
5491 | Habituation. | |
5493 | Synthetic habituation.(Continued 5494.6) | |
5494 | Repeated samples with some sticking. | |
5495 | Synthetic display of habituation and its "inhibition". | |
28-Jan-57 | 5496 | The use of a transformation repetitively in time is a constraint, so structure becomes apparent. |
5498 | "Confluent" defined (as noun). 5512 | |
1-Feb-57 | 5499 | The theory of the determinate machine includes the practical aspects of the theory of the Markovian machine. |
1-Feb-57 | 5502 | Sample space of a whole made from parts by coupling, they having sample spaces of their own. |
1-Feb-57 | 5503 | One system may have many confluants, and many separated systems may have a single confluent |
2-Feb-57 | 5506 | The whole built from random parts, by random coupling, when each part has probability πi that its state is equilibrial, does not go (if not in equilibrium) equiprobably to all states but favours those "near" itself. Summary 5524 |
5507 | Refusal to give a machine (or state, or input-valve, or transformation, etc) a particular value corresponds to talking about a set of machines (or states, or input-values, or transformations, etc). The set has no associated probabilities, but can use the concept of "independence". 5666.7 | |
4-Feb-57 | 5510 | The system that is contained only to have high equilibrium in its parts. |
5-Feb-57 | 5511 | High probability of equilibrium in the parts cuts the whole up into (temporarily) isolated sub-systems. 5522 |
4-Feb-57 | 5522 | Habituation and its relation to equilibrium. |
5523 | The system that habituates must be a flat sheet. (But see 5632) 5545, 5631 | |
5523 | of relations between equilibria in part and equilibria in whole. 5259 (See article for refs) 5317, 5510 | |
12-Feb-57 | 5527 | Relations between equilibria in parts and equilibria in whole collected from the last 130 pages. Review 5983 5667, 6019, 6025, 5436 |
5530 | Reducing major Good to minor goods. 5537, 5532, 5578, 5626 | |
18-Feb-57 | 5533 | Basic meanings of organisation, reducibility, conditionality. 5537, 5675, 5993 |
20-Feb-57 | 5534 | Example of isomorphism in differential equation form. |
5535 | The time-factor insists that genetic adaptations and cerebral-learned adaptations shall be done mostly in the piece-meal way. 5601, 5631 | |
5536 | Where I am now. 5558 | |
22-Feb-57 | 5538 | From essential variables to Grand Outcome, via trials. 5573, 5642 |
23-Feb-57 | 5540 | Feedback cannot be discriminating unless an adequate channel brings the necessary information; (but any particular channel may perhaps be supplementable) 5628.7, 5547, 5584 |
5544 | Systems with super-fast sub-components. | |
5547 | "Thinking things over" in a multistable system. Discriminative feedback requires mere opportunism. 5549, 5584, 5601 | |
27-Feb-57 | 5549 | No general principle can be sufficient guide when selection must be done; some actual channel is also necessary. 5585 |
2-Mar-57 | 5550 | In all cases so far, all arcs are assumed to have some sign that they are, or have recently been, active, and the discriminative feedback hits only those with the sign. 5557, 5584, 5601, 5609, 5628 |
5551 | Unsolved problem. (Strachey's solution, 5559) | |
5555 | The "diffusion" of structure is a manifestation of a whole which is really a chain going to equilibrium. | |
5556 | More on the spread of "structure". | |
6-Mar-57 | 5557 | Others are building machines with discriminative feedback. 5584 |
11-Mar-57 | 5558 | Personal note. |
20-Mar-57 | 5559 | The optimal duration of memory. |
20-Mar-57 | 5559 | A minimal quality of memory is not definable. |
25-Mar-57 | 5568 | Identification by random criteria is (in the defined circumstances) practically as good as accurate dichotomy. |
25-Mar-57 | 5569 | Major strategies are determined at the genetic level, minor at the cerebral. |
28-Mar-57 | 5570 | How this works yields application to psychiatry. 5651 |
5572 | The distinction between aggression and non-aggression corresponds, respectively, to having or not having a regulator. 5694 | |
2-Apr-57 | 5576 | The "essential variables" to a machine with input are those other parameters to it whose change would alter its canonical representation. |
5578 | "System" and "machine with input" are very different. | |
2-May-57 | 5579 | Essential variables in Multistable System 5601, 5625, 5642 |
2-May-57 | 5581 | General formulation of "the environment" for an artificial brain. 5522 |
6-May-57 | 5585 | Solution in principle of the problem of discriminative feedback. 5590, 5594, 5601, 5608, 5631 |
6-May-57 | 5588 | Any question about how something can be achieved is answered: a regulator is necessary; lacking it the achievement is impossible. 5601 |
13-May-57 | 5590 | Serial or sequential adaptation is equivalent, in a sense, to semi-iterated simultaneous adaptation. 5593 |
5591 | General phenomena should be explained by proportionately general mechanisms. | |
13-May-57 | 5595 | What is necessary for the accumulation of adaptations. 5601, 5608 |
18-May-57 | 5600 | From iterated systems to the multistable. 5612 |
20-May-57 | 5605 | What is necessary for fast adaptation by reducibility. Much modified 5608 5736 |
5607 | Random dispersion will not achieve a useful degree of reducibility. 5619 | |
24-May-57 | 5613 | When the set of disturbances is a product set of minor disturbances, each of which has its appropriate reaction unconditionally, accumulation is adaptation is readily obtained. Often, the set of disturbances must be defined explicitly. |
5614 | There are two quite different "lengths of trajectory." Better "transient" | |
5618 | Conservation (or accumulation) of adaptations as deference against imperfect isolation, when the "leakage" occurs in slow discrete steps. 5620, 5746 | |
27-May-57 | 5621 | The multistable system re-viewed. 5733, 5735, 5746 |
27-May-57 | 5625 | How big should an arc be? 5746 |
27-May-57 | 5626 | Why have arcs that are dynamic systems? |
5628 | Reducibility of the essential variables in set theory. 5631, 5642, 5652, 5675 | |
28-May-57 | 5629 | How good a synthetic brain can I make? |
5631 | The principles of search are not altered if what we search for is a decision (about what to search for - at a lower level) | |
30-May-57 | 5634 | One unit for adaptation (in Multistable System) may comprise many portions (arcs) in the cortex. 5653, 5746 |
30-May-57 | 5635 | Optimal duration of trial; optimal time back to make disruptive feedback work. 5642 |
31-May-57 | 5636 | Continuity as a restraint. |
5641 | The natural duration of a trial is the time of transmission of information from step-mechanism round then organism and environment back to step mechanism What is implied by "trail." | |
5643 | Distinguish between Essential and Vital variables. | |
13-Jun-57 | 5650 | Vital variable identified generally; what it is vital to; sub-goals. 5811 |
14-Jun-57 | 5656 | Various ways in which senility may affect the primary function of adaptation. |
5661 | The information given by the behaviour of a whole, may often be insufficient for unique characterisation of its parts or couplings. 5983 | |
5665 | In the relating of properties of the whole to those of the parts, one case (described) is of central importance. | |
17-Jun-57 | 5667 | The unspecified machine. |
18-Jun-57 | 5671 | The extreme cases of the relations between equilibria in parts and whole. 5983, 6025, 6019 |
18-Jun-57 | 5673 | If the stimuli are not restricted, the terminal responses to Limn→∞TnD mark out the areas of the T- confluants. |
5674 | Clearer statements of the theorem on habituation. 5687, 5702.4, 5707, 5730, 6088 | |
24-Jun-57 | 5676 | If variables can't communicate, any operator on them may have to be reducible. |
5677 | When two operators act alternately they still each have power of veto over any proposed state of equilibrium. 5708 | |
5680 | High equilibrium in the parts versus communication of activity between them. | |
5685 | The machine that jumps directly to the answer, by spotting a constraint, extrapolates. It can do this only after having had previous experience with other problems in the same class, and by having a regulator that selects the better extrapolation functions. 5728 | |
11-Jul-57 | 5686 | Complexities in integration and coordination may be shown adequately by some simple evidence of their success. |
15-Jul-57 | 5689 | Program for habituation. 6088 |
15-Jul-57 | 5689 | Normal behaviour is loopy. |
30-Jul-57 | 5692 | The homeostat programmed. |
30-Jul-57 | 5692 | The dynamic cannot claim that the static is just a sub-case of it. |
1-Aug-57 | 5693 | Design for a Brain seems to have been successful. |
5696 | What is meant by "force" in psychology. | |
9-Aug-57 | 5697 | When a set is called for, refuse to answer the question: which of these elements is the "actual" one? |
9-Aug-57 | 5698 | Evidence that learned reactions are related to one another in a primarily random way, order appearing only when the environment selects or enforces it. |
5699 | Example showing how adaptation must be measured against a defined class of problems. | |
9-Aug-57 | 5700 | "Transfer of patterns" demands only a transfer of values. |
10-Aug-57 | 5702 | The structure that is necessary and sufficient if the whole's later behaviour is to be much dependent on its earlier experience. (Note that all this is equivalent to saying that the system has memory) |
12-Aug-57 | 5703 | In habituation I have shown that the operator does matter and the system does not (within broad limits). |
5707 | Implications of "going to equilibrium." | |
16-Aug-57 | 5709 | When the alternation of two stimuli to a machine reaches equilibrium, the two effects and the equilibrium are related. 5724, 5729 |
17-Aug-57 | 5711 | Every absolute system defines a topology, the "confluential", over the set of states. This topology may be similar to some other topology, well known over same set. |
17-Aug-57 | 5713 | For general guidance, one can think of a "topology" as a more complex equivalence relation, allowing degrees of "equivalence." |
5714 | The intermediate degree of the conditioned response being brought "towards" the unconditioned | |
19-Aug-57 | 5721 | Basic theory of the conditioned reflex |
5722 | Some experiments on my theory. | |
20-Aug-57 | 5726 | Simultaneous presentation does not give conditioning. 5730, 5827, 5862 |
23-Aug-57 | 5727 | A very new way of producing "conditioning". |
5728 | Constraints are found by applying information-losing transformations and seeing whether they are still acceptable to the essential variables. 5756 | |
24-Aug-57 | 5730 | If two forcing operators alternate, they will lose their distinction while forcing. |
5731 | Cycles under compound operators. 5734, 5893, 6088 | |
5733 | Arcs are necessary because, for adaptation to progress cumulatively, stores are necessary to hold the information that came from the essential variables. 5746 | |
5736 | The Multistable System of D.f.B. (Design for a Brain) is one whose corrective feedback has already been made discriminating. D.f.B. shows how a system will behave after discriminative feedback has been established in it. 5746, 5766.7 | |
31-Aug-57 | 5739 | How habituation will show in a multistable system of arcs. |
31-Aug-57 | 5740 | An arc may "see" only a certain few out of a sequence of stimuli; these few are then "adjacent" for that arc, and may have unexpected effect, e.g. habituation. 5746 |
31-Aug-57 | 5740 | If a variable is forced to a value, perhaps it does not matter whether the forcing is "discreet" or via an ultrastable, vetoing feedback. |
3-Sep-57 | 5743 | Variety, uncertainty analysis, and information. 5794, 5820 |
13-Sep-57 | 5747 | Basic functional necessities for an arc, or store. |
14-Sep-57 | 5755 | Any restriction on one part of a system is likely to show as "structure" in another part of it, Reducibility exemplifier. |
19-Sep-57 | 5756 | Axiom that the "typical member" identifies the sub-set and the constraint. |
19-Sep-57 | 5759 | Layout for accumulative adaptation. 5766.7, 5775 |
20-Sep-57 | 5760 | Additive mechanisms in the brain. 5763, 5765.1, 5766.1, 5768 |
5762 | The problem of the moving critical states. 5778 | |
20-Sep-57 | 5763 | Psychiatric application of the system that adapts additively. |
20-Sep-57 | 5764 | Importance of information whose changes occur only at long intervals. |
26-Sep-57 | 5765 | Psychiatric application. |
26-Sep-57 | 5765 | Operational meaning of "correct translation". |
26-Sep-57 | 5766 | Mechanisms for memory may well vastly outnumber those for action |
1-Oct-57 | 5767 | Essential variables for adaptation by accumulation. |
1-Oct-57 | 5768 | Complexity of remembering old adaptations is independent of complexity within one adaptation. |
3-Oct-57 | 5771 | Serial adaptation, and flow to the step-mechanisms. |
8-Oct-57 | 5774 | My proof (that adaptation demands step-functions) demands in fact only that there must be entities having a step-function aspect. This aspect may be one that is by no means obvious in the real object. 5781.7 |
8-Oct-57 | 5776 | Design of DAMS. (Corrected 5778) 5779 |
8-Oct-57 | 5777 | I may now use design and regulation freely in building DAMS, provided I admit its introduction. |
25-Oct-57 | 5778 | Layout for DAMS, and for the system that accumulates adaptations. |
28-Oct-57 | 5780 | Under certain conditions, communication between arcs is necessary. |
4-Nov-57 | 5781 | So far I have used essential variables as little more than links determining how the environment affects the step-mechanism. |
5-Nov-57 | 5782 | My claim that step-functions are necessary, must be made conditional. |
25-Nov-57 | 5784 | Step-functions have done their job and may now retire. |
5788 | Index [?] of degree of stability of a whole, and its behaviour. 5800 | |
9-Jan-58 | 5794 | Some systems are not to be understood, or controlled, by the amount of information that can be accepted in 1 man lifetime. 5810 |
11-Jan-58 | 5795 | The symmetrical relation between transmitter and receiver, of McGill and Garner and Woodward, is: between two variables' variations a constraint has been perceived. 5820 |
23-Jan-58 | 5796 | Present position of the machine for solving super-problems. |
5798 | Survival of the fittest, demonstrated in a computer. 5801, 5828, 5961 | |
11-Feb-58 | 5801 | Shrinkage to equilibrium, and adaptation to the operator that produces the shrinkage, are equivalent. 5961 |
5807 | How fast does a system adapt to an operator? "Convergency". | |
17-Feb-58 | 5809 | Spontaneous generation of brain in a computer. 5812, 5816.7, 5958 |
5810 | Another example of how a large, and irreducible, quantity of information may be necessary. | |
22-Feb-58 | 5812 | A variable may be essential to an organism and yet outside of it. |
24-Feb-58 | 5814 | Abstract formulation of "survival" and "essential variable". 5828, 5963, 5984 |
3-Mar-58 | 5816 | (1) A part, may be rich in stable subsets. (2) Death hits both organism and environment. |
5819 | An operator may be thought of as "changing its properties" if it moves from one sub-set to another. 5844, 6109 | |
5823 | McGill and Garner's uncertainty analysis applied to machines. | |
5825 | The D.I.E. (diagram of immediate effects) marks out a subset from the set of all transformations. 5982 | |
25-Mar-58 | 5826 | Habituation and the conditioned reflex as consequences of the law of experience. |
5827 | All that a mechanism for the conditioned reflex needs is a clear bias. | |
27-Mar-58 | 5829 | Survival of the fittest in random operations. 5961 |
28-Mar-58 | 5830 | In the cortex, study only the unspecialised case. |
5833 | Transmission of variety through a random network, Let the net be not a chain but broad. | |
8-Apr-58 | 5835 | When the machine with input is determinate, the output-trajectory determined by a given input-trajectory is stable. |
5836 | Demonstration of how, over any set, any subset can be marked off as having a "natural" grouping. Even bigger batch 5896, 6167 | |
5839 | The trap under a two-valued variation at the input. | |
12-Apr-58 | 5845 | The pattern in the confluents tends to copy the pattern in the input-transitions. Stochastic case: 5873, 5892 |
14-Apr-58 | 5849 | Jennings' law of the resolution of physiological states. 5880, 6101, 6137 |
15-Apr-58 | 5851 | There are complications before "in same confluent" means "moving towards". |
15-Apr-58 | 5854 | The homeostat's confluents. |
5957 | Conditioning on the homeostat examined by the method of confluents. 5877 | |
16-Apr-58 | 5858 | Paradoxical predictions for conditioned reflexes. |
16-Apr-58 | 5861 | Simple, second-order, third order Conditioned Reflexes examined by the method of confluents. 6097 |
16-Apr-58 | 5861 | The conditioned dog must have these relations. |
5865 | Defeat of my attempt to uncover the "secret" of the conditioned reflex. | |
5870 | Restoring single-valuedness of prediction, when parts of a machine with active input are not observable, by taking its history into account. 6050, 6069 | |
21-Apr-58 | 5871 | Constraint in the environment will show (in certain conditions) in the organism's behaviour. |
5872 | Examples of patterns that will spread into the nervous system. 5949 | |
22-Apr-58 | 5875 | Transfer of pattern when input and machine are stochastic. |
24-Apr-58 | 5876 | Fully joined systems must be known k steps back if k variables are unobservable. |
5881 | Relation between adaptation and anticipation. | |
25-Apr-58 | 5885 | "Conditioned" stability can readily be defined rigorously. 6091 |
25-Apr-58 | 5886 | "Conditioned" inaccessibility can readily be defined rigorously. |
5887 | A system may have different subsets conditionally stable when the input has different constraints. 6091 | |
25-Apr-58 | 5888 | Transfer of constraints from the world outside to that inside. |
8-May-58 | 5889 | A machine with input may correspond to an algebra. |
9-May-58 | 5891 | Statistical trends (in stochastic processes) are, to be evolving species, simply a method that may or may not be adapted for the job. Once adopted, they have the force of a law. |
9-May-58 | 5893 | How a relation is transmitted by an operator. |
5895 | ||
5899 | Pattern recognising. 6167, 6305 | |
5902 | ||
12-May-58 | 5905 | Present-day topology is obsessed by continuity, and is therefore of no use to me. (I must evidently develop my own theory of structure. This structure* was identified on 4934, in Bourbal's sense, and I have been developing it ever since, with "laws of experience" and such like. Restricted neither to continuity nor groups, nor numbers, nor algera, nor metric) 5949 * This structure was identified on 4934, in Bourbaki's sense, and I have been developing it ever since, with "laws of experience" and such like. |
12-May-58 | 5905 | |
13-May-58 | 5909 | Program for developing the mathematical theory of machines. |
17-May-58 | 5913 | Rigorous form of what is implied by the operator "let it get to equilibrium before applying the next stimulus". 5994, 6084 |
19-May-58 | 5914 | A new form of independence and the "proxy" relation. |
5916 | Hilton's very wide definition of "isomorphism". | |
19-May-58 | 5922 | "Isomorphism" as one of many relations that may hold between relations. |
27-May-58 | 5928 | The theory of super-relations and the laws of pattern. |
28-May-58 | 5929 | Do not confuse "patterns R are like patterns S", with "there is constraint in [RxS]. 6063 |
2-Jun-58 | 5941 | The relationship S=ΦRΦ-1, studied from various angles. 5946 |
3-Jun-58 | 5948 | |
3-Jun-58 | 5948 | Algebraic form of "[T~'s] trajectories are not more than one step long". |
4-Jun-58 | 5951 | The constraint algebraically when a transition can only be to an "adjacent" state. |
5957 | The set of stable sub-sets forms a lattice on which the representative point moves only downwards. (True both for determinate and stochastic transformations) 6091, 6093 | |
24-Jun-58 | 5961 | How to generate Life and Intelligence with probability 1 |
5965 | Intricate cleverness in an organism can be demonstrated only when the whole has been analysed into plenty of parts. 5985 | |
25-Jun-58 | 5966 | Spontaneous generation of life and intelligence in analogue form. 5967, 5984 |
5968 | The typical, or modal, element from EE will not provide a system showing the spontaneous generation of intelligence. 5984 | |
5969 | A set may be expressed with full generality both by arbitrary labels and by any arbitrary product-set-form. The product set is fully general. Review 5978 | |
5971 | We may see a whole with any set of components we like. Division of a whole into parts is relative, so far as labelling is concerned. Review 5977 | |
5973 | Wholes are divisible into parts specifiable by the observer, arbitrarily. 5984 | |
5976 | Any arbitrary system may allow the demonstration that it contains any arbitrarily selected part. | |
12-Jul-58 | 5984 | A review of the relations between "whole" and "part". 6019, 6025 |
5985 | Abstractness can go too far. 'Adaptation' demands several parts. | |
17-Jul-58 | 5986 | Cortex - not statistical but stochastic. |
19-Jul-58 | 5990 | Imposing a property on the set of input-trajectories will necessarily impose a property on the set of output-trajectories. 6063.4 |
5991 | "Constraint" is a relation between an Observer and a set. | |
5992 | Pidget on conception of space. | |
22-Jul-58 | 5995 | Rigorous form of saying that behaviour is "organised". 6007, 6021 |
6002 | Review of Elsasser. 6046 | |
24-Jul-58 | 6005 | "How much information in a brain?" is best preceeded by consideration of "how much information in a flip-flop?" 6043.8, 6179.9 |
29-Jul-58 | 6007 | Notes from Birkhoff's Hydrodynamics. |
31-Jul-58 | 6011 | Every theory has two informational aspects: its passive, when it is learnt or otherwise acquired; and its active, when it is used as transducer. The two qualities of information are not linked necessarily. |
6014 | The notion of two machines being "similar", or even just "related", has been completely generalised. | |
1-Aug-58 | 6016 | Relations between machines. |
1-Aug-58 | 6018 | DAMS was built by an ignoramus. 6025 |
6019 | Parts that have only one state of equilibrium (for each given input) may build a whole with a multiplicity of equilibria. | |
6020 | In DAMS, I went for the cutting-up; I should have gone for the equilibria. 6028 | |
6023 | Sommerhoff's basic formulation given set theory. 6104 | |
8-Aug-58 | 6024 | Wiener suggests that maths is a dynamic process, that may end in a cycle. |
8-Aug-58 | 6029 | Effect of D.I.E. on maximal equilibria of whole - cuts make the maximal number fall. |
11-Aug-58 | 6032 | Eigen-theory generalised. 6109 |
13-Aug-58 | 6033 | A physical system that is not completely analysable. 6065 |
30-Aug-58 | 6035 | Algebraic property of the machine that transmits without loss of information. |
6039 | Coding a function. | |
9-Sep-58 | 6042 | Certain concepts about a machine demand a set, which can exist only in another machine. Such concepts can hardly be used by the machine if thinking about itself. |
9-Sep-58 | 6042 | Machine whose output is invariant for changes in the speed with which the input is sent in. There must be an intervening stage of memory. |
22-Sep-58 | 6044 | Number of atoms in the brain, and the maximal information it can store. 6179 |
6045 | Distinguish between the qualities, in the brain, of information and of memory. | |
6049 | Finding how much information there is in a brain. | |
6057 | "Memory capacity" is basically channel capacity between times in the same system. Any Black Box provides an infinite number of capacities. 6069 | |
29-Sep-58 | 6058 | Of all the !memory capacities", the maximal value may be of physical interest. 6179 |
6059 | Build devices for demonstration. | |
22-Oct-58 | 6060 | Build small specialist machines, each devised to show one fact with perfect clarity. |
6062 | Blitz-therapy. | |
13-Nov-58 | 6063 | Two sorts of memory are identifiable. 6068 |
19-Nov-58 | 6067 | Irreducible complexity. |
18-Nov-58 | 6066 | A proposition is "atomic" if its user does not propose to break it up. |
18-Nov-58 | 6066 | The brain may be like a digital computer in being error-free by going from equilibrium to equilibrium. 6126 |
19-Nov-58 | 6067 | Simple "relations". |
19-Nov-58 | 6068 | To test whether memory really is permanent. |
6070 | Effect of "memory" is studied by the usual method for studying effect, but the two variables are separated in time (as well, usually, as in space) | |
6072 | A DIE can be demonstrated rigorously in a machine with memory, and by the same basic operations as when there is no delay. Continued 6105 | |
28-Nov-58 | 6073 | Learning by pain is fundamentally simpler (demands less communication ) than learning by reward. |
10-Jan-59 | 6074 | The theory of machines may help with interpolation rather than with long range prediction. 6076 |
6075 | The physicists are not yet clear about what they mean by 'casual' and 'determinate'. | |
17-Jan-59 | 6078 | The value of the new logic of mechanism can easily be over-rated. |
6082 | Equilibria attract. 6267 | |
6083 | The process of inscription is much weaker than I thought on 5844. Continued: 6092 | |
6085 | Operation "go to your basin". 6267 | |
21-Jan-59 | 6088 | Habituation with cycles allowed. 6108 |
6090 | A general method for solving problems in combination dynamics. 6108, 6349, 6334 | |
6091 | Closure under a sequence imposes little restriction on the closures at intermediate stages. | |
23-Jan-59 | 6098 | "Inscription" goes. How a pattern of equilibria is related to the pattern of transitions at the input. 6143 |
6103 | Final conclusions (to date!) about my explanation of Jennings' law. 6347, 6137, 6108, 6143, 6127, 6128, 6269 | |
14-Feb-59 | 6104 | Another way of writing Sommerhoff's directive correlation. 6105, 6284 |
14-Feb-59 | 6104 | Are isomorphisms denser around equilibrium? |
25-Feb-59 | 6105 | Isolating a pure concept is like isolating a pure element. |
6107 | Berge's book shows me I must develop my combinatorial dynamics myself. | |
16-Mar-59 | 6110 | Restriction of an operator to a selected domain may make evident a property that is otherwise inconspicuous. 6137, 6350 |
6111 | Quantum mechanics is moulded chiefly by specific atomic peculiarities, not by general epistemological principles. 6179, 6303 | |
2-Jun-59 | 6116 | Oscillating systems, when coupled, do not necessarily pull together in frequency. |
13-Jun-59 | 6117 | When a simplification is permissible. 6148, Better: 6254 |
13-Jun-59 | 6117 | Today I can say I have solved the problem I set out to solve on 7 May 1928 [31 years prior]. I asked, roughly, whence came the patterning properties of the nervous system. The answer is now clear... |
6118 | ... As the selection gets more intense, and the closed set smaller, so does the relation show more intensely. But also, so does it become more degenerate, until finally, at a state of equilibrium, the degeneracy is complete. Then all - disturbances and responses - meet at zero. The adaptation is perfect, intelligence infallible, all in Nirvana. The final statement. | |
25-Jun-59 | 6119 | General, abstract, nature of "induction", |
21-Aug-59 | 6120 | Threshold combines lots of equilibria with continuity. |
6123 | Possible function for the "functionless" parts of the mid-brain. | |
6123 | The "size" of a system had no unique meaning. | |
15-Sep-59 | 6125 | Isomorphism, homomorphism and now protomorphism. 6150, 6260 |
18-Sep-59 | 6127 | The environment goes much from equilibrium to equilibrium, constant on route but noisy in timing. The brain, appropriately, also goes much from equilibrium to equilibrium. |
6128 | Any part of the brain that behaves, with a characteristic pattern will tend to send that pattern to other parts. 6137, 6143, 6248 | |
19-Oct-59 | 6131 | How the amines may come in. |
6133 | Rapid adaptation in an irreducible whole implies many equilibria in the parts. | |
6136 | Simultaneous forcing of two variables may give a slight tendency to association. 6140, 6197 | |
14-Dec-59 | 6137 | Closure under a sequence, and a property of one operator, implies a corresponding property on the other operators. 6143, 6269 |
18-Dec-59 | 6140 | A more general type of "forcing" operator". 6269, 6247, 6312, 6322 |
6141 | Razran's review reviewed. 6269 | |
18-Dec-59 | 6142 | Set theory: model or language? |
6146 | Given a machine, an input restricted to certain transitions, and a subset closed under all sequences (words) restricted to such transitions, to find the properties of the pattern of transitions at the output. 6152 | |
6147 | The outcome of an infinitely long input can be predicted from a finite number of steps. | |
15-Jan-60 | 6150 | Measuring how much a machine has been simplified. |
4-Feb-60 | 6151 | 'Relations' between patterns. |
5-Feb-60 | 6157 | Input pattern of transition showing as output pattern. |
5-Feb-60 | 6157 | Nearness in time encourages similarity in response. |
19-Feb-60 | 6158 | ... no regulator can be more effective than the state-determined system. |
23-Feb-60 | 6160 | No regulator (other things being equal) can give performance better than the machine with input. |
3-Mar-60 | 6162 | Meaning of H(A)=0. |
11-Apr-60 | 6165 | Example of the coordination that exists at a state of equilibrium. 6350 |
13-Apr-60 | 6167 | When there is no information about the problems that recur, accumulation demands that the activations are small and that the "chance" method be used. 6227 |
6169 | What are grouped together as "equivalent" must be specified; information is required. 6181, 6222, 6305 | |
6173 | When a particular equivalence relation is to be specified, the variety to be suppressed is of the order of |n. 6182 | |
6177 | The concept of feedback being positive or negative is usefully simple only when the system is continuous. 6184 [Goes in small steps - Riguet 6184] | |
12-May-60 | 6179 | Solution of the linear difference equation. |
3-Aug-60 | 6181 | More on self-reproduction. |
5-Aug-60 | 6184 | Selfridge's Pandemonium and pattern recognition. 6222 |
10-Aug-60 | 6185 | I should re-read my Notes, Vol. 5 or so onwards, reading "lots of step-functions" as the more general "lots of equilibria", and lots of step-surfaces" as "lots of boundaries of confluents". |
10-Aug-60 | 6187 | The "general purpose" computer of today is in fact extremely specialised. |
6189 | The general purpose computer, to become a really general machine must simply become a table-searcher. | |
21-Aug-60 | 6192 | Rubin and Sitgreaves' results summarised. 6199 |
22-Aug-60 | 6193 | I must demonstrate, some day, that a heap of manure has as high an organisation as a man. |
2-Sep-60 | 6194 | In a lot of ways a system cannot, strictly, be "self-.....ing". 6566 |
6-Sep-60 | 6197 | Independence of probabilities of equilibrium demands that all loops of connexion be long. 6199, 6333 |
19-Sep-60 | 6198 | Can two fields be very different if both have lots of equilibria? 6248 |
6206 | Properties of the polystable system. 6243, 6248, 6342, 6363 | |
6207 | Estes finds learning to go in jumps. 6542 | |
16-Oct-60 | 6222 | Zato-coding. |
6224 | Pattern-recognising after coding. 6260, 6346 | |
6226 | Form all mappings, and you are performing all pattern-recognitions. 6346 | |
6228 | Adaptation to the recurrent situation demands step-mechanisms with a multiplicity of channels. | |
30-Oct-60 | 6233 | What properties of a brain are specialisation to terrestrial life and what are good absolutely? 6404 |
13-Nov-60 | 6242 | We study "machines" that depend on their immediately preceding states because experience has shown them to be very common in the world around us. 6246 |
6243 | I must write a text book on the Theory of Equilibrium. 6350 | |
6245 | Why systems prefer small responses. 6248, 6250 | |
19-Nov-60 | 6247 | Only restricted types of trajectory or process are suitable for cybernetic studies. |
23-Nov-60 | 6249 | "Association" clarified further. 6269 |
6250 | Sketch of a theory that two coupled systems, in going to equilibrium, tend to prefer regions in their phase-spaces that are topologically similar. | |
24-Nov-60 | 6251 | At equilibrium, with suitable metric, the responses have a bias towards smallness. |
6257 | Machine Σ may be simplified by equivalence Relation [formula] 6260 | |
6259 | Campbell won't allow "genius". 6289 | |
4-Dec-60 | 6262 | [SRS-1] is the "shadow" of R when "projected" by S. It can be inverted back to R if and only if [S-1S=Δ]. 6265 |
6264 | Immediate effect is a reality-shadow reaction. | |
6265 | A machine is a "shadow" of simple progression. | |
16-Dec-60 | 6266 | Meaning of [formula] |
17-Dec-60 | 6271 | A better statement of the equilibrium theory of the Conditioned Reflex and Jennings' law. 6295, 6312, 6323, 6333, 6338, 6347 |
6273 | Theory of Conditioned Reflex and Jennings' law without equilibria under each operator. 6316, 6338 | |
6276 | Review of Suppes' book. | |
8-Jan-61 | 6283 | There is no difficulty in getting from a structure of mere clubbing to a full topology. |
16-Jan-61 | 6284 | Extension of homomorphism. |
17-Jan-61 | 6288 | Directive correlation quite simply. 6297 |
6289 | Specifying the "worst" brain. | |
2-Feb-61 | 6290 | The genius searches. 6335, 6339, 6430, 6570 |
2-Feb-61 | 6291 | Unsolved problem: must systems grow in a way that is grossly self limiting in organisational possibilities? |
6292 | The Hamiltonian is a constraint on the field, therefore uninteresting. | |
6293 | The Hamiltonian is not for me. 6321 | |
12-Feb-61 | 6295 | Energy flow is neither maximal nor minimal at equilibrium; it is just irrelevant. 6321, 6345, 6350, 6365 |
23-Feb-61 | 6296 | If a set is diminished, any set tied to it by any relation will be diminished. |
6297 | Getting from simple equilibrium to directive correlation. 6350 | |
4-Mar-61 | 6298 | What a species can do, it can recognise. |
4-Mar-61 | 6301 | So we have exemplified the fact that laws that are functions of their place of action, will develop different adaptations in different places. 6350 |
18-Mar-61 | 6302 | A species that needs its competitors. 6350, 6355 |
6305 | The dynamics of the wave-function is that of a state-determined system. | |
24-Mar-61 | 6306 | Pattern recognition is arbitrary. 6346 |
2-Apr-61 | 6307 | The "anatomical" body is only one way of identifying the boundary of a system. |
6310 | What "isolated" means. 6349 | |
1-Apr-61 | 6311 | Natural systems, observation, and experiment. |
6314 | ||
6315 | ||
6317 | More on Conditioned Reflex 6323, 6347 | |
15-Apr-61 | 6320 | I read the riddle of [Pavlov's] page 197. 6338 |
6321 | Clear example of how a Newtonian system, with no convergence by Liouville, may show strong convergence if seen by a simpler observer. 6627 | |
16-Apr-61 | 6322 | "Forcing" does not imply "one confluent." |
6325 | Final (?) statement of the lae of anticipation. 6334, 6342, 6347 | |
6331 | Mechanical layout for showing law of anticipation. 6333, 6334, 6342, 6347, 6352 | |
6332 | To show anticipation. 6334 | |
22-Apr-61 | 6334 | Mixing network, one way. |
4-May-61 | 6335 | "Transmission" of selection among the components of equilibria. 6347, 6350 |
11-May-61 | 6337 | In a process of search, knowing the goal, and especially of intermediate goals, can cut the time fabulously. |
6339 | Dickens says eloquence comes from thinking about the subject. | |
6341 | Information when two inputs try to get through one output. | |
6344 | Construction to get many compact confluents. 6347, 6362.9 | |
25-Jun-61 | 6345 | Convergence to equilibrium in Markov chain. |
27-Jun-61 | 6346 | Pattern recognition is arbitrary. |
6349 | Theory of anticipation. 6352, 6374, 6389 | |
6351 | Equilibria and their properties. 6373, 6389 | |
1-Jul-61 | 6352 | The elementary conditioned reflex processes only about 2 bits of information, and needs a mechanism of only that capacity. 6363 |
6354 | Notes on: Finding stored information. 6362 | |
6357 | Example of natural selection and evolution in a computer. 6358 | |
6359 | Survival of the fittest in a computer. | |
6361 | Survival of the fittest in a computer. | |
29-Jul-61 | 6362 | For economy, the brain must store memories at the site of use. 6383 |
14-Sep-61 | 6364 | How to make a multistable system. |
15-Sep-61 | 6366 | The physicist's equilibrium at zero free-energy and the biologist's homeostasis. |
17-Sep-61 | 6369 | A game of chess shows three "organisations" simultaneously. One goes down, one up, and one does not change. 6379 |
27-Nov-61 | 6370 | The great difference between teaching by pain and teaching by pleasure. 6550 |
27-Nov-61 | 6370 | To feel sympathy is to have no assurance that the other entity is really feeling. 6384 |
6371 | It is often forgotten that planning must have a goal. 6401 | |
29-Dec-61 | 6373 | The polystable system tends automatically to find and to use the constraints. |
9-Jan-62 | 6374 | To show anticipation, the operations must be such as lead to a unique state; by what route, whether quickly or slowly, are irrelevant 6389 |
6375 | How a Markov chain shows in Uncertainty Analysis of the triples. | |
9-Jan-62 | 6376 | How many parts produce this trajectory? |
6377 | Proof of previous note. | |
6380 | Organisation and redundancy should be defined, in set theory, as [RR-1'R]. | |
26-Feb-62 | 6381 | [RR-1'R≠0] is a sensitive test for the existence of constraint, but [RR-1'R] does not equal it. |
13-Mar-62 | 6382 | On the subjective. 6384, 6427 |
1-Apr-62 | 6383 | Memory held on constraints. |
6385 | A machine can transmit only ......what? | |
6386 | When [x'=Φ(x)], no convergence anywhere implies div Φ=0 everywhere. | |
6388 | Examples of ideas that demand the pre-existence of other ideas. | |
6393 | Theorem on anticipation. 6394 | |
21-Jul-62 | 6396 | The hard core of "habituation", rigorously. |
21-Jul-62 | 6396 | Two random mappings in succession do not give a random mapping. Nor one used twice, similarly. |
22-Jul-62 | 6399 | The unit that develops anticipation must be tiny. |
1-Sep-62 | 6401 | Specialising the anticipation, may properly go into μ. 6457, 6588 |
12-Nov-62 | 6404 | The designer (or planner) must select among the equilibria. |
6406 | Every faculty is good or bad according to the environment. | |
6409 | The number of circuits traceable round n fully joint parts increases as |n (approx). 6426 | |
27-Jan-63 | 6417 | The theoretical unit is simply a mixer. |
6418 | To build any machine, only a mixer is sufficient. | |
6420 | The Pitts-McCulloch neuron from my atom. | |
6423 | Stability of a mixed net of Ashby atoms. | |
6426 | How big numbers arrive. 6438 | |
6428 | Some peculiarities of the "self" relationship. | |
10-Jun-63 | 6429 | Some problems become non-trivial only when much detailed specification is added. |
6432 | Shannon to Sommerhoff. | |
6435 | How two functions f and g must be related if they transmit the value x independently of the value of y. [DIAGRAM] | |
6435 | Some "geniuses" are just the people who happen to be right. 6570 | |
28-Jul-63 | 6437 | "Thing" and auto-correlation. |
6439 | The topologies on n points number about exp(n2). (Size No. 7 on 6424) 6454 | |
5-Aug-63 | 6442 | Review of Waddington's "Nature of life". |
6443 | Algebraic form of "the behaviour doesn't depend on variables Z". | |
6-Aug-63 | 6445 | "Remembering" as hallucination. |
6-Aug-63 | 6446 | Example of how too much memory can be disadvantageous. |
16-Aug-63 | 6450 | Some details about binary relations from B. Russell. |
6453 | Logical dynamics. 6455 | |
27-Aug-63 | 6454 | Example of how a topology is learned. |
6456 | A memory of a pattern does not have to be stored anywhere. | |
19-Nov-63 | 6460 | Proofs the orders of size. |
6461 | Indefinitely long memory in simple machine. 6470 | |
7-Jan-64 | 6464 | A practical way of getting fairly long trajectories with all ending in states of equilibrium. 6485 says joins need not be invariant in time. |
6465 | The start of |
|
10-Aug-64 | 6475 | Much in "Computers and Thought" is relevant to cylindrance. |
12-Sep-64 | 6477 | In the system that is not richly joined, the cylindrance of the set of initial and terminal states tends to increase exponentially with time. 6485, 6549 |
17-Sep-64 | 6479 | Examples of low cylindrance in everyday life. |
6483 | Movement of Amoeba: parts and whole. 6703 | |
21-Sep-64 | 6484 | Contractile molecules in an Amoeba can readily get coordinated for movement. 6789 |
6488 | If every unit has only k inputs, but may move the k around over all the variables, the cylindrance in the 2n-space X'x X is restricted to k + 1. 6493 | |
6489 | If the inputs are changed infinitely fast, the restriction on cylindrance holds, but no trajectory can be found. 6491 | |
6490 | Simpler proof that seeing k keeps cylindrance, in the 2n space, down to k. | |
6492 | "Interaction" corresponds to the last elements removed as Cp-1R shrinks to R. | |
7-Nov-64 | 6495 | A set may increase in cylindrance if a variable is ignored. 6522 Generalised to n dimensions: 6531 Footnote 6502 |
7-Nov-64 | 6496 | Meaning of "meaning". |
8-Nov-64 | 6498 | If the distinction between two values of a variable is lost (and the relation re-formed by union, i.e. + and 0 counts as +), then cylindrance may increase. 6504 |
8-Nov-64 | 6502 | Effect on cylindrance of adding new values to variables (values that did not occur before in R) |
18-Nov-64 | 6504 | Cutting out a slice cannot make cylindrance rise. |
22-Nov-64 | 6506 | Effect on cylindrance of an equivalence relation when the sections combine by intersection. |
25-Nov-64 | 6509 | If only g variables vary, the cylindrance cannot exceed g. 6509 (foot) |
6512 | Rigorous proof that a set with t points cannot exceed t in cylindrance. | |
6515 | Theorem. | |
5-Dec-64 | 6518 | When they are cylindrance-one sets, composition does not raise the cylindrance. 6519 |
5-Dec-64 | 6518 | Combining sets to form their product does not raise cylindrance. 6824 |
6523 | Composition (or elimination) will not raise cylindrance unless the implied projection raises it. And a proof that projection can raise it. 6826 | |
6525 | Section will not raise cylindrance unless the implied projection raises it. And a proof that section can raise it. | |
6527 | Proof of: As base, so cylinder. Better: 6825 Example of 6494 | |
23-Dec-64 | 6528 | Cylindrance is a generalisation of reducibility. |
24-Dec-64 | 6529 | Defeated. Not this time - see page 6531 |
24-Dec-64 | 6530 | There is no obvious relation between cylindrance and stability. |
7-Jan-65 | 6533 | Example showing how projection may jump the cylindrance up from 2 to any given number. Another example 6829 |
7-Jan-65 | 6533 | The theory of the determinate dynamic system leads naturally to set theory and cylindrance. |
6534 | The man who understands. | |
6539 | Goodwin's results are magnificent, and rigorous; but dangerously specialised. | |
6542 | Estes on the permanence of many traces. | |
16-Apr-65 | 6544 | All the maths we know has low cylindrance. 6551 |
16-Apr-65 | 6546 | Any selection of 1 from more than 101000...(47 zeros)...0 is physically impossible. |
6548 | How information-quality can explode when complicated at the sensory side. 6549 | |
14-Jun-65 | 6549 | Length of sequence increases the uncertainty exponentially. |
21-Jul-65 | 6550 | Learning by pleasure is sophisticated. |
6551 | Almost all the operations used in proving theorems do not raise cylindrance. | |
6553 | Simpler proof of Lemma. | |
25-Oct-65 | 6558 | Extracts from Huxley. |
6559 | p-dimensional projections may not be allowed arbitrarily (if n>2) | |
15-Nov-65 | 6561 | A relation can always be found that has projections including, or not including, in arbitrary fashion, those of a given point. |
6563 | The idea of a system reporting on its own behaviour is better replaced by some much simpler equivalent. | |
6566 | A mathematical virus. | |
6568 | Reduction of high cylindrance to low; examples. 6611 | |
4-Apr-66 | 6572 | Every subset (of a product set) implies a quantity of internal transmission of information. |
6574 | A woeful special case in transmission. 6579 Solved again 7006! | |
7-Apr-66 | 6577 | Analyses of data or relations (Fourier, of variance, into partial correlations, etc) are of use only if the first few terms collect all that is significant. 6615 |