Summary: An actual numerical example showing that a path can be fixed by using later values
of a few observable variables.
Summary: Orders of velocity make complete systems.
Summary: The shift is calculated, of a neutral point as a result of small changes in parameters. Equilibrium shift by parameter Parameter changes of state of equilibrium
Summary: How to use my theoretical discovery for practical purposes. "Organisers, Ltd". "You
want the best organisation, we have them." Society : Application by using a (breaking) machine to discover an organisation with required
properties, e.g. economic, 1477.
Summary: 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
Summary: A superb theorem, much more general than that of 1113, and much more precise. It includes the other theorem as a sub-case.
Summary: A test, and example, for stability or instability of a neutral cycle.
Summary: Reasons for changing the form of the index.
Summary: 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. Summary: "Step-function" is an official word in general use.
Summary: 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)
Summary: The equations of a dynamic system with layers of break surfaces given in completely
continuous form, suitable for general analytic studies.
Summary: 1506 is confirmed, that a change of variables does not generally affect the applicability
of the theorem of 1493.
Summary: Variables cannot be exchanged for derivatives when the conditions of 1493 are to hold.
Summary: The substitution of derivatives for variables is apt to lead to troubles due to multiple
values, and must be used with caution.
Summary: 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!
Summary: 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.
Summary: James stating that a machine cannot vary its behaviour.
Summary: Levy supports my view that knowledge of a real dynamic system is purely empirical. Summary: Notes from Bradley's book.
Summary: The problem of the "distributor" solved, in essence.
Summary: A few notes on the important question of exposition.
Summary: 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.
Summary: Some details about getting a system of my type started.
Summary: A first attempt at a theory of selective operators.
Summary: 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)
Summary: The study of the graduation of adaptation seems to be essentially empirical and unsystematic.
Summary: 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).
Summary: Absoluteness is not altered by separating or joining machines.
Summary: In an absolute system, knowing the behaviour of the parts (and the method of assembly)
specifies the behaviour of the whole; and vice versa.
Summary: Observation provides xi=Fi(xo;t), the derivative form is - er - derived; method given.
Summary: An attempt at the analytical expression of a part-function.
Summary: The least possible join of two absolute systems is that they should share a common
Summary: Convenient equations in the technique of joining and separating parts and wholes.
Summary: A symbolic way of writing step-functions. Summary: 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.
Summary: The mere presence of part-functions in a system allows variables to be active in some
reactions and inert in others.
Summary: In a commutive system with many part functions, distribution will occur, because it
is more probable.
Summary: "Equilibrium" is an invariant. It belongs only to an absolute system.
Summary: If reactions are to adapt independently, the breaks must be restricted to the regions
Summary: A better proof that chance of equilibrium, other things being equal, falls off as
e-kn. This means nothing, for p means nothing definite.
Summary: 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
Summary: Two or more [variables] which are always stable apart may be unstable when joined.
(Inverse, 1658) (Note 1665)
Summary: 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.
Summary: 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.
Summary: 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.
Summary: 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)
Summary: 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. Cortex, sensory layering in Dispersion and layering in
Summary: The layering of the cerebral cortex may be explained as required for wide distribution.
Summary: Collected notes and references on "invariance".
Summary: 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).
Summary: 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).
Summary: 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.
Summary: Disturbances must usually be applied to a system at a slower order of time than its
Summary: Adding regular random disturbances to a commutive system with layers of break-surfaces
increases the probability, at any time, of finding the system with a field of normal
equilibrium. [deleted] Correct, but rewritten.
Summary: 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)
Summary: Any number of unstable systems joined must be unstable.
Society : In organisations in general, particularly economic, the neutral points may have to
be arranged holistically, 1661.
Oddments : Field of parts joined may show features not possible when parts are separated, 1663.
Summary: 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).
Summary: Two machines may form a whole which is stable if they were joined one way, and unstable
if joined the other.
Summary: A review of Craik's book. And a statement of the present position, re publishing,
of my theory.
Summary: An attempt to handle the similarity of machine to machine. "Equiformal" defined.
Summary: A proof is given that the commutive process must increase the mean of K1.
Summary: If K1 and K2 are uncorrelated, then disturbances give fields with K2 always increased.
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Summary: Proof that a non-activated variable, in contact only with other non-activated variables,
cannot become activated.
Summary: A "distributive" system is defined. Three theorems are given, including one showing
rigorously how adaptation can proceed by parts in such a system.
Summary: I am unable at present to get a satisfactorily rigorous test for independence when
there are part-functions present. [But see 1748]
Summary: 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.
Summary: A proof that non-activated variables cannot transmit effects. (Much better proof 1921)
Summary: Much human behaviour is reaction to an internal environment: anxiety. (Cf. 1877)
Summary: A graph of the multiplying factor K1/(1-K2). (Another aspect, 1705)
Summary: 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.
Summary: The distribution of K2 after disturbance is given in terms of the original distribution and the means of
K1 at each K2-value.
Summary: An example of two reactions, each quite adaptive, which are in unstable equilibrium if joined. Psychiatric applications : Actual example of two human reactions which are unstable when joined (sleep and agression)
Summary: 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.
Summary: 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.
Summary: The possibility of giving some of the variables a fixed value and letting others vary
is functionally identical with taking the machine to pieces.
Summary: Some other people's quotations on equilibrium.
Natural Selection : "Adaptation" is an arbitary problem, the time one being "what happens?" (Hypohippus)
1478. Another example (overgrowth of fighting males) 1722.
Summary: 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.
Summary: A proof that step-functions are necessary, as well as sufficient, to get changes of organisation of a subsystem in an absolute