Volume 07 of W. Ross Ashby's Journal
is loading...

Warning: Your browser does not have JavaScript enabledJavaScript has been used to implement many features on this Web site. Unless you enable JavaScript, the following things will not work for you: pop-up image previews, feedback links, random page links, the jump-to-any-page, jump-to-any-volume boxes, and much more. It will annoy you...

1943



Volume 07



1446+03	1446+04



1446+05	1446+06

Summary: 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.

1447	1448



1449	1450



1451	1452



1453	1454



1455	1456



1457	1458



1459	1460


Summary: Complete systems containing complete systems etc, is the same as a chain of dominances.
1461	1462


Summary: Of the methods available for solving my differential equations, some apply generally, and some only to complete systems.
1463	1464


Summary: It is believed that the theorems relating zeros in [f] and [F] to each other is still valid if the system is not complete.
1465	1466

Summary: It is proved that, if they are complete systems, then if A dominates B and B C, then A dominates C.
Summary: It seems best to define whether one variable "affects" another as whether F_i contains (or not) x^o_i
1467	1468

Hour glass system example
Summary: A simple practical example of the "hour-glass" type of organisation. Higher geometry of fields and matrix theory [5]: If some variables in a complete system are unobservable, a path fixed by n t,x combinations can be accertained empirically, by using substitute variables, 1413, numerical example 1470.
1469	1470



1471	1472

Summary: An actual numerical example showing that a path can be fixed by using later values of a few observable variables.

1473	1474

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
1475	1476

Summary: How to use my theoretical discovery for practical purposes. "Organisers, Ltd". "You want the best organisation, we have them." Society [11]: Application by using a (breaking) machine to discover an organisation with required properties, e.g. economic, 1477.
Hyohippus Natural Selection [26]: "Adaptation" is an arbitary problem, the time one being "what happens?" (Hypohippus) 1478. Another example (overgrowth of fighting males) 1722.
1477	1478


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
1479	1480



1481	1482



1483	1484



1485	1486



1487	1488



1489	1490



1491	1492


Summary: A superb theorem, much more general than that of 1113, and much more precise. It includes the other theorem as a sub-case.
1493	1494



1495	1496

Summary: A test, and example, for stability or instability of a neutral cycle.
Summary: Reasons for changing the form of the index.
1497	1498



1499	1500



1501	1502

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.

1503	1504


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)
1505	1506



1507	1508



1509	1510

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.
1511	1512



1513	1514

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.
1515	1516



1517	1518

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!

1519	1520


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.
1521	1522


Summary: James stating that a machine cannot vary its behaviour.
1523	1524

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.
1525	1526



1527	1528

Summary: A few notes on the important question of exposition.

1529	1530

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.
1531	1532

Natural Selection [7]: Similarity of my theory and natural selection, 1533, 1535.

1533	1534

Summary: Fisher's book. Natural Selection [7]: Similarity of my theory and natural selection, 1533, 1535.
Natural Selection [28]: Selective operators 1536. Five discovered by me, 1944.
1535	1536


Summary: A first attempt at a theory of selective operators.
1537	1538

1944


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)
1539	1540

Summary: Two notes on exposition.
Organisation types of organisation
1541	1542



1543	1544



1545	1546


Summary: The elementary ideas on systems and their behaviour is thoroughly tidied up and clarified.
1547	1548



1549	1550



1551	1552

Summary: The properties of non-complete systems are described.
Summary: An attempt to find the effect on the field of permanent zeros in the first Jacobian matrix.
1553	1554

Summary: Two problems for the future are noted.

1555	1556



1557	1558



1559	1560

Summary: A very precise statement of my basic theorems. (but see 1564)
Summary: A proof that finite continuous groups have differential equations not containing t explicitly.
1561	1562


Summary: The word "absolute" seems better than the "complete" already used.
1563	1564



1565	1566



1567	1568


Summary: A very economical proof of the main elementary theorems by defining and using "commutive" systems. "Restricted" equilibrium is defined.
1569	1570

Summary: A useful approximation for finding p and P.
Summary: The smallest value of p ever likely to be used is estimated. Also a common value.
1571	1572

Summary: Theorem B is rejected. Summary: A field.
Summary: The study of the graduation of adaptation seems to be essentially empirical and unsystematic.
1573	1574


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).
1575	1576


Summary: Absoluteness is not altered by separating or joining machines.
1577	1578



1579	1580

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 x_i=F_i(x^o;t), the derivative form is - er - derived; method given.
1581	1582



1583	1584

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 step-function.
1585	1586

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.
1587	1588

Summary: An actual example of "distribution".

1589	1590

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.
1591	1592

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 of part-functions.
1593	1594


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.
1595	1596


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 activated.
1597	1598



1599	1600


Summary: Two or more [variables] which are always stable apart may be unstable when joined. (Inverse, 1658) (Note 1665)
Hover mouse here to display note
1601	1602

Chatelier, Rule of Le examined

1603	1604



1605	1606



1607	1608



1609	1610

Le Chatelier, principle of not necessary

1611	1612

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.

1613	1614



1615	1616

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.

1617	1618


Summary: In a commutive system, if we keep returning x_ρ to a we shall eventually get, and keep, a field which stabilises x_ρ at, or near, a.
1619	1620

The Conditioned Reflex [3]: Simple conditioned reflex as an elementary property of the commutive system, 1621. Still unsolved, 1943. Solved with multistable system, 1982. Further observations, 2064, 2490. Still unsolved, with reasons, 2192, 2243.
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)
1621	1622



1623	1624

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.
1625	1626

Summary: A note on exposition.
Summary: "Disturbance" and "ingressive" are defined. Invariant collected notes
1627	1628

Summary: Collected notes and references on "invariance".

1629	1630



1631	1632



1633	1634

Summary: A proof is given that: If a random displacement y₁ , y₂ , ... , y_n with probability distribution df=Φ(y₁ , ... , y_n) dy₁ ... dy_n is added to a point at X₁, ..., X_n then the probability that it (i.e. X₁+y₁ , ... , X_n+y_n) should still be within a space V is maximal if, and only if, X₁ ... X_n satisfy the equation (8). (See next note).

1635	1636

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 ... X_n (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.
1637	1638

Summary: Disturbances must usually be applied to a system at a slower order of time than its reactions.

1639	1640



1641	1642



1643	1644


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.
1645	1646



1647	1648



1649	1650



1651	1652



1653	1654



1655	1656

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)

1657	1658

Summary: Any number of unstable systems joined must be unstable.

1659	1660

Society [6]: In organisations in general, particularly economic, the neutral points may have to be arranged holistically, 1661.

1661	1662

Oddments [10]: 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).
1663	1664

Summary: Two machines may form a whole which is stable if they were joined one way, and unstable if joined the other.
Summary: Two stable machines may be unstable when joined if either contains more than one variable. Isomorphism Craik's book on
1665	1666

The Conditioned Reflex [14]: Hull's model showing conditioned reflex, 1667.
Summary: A review of Craik's book. And a statement of the present position, re publishing, of my theory.
1667	1668



1669	1670

Summary: An attempt to handle the similarity of machine to machine. "Equiformal" defined.

1671	1672

Summary: A proof is given that the commutive process must increase the mean of K₁.

1673	1674

Summary: If K₁ and K₂ are uncorrelated, then disturbances give fields with K₂ always increased.

Hover mouse here to display note
1675	1678

Summary: Proof that a non-activated variable, in contact only with other non-activated variables, cannot become activated.

1679	1680



1681	1682


Summary: A "distributive" system is defined. Three theorems are given, including one showing rigorously how adaptation can proceed by parts in such a system.
1683	1684



1685	1686



1687	1688

Summary: I am unable at present to get a satisfactorily rigorous test for independence when there are part-functions present. [But see 1748]

1689	1690


Summary: A test of independence both necessary and sufficient, is deduced from x_i=e^tXx^o_i. Although the rigour of application to arbitary functions is doubtful, it leads to the same results as the previous test.
1691	1692



1693	1694

Summary: A proof that non-activated variables cannot transmit effects. (Much better proof 1921)

1695	1696


Summary: Much human behaviour is reaction to an internal environment: anxiety. (Cf. 1877)
1697	1698


Summary: A graph of the multiplying factor K₁/(1-K₂). (Another aspect, 1705)
1699	1700



1701	1702


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.
1703	1704



1705	1706

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 [37]: Actual example of two human reactions which are unstable when joined (sleep and agression) 1708.
1707	1708


Summary: Some details contributed by Carroll.
1709	1710



1711	1712



1713	1714

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.

1715	1716

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.

1717	1718


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.
1719	1720

Summary: Some other people's quotations on equilibrium.
Natural Selection [26]: "Adaptation" is an arbitary problem, the time one being "what happens?" (Hypohippus) 1478. Another example (overgrowth of fighting males) 1722.
1721	1722

Summary: Extracts from a book. Natural Selection [3]: Natural selection actually seen to work in the peppered moth, in Manchester 1723, in Plymouth crabs 1815, in American sparrows 1816, in most mutations 1883, in Drosophila with gene 'ebony' 1886.

1723	1724

Summary: In an absolute system (variables x₁ ... x_K ... x_n) of fixed organisation [x^~_i = f_i(x)], that a subsystem (variables x₁ ... x_K) should itself be absolute (the other variables x_K+1 ... x_n being given all random starting points in the testing) it is necessary and sufficient that f₁ ... f_K should not change for any or all changes of x_K+1 ... x_n.

1725	1726



1727	1728

Summary: A proof that step-functions are necessary, as well as sufficient, to get changes of organisation of a subsystem in an absolute system.

1729	1730

Summary: Pavlov says that adaptation and survival equals equilibrium. Natural Selection [24]: "Shacking together" as selective operator on the shapes of stones, 1731.

1731	1732


Summary: James describes the facts of adaptation = equilibrium without calling it such. Ants Lubbock's observations
1733	1734


Summary: Quotations demonstrating field experiments clearly as examples of my type of system.
1735	1736

Learning and age Natural Selection [25]: Waves on the coast as selective operators, 1737. So is a ratchet, 1836. Erosion and rain has a peculiarity, 1947.

1737	1738

Summary: Known examples in physics of my type of absolute system, one of which shows dominance.
Summary: Two notes from a book. Learning in Insecta Learning in bees Play species that do not
1739	1740

Natural Selection [38]: Selection of audible words in "Russian scandal", 1741.
Natural Selection [22]: Distillation of alcohol and water as selection with two, opposite, "adaptations", 1742.
1741	1742


Summary: A note on exposition. Natural Selection [39]: Rule that "bad money drives out good" as example of selection and "adaptation", 1744.
1743	1744

Summary: Another example of selection leading automatically to adaptation.
Summary: An outline of quantum theory. Quantum theory theory reviewed
1745	1746

Operator embroidery as Pattern (in general) and operators

1747	1748

Independence monograph

1749	1750



1751	1752



1753	1754



1755	1756



1757	1758



1759	1760



1761	1762



1763	1764



1765	1766



1767	1767+01



1767+02	1768



1769	1770



1771	1772



1773	1774



1775	1776



1777	1778



1779	1780



1781	1782



1783	1784



1785	1786



1787	1788



1789	1790



1791	1792



1793	1794



1795	1796



1797	1798



1799	1799+01



1799+02	1799+03

These images are reproduced courtesy of The Estate of W. Ross Ashby. Copyright 1972, 2008 © The Estate of W. Ross Ashby