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Volume 06 of W. Ross Ashby's Journal
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1942
Volume 06
1176+03 1176+04
Summary: A field can be explored easily, but break-surfaces are destroyed by their discovery. This may involve curious philosophical properties.
Break surface exploring
Organisation exploring organisation
1177 1178
Summary: Dynamic systems are, in general, fundamentally irreversible.
Dynamic system irreversible
Reversible process in dynamic system
1179 1180
1943
Summary: The concept of "break" does not need that of "irreversibility".
Break reversible
Reversible process breaks
Summary: Theory has been submitted for publication for the third time.
Meanings of words in my form inhibition, reflex
1181 1182
1183 1184
1185 1186
Summary: The concept of "a reflex" is translated into my organisational terminology.
Reflex in dynamic system
Break surface controlled
Dominance over breaks
Levels controlling breaks
1187 1188
Summary: A dominating system can control the position of break-surfaces of a second system.
Dominance two types
1189 1190
1191 1192
Dominance and velocity
Independence and velocity
Order of velocity
1193 1194
1195 1196
Summary: 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.
Break surface controlling substitution
1197 1198
Reflex in dynamic system
Summary: A discussion of a simple reflex along my lines.
Meanings of words in my form inhibition, reflex
1199 1200
Summary: "Adaptation" is more properly divided into: the adapted state after this has been reached, and the process of finding this state.
Adaptation defined
Mathematics 1+1?2
1201 1202
Adaptation growing
Equilibrium graduation of
1203 1204
Organisation splitting into parts
1205 1206
Part-function defined
1207 1208
Summary: We study how adaptation can increase qualitatively, and are led to define and examine "part-function" and "part-surface". (Continued 1219)
Organisation number of types of
1209 1210
1211 1212
1213 1214
1215 1216
Summary: The number of possible ways of organising n variables is at last answered. It is of the order of |n
Operator example
Substitution (mathematical) example
Summary: An interesting elementary substitution is described. It demonstrates paths going to infinity and neutral cycles. (Better 3776)
Neutral point (of equilibrium - including 'cycle', 'region' etc.) example of cycle
1217 1218
Summary: A property of step-functions.
Step function (not)
1219 1220
1221 1222
Threshold significance
1223 1224
Holism excessive
Summary: 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
Adaptation non-adaptation
Survival failure of
1225 1226
Break surface peculiarities of
1227 1228
1229 1230
1231 1232
Summary: 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.
Book sketch of
1233 1234
1235 1236
1237 1238
1239 1240
1241 1242
Summary: Arrangement and collected materials for my book.
1243 1244
Invariant essence of
Substitution (mathematical) invariants of
Field (of substitution) invariants of
1245 1246
Summary: Discusses the application of the concept of the "invariant" of a substitution.
Organisation number of
Organisation number of types of
1247 1248
Adaptation after previous adaptation
1249 1250
Complex (Freudian) as internal environment
1251 1252
Environment "internal" environment
Summary: Notes on adaptation to "internal" environment; and an example of how a set of adaptations can collapse.
Adaptation and mutations
Adaptation chains of
Evolution as law and chance
Holism in mutations
Natural Selection [13]: In adaptation by heredity there is the recombination effect 1254. Quotation 2163.
1253 1254
Break mostly harmful
Organisation selection of
Selection of organisations
1255 1256
Summary: Huxley's book reviewed, and proof that a holistic set must be altered by infinitesimal steps.
Adaptation growing
Organisation must change only infinitesimally
Equilibrium tends to "normal" type
1257 1258
Summary: We have a right to expect that normal equilibrium will be commoner than other sorts
Part-function further discussion
Step function in substitution
Substitution (mathematical) part-function in
1259 1260
Break as path property
Field (of substitution) special types
Organisation and special fields
1261 1262
1263 1264
Summary: Part-functions and step-functions should be defined as special types of path in a field.
1265 1266
Summary: Whittaker defines "equilibrium" and also a "neutral cycle".
1267 1268
Observable equals projection
1269 1270
1271 1272
Dominance in field
1273 1274
Field (of substitution) dominance in
1275 1276
Hover mouse here to display note
1277 1278
1279 1280
Part-function defined
Step function defined
Summary: We have got a grip of "part-function", finding that it depends simply on zero values of dxi/dt.
1281 1282
Summary: Some points from a book.
1283 1283+01
1283+02 1284
1285 1286
1287 1288
1289 1290
Summary: 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.
1291 1292
1293 1294
Summary: A view of Levy's book. He specifically notices that breaks are an essential feature of matter and not a trivial one.
1295 1296
Summary: 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.
1297 1297+01
Summary: 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)
1298 1298+01
Summary: 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.
1299 1300
Homeostasis Carrel's list
1301 1302
Summary: A review of Carrel's "Man, the unknown".
1303 1304
Summary: 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)
1305 1306
1307 1308
1309 1310
Oddments [16]: Removing excess variables 1311.
1311 1312
1313 1314
Summary: 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.
1315 1316
Summary: "Step-function" in practice is not usually so restricted as on 1279.
1317 1318
Summary: 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.
1319 1320
Summary: Nil.
1321 1322
Summary: A definition of a complete system, and some elementary properties.
Summary: Parameters which are regarded as constant "variables" thereby lose some freedom, perhaps too much sometimes.
1323 1324
Summary: A single permanent zero in [f] introduces a slight, permanent restriction in the field.
1325 1326
Summary: The non-zero elements in [f] correspond, in a sense, to dendrons.
1327 1328
1329 1330
1331 1332
Summary: 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.
1333 1334
1335 1336
1337 1338
Summary: 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.
1339 1340
1341 1342
Summary: The solutions of a complete system form a finite continuous group of order one.
1343 1344
Summary: Notes from Bieberbach on finite continuous groups.
1345 1346
Dominance and velocity
Independence and velocity
1347 1348
Summary: 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!)
1349 1350
1351 1352
Summary: The relations of "complete sets which contain complete sets which ..." can be shown accurately by an isomorphic diagram.
1353 1354
1355 1356
Summary: 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.
Hour glass system defined
1357 1358
Summary: An unsolved problem in organisation. (Now see 1420)
1359 1360
1361 1362
1363 1364
1365 1366
Summary: 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)
1367 1368
Summary: 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)
1369 1370
Summary: The 1st Jacobian Matrix (1) cannot be filled in arbitrarily (2) does not accurately specify a dynamic system.
1371 1372
Summary: 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.
1373 1374
Summary: As first approximation, the "largest of a sample of n" tends to increase as log n.
1375 1376
Summary: 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!
Input control possible
Parameter degrees of freedom
Summary: Note from Eddington.
1377 1378
1379 1380
Reducibility defined
Oddments [15]: A "Reducible" complete system defined 1381.
1381 1382
1383 1384
Oddments [6]: "Almost absolute" systems, defined 1409, some properties 1386.
1385 1386
1387 1388
Summary: The problem of several complete systems joining into an interacting system without losing (entirely) their completeness is discussed and partially solved.
1389 1389+01
1389+02 1390
Summary: 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).
1391 1392
1393 1394
Summary: A proof, with modern technique, of the old problem, showing that two stable machines can be joined to form an unstable one.
1395 1396
1397 1398
Summary: A test to see whether a neutral point is stable or unstable. (Test for neutral cycle, 1494)
1399 1400
1401 1402
1403 1404
1405 1406
Summary: 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.
1407 1408
Summary: Contrary to p.____ [0599], the concept of equilibrium does not depend on a circuit.
Oddments [6]: "Almost absolute" systems, defined 1409, some properties 1386.
Summary: Definition of an "almost" complete system.
1409 1410
Memory and unobservables
Unobservables replacement by other observations
1411 1412
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.
Summary: 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)
1413 1414
Summary: 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.
1415 1416
1417 1418
Summary: 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.
Hour glass system properties
1419 1420
1421 1422
Summary: It is shown that the "hour-glass" type of organisation will differ little from others in its properties of adaptation.
1423 1424
Summary: If, in a system of n variables complete or not, we are given n coordinate-time pairs, the particular path is fixed.
Higher geometry of fields and matrix theory [4]: A path is fixed (in a given field) by any n combinations of t and x, 1425.
1425 1426
Summary: Notes from Eisenhart. (Ref. 476)
1427 1428
1429 1430
Summary: Six definitions of a "complete" system are given and are all proved equivalent.
1431 1432
Summary: Some references to amoeboid activity in nerve cells.
1433 1434
Summary: 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.
1435 1436
1437 1438
Summary: Stabilising some variables almost certainly stabilises those other variables connected with them.
1439 1440
Summary: More notes on the "hour-glass" case.
Summary: A definition of transient and permanent equilibria.
1441 1442
Summary: The projections of a path, and the solutions xi=Fi(xo,t) are two forms of the same thing.
1443 1444
1445 1446
1446+01 1446+02

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