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Mapping composition of random mapping Random mappings Summary: The hard core of "habituation", rigorously. Summary: Two random mappings in succession do not give a random mapping. Nor one used twice, similarly.
Genius Summary: How two functions f and g must be related if they transmit the value x independently of the value of y. [DIAGRAM] Summary: Some "geniuses" are just the people who happen to be right. 6570
Homeostat Grodins' book Servo-mechanism biological Summary: A practical way of getting fairly long trajectories with all ending in states of equilibrium. 6485 says joins need not be invariant in time.
Summary: 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
Summary: 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
Summary: If the inputs are changed infinitely fast, the restriction on cylindrance holds, but no trajectory can be found. 6491
6488
6489
Summary: Simpler proof that seeing k keeps cylindrance, in the 2n space, down to k.
Summary: 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
Cylindrance composition and Summary: When they are cylindrance-one sets, composition does not raise the cylindrance. 6519 Summary: Combining sets to form their product does not raise cylindrance. 6824
Cylindrance composition and Summary: Composition (or elimination) will not raise cylindrance unless the implied projection raises it. And a proof that projection can raise it. 6826
6522
6523
Cylindrance section and Summary: Section will not raise cylindrance unless the implied projection raises it. And a proof that section can raise it.
6524
6525
Summary: Proof of: As base, so cylinder. Better: 6825 Example of 6494
Cylindrance and stability Stability and cylindrance Summary: There is no obvious relation between cylindrance and stability.
6530
6531
1965
Cylindrance and determinate system Dynamic system determinate and cylindrance Summary: Example showing how projection may jump the cylindrance up from 2 to any given number. Another example 6829 Summary: The theory of the determinate dynamic system leads naturally to set theory and cylindrance.
Summary: p-dimensional projections may not be allowed arbitrarily (if n>2)
6558
6559
Summary: A relation can always be found that has projections including, or not including, in arbitrary fashion, those of a given point.
6560
6561
Self-describing system can be reformulated in simpler form Summary: The idea of a system reporting on its own behaviour is better replaced by some much simpler equivalent.
Summary: 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
6576
6577
Cylindrance using low cylindrance Summary: Transforming sets of low cylindrance to a "simpler form". 6679
Summary: Anticipation forced on the "pin-table". 6594
Summary: Though the designer of an anticipator must look at it in detail, its demonstration demands a great and deliberate reduction
in the quantity of information emitted. 6596
6590
6591
Archer dream of Dream and "self" Self-awareness impossible Summary: "I", in a dream, is not necessarily the site of intellectual activity.
Organisation and parts Part and whole, independent Summary: Parts isolated (with an experimenter) and parts in a whole (with other parts as disturbers) are not directly comparable.
