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And in my experience many of the intellectually most interesting aspects of technology emerge only when one actually tries to build technology for real—and they are often in a sense best captured by the technology itself rather than by a book about it.
Poincaré recurrence
Systems of limited size that contain only discrete elements inevitably repeat their evolution after a sufficiently long time (see page 258 ).
But experiments—the most direct of which are based on looking for quantization in the measured decay times of very short-lived particles—have only demonstrated continuity on scales longer than about 10 -26 seconds, and there is nothing to say that on shorter scales time is not in fact discrete.
But with all the first million initial conditions, only one other structure is produced, and this structure is again one that does not move.
But the point is that the large domains of black and white that form have boundaries which move only rather slowly.
The connections between these cells are set up so that a given cell in the visual cortex will typically receive inputs only from cells in a fairly small area on our retina.
Thus for example in first case shown only strings containing nothing but black elements are ever produced.
In the distant past humans were presumably exposed only to features generated by ordinary natural processes. … For example, while repetition has been much emphasized for several millennia, it is only in the past couple of decades that precise nesting has had much emphasis.
In addition, affine transformations can readily be generalized to any number of dimensions, while complex numbers represent only two dimensions.
Experimental data [on fracture]
To investigate the model in the main text requires looking not only at the path of a crack, but also at dislocations of atoms near it.