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In general, the more systematic the proofs in a particular area become, the less relevant they will typically seem compared to the theorems that they establish as true.
Significantly less work has been done on the problem of finding initial conditions for rule 30 than on the problem of factoring integers.
The increases have tended to become less significant over the years, as the on-chip memories of microprocessors have become larger, and the time necessary to send data from one chip to another has become proportionately more important.
With vectors of length n it generically takes about n 2 steps to compute u given v , and a little less than n 3 steps to compute v given u (the best known algorithms—which are based on matrix multiplication—currently involve about n 2.4 steps).
And outside of physics, I have tended to find still less reliability in the results of complex experiments.
Beyond a few thousand cells, however, individual cells seem to be less relevant, and instead what appears to happen is that chemicals such as retinoic acid (a derivative of vitamin A) produced by particular cells diffuse to affect all cells in a region a tenth of a millimeter or so across.
But in a field like biology, the principle has usually been regarded as much less successful.
But from my discovery that complex and seemingly random behavior is in a sense easy to get even with very simple programs, the phenomenon of fluid turbulence immediately begins to seem much less surprising.
And more or less the same is true of descriptions based on ideas like natural selection in biology.
Indeed, it seems that the system just never settles down, but rather continues to fluctuate forever, sometimes becoming less orderly, and sometimes more so.