Reducible quotes

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Stephen_Wolfram

Computational Irreducibility

“I’ve increasingly come to view the whole fundamental story of science as being about the interplay between computational irreducibility and computational reducibility. The computational nature of things inevitably leads to computational irreducibility. But there are slices of computational reducibility that inevitably exist on top of this irreducibility that are what make it possible for us — as computationally bounded entities — to identify meaningful scientific laws and to do science.”

Simple Purpose

“Whenever there’s computational irreducibility we can think of it as exerting a powerful force towards unpredictability and randomness... So for a system to achieve an overall “computationally simple purpose” this computational irreducibility must in some sense be tamed, or at least contained. And in fact it’s an inevitable feature of computational irreducibility that within it there must be “pockets of computational reducibility” where simpler behavior occurs. And at some level the way computationally simple purposes must be achieved is by tapping into those pockets of reducibility. When there’s computational irreducibility it means that there’s no simple narrative one can expect to give of how a system behaves, and no overall “mechanism” one can expect to identify for it. But one can think of pockets of computational reducibility as corresponding to at least small-scale “identifiable mechanisms”... When there’s a “simple overall purpose” being achieved these mechanisms tend to become more manifest.”