[FOM] P =? NP: A practically important breakthrough

[Andrew Butterfield]

Worth looking at is "A New Kind of Science" by Stephen Wolfram,
which has an extensive discussion of the whole randomness issue
 - in particular how simple rules can produce very complex behaviour
but also the difference between internal and external randomness...

A key thesis of that book is that physical systems in general, even if following simple
deterministic rules can exhibit behaviour that looks(*) very random.


(*) Some of the sequences produced by the cellular automata he discusses a lot
can be shown to be random by almost every definition of randomness except
the Kolmogorov one: a sequence is random if it is its own shortest description.


> On 20 Jan 2016, at 00:09, W.Taylor at math.canterbury.ac.nz wrote:
> 
> Quoting Josef Urban <josef.urban at gmail.com>:
> 
>> Or does quantum theory really
>> clearly show randomness of the "physical world"?
> 
> Interestingly, the (so-called) "many worlds" interpretation of quantum theory
> both supports and denies the existence of physical randomness.  It supports
> it in that its (appropriate) observables are indistinguishable from random,
> by you, the observer there.  But denies it in that all possible outcomes
> (along with all possible sequents and parallel cases) do actually really
> physically occur, here in our own piece of space-time, but indetectable
> by us once sufficiently de-cohered.  And OC there are other versions of
> all of "us" in those other "worlds" who see it exactly the reverse.
> 
> Whether or how this blends in with whatever Kreinovich and others adduce
> to be the effect of physical randomness on abstract math, is unclear,
> but might well lead to some interesting insights.
> 
> Bill Taylor
> 
> 
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Andrew Butterfield
School of Computer Science & Statistics
Trinity College
Dublin 2, Ireland