the Universe, Computability, and the Singularity

EDIT at Karma −5: Could the next “good cit­i­zen” to vote this down leave me a com­ment as to why it is get­ting voted down, and if other “good cit­i­zens” to pile on af­ter that, ei­ther up­vote that com­ment or put an­other com­ment giv­ing your differ­ent rea­son?

Origi­nal Post:

Ques­tions about the com­putabil­ity of var­i­ous phys­i­cal laws re­cently had me think­ing: “well of course ev­ery real phys­i­cal law is com­putable or else the uni­verse couldn’t func­tion.” That is to say that in or­der of the time-evolu­tion of any­thing in the uni­verse to pro­ceed “cor­rectly,” the phys­i­cal pro­cesses them­selves must be able to, and in real-time, keep up with the com­plex­ity of their ac­tual evolu­tion. This seems to me a proof that ev­ery real phys­i­cal pro­cess is com­putable by SOME sort of real com­puter, in the de­gen­er­ate case that real com­puter is sim­ply an ac­tual phys­i­cal model of the pro­cess it­self, cre­ate that model, ob­serve whichever fea­tures of its time-evolu­tion you are try­ing to com­pute, and there you have your com­puter.

Then if we have a phys­i­cal law whose use in pre­dict­ing time evolu­tion is prov­ably un­com­putable, ei­ther we know that this phys­i­cal law is NOT the only law that might be for­mu­lated to de­scribe what it is pur­port­ing to de­scribe, or that our the­ory of com­pu­ta­tion is in­com­plete. In some sense what I am say­ing is con­sis­tent with the idea that quan­tum com­put­ing can quickly col­lapse down to plau­si­bly tractable lev­els the time it takes to com­pute some things which, as clas­si­cal com­pu­ta­tion prob­lems, blow up. This would be a good in­di­ca­tion that quan­tum is an im­por­tant the­ory about the uni­verse, that it not only ex­plains a bunch of things that hap­pen in the uni­verse, but also ex­plains how the uni­verse can have those things hap­pen in real-time with­out mak­ing mis­takes.

What I am won­der­ing is, where does this kind of con­sid­er­a­tion break with tra­di­tional com­putabil­ity the­ory? Is tra­di­tional com­putabil­ity the­ory limited to what Tur­ing ma­chines can do, while per­haps it is straight­for­ward to prove that the op­er­a­tion of this Uni­verse re­quires com­pu­ta­tion be­yond what Tur­ing ma­chines can do? Is tra­di­tional com­putabil­ity the­ory limited to digi­tal rep­re­sen­ta­tions whereas the de­gen­er­ate build-it-and-mea­sure-it com­puter is what has been known as an ana­log com­puter? Is there some­how a level or mea­sure of ar­tifi­cial­ity which must be pre­sent to call some­thing a com­puter, which rules out such brute-force ap­proaches as build-it-and-mea­sure-it?

At least one imag­in­ing of the sin­gu­lar­ity is ab­sorb­ing all the re­sources of the uni­verse into some max­i­mal in­tel­li­gence, the (pos­si­bly asymp­totic) end­point of in­tel­li­gences de­siging greater in­tel­li­gences un­til some­thing makes them stop. But the uni­verse is already just hum­ming along like clock­work, with quan­tum and pos­si­bly even sub­tler-than-quan­tum gears turn­ing in real time. What does the sin­gu­lar­ity add to this pic­ture that isn’t already there?