# 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?

• 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 is only true if the uni­verse it­self is com­putable, right? In fact, it’s triv­ial if the uni­verse is com­putable be­cause any phys­i­cal pro­cess could be de­ter­mined by us­ing the fi­nal physics- so of course an un­com­putable piece­meal the­ory wouldn’t be the only law that could de­scribe the phe­nomenon.

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?

My guess is that the down votes are com­ing be­cause it sounds like you’re mak­ing deep and im­por­tant claims about the uni­verse based com­putabil­ity the­ory while also re­veal­ing a lack of un­der­stand­ing of com­putabil­ity the­ory. It also isn’t clear what your point is. Then you bring up the Sin­gu­lar­ity and peo­ple here are pretty sen­si­tive to Sin­gu­lar­ity talk mixed with ram­bling about sci­ence the writer doesn’t re­ally un­der­stand.

It isn’t re­ally my field though, so some­one who un­der­stands com­putabil­ity the­ory bet­ter than I should con­firm my sus­pi­cion.

• 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?

There’s a large set of com­putabil­ity mod­els, but if you don’t get into hy­per­com­pu­ta­tion they all pro­duce the same set of com­putable func­tions. Quan­tum com­pu­ta­tion doesn’t change this pic­ture; any­thing com­putable by a quan­tum al­gorithm is com­putable by a clas­si­cal al­gorithm, al­though of­ten less effi­ciently.

Whether or not the phys­i­cal laws of the uni­verse in­volve any un­com­putable op­er­a­tions is an open ques­tion, al­though none, as far as I know, have been proven to ex­ist.

• I voted it up as not un­suit­able for the dis­cus­sion sec­tion, for what it’s worth. There aren’t a lot of com­ments, but they’re de­cent enough. It’s not against the mis­sion state­ment.

• I don’t know enough to know why this topic is down­voted. Is it be­cause no un­com­putable phys­i­cal laws have been dis­cov­ered, or is it be­cause the last para­graph doesn’t make much sense, or some­thing else?

• There is a whole field of hy­per­com­pu­ta­tion. Ob­vi­ously any Tur­ing-com­putable pro­gram can be run by a Tur­ing-com­plete com­puter and a hy­per­com­putable pro­gram can be run by a hy­per­com­puter of the same place in the ar­ith­meti­cal hi­er­ar­chy. The Church-Tur­ing the­sis can be ex­pressed as stat­ing that the uni­verse is Tur­ing-com­putable, which is a ques­tion about the uni­verse, not just about com­pu­ta­tion. You may also be in­ter­ested in Banana Scheme, which pro­vides an short in­tro­duc­tion to hy­per­com­pu­ta­tion.

• Basilisk!

No sorry, I’m sure its not that. I would also like to know why.

• What are you refer­ring to?

• Sorry that was a re­ply to the com­ment above ac­ci­den­tally hit the wrong “Re­ply” but­ton. The com­ment was flip­pant any­way I’ve re­moved it.

• Wouldn’t a pro­gram (like a com­pu­ta­tion of the laws of physics) writ­ten within the con­fines of the uni­verse be nec­es­sar­ily less com­plex than the uni­verse it­self, or am I miss­ing the point of your post?