New FQXI essay contest Is Reality Digital or Analog?

[D H]

We use digital computers to approximate solutions to systems of differential equations. They do not solve them. They give answers that are very close to a solution. Way back in the day, scientists used analog computers that at least conceptually could yield exact solutions to systems of different equations.

You are assuming that the universe is computable and then using that assumption to prove that the universe is computable. That of course is not a valid line of reasoning.

 

[friend]

No. Allowing the continuum means that the universe is not computable. Computable here has a specific meaning and is related to the answer to the question "Is the universe a giant computer (a giant digital computer, to be specific)?"

Just because we humans cannot calculate to infinite precision doesn't mean that there cannot be a relationship between infinitesimal distant spacetime points. Perhaps all of physics is derived from nothing more than a conjunction of an infinite set of points, each infinitesimally distant from its neighbor with no other relationship to calulate implied. To suggest that there are any gaps at all between adjacent points creates the delemma of asserting that something that is not real (the gaps) actually exists.

 

[Fra]

Just because we humans cannot calculate to infinite precision doesn't mean that there cannot be a relationship between infinitesimal distant spacetime points.

I agree, BUT, as I see it, the question is how any observer/system can make the inference and establish this? My conclusion is that such an inference must involve an infinity of processing and representation - making it unphysical. This is what I mean with non-inferrable.

Something beeing non-inferrable, doesn't mean it doesn't exists.

creates the delemma of asserting that something that is not real (the gaps) actually exists.

Yes, but as I see it at least, it's irrelevant wether it exists, if the action of the computer only depends on it's current state of knowledge/information.

Thus, the observers action, should be invariant with respect to wether whatever is "in between the points" exits or not :) So there is no dilemma as I see it.

/Fredrik

 

[Fra]

Just like (a bit simplified)

~ an electrically neutral particle simply doesn't respond to en electric
field, that particle is quite indifferent to wether there IS an an electrical field or not.

~ all particle though, respond to gravity (which is a hint), no particle can be indifferent to gravity

~ a poker players instant actions is indifferent to what cards the othre players REALLY have, becuase all that matters is what cards he THINKS they have

There are several analogies like this... I think this extends also to the digital/analog question we discuss here.

I think the key, we must not forget, that the question is not in some unscientific sense wether there "IS" a continuum or not. The real queston, as I see it is HOW a physical systems ACTS. Ie the action. This is what makes a different.

If a system acts as if it has discrete information, THEN that is what's physical. To embedd this into some continuum model simply doesn't add anything useful. It rather blurrs up what's continuum ghosts and what's physically distinguishable states as judged in the sense as how the action is.

I'd say that MY actions, is indeed coloures by MY own ignorance and incompleteness. So as far as my rational action concerns, it's completely irrelevant to ponder wether there is something that I do not know about that should (if I knew it) affect my decisions :)

/Fredrik

 

[S.Daedalus]

We use digital computers to approximate solutions to systems of differential equations. They do not solve them.

If an analytic solution is possible, a (digital) computer is as capable as a scientist to solve it. And if not, then it might just be that no exact solution exists -- not for you, not for the computer, not for nature. Indeed, such a solution corresponds to hypercomputation (at least in some cases). Take the gravitational many body problem: if you had an exact solution, you could solve the halting problem. Why? Because you can build a computer out of such a system (IIRC, a three body system suffices), and with your analytic solution, could find out for any given evolution of the system whether it ever reaches some halting state.

They give answers that are very close to a solution. Way back in the day, scientists used analog computers that at least conceptually could yield exact solutions to systems of different equations.

Conceptually, yes, if you neglect finite measurement precision. In practice, analog computers work maybe to three or four digits precision.

You are assuming that the universe is computable and then using that assumption to prove that the universe is computable. That of course is not a valid line of reasoning.

I just observe that every process in the universe (that we've come across so far, at least) can be arbitrarily well approximated using computational means -- i.e. that no matter how big my magnifying glass, I could not observe any deviation that I could not in principle compute. That reality then is computable is just the most conservative hypothesis to go with. The real numbers might have seemed a natural choice when they were first introduced into physics; however, from today's perspective, with the benefit of a theory of computation, they seem like almost alchemistic constructs.

And I'm still not sure I get in what way you claim that Newtonian mechanics, etc., are non-computable theories. One can completely recast these theories in terms of Turing machines, or partial recursive functions from initial to final values. That they are formally defined over the reals plays no role, as everything we do with them happens entirely within a computable subset thereof; and neither does the fact that they involve differentiation, which is in the end just a limit, which exists precisely if it is computable. In the end, anything that can be reduced to manipulating symbols on a sheet of paper according to a certain set of rules is computable, and I don't think there's any theory that can't be thus reduced.

 

[Fra]

And I'm still not sure I get in what way you claim that Newtonian mechanics, etc., are non-computable theories. One can completely recast these theories in terms of Turing machines, or partial recursive functions from initial to final values.

Of course to just talk about what's computable given infinite time seems like a useless classification.

The optimal action/decision problem is that you need to process a certain amount of information and use a finite computational device/brain to find your "best choice" and this must be done at a rate that is on par with the dataflow or there will be overflow. If the decision takes too long that equals no action, and the system will be torn apart by it's own environment.

With continuum models, if the convergence rate of the limits you mention is FAST enough, then the model is FIT, as the overflow will not destabilise things, if not, or of the overflown data completely fail to give priority as to WHICH data that's discarded the algorithm will not survive.

It's true that to discusse this more seriously one has to introduce the ORDER that's implicit in the dataflow and thus indirectly time.

Edit: like in crise handling, there is always a tradeoff/balance between making the RIGHT decision and making SOMETHING at all, because everyone understands that you can't sit forever and analyse what's the best action to take in the middle of the field in say a war (or chaos). You have a split second to make a decision. Errors will be made. And whoever lives through have made the right priorities. (this is also a good analogy to I how I see physics, ssytem stabilisation)

/Fredrik

 

[friend]

Edit: like in crise handling, there is always a tradeoff/balance between making the RIGHT decision and making SOMETHING at all, because everyone understands that you can't sit forever and analyse what's the best action to take in the middle of the field in say a war (or chaos). You have a split second to make a decision. Errors will be made. And whoever lives through have made the right priorities. (this is also a good analogy to I how I see physics, ssytem stabilisation)

/Fredrik

That's pretty close to saying that angels and demons fight it out for what's going to happen.

 

[Fra]

That's pretty close to saying that angels and demons fight it out for what's going to happen.

That's not what I meant though, the undecidability with respect to the observer does not imply that everything is then decided by some external entiyry: god, or demon, it just means that all we have is expectations, and all we need to do is place our bets and collect the feedback.

There is no shortcut, or simplification where you can simulate the entire universe in a pocket calculator. Instead I think that nature fundamentally works so that, all that any subsystem does is act rational according to it's expectations, and there is an oversall undecidable evolution that takes place.

It's the basic premise that everyhing has to be decided - somewehere by someone or something, be it a birds view, angels or demsons - that I think is wrong. My point is that as I see it, not all things are decidable, and the main point is that it does not have to. I even think that the fact that not everything is decidable, is at the orgin of the arrow of time, the entire arrow of time is like a spontaneous computation; but without global simplification that can be captures by an inside subsystem.

/Fredrik

 

[unusualname]

Competition closed on 15th February, although there seems to be a whole load of late submissions, you can read them all here:

http://fqxi.org/community/forum/category/31417

there are certainly some really crazy and unusual ideas out there

at least one frequent poster here has submitted an essay (looks like he got it in just on time)

 

[qsa]

Competition closed on 15th February, although there seems to be a whole load of late submissions, you can read them all here:

http://fqxi.org/community/forum/category/31417

there are certainly some really crazy and unusual ideas out there

at least one frequent poster here has submitted an essay (looks like he got it in just on time)

something has gone wrong with the website, can't read the articles. also it is strange that nobody has commented on the articles which I think summerizes all the possible ideas that could solve QG. I will do that as soon asI am able to read the articles again.

 

[Fra]

something has gone wrong with the website, can't read the articles. also it is strange that nobody has commented on the articles which I think summerizes all the possible ideas that could solve QG. I will do that as soon asI am able to read the articles again.

Seems to work now.

/Fredrik

 

[qsa]

String, LQG and the rest are great, but tweaking standard ideas to achieve full unification from the very small distance to the cosmological one is very clearly has not been able to do that. Because QM and GR fail to apply in those regimes. It is time to look at different conceptual alternatives in a serious way.

http://www.fqxi.org/community/forum/topic/950

http://www.fqxi.org/community/forum/topic/867

http://www.fqxi.org/community/forum/topic/821

http://www.fqxi.org/community/forum/topic/803

http://www.fqxi.org/community/forum/topic/884