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In this video, a physics theorist talks with his collegues claiming to have found evidence for Simulation Theory. I'm not here to ask about the various proofs for and against ST - that's basically in the realm of philosophy at this point.

But one of the physicists claims that because of the nature of mathematics, it's impossible to simulate a particular aspect of our universe: infinite divisibility of time. The theorist responded that math can be used to describe infinite time division, which is all the simulation would need to do.

My question is this: In Computer Science, can we determine whether it is or is not possible through any currently known medium of computing to create a simulation in which the inhabitants would be able to observe infinite time divisibility?

Elaboration:

If you simulate things at a rate of infinite divisions per second of simulated time, you could never simulate the entire second right? The simulation would hang infinitely? The question is whether you could simulate based on something other than an interval, like in quantum physics, things (seem to) happen more or less precisely on a small level based on whether or not they're being observed (Disclaimer: that's a severe oversimplification).

Whether in CS this method of simulation (resulting in observed but perhaps not literal infinite time divisibility) is fundamentally possible via the computing formats we're aware of is my question. I think it's quite an interesting fundamental CS question.

Somehow the simulation would have to describe the occurrence of events via functions, not increments, which make it look like to an observer within the simulation that there is no smallest increment.

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    $\begingroup$ Please describe what "infinite divisibility of time" means; this is not a physics board. Please describe how you think computer science model are in any way affected by this. Please fix the model of computation you want to assume. $\endgroup$ – Raphael Jul 18 '16 at 7:25
  • $\begingroup$ @Raphael time: The frequency by which the state of the computer stimulation can be measured (or in this case, "observed" by an object bound within the simulation). Infinite would mean that for any given action an object makes in the simulation, limitless states can be observed by that object if it were to analyze the action. As for model of computation, I guess you mean quantum or binary - Well I didnt want to rule out an interesting answer like: Well in conventional computing models it isnt possible but in a different model it actually is. $\endgroup$ – Viziionary Jul 18 '16 at 8:23
  • $\begingroup$ It's pretty clear that for the purpose of algorithmic simulation, you can choose whatever time interval you desire. The problem will be that we don't know the physics to compute the changes of things over arbitrarily small time steps. $\endgroup$ – Raphael Jul 18 '16 at 10:31
  • $\begingroup$ @Raphael Well, "any time interval" really is a whole different thing from infinite inwardly observable divisibility of time. That's what makes this interesting in terms of CS. If you simulate things at a rate of infinite divisions per second of simulated time, you could never simulate the entire second right? The simulation would hang infinitely? The question is whether you could simulate based on something other than an interval, like in quantum physics, things (seem to) happen more or less precisely on a small level based on whether or not they're being observed. (cont) $\endgroup$ – Viziionary Jul 18 '16 at 19:09
  • $\begingroup$ @Raphael (cont) Whether in CS this method of simulation (resulting in observed but perhaps not literal infinite time divisibility) is fundamentally possible via the computing formats we're aware of is my question. I think it's quite an interesting fundamental CS question. Somehow the simulation would have to describe the occurrence of events via functions, not increments, which make it look like to an observer within the simulation that there is no smallest increment. Do you see how this is a legitimate CS question now? $\endgroup$ – Viziionary Jul 18 '16 at 19:10
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Yes, you can compute over continuous quantities. Calculus is an example.

If it was actually impossible to compute how a continuous system would behave, then how did this physicist end up believing reality is continuous? How did they make predictions that were confirmed by experiment, scientifically justifying their belief, if they weren't able to calculate any predictions?

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  • $\begingroup$ Simple - they performed a quantized approximation of their continuous model, then compared that to the quantized approximation of the same model the creator of this universe had in mind. $\endgroup$ – John Dvorak Jul 18 '16 at 7:08
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    $\begingroup$ @JanDvorak If you can make approximations like that, then it sounds pretty computable to me. And if the approximation breaks down, as in cases like Chaitin's constant, then you stop being able to distinguish the continuous case from the discrete case. $\endgroup$ – Craig Gidney Jul 18 '16 at 7:29

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