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I guess that this is a chaos, randomness and modelling question. Can it be conceived that a sufficiently powerful (perhaps quantum) computer might be able to accurately predict the scores on a physical die tossed from a cup?

I understand that dice land the way they do because of highly complex and chaotic interactions between the die and whatever it hits. There is a concept of total physical modelling (that I don't know the technical term for) that aims to model a real item on an atomic level. This would require great computational power and storage.

Is such modelling possible, or are there fundamental (perhaps quantum) nuances that will always prevent this? They say the weather is chaotic and unpredictable, yet the Met Office now says that today's three day forecasts are as accurate as yesteryear's daily forecasts. Advances seem to be possible...

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  • $\begingroup$ A computer that simulates the whole universe (under assumption that our universe is computable) would easily do that. Universe computability is open question, but quantumness is not thought as huge boost to TM (a few speed ups, but not more than that). $\endgroup$
    – rus9384
    Commented Sep 29, 2017 at 14:09
  • $\begingroup$ @rus9384 Err, what's TM? $\endgroup$
    – Paul Uszak
    Commented Sep 29, 2017 at 14:17
  • $\begingroup$ I meant bounded Turing machine. So, I mean that we think that quantumness does not help solving undecidable problems. $\endgroup$
    – rus9384
    Commented Sep 29, 2017 at 14:18
  • $\begingroup$ I think this question is for Physics. Without them knowing what's happening there, how can we know whether we can simulate it? $\endgroup$
    – Raphael
    Commented Sep 29, 2017 at 20:56
  • $\begingroup$ FWIW, mathematical randomness can not be predicted, algorithmically or otherwise. $\endgroup$
    – Raphael
    Commented Sep 29, 2017 at 20:56

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I believe it could be predicted assuming technological limits of sensors and computation were overcome. A die is too large for quantum effects and a simple enough system.

Related paper

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You wouldn't need a quantum computer to solve this problem; you'd need a complete set of inputs and assumptions, and a reasonable expectation. I think the question may be under-specified.

Why quantum computing?

If you are trying to solve this in real time while watching someone toss the die, e.g. to make money at a casino, there are likely too many variables to ever accurately predict before the die actually falls.

What do you mean by "tossed from a cup"?

Is this a controlled experiment? Will the cup, force used to move cup, the die shape, the surface material be consistent? If you'd like to predict for all situations, then there is likely only 1 computer, i.e. the universe, capable of determining the outcome. Otherwise, that is an interesting problem!

What do you mean by "accurately"?

If you are looking for the correct prediction for 1000 tosses by 1000 different people , then we could likely say, "nope, can't be done." If accurately means "80% of the time the model predicts the outcome of a toss," then that is an interesting question!

Next up ... FEA?

The physics of rolling a die are well understood. The complete set of inputs and assumptions make a good model, and could be used to predict a single die's rolled value with some confidence. The model would likely be limited to a very fine set of criteria, material of the cup, force used to move cup, curvature of the corners of the die, the material of the ground, etc.

Here's an example of some documentation for a detailed Finite Element Analysis of explosives. I didn't have time myself to go through it, but it looks good enough. The best thing about FEAs are the movies.

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"Sufficiently powerful" means just that - if you can't predict the dice roll, it would not be because of lack of computing power.

You need to measure the initial conditions, and model how the initial conditions lead to the outcome. That measurement will have some margins of error. If you measured initial conditions C, the real initial conditions will be C + eps for some unknown eps. The question is then: Given different initial values C' that are consistent with your measurements, are different outcomes possible? If yes, then your "sufficiently powerful" computer cannot help.

Instead of dice, take planet movements. The last calculation that I read about showed that planet movements are not predictable for the next 25 million years, because of measurement errors in the initial conditions, not because of any lack of computational power.

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  • $\begingroup$ I'm interested in your planets but don't understand them. We successfully send probes to all the planets for rendezvous and they appear to be where they're meant to be. Can you elaborate? $\endgroup$
    – Paul Uszak
    Commented Sep 29, 2017 at 23:20
  • $\begingroup$ If you sent a probe on a long path to arrive on Neptune 25 million years from now, it won't be where you expect it. Next year is fine. 100 years are fine. 25 million years are not. And it's not because of computing power. We know within 10 meters (or so) where it is right now and how fast it is moving. That's not enough precision for a 25 million year prediction. If we knew the position right now within 1 meter, we could predict further on. We can predict quite precisely where a dice will be 1 millisecond after it leaves your hand. $\endgroup$
    – gnasher729
    Commented Sep 30, 2017 at 12:32

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