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Free Will Is Real And You Better Believe It (philosophyofbalance.com)
submitted 1 year ago by to c/philosophy@lemmy.world
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[–] 2 points 1 year ago (5 children)

Perhaps I don’t quite understand the chaos argument. Some of those systems that you mentioned, particularly famously the double pendulum, have been simulated using computers running deterministic programs.

A computer can determine the current state of a double pendulum by using information about the past state, so doesn’t that mean that the system is not chaotic?

Is there something fundamentally different about double pendulums in reality vs ones that we can simulate? And how would such a difference be proven?

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  • [–] 2 points 1 year ago* (last edited 1 year ago) (4 children)

    There is a big difference between solving numerically, and being able to use current information to predict into the future for arbitrary time.

    Take for example the two body gravitational problem, given the appropriate current information, you can predict the state of the system at any point in the future.

    In the three body problem, you have to calculate small steps in time over and over to get the future state. This has limitations, as the error grows over time, this is why NASA etc refine the predictions as more measurements are taken.

    Chaos doesn't mean we know nothing, it means we can't predict arbitrarily far into the future. We can't "solve" chaotic systems.

    Another example is weather prediction; if we could "solve" chaotic systems, we could predict the weather far in advance, think months or even years. We have 10 day predictions now, but this is mainly driven by throwing more compute at it and solving the system over and over and over again for small time jumps....yes the models have gotten more sophisticated; but brute force is the bulk of it.

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  • [–] 2 points 1 year ago* (3 children)

    Ok, so from what I understand, the key difference between reality and our simulations of chaotic systems, is that in our simulations, we need to use a discrete time step to do the calculations (over and over) to find future states.

    Reality, on the other hand is continuous, so these models are only approximations that get more and more accurate as we decrease the time interval of the steps in the simulations. It’s impossible to exactly model these systems because we can’t use an infinitesimal interval in a simulation. The amount of steps we need to calculate grows towards infinity.

    However we haven’t been able to confirm that time is actually continuous (www.clrn.org/is-time-discrete-or-continuous-data/). If time is not continuous, then it would be possible to use a discrete model to predict these chaotic systems arbitrarily far into the future in our universe.

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  • [–] 2 points 1 year ago (2 children)

    Well done; that is exactly correct. As we want to model the systems more accurately the computational resources get insane.

    If time is not continuous, then it would be possible to use a discrete model to predict these chaotic systems arbitrarily far into the future in our universe.

    Not necessarily; in fact (in my opinion) all that would do would set a lower bound on the time step required in your numerical simulation to achieve a "perfect" model. You would still have to solve the equations over and over again to know the future state.

    Quantum computers may be able to help us solve certain classes of problems much more efficiently. But even these don't change the fundamental nature of reality; there are still unknowable future states.

    It also doesn't matter if time is discrete or continuous; since we live inside time, we cannot experience the difference. The universe could run for a second, then stop for a year and then run again for a second, we would experience it as two continuous seconds.

    Maybe in the future we will work out some way to step outside the normal flow of time and answer that question.

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  • [–] 2 points 1 year ago (1 child)

    Ah, I think I wasn’t quite careful enough in the wording. Being able to predict a future state is different from being able to determine it. If time is discrete, and a chaotic system requires every state in between the current and some future to be calculated, then it is impossible to compute a future state sooner than that future time. This means that chaotic systems can’t be predicted.

    What I meant to say is that if time is not continuous, then it is possible to determine the state of a chaotic system at some arbitrary time in the future. There is a lower bound on the time step required in the numerical simulation, so that means there is an upper bound on the amount of steps that would need to be computed for a perfect simulation. If there are a finite number of steps, then it can be calculated, and determined.

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  • [–] 3 points 1 year ago

    I see where you are coming from.

    Basically you are saying if time is discrete. There are a finite number of states. And in theory, we could compute any arbitrary future state, based on the current state.

    Quite possibly, the only caveat to that is it may not be computable, given a finite universe.

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