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> This seems like a mathematical trick -- pretending like perfectly smooth functions exist in reality -- which is then extrapolated from in bizarre and unillumi

> This seems like a mathematical trick -- pretending like perfectly smooth functions exist in reality -- which is then extrapolated from in bizarre and unilluminating ways. Given that it is common to make certain claims about the model of NM (e.g. determinism and reversibility) a mathematical trick that demonstrates this is not true is a valid refutation of claims about the model. You can use NM to model other physically impossible systems (such as objects with arbitrarily high rigidity or arbitrarily low friction), but they are not internal contradictions within the NM model, so are less valid for criticism of NM.

ajkjk 3y ago
This example is not practically that different from chaotic systems e.g. the double pendulum, which end up in states that can't be time-reversed back to the initial state without infinite precision. In the case of a double-pendulum pointing straight up at t=0, the same argument holds: it will eventually move in an indeterminate direction. In both cases, reversing time to recover the initial state is impossible without infinite precision. I don't think anybody is losing sleep over the non-determinacy of a double-pendulum. It's just understood as evidence that your model is only as deterministic as your ability to say that something happens at t=0 or x=0 instead of |t| < epsilon or |x| < epsilon.
- aidenn0 3y ago
  > This example is not practically that different from chaotic systems... This is wildly different from chaotic systems in that it cannot be time reversed even with infinite precision. For cryptography, compare to a one-time-pad. There are plenty of practical attacks on one-time-pads, but they are theoretically unbreakable. If someone were to show an actual weakness in OTP in theory it would be a big deal, even if (in practice) OTPs are seldom used due to practical considerations.
  - ajkjk 3y ago
    Well I agree that it's not "theoretically" different from chaotic systems, that's why I said "practically". Practically, infinite precision doesn't exist. Just saying. Doesn't really affect anything, though.

ajkjk 3y ago

This example is not practically that different from chaotic systems e.g. the double pendulum, which end up in states that can't be time-reversed back to the initial state without infinite precision. In the case of a double-pendulum pointing straight up at t=0, the same argument holds: it will eventually move in an indeterminate direction. In both cases, reversing time to recover the initial state is impossible without infinite precision. I don't think anybody is losing sleep over the non-determinacy of a double-pendulum. It's just understood as evidence that your model is only as deterministic as your ability to say that something happens at t=0 or x=0 instead of |t| < epsilon or |x| < epsilon.

aidenn0 3y ago
> This example is not practically that different from chaotic systems... This is wildly different from chaotic systems in that it cannot be time reversed even with infinite precision. For cryptography, compare to a one-time-pad. There are plenty of practical attacks on one-time-pads, but they are theoretically unbreakable. If someone were to show an actual weakness in OTP in theory it would be a big deal, even if (in practice) OTPs are seldom used due to practical considerations.
- ajkjk 3y ago
  Well I agree that it's not "theoretically" different from chaotic systems, that's why I said "practically". Practically, infinite precision doesn't exist. Just saying. Doesn't really affect anything, though.