[randphys]

I can recommend taking this blog post with a grain of salt. I'm a physics masters student and after working through the math myself I believe the Lipschitz continuity violation that Gruff rejects as a red herring is actually the real source of the nondeterminism, and is not just some mathematical fluff.

The first law and stitching arguments he makes appear to both be flawed. Having non-zero derivatives of force in combination with zero velocity and zero force is perfectly in accordance with Newton's first law. And in his frictionless ball counterexample, his equation is incorrect because it violates Newton's second law, not because two solutions are stitched together.

Lipschitz continuity is required for guaranteed uniqueness of differential equation solutions, and non-uniqueness can appear as nondeterminism or incompleteness.

I think he reaches the right conclusion but his reasoning is flawed.