Problem in Newtonian Determinism?

[petermarkley]

Today YouTube recommended this video to me:

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After watching, I made this comment under it (pasted below). What do you all think?

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My comment:

I think the reason it feels wrong is because we imagine the ball spontaneously moving, but I don’t think that’s what the math describes. Mathematically, for the ball to be at rest and then spontaneously move, it would have to switch states from the rest equation to the rolling equation.

Without external forces (like a tiny vibration or waft of air nudging it) the ball can only ever be in one of the two solutions, not both. If we are observing the ball roll, it’s obviously in the rolling case; but if we are observing the ball resting balanced, it’s in the “balanced forever” case. The existence of the rolling solution does not require that it previously be at rest, unless a negative value for ‘t’ gives a result of zero.

 

[Retro]

Watching that video, it looks like a potential flaw in Newtons equations, not too dissimilar to how general relativity breaks down at a black hole singularity when the equation goes to infinity, so we know that it's incorrect in some way.

We already know that Newton's equations are an approximation anyway, so it seems quite likely to me that this is a flaw in them.