>I have no idea why you bring up functors. Are you thinking of functionals?

https://en.wikipedia.org/wiki/Functor. The functor is a generalization of the concept of changing "space". It specifically refers to the mapping between these spaces. For example changing from json to xml, or changing from cartesian coordinates to polar coordinates, euler angles to quaternions or changing from Newtonian mechanics to Lagrangian.

I am saying there's no point in using a functor if the point is already proven. You gain no ground and telling me to change space because of entropy. Things may be easier in the secondary space but because of information entropy there may or may not be a loss of information and this loss definitively leads to less capability of proving anything.

>I did, and he does not. The fact is that in Newtonian mechanics, an object at rest cannot start moving without a change in the applied forces. By definition, if it does, then it does not follow Newtonian mechanics.

Doubtful as you didn't even address his point. You stated your point as if his counterpoint didn't even exist. Either way a discontinuity is undefined but it is 100% legal to talk about the points where it is defined. The limits are legal to address mathematically as there is no math stating that those points are singularities or non-existent or anything like that. You statement of it being unfounded doesn't move your argument in any direction. You need to prove your point or disprove Nortons point.

>But that would not happen, because it is non-Newtonian. What he does in fact demonstrate is that a ball with exactly the right energy does not arrive at the apex in a finite time. He got the contradiction right, but sided the wrong way. Besides, he even mentions himself that the ball would not arrive in a finite time, and we are supposed to believe that this trajectory is the time-inversion image of a ball that definitely leaves the apex in a finite time.

Maybe instead of reading the entire article really quickly and missing the entire point you should read it more carefully. He is talking about the spherical dome. The ball not arriving at finite time is for the perfect hermsphere. For Nortons Dome such an action is 100% possible under newtons model.

>>The whole dome setup is a troll. There is nothing in the principles he mentions that would not work with an ordinary, half-spherical dome, if it did in fact work. His specific dome sounds suspiciously like an artificial setup to get people hung up in irrelevant mathematical details (on top of being generally unphysical).

Again you didn't read. He does mention this. The particle will not move when placed upon the spherical dome and the math for the time inversion version replicates the inverse behavior. Whether the whole thing is physical or unphysical is besides the point he is talking about nondeterminism of Newtonian mechanics itself.

>There is just too much wrong in this example, and I suspect you are in way over your head.

Well you suspect wrong. But that's your prerogative. I suspect you're not even really reading the relevant material and just arguing for arguing sake but that's my prerogative. Your judgement makes me suspect you defer to authority, in which I will reply to you that there are many many scholarly papers on the topic of Nortons Dome and There is no definitive consensus among experts on what the dome itself proves about Newtonian Mechanics. Such a self assured stance coming from you literally flies in the face of many experts who have considered the problem far more thoroughly than you or I.