[Hank Kerchief]

The points on it's axis are instants

That's right, and also Peter Lynds "point." Points, like instants, are conceptual fictions, useful in geometry and mathematics as methods, but without onotological existence.

Ontologically, no segment of anything is "infinitesimal," which is the equivalent of zero. The calculus is nothing more than a clever scheme that allows division by zero, by pretending that zero is just an infinitely small fraction. Like the imaginary roots of negative numbers, the "infinitesimal" is a very useful method, but to conclude that these fictions have actual existence is madness, a common condition of hatters and mathematicians. It was mecury vapor that caused the condition in hatters, it is reification that causes the condition in mathematicians.

Hank

[headsonpikes]

" it is reification that causes [madness] in mathematicians."

Like W.V.O. Quine, some of us prefer desert landscapes. ;^)

[JasonC]

No modern calc explanation needs instants of any kind, that was all solved in the 19th century when analysis was made rigorous. It is true there was an era of flying by the seat of the pants, mathematically speaking, before then, from Galileo to Cantor, to put it at its maximum span. But all settled.

The reason the pros appeared to be interested is not the garden variety Zeno, which anyone who gets through analysis gets straight, but instead a "cat can look at a king" value seen in his critical comments directed at real physicists proposing quantized time. (With the tendency that such proposals, by others, are not needed and make the rest of the QM machinery less consistent not more).