First, it's useful to point out an interpretation of QM that brings it closer to classical mechanics; and this is the Bohmian Model in which particles move in a random walk; this is directly comparable to the Lucretian view that particles move randomly in themselves and not due to impacts ie the *clinamen*.

In Euclid one recalls that his definition of a point is

that which has no parts

Which directly recalls the notion of an atom as that which has no parts; parts meaning being seperable; but not distinguishable.

For Euclid, a line is not made up of points as we understand it; it is a synthetic object. Points mark the ends of a line or where one line crosses another; they are markers of position.

Hence, one can feasibly say that the first synthesis of lines and points is to conceive lines as points.

Now a particle is simply a point in motion; and a wave is a line in motion.
Concieved as points, a wave is just particles moving up and down; this might conceivably called the first synthesis of particles and waves.

But what about QM? After QM, physics began to posit *extended* objects - vortices, strings and branes; one might say they began to explore the possibility that conceiving particles as points was the basic mistake - a mistake that can be traced to The Euclidean definition of a point.

The first atomists were clear that their atoms had extension since they were modelled as Platonic solids; so, in a sense we've returned to an older tradition.

So yes; the point is, that points aren't simply points; that they don't have extension or parts; but that they have extension.

Aristotle pointed out that the actual infinite could not physically exist; but he did admit infinite divisibility; but this isn't the infinitely small; and the contrary appears to be true; that the infinitely small does not either in any aspect, be it space, time, matter or energy, exist; doing so leads to errors.

I've re-revised your edit (no need to edit just by adding). I'm going to reopen it, but .... I think jobermark has the right idea of why this should have no implications. You also might want to review your QM as to

rangein which the uncertainty happens and thus the degree to which this changes anything for normal scale objects. – virmaior – 2015-04-26T02:34:27.957@virmaior Thanks for the re-revision! As to the exhibition of wave properties, you are right, observable

de Broglie wavelengthis attributed only to small mass objects with large speed; the more precise the measurement of one of the conjugate coordinates the larger the uncertainty in the other, so that their product is always smaller than half the reducedPlank constant. – Ziezi – 2015-04-26T09:23:40.263