And if so, are there any interesting implications? According to the storyline, Galileo launched modern science by declaring the necessity of rendering physical events countable. What is countable must be "defined" or literally translated into finite units.
Newton's great leap followed this maxim, notoriously placing a countable limit on the infinite Zeno-like regress of divisions arriving at "points" on a curve. Rendering motion countable. It worked! It worked so marvelously that all the metaphysical debates about it at the time were happily allowed to expire.
But what is the status today of the old philosophical bugbear of "the infinite"? Cantor's set theory produced a kind of "countable" definition of "infinity." But this was originally a disturbing turn for many and, as far as I know, does not have many if any applications in physics.
So, what is the status of "infinity" in philosophy and science now? Is it more or less accepted that science can only get going by performing the (I am tempted to say castrating) act of "defining" to enable counting? And Cantor sealed the deal by defining infinity itself in terms of counting?
(I ask in part because I am always a bit uneasy with modern cosmology and statements like "countable" hydrogen atoms in the "universe.") In any case, are there interesting current controversies about infinity in physics, math, and philosophy these days? Preferably understandable to the amateur.