Calculus is an idealization where we take limits like
lim h → 0 (1+h)(x/h).
(This is a compound interest formula. It appears in the movie
The Bank.
Can we really do that? Early philosophers have thought
about this: Zeno of Elea (490-430 BC) was worrying about that
200 years before Archimedes (287-212 BC).
What if an
arrow is located at a fixed position at any moment of time,
how can it move? The concept of velocity deals with rate of
change which is a limit
limh →0 [f(x+h)-f(x)]/h. An example is for
f(x) = sin(x), and x=0, where sin(x)=0, so that
we want to understand the limit
limh →0 sin(h)/h. The fundamental theorem
of trigonometry assures that this is 1. Here is a hollywood
picture The Ant man and the wasp (2018)
illustrating the quantum realm which somehow still
suggests that the world can be scaled arbitrarily. A the end,
Scott gets trapped in the quantum world. (The story then gets
concluded in Avengers Endgame.)
