Ohhh man, you guys quibbling about units of distance, discrete or continuous ought to read up on quantum mechanics--it'll blow your mind.
If you're familiar with orbitals, or remember them from chemistry, you know that electrons "jump" from orbital to orbital depending on energy levels of the molecule. One very interesting example is fluorescence. . .
You have a substance which is hit with photons (the discrete particles of light), the photons add energy to the electron, which then jumps into higher level orbitals. Fluorescence, the observed phenomenon of an item glowing in the dark is electrons returning to the lower energy orbital and releasing the photon previously absorbed.
The interesting thing about the electron jump--and the wackiness that is quantum physics: The electron does not travel in a continuous fashion to the other orbital, the electron absorbs the photon and
instantaneously appears in the other orbital. I remember learning this and thinking, wow, I could understand if it were 10^-576 seconds, but it's instantaneous.
I asked the professor about this, and you get into some crazy particle-wave duality issues as well, but in essence, everything acts on a quantum level, but our senses are not geared finely enough to ever experience this.
One of my nuttier theories is that I think that since we are born with senses that are attuned to the macro world, and our education is, of course, attuned to the same world--that we go about science education in the wrong order. While children are young and have the "sponge" for a brain and can absorb some of these realities of the world of particles is when they should be taught it. We shouldn't teach classical physics first because it makes it far more difficult to comprehend the quantum world.
Personally, I didn't learn anything significant about it until college. In my weird opinion, some of the basics should be taught in elementary school. I have this whole idea for a curriculum for children and, well, I feel sorry for any child I might someday have.