Maybe it was a Greek maxim about running a race. Oh yeah, the atom. Where a runner runs half a race, then half of half, and half of, etc and eventually you’d get to a point where you can’t split it anymore. And thus, the atom. And forgiving a few whack jobs we know this isn’t true, with the atom being splitting over two Japanese cities etc, etc. Now we know, or at least conceptualize, the Planck as the most finite distance of travel. But lets not get worked up on names and instead return to our race runner. Who has about a foot left to travel to the end of the race. Then half a foot, then a quarter, then a few inches, then an inch, then half, then a quarter, then a few millimeters, then half, then a quarter, then a few nanometers, then well you get it. But, seeing as that there is just as many halves left to go, as halves he’s already overcome, I question. And fear the parables and physics has left me to question, as if getting to the last 99% of the story I would figure out the rest. How do you ever get to a final half, and over the finish line? Is there just a probability threshold to overcome in which you go from infinite halves on one side of the line, to infinite other halves on the finish side? There’s as many pieces of one as there are ‘ones’. Its like as x -> infinity in the denominator, math sort of gives up y’know and you put a big DNE on your test in calc II and get full marks.
I guess I better understand activation energies for chemical reactions, if I don’t say so myself. Y’know, heat water and eventually you give enough energy to the water molecules to go from liquid to solid. There’s an energy threshold, with binary states of solid, liquid, gas, and each temperature and pressure dependent. That somehow makes more sense to me then ever getting to the finish line. The infinite abyss between the last step and the finish line feels insurmountable and taken for granted. Does it work the same way? Do you add enough steps to the race that your binary state goes from not finished to finished? Hang on hang on, the last Joule of energy in the near boiling water needs another 2 half Joules and 4 quarter Joules and 8 8th’s of a Joule, oh god. Oh god. How do we ever go from one state to another???