If you’ve read my previous “stuff” on mathematics you already know I am no academic in the field. Nonetheless philosophical mathematics interests me. I was reading a book titled “number: the language of science” by Tobias Dantzig and a debate was presented stemming from Greek philosophers about space and time and our perception of it. I am so confused now. Here’s the deal, put simply:
You are on a track. Now, you can run around the track and get from the start line back to the start line for one revolution. Correct? Okay. Now, if we consider that we can divide the track infinitely, meaning we can continue to divide an oval into segments infinitesimally small. Now, to traverse each segment takes an amount of ‘time’. Which means if you divide a track into an infinite amount of segments then it is impossible to make a single revolution.
This gets my mind twisted up because while I cannot comprehend infinity I can and do walk a track regularly and my knees tell me I have walked too many revolutions. Is this because I have walked an infinite amount of time? I am sure I have not. Clearly I misunderstand.
But I have to wonder about this concept because if I can see a circle as nothing more than an infinite amount of points and a track as nothing more than an infinite amount of segments than to walk a revolution on either means that I have traversed an infinite amount of time as well as segments and now I must question time. I must. If infinity can be summed up into a track, a loop, then why cannot other concepts that have to do with time? Is our Universe but one segment of a track that Gods walk upon daily in some reality that is fractally bigger than this one?
While it is fun to speculate on such things, I have to admit I find no place this in reality so I give up on the imaginary in favor of imagination that ends where I comprehend. I walk a track that ends at the same space where I began. Nothing more.