Exact Numbers

Recently I have been counting steps as I walk. I pick particular short stretches along frequently traveled routes and count each time I walk them. The numbers vary quite a bit. I can't say, for example, that a stretch of sidewalk is 54 steps long, but I could give a pretty good guess of the mean at 54 and the shape of the distribution.

It's natural to believe that the exact number of steps does not exist, because once you walk it, it vanishes. Each time you try to count it, you will get a different number. The distribution eventually takes a characteristic shape, but each time you walk it, the outcome is unpredictable.

Now another counting problem. Count the number of ants in New Brunswick. You can't actually go and find every single ant. Even if a team of 100 people committed a year to it they wouldn't find every single ant. You'd have to get some kind of an estimate. And it wouldn't be exactly right, and every time you did it, you'd get a slightly different estimate.

Now the question is, does the number of ants exist? First, a slightly less weird question: is there any way to observe the exact number of ants directly? My inclination to this question is no, simply because I haven't thought of a way to do so. Then a slightly harder question: is there a way to observe the exact number of ants indirectly? Another way to put it, is the number of ants divisible by three, and how would we ever know? The question this is getting at is, is there any way in which whether the number of ants is divisible by three will affect our experience in a way that is observable to us? This is the really careful way of asking, is the world in which the number of ants exists any different than the world in which that number does not exist? Which is yet again a really careful way of asking, does the number of ants exist? Again my inclination is no, but only because I haven't thought of a way to make it exist.

Anyone who thinks we live in a deterministic world hasn't looked around them recently enough.