unnatural numbers – the short version

So the short version goes something like this: “natural” numbers (the non-negative integers we use for counting) are a man-made invention, and do not connect deeply with the fabric of our existence. There, I’ve said it.

I can’t tell you what a relief it is to finally say that out loud. So to speak.

Why do I emit such drivel? Well, it’s a rather long story, and I’ve been writing about it on again/off again for the past couple of months, and I have yet to sufficiently refactor my reasoning such that I am comfortable exposing it to public scrutiny. So I wanted to at least lead here with the short version so that I could briefly touch on some of the troubling consequences of this belief.

The biggest trouble is that I am now unable to map conclusions reached through any formal system – including, tragically, that old standby of geometry – back to the real world with any deep sense of certainty.   If the axioms on which these formal systems are based don’t have a basis in the real world, how can we trust that the theorems we derive with them have any semblence of Truth when mapped back to the natural universe?

But surely, natural numbers must exist, you say.  Why, look here: I have exactly 5 fingers on each hand.  And I have exactly one car that I drive to work.  And three quarters in my pocket.  And so on.  I’ll have to save my expanded reasoning for the long version of this story, but basically, I say that’s not true.  In your mind, you have elected to partition a specific clump of spacetime and model it as “your car,” and for the purposes of reasoning (in your own mind) you find it convenient to think of all the components of the car as making up a single entity.  But the idea that all of those components actually comprise a single, atom entity is a figment of your mind alone.  The universe has no need to oversimplify patterns of matter such that they may more easily be manipulated by logic, and so doesn’t see things that way.  I’ll look forward to digging into the reasons I think this is true later on.

For now, I’m just happy to have that zinger off my chest.