Do you believe in god or math?

[Categories+Sheaves]

The only thing the math does is give 10 equal horses. After quantifying them in terms of money, we can let the math shine with much more detail. 1 prize stud worth $250,000 (who ran away) and is hanging out with 9 scrub mares worth $800 each. We shall have to see if they gave him some bad horse disease that brings his value down to 0 however.

Not to necro, but I want to nitpick this.
Of course turning things into numbers kills off a bunch of details. That's arguably what math is all about: getting the maximum mileage out of a very small bit of information (and conversely figuring out how little you can know while still being able to deduce something). We might lose a lot of information when we turn a knot into a polynomial (e.g. Alexander Polynomial, Jones Polynomial). But we do it anyway, because they're easier to work with than a horribly tangled diagram.

And if the health of the horses is something we find particularly important, we can find some notation of keeping track of that as well. Not all functors need be so forgetful.

So if I throw ten tennis balls into a bin, they aren't exactly the same as they were before I threw them? Ok. I can live with that. Math is supposed to be a description of reality after all, not the other way around.

I agree that math isn't completely objective. But I can't see where this subjectivity has any teeth. "I'm drank some coffee before I typed this sentence" was surely made from the same subjective basis. And I'm sure my coffee has some things in it (plastic leeched from the mug, maybe some of my hair?) that I don't consider to be coffee. My conception of coffee is no less perfect that my conception of n tennis balls in a bin. But I fail to see how we could insist on the existence of coffee while questioning the existence of numbers. I mean, coffee does exist, right?