Supernatural Math

bysaturn10y19th May 200958 comments


Related to: How to Convince Me That 2 + 2 = 3

This started as a reply to this thread, but it would have been offtopic and I think the subject is important enough for a top-level post, as there's apparently still significant confusion about it.

How do we know that two and two make four? We have two possible sources of knowledge on the subject. Note that both happen to be entirely physical systems that run on the same merely ordinary entropy that makes car engines go.

First, evolution. Animals whose subitizing apparatus output 2+2=3 were selected out.

Second, personal observation; that is, operation of our sense organs. I can put 2 bananas on a table, then put down 2 more bananas, and count out 4 bananas; my schoolteachers told me 2+2 is 4; I can type 2+2 into a calculator and get 4; etc.

Now, notwithstanding the above, does 2+2 really equal 4, independent of any human thoughts about it? This way lies madness. If there is some kind of pure essence of math that never physically impinges upon the stuff inside our heads (or, worse, exists "outside the physical universe"), there's no sensible way we can know about it. It's a dragon in the garage.

The fact that our faculty for counting bananas can also be used to make predictions about, say, the behavior of quarks is extremely surprising to our savannah-adapted brains. After all, bananas are ordinary things we can hold in our hands and eat, and quarks are tiny and strange and definitely not ordinary at all. So, of course, the obvious thing that comes to mind to explain this is a supernatural force. How else could such dissimilar things be governed by the same laws?

The disappointing truth is that bananas are quarks, and by amazing good fortune, the properties of everyday macroscopic objects are sufficiently related to those of other physical phenomena that a few lucky humans can just barely manage to crudely adapt their banana-counting brain hardware to work in those other domains. No supernatural math required.