A very odd thing about math — which, after all, is a realm of pure reason, or as close to one as we can get — is that it makes a lot of people angry.
Ackerman’s function had this effect on one of my readers.
What is the POINT of numbers that big? Why do they bother to exist? They are no conceivable use for anything . . .
I’m not unsympathetic, and the question is quite a profound one. The real world seems to have no use for such numbers. It is in fact an odd thing that the universe, in relation to ourselves, limits itself to numbers of just a dozen or so digits, in both its spatial and temporal dimensions. I can’t see any reason why it shouldn’t be A(4, 3) years old, or A(A(A(A(4, 3), A(4, 3)), A(A(4, 3), A(4, 3))), A(A(A(4, 3), A(4, 3)), A(A(4, 3), A(4, 3)))) for that matter, but it chooses to be a mild, comfortable, easily imaginable 13.7 billion years old. Strange. I have ruminated on this topic at more length here.