User blog comment:Vel!/Yudkowsky on googology/@comment-5529393-20140321133053

I guess I largely agree that those conjectures are the reasons most mathematicians would give for not taking googology seriously (particularly #3). While I can see people might believe #1, I'm not sure that it is actually valid in practice. Usually, it is either easy to see that one number is bigger than another, or in cases where it is difficult to see, it is because something interesting is going on mathematically. Of course, "seeing" that one number is bigger than another is different from a rigorous proof;  it may be quite difficult to prove, say, tree(4) > Hydra(10), even though it is easy to see which is almost certainly larger by comparing ordinals.


 * 1) 3 is a difficult objection to deal with; honestly, I would have trouble explaining my obsession with large numbers.  There's a sort of mind-expanding vastness that comes with dealing with larger and larger structures, each new ocean turning the previous one into a little wading pool.  As a bonus, the mathematics that comes out of it is pretty cool, niche as it may be.  I don't think most people would be persuaded by this, though.  At least for #2, we can say that there are certain specialized fields (proof theory, recursion theory, Ramsey theory, combinatorics) where these large numbers can enter in.  But I don't know how to persuade someone who asserts #3.