User blog comment:Maxywaxy/how do five argument beaf arrays work/@comment-30754445-20181122155711/@comment-30754445-20181123115538

I guess that "infamous" wasn't the word I meant to use here (should have simply been "famous").

Though the media hype sorrounding Graham's Number is, indeed, infamous in googological circles,.because:

(1) It wasn't the actual number used in Graham's proof. The number which was actual upper bound is known as "Little Graham" (look it up). The famous number with the 64 layers of arrows actually served no mathematical purpose what-so-ever.

(2) It just isn't that big. I mean, yes, it is huge when compared to everyday numbers or even power towers, but you can construct it with a single diagonalization plus a single recursion.

(3) The Little Graham is just an upper bound. The actual solution for Graham's problem is believed to be less than 100. So it's a poor example of a large number actually appearing in a solution to a mathemical problem.

I think a better target for all this hype would be TREE(3). It is so huge (above SVO-level) that you can't even begin to explain how big it is to a person without getting into pretty deep stuff. And more importantly: it isn't just an upper bound. It is the actual solution to a fairly simple problem.