User blog comment:Maxywaxy/how do five argument beaf arrays work/@comment-30754445-20181122155711/@comment-30754445-20181126195542

Yeah, that's the official explanation, which - quite honestly - doesn't make much sense.

It does explain why Graham's Number is solely built with 3's (unlike the Little Graham)... but why 64 layers of arrows? 8 layers would have been sufficient to surpass the Little Graham (and therefore sufficient to be a valid upper bound of Graham's problem), and changing the "8" to "64" doesn't simplify anything.

I suspect that the only reason that Graham did that, was to make his number more impressive to the layman.

From a googological point of view, by the way, this is kinda funny. Because in reality, the number of layers doesn't really matter. What matters is the kind of recursion that your function does (in Graham's case, doing layers of arrows). Whether you do it 8 times or 64 times or a million times or even a googolplex times, it doesn't really change the general ball park of how large your number is.

Here are the Psi Levels of these four examples, just to illustrate my point:

8 layers - PL 12.9

64 layers - PL 13.2

a million layers - PL 13.4

a googolplex layers - PL 13.5

As you can see, in general any Graham-like number will score around 13 on the Psi Level Scale (though you can get to Level 14 by setting the number of layers to Graham's Number)