User blog:SuperSpruce/How I think the growth rate of the “array of” operator in BEAF is

BEAF (Bower’s Exploding Array Function) is ill-defined after tetrational arrays. There are many ways people think how powerful the “array of” operator is. And here is my take on that:

w=lowercase omega, W=Capital Omega, e=epsilon, P=phi

You know how something like (10^10)&10 has a growth rate of f_w^w^w[10] in the Fast-Growing Hierarchy (FGH). It turns out that 10^10 is g_w^w[10] in the Slow-Growing Hierarchy (SGH). Also, (10^^10)&10 is f_e_0[10] in the FGH and 10^^10 is g_e_0[10] in the SGH.

So here is my idea: A&B=f_w^C[n], where A=g_C[n]. In the first example C was w^w, and in the second example C was e_0. This means that (10^^10]&10&10 should have a growth rate of the BHO, for example.

Since the most common form of the SGH catches up with the FGH at P(W_w), then {n,n / 2} should have a growth rate of P(W_w).

I’ll continue this post later. Feel free to comment on this post, and I encourage you to make Recursion levels in the FGH past legion arrays, to ligions and lugions and legattic arrays and whatever Jonathan Bowers made after legion arrays. I have tried to provide a simple explanation of what I think the growth rate of simple legion arrays are, and I hope this helps people think how powerful Bower’s ill-defined arrays actually are.