log* doesn't beat Knuth arrows. See that log*(e ↑↑ n) = (n-1) log*(e) = n So log* is just the inverse of e ↑↑ n. That makes sense. Logar

log* doesn't beat Knuth arrows. See that log*(e ↑↑ n) = (n-1) log*(e) = n So log* is just the inverse of e ↑↑ n. That makes sense. Logarithm is the inverse of exponentiation. log* is iterated logartithm-ing, and (↑↑) is iterated exponentiation (aka tetration). (↑↑) builds up a stack of powers, and log* tells you how tall that stack is.