Apart from differentiating log (n²) from (log n)² in "log en squared", that at least makes sense without overloading the superscript-2's meaning. You cannot "square" a function (rather than the result of a function) and whilst I acknowledge that trig functions are so notated (at least with the likes of sin²(x), but not sin-1
(x), and sin-2
(x) could therefore be considered confusing), "iterate twice", i.e. "log of log of n", is really the only way I would understand this, without guidance to the contrary.
It doesn't help if it's pronounced
as "log squared en", as (unless we're breaking into perhaps some sort of Polish notation - thus log (n²)?), it really should be said as "log twice en" or nothing... Like log-1
is "unlog n", if that weren't "(unstated base) to the power of n", anyways (also highlighting trouble with "logb2
(n)" notation), and the reciprocal of the log is often better written otherwise ("1/log n"? "1
"? "(log n)-1
"? and also a proper TEX layout - according to availability in the medium being written in...).
I'll admit that I've never actually done much log of logging, or else squaring of logging, in a pure maths-theory environment where this may be necessary to understand the inconvenient precedents for (as per trigs). In coding, nested parentheticals make it clear(er!) what is meant, in a different manner. The "in the order of" notation of programming theory
just has never required me to delve into this inconvenient version of alternate applications of notation until now... I just have a sense that somebody, somewhere has got it wrong, and obviously it aten't me...