Infinite tetration and superroot of infinitesimal

[GFR]

Hi Ivars!

Concerning:

I have a question:
Since we have h(e^(pi/2)) = h(i^(1/i)) = h( (1/i)^i) = -i (or, perhaps, also +i, but that is not so important at this stage), and we interpret it as Andrew did it:

if -i is a hypervolume of length e^(pi/2) being tetrated infinitely - kind of building up higher dimensions of immeasureable (transcendental or not?) edge e^pi/2,

With "rho" and "pi": Greek letters, let me try to put it like this:

- pi = 3.1415592654.. : the famous constant universal ratio;
-+/- i = sqrt(-1) : the two (constant!) square roots of -1;
- rho = e^(pi/2) : a critical base for an "infinite tetrate";
- h = {-i, +i} : the imaginary conjugate units.

Well, we have:

rho#(+oo) = [e^(pi/2)]#(+oo) = {-i,+i}
rho = i^(1/i) = i^(-i) = (-i)^(-1/i) = (1/i)^(i) = e^(pi/2)

Concerning a possible mnemonical and amusing math-fiction model, we might say that -i and +i are the two possible symmetrical (conjugate) imaginary unit heights of a tower with base "rho" and an infinite number of stores. In other words, {-i, +i} are the two softly collapsed heights of an infinite tower with base (and not an "edge") rho.

But, it is not reasonable to measure the actual "volume" of this kind of "towers" and, particularly, their external "surfaces". These are, in my opinion, label concepts without any specific mathematical meaning.

GFR