Dvali's and Avogadro's Numbers

This is not the first time that we are confronted with huge numbers in physics. Many years ago Boltzmann, forced us to consider the number of atoms in a grain of salt (10²³)to the dismay of Mach. Now Dvali wants us to think of 10³² to the dismay of most of us.

Is there any fractal structure here?

We are made of 10²³ parts, and the parts are made of 10³² parts.

So, naturalists observe, a flea
Has smaller fleas that on him prey;
And these have smaller still to bite ’em;
And so proceed ad infinitum.

Jonathan Swift (1667-1745)