Why does 3/2 show up everywhere in physics and quant ratios?

The ratio is the volume of a sphere to the surface area, log(r^3)/log(r^2), so that number will be closely related to the quant ratios you need for maximum entropy, and in the signal to noise, a ratio of energy, you will see looks like r^3/r^2 everywhere. So maximum entropy theory will tell us that at some point, we can do just as well by treating a collection of packed bubbles as one spherical bubble. Namely when log2(1+r), and r > .5, you can do better by bumping your quant rate and carrying fractions.

3/2 is log(r^3/r^2) is 3/2*log(r). So 3/2 is the optimum quant ratio to make a digit system for spheres. That means, breaking up a sphere along the radius by units of (3/2)^n will give you the minimum number of digits you need, so multiply is the most efficient.

The topologist who discovers the maximum packing theorem for three types of bubbles will tell us that story when he gives speeches to the Swedish Banana Society.