Combinatorics and how Phi makes Pi, how nature does log and the theory of everything

We have this:

4^Phi = 3*Pi, Phi being the Fibonacci constant.

The reason for this, skipping the 3 for a moment, is the Phi is composed of:

1/Phi + 1/Phi^2 + 1/Phi^3....

What this means, in terms of Lucas angles, that a system which combines two previous sets to make the next set of things will be minimally dense when the sets of things grow by Phi^n.

The 4 results here because in the Lucas angles, 1/Phi^n are created by cosh(n)-sinh(n), and each of the cosh and sinh are combined from the two previous sets, each set composed to two types of things.  When all the things are combined along the chain and density is minimized, then we have:

log(4^Ph) = the sum of log(4^[1/Phi^n]), for each of the n, to Nmax

Let density, D, be defined as the overlap of things, as if they were bubbles.
Then, at the point the sum of D'/D along the chain is log additive base 4. So any additional combinations will no longer be evenly dense along the chain.  Pi, is an outcome of combing two previous sets of thing. It has nothing to do with circles, we humans made that up. Stability is D'/D being the least redundant motion. That is there is no exchange which reduces density along the chain.

This, then, is the essence of the theory of everything: local combinatorics,  least redundant motion, and maximum divergence.

What if we reach back and combine three previous sets? Dunno, wonder what the pros say? Left to the reader.

Now the reason we have cosh(4^Phi/3) = (1/fine structure)^1/2 has to do with quasars. They are not strong enough to compress the vacuum past some dimension Nmax, which gives the uncertanty in divergance, and minimal redundancy. 

If you want to work this use:

Mainly because reaching beyond Pi/2 is reversing causality. Right now we are limited to Pi/2.


Maybe there are some quasars than can do better, dunno. Go look for them with your telescopes.

Great, now let me make my pitch.  Large companies with lots of money need to higher all the mathematicians who are good at this, and these folks are friggen brilliant.  This theory makes AI, does optimum search engines, makes banker bots and everything else. Go get yourself some mathematicians and you will not over pay them, they are worth every dollar.