Saturday, March 22, 2014

Fibonacci coding and Wiki to the rescue

I get this feeling sometimes that mathematicians read my puzzlement and post results on Wiki, as if this the unified theory is a community project.
In mathematics and computing, Fibonacci coding is a universal code which encodes positive integers into binary code words. It is one example of representations of integers based on Fibonacci numbers. Each code word ends with "11" and contains no other instances of "11" before the end.
This is what we want.

I am going to show a sequence from Nyquist to symmetric to asymmetric.


(-1.57,0,+1.57). Is Nyquist, there are only waves.
(-1.94, 0,+1.94) is symmetric packing, nulls balance phase.
(-2.09,0,+2.09) is asymmetric packing, more null measured than phase.
They all can be resolve to (-1,0,1), which makes the Fibonacci sequence.
-3,-2,-1,-1,0,1,1,2,3. How can that be?

It is what they measure, each assumes a different curvature of the universe, which is measured by something called the hyperbolic functions.  Nyquist assume the universe is made of balanced sine waves. And so I will show the quantization levels are Fibonacci encodings and obey the Shannon condition. We get integer arithmetic.  The layout or our complete sequence should obey the hyberbolic functions.

That is my direction, wish me luck.


This is the hyperbolic.  Take the first form and split it up:
(1/2) (e**x -1) - 1/2(e**-x -1)
Both parts obey the Shannon condition by converting loge to log2.  They which are the negative/positive halves of a quant level, and become: SNR when treated separately. Half the energy from negative phase, half from positive.

The base you convert to is determined by how flat you think the world is.Here is Wiki:
The first few Fibonacci codes are shown below, and also the so-called implied distribution, the distribution of values for which Fibonacci coding gives a minimum-size code.

So we have a basis to combine quantization and SpaceTime. And this note:
It can be shown that such a coding is unique, and the only occurrence of "11" in any code word is at the end i.e. d(k−1) and d(k). Note that the penultimate bit is the most significant bit and the first bit is the least significant bit. Note also that leading zeros cannot be omitted as they can in e.g. decimal numbers.

Zeros are our null points. Matter must exist.So we add Fibonacci to our list of great scientist of the world.

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