Thursday, January 1, 2015

How's the mathematic you ask? And more

I am taking the approach that a Weiner process is local, and local processes are minimally redundant. So I take this equation:

1: (integral) tanh f(x) dx = (1/f(x))ln (cosh f(x)) + C

and make if look like this:

2:




Where f(x) is some polynomial that creates a Weiner process, or one stage of the Schramm-Loewner.

That gets me something like this:

3:   f'(x) * (integral) tanh(f(x) -f(x)/2 = ln(cosh(f(x))

This tells me the following. If the electron were a geodisic sphere, a multi-mode string, or a deformable bubble, then  then it is a digit system.

4: 2a1+1,2a2+2,2a3+3 etc

So, equation three above tells me that the unit sphere  fill up to a certain point then jumps to the next exponent in the digit system in 4.  The rate by which it fills is determined by the Weiner mode, and that is minimal because of equation 2.  Equation 3 gets me my values for the a1,a2,a3... So this is my approach to combining the Schramm Loewner and hyperbolic sphere packing.  There is a tangent and a cotangent move, and equivalent move using the coth(f(x)).   So the string or geodesic is a 12 sided thing, because I already know that f(x) is ax with a = ln(Phi) . The quarks are cramped, so they have larger angles but the angles are complementary, they are a multi-process Weiner process.

What about sets?

I am doing the same.  I start with plain vanilla names, unique and ordered, called primes: a,b,c,d.  They combint in order: a,b,ab,ac,bc.abc.. The names mean nothing, they just combine to exhaust the possible sets.  I even include powers like aa,aaa,bb, etc The primes count sets as a two bit number, as you can see. So I have the same problem.  Except that instead of imposing a Weiner sphere packing motion I impose something called the 'human multiply', and I match the exhausted set with the multiply motion. I use the multiply motion to bounce along the exponents and re-arrange the countable sets into a 'multiply' set.


So, making a multiplier.

I have the exhaustive number of possible sets using some N primes identified, and I know the total number of sets created.  I now want to make a multiplier graph bu applying the rules of multiplication.

So, for example, the prime sequence 3*3*3 appears 1/27 times in my multiplier sequence.  And 3*3 appears 1/9 - 1/27 times, I am applying the power rules and discovering the probability of occurrence.

I do thsi for all the primes, and scale the probability of  occurrence by the total number of sets.  Now I can compute -iLog(i) for all my primes.  I treat my multiplier as an information channel. The total number of sets are unique and treated as a unitofrm distribution.  For each of the sets, the send wants to encode the primes making u0p the set and deliver them to the multiplier, whcih then decodes them into the individual primes.  The number of bit allocated to each prime is the -Log(i), where i is the absolute probability of occurrence for nth prime, for example.   But -Log(i) is irrational. However, I can set the precision of the -Log(i) such that each prime can be identified to come precision.

So, my sender picks one of the sets, enco0des the sequence of primes, and send them.  The receiver takes the encoded prime and runs it through the decoder tree, and determines the exact prime, and one of the bits in the set identifier is set. When the sequence of primes for the set has been received, the bits set identify the actual set to some probability.  Hence, I have the minimum spanning tree for my multiplier up to some finite length number line.  But that tree is minimal, and any real digital multiplier should have the dual of that tree.  But I know what digital multiplier trees look like, and I know how they are recursively expanded as the number line grows in finite length.  So, I should be able to reveal the spasity of primes, for some selected precision, as the number line grows.  I have decomposed the prime number problem, at least to some variable amount of precision.

That is the theory, anyway, and it is based on the idea of minimally redundancy bveing unique and supporting a locally recursive Weiner process.






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