Saturday, May 10, 2014

Straightening out my number line

In this exercise, I have dual quantizations in powers of my index, the X axis. One is a power of two, the other the Fibonacci rate. So, I set the scale factors of my integers to get both quantizations matching the prime numbers up to 3001. My question is why do they only match up to the last prime in my list?  It is an error in my method. My spreadsheet, counting up, does not know what is next, the only thing relevant is the spacing of primes relative to the X axis.

What is that crossover point, the point where dual quantizations need another prime?  Both twos and Fibonacci are strongly divisible, I think. Are there other quantization rates for X I can try?

I have 436 primes in the list. My theory of primes tells me I can scale the number line with a 436 degree polynomial in X and make the number line have all those axii of symmetry and keep the error between two operators within a range. If I want, I can skip some separable groups, and make a shorter polynomial.  Say, for instance, if the King prohibited all groups composed of 23 elements.

What I am really doing is picking two reasonable operations I want to perform. then creating a finite number line so the number of integers and the number of fractional ticks between integers match the operators I want to use. I am minimizing the redundancy in my finite number line. That sharp cross over point results because my number line was scaled to match a particular number of separable groups, so when I exceed that number, I get sudden redundancy.
Work though the method and you will see this is just a method to do the Zeta function up to a finite limit.

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