Factoring the product of primes .
14 Dec 2009
Iterative systems are needed to get results .
The physical solution .
Take a number N . Make a circular mirror where Circumferance=N. Shine a sharp light from anywhere on the inner rim and rotate it , shining the light around the circumferance. Have a light-sensor at the back of the light-source . If the sensor shows a maximum , stop . The factors can then be calculated .
The Point :
This is an in principle argument .
Anything that can be done like this should be possible using mathematics .
This is a fundamental assumption in present society . Not even mentioned , usually .
Yet , RSH and other systems use the difficulty of factoring the product of large primes as secure systems .
But if a known physical solution cannot be described in mathematical terms , we are in deeper doo-doo than a few encryption problems .
Iterative systems .
See http://andreswhy.blogspot.com "The inside of zero"
The multiplicative system can be described as :
Sin(pi/(n+2)) = Sin(pi/(n+1)) + n^2/N *tan(pi/(n)) … an iterative process .
Where N is the number to be factored , and n a factor .
This can be stated by
Y = Sin(pi/(n+2)) –Sin( n(pi/(n+1))) - n^2/N *tan(pi/(n))
Using Newtonian approximation . AsY->0 , n->factor .
Any N can be factored .
This is a double application of iterative processes , using the interchangeability of n and the counter . (A neat cheat.)
But what does it mean ?
At least two infinite processes are needed to get some meaningful results that a physical experiment gives immediately .
It means that no theory of everything is possible . Any description will always be two infinities behind . Regardless .
As expected .