Utility of integer factorization.
Other than the obvious, RSA and P:NP, how would the ability to factor integers of any magnitude affect the sciences?
A natural extension includes factors such as complex (Gaussian) primes and quotients.
Will such a tool provide deeper insight into the results of numerical calculations, fundamental physical or mathematical constants?
PSLQ has provided insight into some structures and Plouffe (unsuccessfully as far as I am aware) attempted the same for some physical constants. (Regarding constants, Steven Finch's expositions are a good complementary reference.) The work of Mandelbrot and Thom has helped to conceptualize order from apparent disorder and I was wondering if `reversing the multiplicative process (a solid notion of primality is crucial)` would have a similar effect. Mandelbrot's, "The Fractalist", is a bargain in paperback and for those with some time, any of the books in the "Library of Living Philosophers" are worth [the] while. As usual, Google and Wikipedia will point and introduce the sources but will not replace them. Rational creativity, I guess, would be a way of encapsulating the above.
Looking at "Wired's" review of Mandelbrot's memoir, this point is a carryover from prior thread, "... Mandelbrot was a brilliant idealist who struggled with the gap between thought and language..." which may be
considered as an aspect of the SW hypothese.
Last fiddled with by jwaltos on 20150513 at 16:56
Reason: corrections
