Mathematics in Sci-fi

6/6/12 Divergence, Tony Ballantyne, 2007. It started slowly with too many characters, but then zoomed off into the depths of the story with all its philosophical issues and amazing details. The ending, as was to be expected, verged on the psychedelic symbolic images of 2001 the movie, but did not go over that abyss. Too many great ideas were contained in the processing space of this trilogy to mention them all but a few of my favorites were: “... so what if your mind is a TM? You are greater than the sum of your parts.”; the dark plants being fixed in space by the observation of an intelligence; the n-string game and Schroedinger’s Cat’s Cradle; “There are different levels of programming languages, so why not one specifically for the soul?”
A you would expect from an author who taught math and IT, these books are full of mathematical references. Although the story is built mostly on computer science and artificial intelligence, it mentions stellated icosahedrons and dodecahedrons, the Sierpinski Gasket and the Mandelbrot set, the golden ratio, Riemannian transforms, and Hilbert space. It even includes the formula for Heisenberg’s uncertainty principle! One of the characters sails off in a spaceship called the Fourier Transform, on which the classical mathematical impossibilities are no longer impossible: creating a formal way for determining a proof, finding an even number that is not the difference of two primes, having a recursive set for everything, a solution for an NP complete problem, and all the other NP problems tumbling into P.