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Exhibiting Randomness in Arithmetic Using Mathematica and C

G. J. Chaitin
Organization: IBM Research Division
Journal / Anthology

Year: 1993

In my book Algorithmic Information Theory I explain how I constructed a million-character equation that proves that there is randomness in arithmetic. My book only includes a few pages from the monster equation, and omits the software used to construct it. This software has now been rewritten in Mathematica. The Mathematica software for my book, and its input, are here in their entirety. The Mathematica code is remarkably compact, but it sometimes is slow. So one C program plus equipment for automatically generating another is also included in this software package. I used Version 2.1 of Mathematica as described in the second edition of Wolfram's book Mathematica -- A System for Doing Mathematics by Computer, running on an IBM RISC System/6000 workstation. Since the APL2 character set is not generally available, I decided to change the symbols that denote the primitive functions in the toy LISP that I use in Algorithm Information Theory.

*Mathematics > Discrete Mathematics > Cellular Automata