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## Human ecology

# Godel's Theory - other versions

From Casti (1991)
- Turing Machine Version

No computer program can ever generate all the true statements of
arithmetic. (p.348)
- Complexity Version

There exist numbers having complexity so great that no computer
program can generate them. (p.356)
- Computer Program Version

There is a computer program P* such that if P is a correct program,
then P* applied to P yields a truth omitted by P. (p.383)
- Diophantine Equation Version

There exists a Diophantine equation having no solution - but no
theory of mathematics can prove the equation's unsolvability (p.387)
- Dice Throwing Version

There exists an uncomputable number (omega) whose digits correspond
to an infinite number of effectively random arithmetic facts. (p.390)

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Created 3/3/99