Mind of God: The Scientific Basis for a Rational World by Paul Davies

Author:Paul Davies [Davies, Paul]
Language: eng
Format: epub
Tags: Religion, General, Science, Philosophy & Social Aspects
ISBN: 9780671797188
Google: 2us7445YjgMC
Amazon: 0671797182
Publisher: Simon & Schuster
Published: 1993-03-05T08:00:00+00:00

In spite of these difficulties, it might be possible to find a 10-percent approximation by nonalgorithmic means. The point about an algorithmic construction is that one can lay down a finite set of standard instructions at the outset; it is then purely a mechanical matter to work through those instructions to obtain the desired result. In the case of a computable number such as pi, one can imagine a computer churning away, generating a sequence of ever better approximations and including in the output at each step precisely how good that particular approximation was. But as we have seen, this strategy won't work for an uncomputable number. Instead the theorist would have to approach each level of accuracy as a new problem, to be tackled a different way. By some clever trick it might be possible to find a 10-percent approximation to x. But the same trick wouldn't necessarily work to reach the 1-percent level. The theorist would be obliged to try some totally different strategy. With each improvement in experimental accuracy the poor theorist would need to work harder and harder to find a matching approximation for the predicted value.

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