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Then and now: the challenge of irrationality in the ancient world and today

I was listening to the 'In Our Time' discussion about Boethius this morning and something that was said brought the following idea into my mind.

We are told that the Pythagoreans were horrified to discover that there are irrational numbers, such as the square root of 2, that cannot be expressed by a fraction. This seemed to them to be a threat to the rationality of the universe.

Is there a parallel here to Einstein's conviction that there must be something wrong with quantum mechanics, which he expressed in the famous phrase 'God does not play dice'?

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