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[It follows that there is] an upper bound of ~10^122 on the number of bits that can ever be involved in any computation in our world […]


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    The transition from ‘difficult, but provable’ to ‘mathematics says no’ in busy beaver numbers is one of those great little ah ha! moments. It’s got a similar feeling to the outline proof of Gödel’s incompleteness - that “oh sure, lets just embed a logic in our system of arithmetic, what could possibly go wrong?!” moment.