The Berry paradox is related to famous liar’s paradox (“this statement is false”), Berry as well as a number of paradoxes in set theory explored by Bertrand Russell and paradox Kurt G¨odel. The Berry paradox shows indirectly how the notion of Kolmogorov complexity can be difficult and subtle. Consider describing positive integers by means of sentences, for instance “the number of fingers on a human hand,” or “the number of primes less than a million.” Explain why the definition “the least number that cannot be defined in less than twenty words” is paradoxical, and informally how this relates to the difficulty in computing Kolmogorov complexity

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Asked Mar 3, 2020
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The Berry paradox is related to famous liar’s paradox (“this statement is false”), Berry as well as a number of paradoxes in set theory explored by Bertrand Russell and paradox Kurt G¨odel. The Berry paradox shows indirectly how the notion of Kolmogorov complexity can be difficult and subtle. Consider describing positive integers by means of sentences, for instance “the number of fingers on a human hand,” or “the number of primes less than a million.” Explain why the definition “the least number that cannot be defined in less than twenty words” is paradoxical, and informally how this relates to the difficulty in computing Kolmogorov complexity

 

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