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NancyLebovitz comments on Crazy Ideas Thread - Less Wrong Discussion
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One definition of random is compressible-- it's shorter to say forty birds mentioned in Shakespeare than to list the birds.
I'm pretty sure the choice of writer wasn't random-- Shakespeare is tremendously respected by a lot of English speakers, but the idea of exporting British birds to North America to make it seem more homey seems very random.
A sequence of 40 zeros is highly compressible, but does not look random.
You mean a sequence "looks random" if it's not very compressible -- right? That is, the sequence is a member of the appropriate typical set:
https://en.wikipedia.org/wiki/Typical_set
Or maybe you meant "looks random" means "compressed already." (???) A zipped file expressed as a bit sequence looks random.
I'm sorry, I meant to say that randomness is not compressible.