This could be tested by finding someone who has seen some of my tweets but not this one, and getting them to give probability distributions over the each character in the tweet (where they can see all the previous characters). I am unlikely to carry out this test.
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Each letter in a typical English sentence has around 1 bit of information. 2^140 is around 10^42. I’m not sure how much information can be gained from knowing who’s the tweeter.
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My tweet was less than 140 characters.
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The space of potential tweets over which the prior is distributed should be the reference class, not the actual length.
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Short tweets are more likely than long tweets. You can tell because there are many more possible short tweets than possible long tweets, but among actual tweets, short tweets are still common.
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I think you got something the wrong way around.
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Oops, yes. Many more possible long tweets than possible short tweets.
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No, even accounting for the lower probability on false (but comprehensible and plausible) statements.
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Do you think 10^-30 was too low or too high?
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Too low. Tweets about their own probability merit at least 10^-10; conditional on that subject, the particular tweet is at least 10^-10.
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I'd guess there are more than 10^10 ways to write a tweet about its own probability.
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But what sane prior will put a lot of mass on "The probability of this tweet is [HIGH KOLMOGOROV COMPLEXITY REAL IN (0,1)]."?
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Oh, that also gives you more than 10^10 possibilities, but it isn't what I had in mind. I don't think varying the real parameters accounts for the majority of the entropy of tweets that are about their own probability.
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Really? Think about 10^5 syntax trees (or sequences of trees) and 10^5 different realizations of each.
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