13/ model the Big World as set of all Turing machines, can do this without loss of generality. Each is equally real regardless of length.
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Replying to @MoralOfStory
14/ however, short Turing machines are often embedded in long Turing machines and called as (potentially non terminating) subroutines.
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Replying to @MoralOfStory
15/ this gives some sort of over representation factor (ORF) for short Turing machines, they have higher than expected density.
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Replying to @MoralOfStory
@MoralOfStory But this ORF is not a well-defined number.1 reply 0 retweets 0 likes -
Replying to @ObjectOfObjects
@ObjectOfObjects should roughly scale with 1/2^(len a - len b)?. Sample larger numbers of Turing machines to get better estimates.2 replies 0 retweets 0 likes -
Replying to @MoralOfStory
@MoralOfStory Sample Turing machines from what distribution?1 reply 0 retweets 0 likes -
Replying to @ObjectOfObjects
@ObjectOfObjects an exponential distribution, increasing the parameter so that in the limit you would sample the infinite space.2 replies 0 retweets 0 likes -
Replying to @MoralOfStory
@MoralOfStory The value of the limit will still depend on your initial choice of UTM that you're calculating the lengths with respect to.1 reply 0 retweets 0 likes -
Replying to @ObjectOfObjects
@ObjectOfObjects things get very complicated when you want to consider all models of computation, but I don't think that dooms this1 reply 0 retweets 0 likes -
Replying to @MoralOfStory
@MoralOfStory Dooms what? What is your actual goal here? Finding a "true" or "canonical" prior distribution over Turing machines?2 replies 0 retweets 0 likes
@ObjectOfObjects just exploring what it means to live in a Big World.
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