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> 0.5 is a real number. Its series of bits is not random at all Would you say that an (arbitrarily long) sequence of coin tosses that all come up heads "is not
by chriswarbo 8y ago
> 0.5 is a real number. Its series of bits is not random at all
Would you say that an (arbitrarily long) sequence of coin tosses that all come up heads "is not random at all"? I'd say it's vanishingly unlikely to occur (if the coin is actually 50/50), but just as unlikely as any other particular sequence of the same length. It's like if a lottery gave out [1, 2, 3, 4, 5, 6]: it's a remarkable pattern, but no more or less likely than any other particular result. The same goes for the never-ending decimals of 0.5 and sqrt(2), and it's misleading to draw general conclusions from such specifically-chosen examples.
- ethagnawl 8y ago> It's like if a lottery gave out [1, 2, 3, 4, 5, 6]: it's a remarkable pattern, but no more or less likely than any other particular result. Do you know if there's a name for the fallacy you've alluded to? (Assuming that an ordered sequence is less likely than any other.)
- gowld 8y agoInterestingly, the fallacy is actually good reasoning. Even though every permutation is equally likely, the permutations fall into equivalence classes of "notoriety", and the class of ordered sequences is far smaller (== less likely) than the class of disordered sequences (which are all equivalently noninteresting). (This is entropy, as it applies to both information and the physical world.)
- tzs 8y agoAs of the end of April 2018, we've had 400 consecutive months where the world's temperature was hotter than average for that month, yet a whole lot of politician say that's just due to random variation. I bet they could take a long run of heads in stride without thinking that maybe they have a biased coin.