Overheard at brunch at the table next to us: Some millennials talking about pi day and how many digits of pi they can recite.
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“Once you get past the first five you can just make them up. No one can tell.”
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Replying to @johncarlosbaez @divbyzero
Indeed. If you had to make up a sequence quickly, an alert mathematician should I think be able to tell fairly quickly that it has statistical anomalies that make it very unlikely to be an early part of the decimal expansion of pi.
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Simulating randomness is perhaps what humans do worst. Understanding randomness may be a close second, though. I once had a student who would offer a "random" sequence of digits that began: 4, 4, 4, 4, 4, 4, and so forth. When others objected, he counseled them to wait a bit.
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Replying to @MathPrinceps @wtgowers and
Pi is not known to even be normal, much less satisfying stronger randomness properties.
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This is of course true, but its bearing on human abilities to simulate and to grasp randomness seems to me unclear.
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Replying to @MathPrinceps @wtgowers and
Well, somehow the preceding discussion implied that one ought to be able to detect made up pi digits due to them not being random enough.
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There is certainly at least some empirical evidence of normality, though, would you not agree? And perhaps that is enough to justify suspicion of any putative digit string that seems pretty clearly to privilege some digit over others?
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Replying to @MathPrinceps @wtgowers and
Yes I agree about the empirical evidence for normality. And of course I would be suspicious about some particularly outrageous strings. But generally I would be less suspicious about a string be part of pi expansion than it being random.
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