He Say, He Sigh, He Sow #20

“In 1997, Fabrice Bellard announced that the trillionth digit of π, in binary notation, is 1.” — Ian Stewart, The Great Mathematical Problems (2013).

6 thoughts on “He Say, He Sigh, He Sow #20

    • It seems you can find any string there if you search long enough, as I suggested in “Kopfwurmkundalini”. But the point above about the trillionth binary digit being 1 is that there’s a formula to calculate it without finding any of the previous digits:

      The same formulas can be used to find isolated digits of π in arithmetic to the bases 4, 8 and 16. Nothing of the kind is known for any other base; in particular, we can’t calculate decimal digits in isolation. Do such formulas exist? Until the Bailey-Borwein-Plouffe formula was found, no-one imagined it was possible in binary. — Ian Stewart, The Great Mathematical Problems (2013).

      • It seems you can find any string there if you search long enough, as I suggested in “Kopfwurmkundalini”.

        Yeah, but it’s interesting to think about exactly how many digits you’d need to have a good chance of reproducing something, whether it’s a sentence, a story, or a computer program (it’d probably be relatively easy to find a simple program written in a language like Brainfuck)

        I still find it strange to think about irrational numbers because, in a sense, they mean nobody is actually creating anything. We’re only producing “decoded” copies of things that are already in irrational numbers. James Havoc, for example, is not the author of Teenage Timberwolves. He merely re-typed a story that existed at the nonillionnonillionth position (or wherever) in Pi, which existed since the beginning of time.

        But the point above about the trillionth binary digit being 1 is that there’s a formula to calculate it without finding any of the previous digits:

        I must be missing something, but does this suggest that the digits of pi are not, in fact, random?

      • I still find it strange to think about irrational numbers because, in a sense, they mean nobody is actually creating anything. We’re only producing “decoded” copies of things that are already in irrational numbers. James Havoc, for example, is not the author of Teenage Timberwolves. He merely re-typed a story that existed at the nonillionnonillionth position (or wherever) in Pi, which existed since the beginning of time.

        The entire universe and all its history is encoded in π too, so Havoc is there as a whole, complete with praise for Oasis and Barbie obsession. Horrendous thought. But meaning comes into it too. Havoc knows what he’s doing, whereas π doesn’t, unless it’s conscious in some sense. You could see Havoc as a meat computer running a program to realize a particular meaningful stretch of the digits of π, à la Douglas Adams’ idea about the earth and 42. This raises the question of consciousness, tho’, and whether it’s an epiphenomenon. Can “meanings” in consciousness, as distinct from patterns representing those meanings in the physical basis of consciousness, influence our behaviour? I can’t see how, but if they don’t there’s a puzzle to solve.

        But the point above about the trillionth binary digit being 1 is that there’s a formula to calculate it without finding any of the previous digits:

        I must be missing something, but does this suggest that the digits of pi are not, in fact, random?

        It depends on the definition of random. All the digits of π or √2 are absolutely determined in advance, but you couldn’t bet successfully, given a particular digit and not knowing what position it occupied, which digit would come next. That’s assuming they’re “normal” numbers, i.e. that all possible n-length combinations of digits occur with equal frequency in the long run (and possibly other conditions have to met too — I’m repeating what I read in David Wells’ The Penguin Dictionary of Curious and Interesting Numbers). Whether randomness can truly exist is another interesting question. I don’t see how it can, because it would seem to demand existence ex nihilo, just as free will does.

        I replied here, btw, if you didn’t see it, but the reply ended up in trash for some reason:

        Who Guards the Guardianistas?

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