My recollection of the plot point is that the message in question was a patch of digits whose length was a smallish prime square, something like 121 or 169. These digits were all zeroes and ones, and when laid out in a square formed a crude bitmapped image of a circle with the center marked. One would expect such a figure somewhere in the first 11^121 or 11^169 places, and although Sagan is intentionally vague about where the message is found, it's clearly nowhere near that late. The miracle is of an extreme enough order that Divine intervention is the only "plausible" explanation. But the whole episode is a casual throwaway. On Nov 25, 2018 5:36 PM, "David Wilson" <davidwwilson@comcast.net> wrote: Presuming pi is normal in all bases, aren't all possible (finite) messages somewhere in there?
-----Original Message----- From: math-fun [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of James Propp Sent: Sunday, November 25, 2018 1:11 PM To: math-fun Subject: [math-fun] Messages in pi
Keith Lynch writes:
“Carl Sagan’s 1985 novel _Contact_ is a classic, though not very
original, SETI novel. Unoriginal except for a subplot about the
aliens having discovered messages hidden in the base-eleven digits
of pi, which was unfortunately left out of the 1997 film of the same
name. I find it an interesting question whether evidence for such a
message in pi can ever overcome the possibilities that it's either an
astonishing coincidence or someone hacking the computer that's doing
the calculation. Presumably if there really was such a message, it
would have to be from God, rather than from advanced aliens.”
I’m not sure if we’ve discussed this before on math-fun, but I’ve never found this aspect of Sagan’s novel compelling or even coherent. I can imagine a God who intervenes in ways that locally violate the laws of physics, or a God who chooses the laws of physics, but not a God who chooses the laws of mathematics. Is there anything that this might mean?
My guess is that, even though Sagan acknowledges in the novel that pi is a mathematical constant rather than a physical one, he didn’t really understand what this entails. Hiding a message in the digits of the base ten expansion of pi is no different from hiding a message in the digits of the base ten expansion of seventeen. (“Mathematicians will tell you that it’s all zeros after the decimal point, but how far out how they really checked?”)
I know that the mathematician and science-fiction novelist Greg Egan plays thought experiments with the mutability of math, but I always get the sense with him that at least a fraction of his tongue is in his cheek when he does this, whereas I think Sagan was invoking mathematical ideas in an attempt to convey a sense of transcendence, much as Arthur C. Clarke had done in _2001: A Space Odyssey_ (when the newly transhuman Bowman chides his recently human self for failing to imagine that the numerical pattern governing the proportions of the monolith were limited to three dimensions).
Trying to convey something beyond human comprehension is a tricky business; it’s akin to designing good technobabble, but harder.
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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