Julia Robinson has a good quote: "What is proved about numbers will be a fact in any universe." Though I suppose there could be universes harboring intelligent life in which the laws of physics are such that pi isn't seen as a very interesting number until fairly late in a culture's development, and facts about pi are seen as arcane and boring. By the way, have any of you read the R. A. Lafferty short story in which some people discover some small integers (less than ten) that had hitherto gone unnoticed? The relevant phrase is something like "involutive number series" but I couldn't dig up any information with Google. Jim Propp On Sun, Nov 25, 2018 at 8:50 PM D J Makin via math-fun < math-fun@mailman.xmission.com> wrote:
Assuming that Divinity is necessary is limiting the possibilities with respect to other intelligences - “God" could even be a technologically advanced human, maybe even one with the tech but no knowledge of how to reproduce it, see “World of Tiers: ;)
On 25 Nov 2018, at 18:11, James Propp <jamespropp@gmail.com> wrote:
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.
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