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
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
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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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.
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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.
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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On Nov 28, 2018, at 11:31 AM, James Propp <jamespropp@gmail.com> wrote:
Julia Robinson has a good quote: "What is proved about numbers will be a fact in any universe.”
This still suffers from the bias that “intelligent life” runs on a platform that is “open” in the sense of physics, where there is a sense of “now” that runs unidirectionally into the future. For example, if some form of life was effectively a closed system, with perfect symmetry under time reversal (i.e. unitary evolution), I very much doubt that questions involving the operations of arithmetic or logic, most of which are not reversible, would arise (be considered interesting). The only work of fiction I know of that brings up this bias is Vonnegut’s Slaughterhouse Five, in which the Tralfamadorians have managed to become “unstuck in time”, that is, they experience the events on their world-lines not in sequence but as a single entity. We have the means, in principle, to build new kinds of AIs that are not subject to this bias. Whether there is anything interesting to talk about with them, or whether there is even a sense in which we could carry on a conversation, is another question. -Veit
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
Ted Chiang's novella "Story of Your Life" had a similar theme; it was recently made into the movie "Arrival". I'm very skeptical that anything we would call "life" could exist in a really time-symmetric environment. What we call life is very complicated, and achieved its current complexity due to natural selection. I don't think the concept of natural selection is coherent in a time-symmetric environment, and can't think of any other effect that would favor such complexity. On Wed, Nov 28, 2018 at 1:01 PM Veit Elser <ve10@cornell.edu> wrote:
On Nov 28, 2018, at 11:31 AM, James Propp <jamespropp@gmail.com> wrote:
Julia Robinson has a good quote: "What is proved about numbers will be a fact in any universe.”
This still suffers from the bias that “intelligent life” runs on a platform that is “open” in the sense of physics, where there is a sense of “now” that runs unidirectionally into the future. For example, if some form of life was effectively a closed system, with perfect symmetry under time reversal (i.e. unitary evolution), I very much doubt that questions involving the operations of arithmetic or logic, most of which are not reversible, would arise (be considered interesting).
The only work of fiction I know of that brings up this bias is Vonnegut’s Slaughterhouse Five, in which the Tralfamadorians have managed to become “unstuck in time”, that is, they experience the events on their world-lines not in sequence but as a single entity.
We have the means, in principle, to build new kinds of AIs that are not subject to this bias. Whether there is anything interesting to talk about with them, or whether there is even a sense in which we could carry on a conversation, is another question.
-Veit
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
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On Wed, Nov 28, 2018 at 9:31 AM James Propp <jamespropp@gmail.com> wrote:
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.
That's still the case for the vast majority of humans. In hyperbolic space, the circumference is 2 pi R sinh r/R, where R is the Gaussian curvature of the plane, so perhaps an inhabitant of such a space would consider (pi R) more fundamental. Also seems like a q-deformed exponential function wouldn't have period 2 pi. So while pi would still be pi, it wouldn't necessarily have the same physical significance.
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.
There's a popular hypnosis trick where people are made to forget a number below ten and then count their fingers: https://www.google.com/search?q=hypnotized+to+forget+the+number+6 -- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike https://reperiendi.wordpress.com
Here's a list of Lafferty's work, in case it might jog your memory. Short stories near the bottom. http://www.isfdb.org/cgi-bin/ea.cgi?36 On Wed, Nov 28, 2018, 10:31 AM James Propp <jamespropp@gmail.com> wrote:
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.
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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I just consider that the Unifying theory is Mathematics - the physical specifics for one (hyperverse set?) Universe merely being data ;)
On 28 Nov 2018, at 23:05, Paul Palmer <paul.allan.palmer@gmail.com> wrote:
Julia Robinson has a good quote: "What is proved about numbers will be a fact in any universe."
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.
Probably not the story you have in mind, since it's not by R A Lafferty and doesn't include anything much like "involutive number series", but there's "The secret number" by Igor Teper: http://strangehorizons.com/fiction/the-secret-number/ -- g
Rudy Rucker has a short story about missing 4. --Rich Quoting Gareth McCaughan <gareth.mccaughan@pobox.com>:
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.
Probably not the story you have in mind, since it's not by R A Lafferty and doesn't include anything much like "involutive number series", but there's "The secret number" by Igor Teper: http://strangehorizons.com/fiction/the-secret-number/
-- g
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participants (9)
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Allan Wechsler -
D J Makin -
David Wilson -
Gareth McCaughan -
James Propp -
Mike Stay -
Paul Palmer -
rcs＠xmission.com -
Veit Elser