Re: [math-fun] Mathematics of SETI protocols ?
Henry Baker <hbaker1@pipeline.com> wrote:
The problem is: how do you establish communication with someone you don't know, and someone who doesn't speak the same language ?
Somehow, when we are babies, we manage to figure out how to communicate with our parents.
Good question, though I'm not sure that it's math. I've never heard of parents proving their intelligence to their newborn, or vice versa, by generating a prime number sequence or the digits of pi. Probably it's mostly pointing at things while speaking their name. Some linguists suggest that much of language is genetic, as proven by the fact that all human languages allegedly have certain features in common, rather than being random points in the space of all possible languages. Decades ago, I asked Chomsky, in person, whether Lojban, a constructed spoken language, follows his rules for all natural languages. He didn't know enough about Lojban to answer. (Some people are fluent in Lojban. As far as I know nobody has tried to teach it to a very young child. It would probably be unethical to raise a child exclusively in that language.) People also have the ability to recognize other languages, despite utterances in them not usually being prefaced by "I'm about to speak in ..." in a language they know. As for SETI, the best suggestion I've heard is to send a semi-prime (product of two primes) number of on-off pulses which when assembled into a rectangle in one of the only two possible ways form a coherent image. Sending the sequence of prime numbers would communicate only the fact of intelligence, not any content. Sending the digits of pi would at best do the same. But in which base should pi be sent? And maybe the aliens consider 1/pi, 2pi, or sqrt(pi) the constant, and maybe they use continued fractions, Egyptian fractions, or something we never thought of instead of a base number system.
Each TM can't assume that there is only 1 other TM that wants to establish communication -- i.e., TM#1 may get confused if TM#2 and TM#3 both try to establish communication with TM#1 at the "same" time.
One rather silly suggestion is that there are so many aliens trying to communicate with us that they are jamming each other's signals.
Does any of this discussion ring a bell? Surely, someone must have studied this sort of problem before?
Plenty of good science fiction (and of course far more bad science fiction) has dealt with this. H. Beam Piper's 1957 short story "Omnilingual" is about human archaeologists on Mars, and how they used a Martian periodic table of the elements and other Martian scientific literature as a Rosetta stone to gradually figure out the extinct Martians' written language. Robert Forward's 1980 novel _Dragon's Egg_ portrays the interaction between the inhabitants of a neutron star and a human mission in orbit around it. It's complicated by the fact that the metabolism and thinking speeds of the neutron-star creatures are millions of times faster than ours. During the brief human mission, they evolve from savagery to a civilization much more advanced than ours. Ted Chiang's 1998 novella "Story of Your Life" depicts an alien language so alien that the consciousness of any person learning it comes unbound to time. They remember their future along with their past. The title comes from the chief scientists remembering their marriage to each other and the whole of the life of their daughter, despite neither having happened yet. Even if you think that's absurd, their discussion of variational principles in physics as an alternative to cause and effect is worth reading. It was made into a movie, _Arrival_, in 2016. Carl Sagan's novel 1985 _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. In the 1974 novel _The Mote in God's Eye_ by Larry Niven and Jerry Pournelle, people visiting an alien planet find an automated museum intended to provide knowledge to reboot civilization. They correctly conclude from that that the alien's civilization is prone to repeatedly crashing long and hard, something the aliens didn't want known. Math can be something aliens communicate with us about. And of course mathematical physics and information theory are essential for designing any method of communicating over interstellar distances. It's recently been suggested that we should look in the optical rather than the microwave part of the spectrum. With higher frequencies, there's linearly more quantum noise (i.e. fewer photons per joule of energy), but quadratically better ability to aim a beam from a given aperture. Stars are much noisier in the optical than in the microwave range, but are easily nulled out with a good interferometer. Anyhow, stars have a very broad spectrum, but an optical signal can rise above the noise by having either a very narrow bandwidth or a very short pulse time, and if the former, by being in the middle of one of the star's dark Fraunhofer lines. Also, the optical part of the spectrum has far more bandwidth, hence channel capacity. With just a few kilowatts total power, everyone on Earth could send an email the size of this one every day to someone near any nearby star. Greg Egan takes this to an extreme, by having people communicate over interstellar distances by gamma ray laser. They sometimes even transmit the locations of every atom in their body, as a form of travel.
Not really “Mathematics” as such - but how do we do it when the part or parts of the electro-magnetic and/or chemical and/or even base quantum or other physical manifestations of existence the aliens use to communicate or just plain sense, is unknown ? Assuming we allow for multiple “sense” options it makes perfect sense! that each presentation method may affect the possibilities with respect to the math behind communication i.e. work out the method/s first, then the math.
On 22 Nov 2018, at 06:04, Keith F. Lynch <kfl@KeithLynch.net> wrote:
Henry Baker <hbaker1@pipeline.com> wrote:
The problem is: how do you establish communication with someone you don't know, and someone who doesn't speak the same language ?
Somehow, when we are babies, we manage to figure out how to communicate with our parents.
Good question, though I'm not sure that it's math. I've never heard of parents proving their intelligence to their newborn, or vice versa, by generating a prime number sequence or the digits of pi.
Probably it's mostly pointing at things while speaking their name.
Some linguists suggest that much of language is genetic, as proven by the fact that all human languages allegedly have certain features in common, rather than being random points in the space of all possible languages.
Decades ago, I asked Chomsky, in person, whether Lojban, a constructed spoken language, follows his rules for all natural languages. He didn't know enough about Lojban to answer. (Some people are fluent in Lojban. As far as I know nobody has tried to teach it to a very young child. It would probably be unethical to raise a child exclusively in that language.)
People also have the ability to recognize other languages, despite utterances in them not usually being prefaced by "I'm about to speak in ..." in a language they know.
As for SETI, the best suggestion I've heard is to send a semi-prime (product of two primes) number of on-off pulses which when assembled into a rectangle in one of the only two possible ways form a coherent image.
Sending the sequence of prime numbers would communicate only the fact of intelligence, not any content. Sending the digits of pi would at best do the same. But in which base should pi be sent? And maybe the aliens consider 1/pi, 2pi, or sqrt(pi) the constant, and maybe they use continued fractions, Egyptian fractions, or something we never thought of instead of a base number system.
Each TM can't assume that there is only 1 other TM that wants to establish communication -- i.e., TM#1 may get confused if TM#2 and TM#3 both try to establish communication with TM#1 at the "same" time.
One rather silly suggestion is that there are so many aliens trying to communicate with us that they are jamming each other's signals.
Does any of this discussion ring a bell? Surely, someone must have studied this sort of problem before?
Plenty of good science fiction (and of course far more bad science fiction) has dealt with this. H. Beam Piper's 1957 short story "Omnilingual" is about human archaeologists on Mars, and how they used a Martian periodic table of the elements and other Martian scientific literature as a Rosetta stone to gradually figure out the extinct Martians' written language.
Robert Forward's 1980 novel _Dragon's Egg_ portrays the interaction between the inhabitants of a neutron star and a human mission in orbit around it. It's complicated by the fact that the metabolism and thinking speeds of the neutron-star creatures are millions of times faster than ours. During the brief human mission, they evolve from savagery to a civilization much more advanced than ours.
Ted Chiang's 1998 novella "Story of Your Life" depicts an alien language so alien that the consciousness of any person learning it comes unbound to time. They remember their future along with their past. The title comes from the chief scientists remembering their marriage to each other and the whole of the life of their daughter, despite neither having happened yet. Even if you think that's absurd, their discussion of variational principles in physics as an alternative to cause and effect is worth reading. It was made into a movie, _Arrival_, in 2016.
Carl Sagan's novel 1985 _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.
In the 1974 novel _The Mote in God's Eye_ by Larry Niven and Jerry Pournelle, people visiting an alien planet find an automated museum intended to provide knowledge to reboot civilization. They correctly conclude from that that the alien's civilization is prone to repeatedly crashing long and hard, something the aliens didn't want known.
Math can be something aliens communicate with us about. And of course mathematical physics and information theory are essential for designing any method of communicating over interstellar distances.
It's recently been suggested that we should look in the optical rather than the microwave part of the spectrum. With higher frequencies, there's linearly more quantum noise (i.e. fewer photons per joule of energy), but quadratically better ability to aim a beam from a given aperture. Stars are much noisier in the optical than in the microwave range, but are easily nulled out with a good interferometer. Anyhow, stars have a very broad spectrum, but an optical signal can rise above the noise by having either a very narrow bandwidth or a very short pulse time, and if the former, by being in the middle of one of the star's dark Fraunhofer lines. Also, the optical part of the spectrum has far more bandwidth, hence channel capacity. With just a few kilowatts total power, everyone on Earth could send an email the size of this one every day to someone near any nearby star.
Greg Egan takes this to an extreme, by having people communicate over interstellar distances by gamma ray laser. They sometimes even transmit the locations of every atom in their body, as a form of travel.
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As an aside I guess hoping that the aliens’ form of communication/sensing is as different from our own as possible because in that scenario the chance of competing species is probably reduced ;)
On 22 Nov 2018, at 10:42, D J Makin via math-fun <math-fun@mailman.xmission.com> wrote:
Not really “Mathematics” as such - but how do we do it when the part or parts of the electro-magnetic and/or chemical and/or even base quantum or other physical manifestations of existence the aliens use to communicate or just plain sense, is unknown ?
Assuming we allow for multiple “sense” options it makes perfect sense! that each presentation method may affect the possibilities with respect to the math behind communication i.e. work out the method/s first, then the math.
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:) I didn’t mean to start a debate about the existence of aliens or not or Fermi’s Paradox, really just to point out that the content/math of any message/s would need to be modified based on the method/s of communication. Having said that, as to the definition of “intelligent” creature, I’d say one that could comprehend the meaning of “I think therefore I am” in whatever language - of course that’s if it’s translatable, it assumes a concept of self which may not actually be necessary for actual intelligence ? I guess an understanding of math beyond just +-*/ would do. With respect to types of alien, I don’t exclude anything really - including the intelligent nebula in Van Vogt’s “The Voyage of the Space Beagle”.
= D J Makin it assumes a concept of self which may not actually be necessary for actual intelligence ?
See the works of SF author (& former marine mammal biologist) Peter Watts [1]. His novel "Blindsight" [2], for instance, features an advanced alien civilization of intelligent beings that wholly lack consciousness, much less possess a sense of self. [1] https://en.wikipedia.org/wiki/Peter_Watts_%28author%29 [2] https://en.wikipedia.org/wiki/Blindsight_(Watts_novel)
participants (3)
-
D J Makin -
Keith F. Lynch -
Marc LeBrun