Henry Baker <hbaker1(a)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.
