I haven't read the book "Contact", but I did see the movie -- good flick! I purposely made a substantive change in the model -- I eliminated the speed-of-light problem for communicating across 10's/100's/millions of light years, and posited short latencies. This is because I suspect that many "rounds" are going to be required to "settle" into some mutually agreed communications protocol. However, all of that cleverness about prime numbers, etc., is useless until you've established more basic communication mechanisms -- e.g., what is the approximate clock rate? What distinguishes *your* signal from everyone else's? For example: if a 21st Century TM wants to communicate with *me*, it has to wait *eons* -- e.g., more than 10^9 cycles -- for any sort of reply. This isn't a latency thing, but a time scale thing. Furthermore, my bit rate is also slower than its own by 10^9, so this TM could probably be simultaneously probing 10^6 or more people for some sort of response. So the first order of business is to establish an appropriate time scale. Ditto if humans wanted to talk with some non-human race: we don't know if their neurons operate in the millisecond range, the nanosecond range, or the century range. Here's a place for math: I said that 1) TM#1 wants to send out a whole bunch of test signals with different clocks and different time-of-day sequences; and 2) TM#1 needs to *remember* all of these signals so that if any of them come back again, TM#1 can recognize them. So an interesting math problem: what kind of data structure could be used to emit a huge number of different types of signals, while simultaneously scanning the channel for delayed copies? It sounds very much like a sort of lossless compressor -- e.g., gzip or equivalent. Of course, gzip assumes that one already knows the appropriate clock signal, while our TM's still don't know these, yet. Better yet would be some sort of sequence which incorporated the appropriate test sequences as subsequences. Perhaps some sort of De Bruijn sequence, which could quickly be indexed upon receipt to figure out when it was sent. At 06:38 PM 10/31/2018, Mike Beeler wrote:
The movie "Contact" (1997) deals with this, plus lots of drama to make it commercially viable entertainment.
The first step is that the signal is bursts of "noise", clustered in groups of 1, 3, 5, 7, 11, 13, Â 137(?) bursts, then repeating.
The sequence convinces the team that it's not a natural phenomenon.
Then they discover an old signal from earth embedded, like your idea of playing back part of the other entityâs identifier.
Then discovery of how some more images are coded, then how the images go together, etc.
Not a lot of math, butÂ
Bassed on a story "Contact" (1985) by Carl Sagan and Ann Druyan.
 Mike
On 31 Oct 2018 at 7:32, Henry Baker wrrote:
I've been thinking about the following problem for a while, and hope that others have also.
The problem is: how do you establish communication with someone you don't know, and someone who doesn't speak the same language ?