Posted by Detecting a signal would be the easy half. The hard half starts the morning after, when a room full of very clever people sits down in front of a stream of pulses from another star and has to work out what any of it means. There is no dictionary, no shared history, no common body plan, possibly not even a shared sense of what counts as an obvious idea. This is why mathematics keeps coming up whenever anyone talks seriously about extraterrestrial communication: numbers look less like a human invention than like a description of how the universe is put together, and a species that builds transmitters has almost certainly noticed the same relationships we have.
That is the hope, anyway. It deserves more scrutiny than it usually gets.
Why no human language survives the trip
English works because a few billion people spent centuries agreeing that certain noises point at certain things. Strip away the shared bodies, the shared planet and the shared evolutionary accidents, and the agreement evaporates. A receiving civilization might not hear, might not see in anything like our range, might not experience time in units that make our grammar of tenses meaningful. Even our metaphors would betray us — “grasping” an idea assumes hands.
A message therefore has to teach its own rules on the way in. Whatever it opens with must be recognizable without any prior agreement, and then everything after that has to be built on top of the recognition. Hans Freudenthal, a Dutch mathematician, tried to design exactly that in 1960 with Lincos, a constructed language that begins with pulses standing for numbers, introduces equality and arithmetic through worked examples, and only much later reaches for concepts like time, behaviour and social relations. Lincos has never been transmitted. It remains the most thorough attempt anyone has made to think the problem through from first principles.
Primes, and why they keep getting sent
Prime numbers show up in nearly every proposed interstellar message, and the reason is narrow but solid: a run of 2, 3, 5, 7, 11, 13 with no gaps and no errors is not something a cloud of hydrogen produces by accident. Pulsars can beat out a rhythm more precise than a laboratory clock, so raw regularity proves nothing at all. What natural physics does not do is count.
Frank Drake tested this in 1961 by handing colleagues a string of 551 bits and asking them to make sense of it. The number is the product of 19 and 29, both prime, which is the hint: lay the bits out in a rectangle with those dimensions and a crude picture appears. Even scientists who knew in advance that a message was hidden in there found it hard going. That result should temper anyone’s confidence about how self-evident a mathematical message really is.
Thirteen years later Drake and Carl Sagan scaled the same trick up for the ceremony marking the resurfacing of the Arecibo dish. On 16 November 1974 the observatory beamed 1,679 bits toward the globular cluster M13. Once again the length is a product of two primes, 73 and 23, and once again the arrangement into a 73-by-23 grid is meant to be the puzzle’s only key. The picture that emerges contains the numbers one to ten, the atomic numbers of hydrogen, carbon, nitrogen, oxygen and phosphorus, the double helix, a stick figure, the Solar System and the dish that sent it.
Building meaning one layer at a time
Getting a receiver to recognize numbers is step one of maybe twenty. The genuinely difficult move is attaching those numbers to things.
Say a transmission contains the value 1,420,405,751. On its own it is just an integer. To us it is instantly the frequency in hertz of the hyperfine transition of neutral hydrogen — the 21-centimetre line, the most common radio note in the universe, measurable by anyone with the right receiver and the same laws of physics. That single number can bootstrap a unit of time and a unit of length simultaneously, which is precisely why the plaques bolted to Pioneer 10 and 11 in 1972 and 1973 use the hydrogen transition as their tick mark before doing anything else. The same plaques locate the Sun using a starburst of lines pointing at fourteen pulsars, each labelled in binary with its period, a scheme that works as a galactic address and a rough timestamp at once.
From physical constants you can climb toward chemistry, then toward planetary conditions, then, in principle, toward biology. Each rung depends on the one below it holding. Skip a step and the receiver is left with a number and no idea whether it means a distance, a temperature or a population.
Binary, redundancy and the messages we actually sent
Almost every serious design encodes in binary, not because aliens must think in twos, but because two clearly different states are the least you can ask a noisy interstellar channel to preserve. Pulse or silence, one frequency or another — a receiver only has to tell two things apart before it can start hunting for structure.
The Cosmic Call transmissions, sent from the Evpatoria radio telescope in Ukraine in 1999 and again in 2003, took the engineering seriously in a way the Arecibo message did not. Yvan Dutil and Stéphane Dumas built their message out of pages of 127 by 127 pixels, taught a symbol set page by page, and deliberately padded the whole thing with redundancy so that bits lost to interstellar static would not destroy the meaning. It was an attempt at extraterrestrial communication designed like a real transmission protocol rather than a commemorative gesture.
Whether either message will ever be read is a separate question. Arecibo’s target sits about 25,000 light-years away, and the cluster will have shifted position by the time the pulse arrives.
The part where the universal language stops being universal
Mathematics gets you a handshake. It does not get you a conversation.
Marvin Minsky argued that any intelligence facing limited time, limited memory and the same physical universe would converge on similar ways of carving up problems, which would make an alien message far more tractable than pessimists assume. Others point out that human mathematics carries fingerprints of human cognition all over it — our notation, our fondness for base ten because of our fingers, our particular history of which branches got developed first. A species living in a dense atmosphere, or one that evolved without discrete countable objects in its environment, might have built its formalism around continuous quantities or topology and find our arithmetic-first approach quaint.
The claim worth defending is narrower than the slogan. Mathematical truth is probably shared. Mathematical writing almost certainly is not. A message has to survive that gap by carrying its own instructions, which is a design problem more than a philosophical one.
And nothing here touches the categories a message might actually want to convey. Two civilizations can agree perfectly on prime factorization and still have no route to discussing grief, or governance, or why anyone bothered to transmit.
What a decoded signal would really prove
Suppose a candidate turns up: narrow in frequency, fixed to one spot on the sky, confirmed by a second observatory that would love to embarrass the first, and carrying a nested arithmetic structure nobody can reproduce with plasma physics. Machine learning would be thrown at it immediately, and it would be useful for the statistics — spotting repeats, guessing at hierarchy, ranking candidate segmentations. It would not hand anyone a translation. Too many readings fit any short sample, and choosing among them is a judgement call that still lands on human researchers.
Even so, the first message might not need to say anything at all. A sequence that demonstrates the sender knows what a prime is, and what hydrogen does, would already carry the only content that matters on arrival: somebody else worked out the same structures, under a different sun, without ever meeting us. SETIworld follows the search, the decoding attempts and the arguments about what we should send back — worth keeping an eye on if this is the kind of problem that keeps you up.
