How do you find someone who is also looking for you if you can’t communicate with them?

I was reading the Wikipedia article on the water hole concept in SETI, and saw under “see also” the entry “Schelling point“. Investigating led me to a fascinating bit of history.

Thomas Schelling is a heterodox economist and foreign policy expert who won the Nobel Prize for applications of game theory to conflict. His analysis of the game theory behind nuclear warfare led to the concept of “mutually assured destruction” (with the appropriate acronym MAD) which had great influence (for better or for worse) on the nuclear arms race. His demonstration of the power of being “credibly irrational” does a lot to explain North Korea’s foreign policy. His concept of “tipping” explained how racial segregation can arise from small preferences even in the absence of government-sponsored redlining, which continues to have strong influence on housing policy.

In his seminal 1960 work The Strategy of Conflict he described a game in which the players must cooperate but cannot communicate. In order to work together, they must guess at each others’ strategies, and make sure that their own strategies are guessable. This means they should not pick the objectively best strategy, necessarily, but they should pick the strategy that is most likely to be guessed by the other—assuming they think the same way, one ends up with an infinite recursion! But all is not lost: if you have something in common with the other player some strategies are clearly superior to others.

For instance, suppose the game is to find the other player in New York City. They are also looking for you, but you two have no way to communicate with each other. Is it reasonable to wait in a restaurant at the corner of 3rd Ave and E 56th street until they show up? No—not only is that not a particularly meaningful place, if they similarly pick a (different) random spot in the city and wait for you, you will never find each other. But there are better strategies: if your partner in the game knows anything about New York (and since they are somewhere in New York, they could ask even if they don’t) then there are certain places and times they are more likely to guess. Landmarks like Grand Central Station and the Empire State Building are more likely common guesses than random restaurants, and times like noon are more likely for meeting up than 3:12am.

In other words, by thinking about the sorts of common knowledge you share with your partner, you can narrow down the infinite range of possible strategies and have a fighting chance of finding your partner. The point isn’t that you could win this particular game, it’s that even in the absence of coordination there is a hierarchy of strategies, and they have more to do with the players (what they know) than the game itself. It was a brilliant insight, and the concept today is called a “focal point”. This already has an unrelated definition in astronomy, so I prefer the (also common) term “Schelling point”.

Incredibly, even though the book was published in 1960, it contains a footnote about SETI, which had its first paper published in 1959! He writes:

[A good example] is meeting on the same radio frequency with whoever may be signaling us from outer space. “At what frequency shall we look? A long spectrum search for a weak signal of unknown frequency is difficult. But, just in the most favored radio region there lies a unique, objective standard of frequency, which must be known to every observer in the universe: the outstanding radio emission line at 1420 megacycles of neutral hydrogen” (Giuseppe Cocconi and Philip Morrison, Nature, Sep. 19, 1959, pp. 844-846). The reasoning is amplified by John Lear: “Any astronomer on earth would say ‘Why, 1420 megacycles of course! That’s the characteristic radio emission line of neutral hydrogen. Hydrogen being the most plentiful element beyond the earth, our neighbors would expect it to be looked for even by tyros in astronomy'” (“The Search for Intelligent Life on Other Planets,” Saturday Review, Jan. 2, 1960, pp. 39-43). What signal to look for? Cocconi and Morrison suggest a sequence of small prime numbers of pulses, or simple arithmetic sums.

This is amazing! I’m guessing Schelling was reading his weekly Saturday Review when he came across the article, thought it was a great example of his point, and added the footnote to his manuscript for the book, which was published later that year.

This idea has been re-invented over and over in the SETI community. Filippova called it a “Convergent strategy of mutual searches” in 1991, and before that in 1980 Makovetskii called it a “mutual strategy of search,” and a “synchrosignal” in 1977. Guessing the “magic frequencies” at which ET might be transmitting (it was “pi times hydrogen” in Contact), where they might be transmitting, and when they might be transmitting is an exercise that founds many SETI papers.

My favorite example is Kipping & Teachey’s suggestion in their “laser cloaking” paper. The paper is mostly about how lasers could be used to sculpt transit light curves to hide or amplify the signs of biology or technology (or of the planet itself!), but it also points out that the best time to transmit is during the time your target would see your planet transit your star (so stars exactly 12h from the Sun; especially those on the ecliptic). This is a great Schelling point: it is an obviously special time in a planet’s orbit, it doesn’t require the transmitter or receiver to know the precise distance to each other to account for light-travel time and synchronize their efforts, and has the bonus that one might catch the attention of astronomers observing the transit for purely natural scientific reasons.

But this all goes back to Schelling and brings us to the central insight: if there are alien civilizations out there trying to get our attention, we are more likely to find their signals if we can “think like them” and ask “what can we assume they know about us?” The logic that if we have radio telescopes we will know about the 1420 MHz line is pretty solid. Mathematics seems like something we must have in common if they are technologically advanced enough to send interstellar signals, but I’m skeptical that they would find find primes as fascinating as we do (and if we assume they like pi we miss out on them if they are actually tauists).

It’s a nice illustration of how SETI forces us to look inward, as well as out, and question what it means to be human, so we can imagine what it might mean to be an alien. Since these are questions of the social sciences, it shows that SETI is much more than a physical science or engineering challenge, and needs to include anthropologists, linguists, mathematicians, and others.

You can read more examples of people suggesting Schelling points in SETI in my review chapter on exoplanets and SETI here.