Massachusetts Institute of Technology, Cambridge, Massachusetts

A quantum mechanic considers how we might ‘talk’ to aliens

So it finally happens. After hundreds of years of humans attempting to communicate with extraterrestrial beings, our descendants receive a message back. But it looks like utter gibberish. What to do? Earthlings might, for example, find some middle ground by sending the aliens a stream of circularly polarized photons to explain what we mean by left handedness. Or maybe the aliens would be able to decipher simple mathematical formulae, encoded in a binary alphabet, through which we could gradually build up a mutual understanding of mathematics, logic, and so forth?

That might work, but what if the replies are still nonsensical? Brendan Juba and Madhu Sudan recently supplied a mathematically precise answer to this question (B. Juba and M. Sudan Symp. Theor. Comput. 123–132; May 2008). Using the theory of interactive proofs, which shows how parties who possess different pieces of a theorem’s proof can cooperate to construct a full proof, they show that as long as aliens are not completely indifferent to communications from Earth, we will quite quickly be able to ascertain whether or not they have knowledge that is useful to us.

The technique that Earthlings should use goes like this: Bob, the human, systematically encodes questions about a class of problems in a form that any computer can interpret. He then repeatedly sends the encoded questions to Alice, the alien, and carefully parses the apparent gobbledygook that she sends back. Juba and Sudan prove that if Alice knows the answers to Bob’s questions (that is, were the questions asked in her own language), and actually answers some non-neglible fraction of those questions (again, in her own language), Bob can determine what she means.

So communicating with aliens is possible in principle, no matter how unpromising the task may seem. I find that reassuring.