Mathematical Methods for Deciphering Alien Messages

In 1974, the Arecibo radio telescope sent a message to space that contained 1,679 bits of information. If extraterrestrial life sent us something similar, how would we begin to decode it? A new mathematical approach by Hector Zenil, a computer scientist at the University of Cambridge and founder of Oxford Immune Algorithmics, proposes a solution. The method looks at every possible combination of dimension number and size, and then measures the orderliness of each possible configuration in terms of local and global order to determine the most likely configuration. Zenil tested the approach on the Arecibo message and other forms of encoded information, including a 3-D MRI scan.

To interpret the Arecibo message, you would first need to understand that it was an image consisting of 23 pixels in width and 73 pixels in height. The radio antenna encoded the 1,679 bits by flipping between two frequencies that represented 1 and 0. Lining up the bits differently without realizing the image's dimensions would make it seem like random noise. However, the Arecibo scientists built a clue into the transmission: 23 and 73 are both prime numbers - a pattern that other intelligent life may recognize. But, Brian McConnell, a computer scientist at Notion Labs, points out that alien messages could take on various forms and dimensions.

Zenil's approach analyzes each possible configuration's orderliness and potential to be the correct one, taking into account local and global order. The team tested the method on the Arecibo message expanded to six times its size, and it showed success in detecting the correct configuration. This approach not only works with encoded messages that contain bits, but it also has the potential to analyze a continuous signal sent by aliens. It could help find the right sampling frequency for digitizing it.

According to Zenil, this method could revolutionize how we interpret messages from extraterrestrial life. The message would effectively tell us its own geometry and save precious time that would otherwise be spent trying to figure it out. Overall, by identifying variations in geometry, we can potentially recognize patterns and better understand the universe.

“What I like about it is that it’s a mathematically rigorous approach to characterizing a transmission,” McConnell says of the technique, which has not yet been peer reviewed. What’s more, “most of the people in the SETI community” — referring to the search for extraterrestrial intelligence — “focus on signal detection. They don’t tend to give a lot of thought to what would come after that.”

SETI researcher Douglas Vakoch, the president of METI International, a nonprofit that studies how we might message extraterrestrial intelligence, notes that the new approach frees prime numbers to serve a secondary purpose in parsing a message. “Instead of being a guide to discover the format, they can now be used to confirm that the decoders found the correct solution,” Vakoch wrote via email.

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(“Primes are somehow very special in a mathematical sense,” Zenil notes, “because they can be thought of as a compressed version of the natural numbers.” But there are also other types of interesting numbers to choose from, many listed in the On-Line Encyclopedia of Integer Sequences.)

Of course, even if we could detect and format the message, we’d still need to interpret it correctly. Might a shape indicate an alien body, a spacecraft, an equation or a smudge?

Zenil notes that the approach has potential terrestrial applications, for instance in deciphering intercellular signaling. He’s also already used conceptually similar methods to identify important components in gene regulatory networks — if you perturb one part, does it make the overall system less intelligible? An algorithm that pieces together smaller algorithmic components in order to explain or predict data — this new method is just one way to do it — may also help us one day achieve artificial general intelligence, Zenil says. Such automated approaches don’t depend on human assumptions about the signal. That opens the door to discovering forms of intelligence that might think differently from our own. 

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