Here’s how we could start deciphering an extraterrestrial message using math

One of the most famous messages ever sent into space was a string of 1,679 bits sent by the Arecibo radio telescope in 1974. But if ET sent us such a string, how could we earthlings even begin to decode it? A new mathematical approach suggests a way.

Anyone attempting to interpret the Arecibo Message—a drawing that shows, among other information, a person, the DNA double helix, the solar system, and the telescope itself—must first understand that it is a picture at all, and that The image was 23 pixels wide and 73 pixels high.

A vertical image showing the Arecibo Message.  The image consists of several different colored small squares grouped on a black background.
The Arecibo message, broadcast from Earth in 1974, was sent as 1,679 bits, making an image 23 pixels wide by 73 pixels high (color has been added here to show the parts of the message).Johannes Rössel/Wikimedia Commons (CC BY-SA 3.0)

When transmitting the signal, the radio antenna encoded the 1,679 bits by alternating between two different frequencies, each representing one and zero. If you rearrange the bits differently – that is, place more or less than 23 pixels per line – the image looks like a random jumble.

We would face a similar challenge if extraterrestrials sent us a message. How do we know the number and size of its dimensions?

The Arecibo scientists built a clue into the translation: 23 and 73 are prime numbers—a scheme that other intelligent beings might recognize if they too find prime numbers interesting. But extraterrestrial messages could come in many forms and dimensions, says Brian McConnell, a computer scientist at Notion Labs in San Francisco and author of The Alien Communications Manual. A message can be a database in which each item is not just a value but a list of values ​​or a list of lists. A message in the form of a physical simulation might contain a set of measures for any point in space-time.

The new decoding method, developed by Hector Zenil, a computer scientist at Cambridge University and founder of Oxford Immune Algorithmics, and colleagues, takes a sequence of bits – an incoming message – and examines every possible combination of dimension number and size. For example, 100 bits could be 1×100 or 10×10 (two dimensions) or 4x5x5 (three dimensions) or 2x2x5x5 (four dimensions) and so on.

Then the regularity of each possible configuration is examined in two ways. To get a measure of local order, the message is divided into patches. For each patch, it searches a catalog of trillions of tiny computer programs that the researchers previously created to explore algorithmic space, and counts how many programs generate an identical patch. (The programs’ outputs were precalculated and stored, which speeds up searching.) The more programs that create an identical patch, the higher the patch’s local order score. The patch scores are averaged to obtain an overall local order score for the entire configuration. The researchers also measure the global order of each possible configuration by seeing how much an image compression algorithm can shrink it without losing information – mathematically, randomness is less compressible than normal patterns. By combining the local and global values, researchers get a sense of how likely each configuration is to be correct.

An image with a black background and a rainbow of different colors scattered across the frame.
Arranging the Arecibo bit sequence in an image that is 73 pixels wide and 23 pixels high would distort the intended visual representation (color added). But a mathematical approach could still reveal the message.Jarmo Kivekas/Wikimedia Commons

The team tested the method on a version of the Arecibo message that had been expanded six times its size, so the width was now 138 pixels. In an analysis, the researchers arranged the bit sequence into images ranging from 0 to 200 pixels wide, a subset of possible configurations. When plotting the image width on the an audio file and a 3D MRI scan.

The new approach could also deal with the kind of noise that might be generated when a message travels through space. In another analysis, the original Arecibo message’s width of 23 pixels stood out, even though a quarter of the bits had been flipped from 1 to 0 or vice versa.

“This work is quite exciting because we have shown that information that is not entirely random actually encodes the original space in which it was intended,” says Zenil. In other words, the message tells you its own geometry. He notes this in Carl Sagan’s science fiction novel Contactand the movie based on it, the characters spend a lot of time trying to figure out that a message received from aliens is in 3D (particularly a video). “If you had our tools, you could solve this problem in seconds and without human intervention.”

Even if aliens send a continuous signal instead of bits, the method could help find the right sampling frequency for digitization, he says. It would just add more configurations to try out.

“What I like about it is that it’s a mathematically rigorous approach to characterizing a transmission,” McConnell says of the technique, which has yet to be peer-reviewed. Additionally, “most people in the SETI community” — in terms of the search for extraterrestrial intelligence — “are focused on signal detection. They don’t tend to give much thought to what comes after.”

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

(“Primes are somehow very special in a mathematical sense,” Zenil notes, “because you can think of them as condensed versions of the natural numbers.” But there are other types of interesting numbers to choose from, many of which are listed in the online Encyclopedia of Integer Sequences.)

Of course, even if we could recognize and format the message, we would still need to interpret it correctly. Could a shape indicate an extraterrestrial body, a spaceship, an equation, or a speck?

Zenil points out that the approach has potential terrestrial applications, for example in deciphering intercellular signaling. He has also used conceptually similar methods to identify important components in gene regulatory networks – does disrupting one part make the overall system less understandable? An algorithm that stitches together smaller algorithmic components to explain or predict data — this new method is just one way to do that — could also one day help us achieve artificial general intelligence, Zenil says. Such automated approaches do not depend on human assumptions about the signal. This opens the door to discovering forms of intelligence that may think differently than we do.

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