When the esteemed German mathematician Carl Friedrich Gauss contemplated communication with extraterrestrials at the beginning of the 19th century, targeting the moon seemed obvious. Our planet’s natural satellite provided the nearest plausible home for life beyond Earth.

The form and content of the message we could send was equally clear to Gauss. He is credited with the idea of communicating with inhabitants of the moon by clearing large swaths of the Siberian forest of its trees and in their place planting massive wheat fields in the shape of carefully arranged geometrical shapes, which would be visible from the moon. Specifically, he wanted to show Lunarians that Earthlings are familiar with the Pythagorean theorem by creating massive landscapes demonstrating that the sum of the squares of the legs of a right triangle equals the square of the hypotenuse: a2 + b2 = c2.

Nearly two centuries after Gauss’s proposal, our team has turned to him for inspiration, using math as a universal language for interstellar communication by radio.

We of course now know that our moon is inhospitable to life. But in the last two decades we have learned of the existence of planets around other stars. Some of these exoplanets orbit within their star’s “Goldilocks zone,” where it is not too hot, and not too cold, but just right to allow for the existence of liquid water—a prerequisite for life as we know it. Recently we sent a series of radio messages that included a numerical description of the Pythagorean theorem to one such exoplanet, in the hope of eliciting a response from any geometry-savvy inhabitants.

CALLING E.T.

The exoplanet is a super-Earth named GJ 273b, which orbits Luyten’s Star, a red dwarf only 12.4 light years from our solar system. It has the distinction of being the nearest known exoplanet that is potentially habitable while also being in view of the two-megawatt transmitter of the European Incoherent Scatter Scientific Association (EISCAT) in Tromsø, Norway, north of the Arctic Circle. On three successive days in mid-October 2017, a project dubbed “Sónar Calling GJ 273b” celebrated the 25th anniversary of Barcelona’s Sónar music festival with radio transmissions from EISCAT, which included a sampling of music by the festival’s artists.

To increase the intelligibility of the signals, we at METI—a research organization dedicated to Messaging Extraterrestrial Intelligence—crafted a mathematical and scientific tutorial within the transmissions. METI’s tutorial differs from earlier interstellar messages in several ways. Past messages—like the radio message transmitted from a radio telescope in Arecibo, Puerto Rico, and the Golden Record onboard NASA’s Voyager spacecraft—have attempted to be encyclopedic in scope. The downside of trying to say everything in an interstellar message is that we are communicating so much information that it may come across as an incoherent jumble. METI’s message takes the opposite approach, explaining a few essentials of math and science with greater depth and clarity.

SIMPLE STEPS TO LINK FORM AND CONTENT

In past interstellar messages, the link between the form and content of the message has been arbitrary, making decoding by any intelligent recipients all the more challenging. In METI’s tutorial, we focus on concepts we can directly demonstrate through the radio signal itself. We explain time through pulses that have a clearly defined duration—one that can be described numerically, as well as directly shown by pulses of corresponding duration. We expand into the realm of electromagnetic phenomena by discussing the fact that radio waves have specific frequencies, doing so by pointing to the two frequencies we used for the transmission itself.

Throughout, we build step-by-step from simple to more complex concepts. After counting, we introduce arithmetic. Combinations of numbers that illustrate the Pythagorean theorem let us move into trigonometry. Once we can describe the relationships between the sides of a triangle—though simple division—we can describe sine waves, and thus radio waves themselves.

In a second round of transmissions set for April 2018, we will expand our tutorial to demonstrate fundamental elements of musical melodies—by turning the transmitter into a musical instrument capable of sending signals at several different frequencies, not just two frequencies as in our first set of messages. By expanding the range of frequencies at which we can transmit, we will mimic the relationships between musical notes, which are separated from each other by specific, mathematically precise intervals. Through some basic math and physics, we will introduce aliens to human melodies.

We have gone to great pains to send messages that will come out intact after a journey of more than 70 trillion miles. On each of the three days that we transmitted in October, we sent our METI tutorial three times. This provides alien codebreakers on GJ 273b with a simple rule to deal with the inevitable errors that will creep into the message as it traverses the vast distances between the stars. The recipient only needs to recognize that the message is sent three times; line up the three versions, one on top of the other; and finally, look for any discrepancies. Whenever there is a difference between the three parts, the extraterrestrial cryptographer has a simple rule to figure out what we intended: go with whatever appears two out of three times.

KEYS TO UNDERSTANDING

Our new METI tutorial provides novel features designed to increase comprehensibility, but it is not the final word. Instead, to craft increasingly sophisticated messages in the coming years, we should learn lessons from the history of the Search for Extraterrestrial Intelligence, or SETI. In 1960 astronomer Frank Drake conducted Project Ozma, the first SETI experiment. The 1960s and 1970s saw a handful to additional searches, each relatively limited in the number of stars observed, as well as the range of frequencies. No signs of intelligence beyond Earth were detected. With the completion of each project, however, astronomers and engineers became increasingly sophisticated in developing signal processing algorithms, ruling out false alarms, and articulating a case for each of their chosen target stars.

The power of today’s SETI searches is easily a trillion times as great as that of Ozma, thanks to more sensitive antennas that can search at billions of frequencies rather than only one. But has our sophistication in creating interstellar messages increased over the same time by even a factor of 10? I doubt it.

Using as an analogy the history of SETI, in which much was learned by conducting a series of modest follow-up searches, the best way to develop increasingly sophisticated messages is to keep targeting additional stars, each getting its own distinctive message. Rather than simply replicating the messages that have been sent in the past, we should continually explore alternatives for both form and content.

An interstellar message is like a treasure chest, offered by one civilization to another with the hope it will have value. Much of this value comes after the recipient can unlock the message’s secrets. But what may seem an obvious clue to us about how to do so may be obscure to an extraterrestrial. In our future messages, we would do well to include multiple keys, each providing a unique way to open the message. These efforts may one day let intelligent extraterrestrials begin to see the universe from a truly human perspective.