Last July, the Russian billionaire Yuri Milner launched a campaign called the Breakthrough Initiatives, a $100-million dollar donation to be doled out to scientists working on the Search for Extra Terrestrial Intelligence (SETI). This donation didn’t just provide some much-needed legitimacy to a field that has, since its inception, often struggled to be taken seriously. It also helped to alleviate one of SETI’s largest problems, second only to actually locating aliens: finding the funding to continue the search. Scanning the cosmos for intelligent life isn’t cheap, and there’s a lot of work to be done to prepare for first contact—which some scientists, like Seth Shostak, the director of the non-profit SETI Institute in California, expect to happen within our lifetime.

Milner’s donation will go a long way in footing the bill as SETI scientists work to make this contact a reality, yet there are some SETI problems money alone can’t solve. In this sense, perhaps the most pressing issue faced by SETI researchers is figuring out not only what we would say when ET calls, but more fundamentally, how we would go about saying it.

Astronomers and SETI scientists have been mulling over this particular communication problem for a while and have come up with a few ideas, some more outlandish than others. One of the earliest solutions was suggested in the early 19th century by the Austrian astronomer Joseph Johann Von Littrow, who proposed digging massive trenches in the Sahara desert, filling them with water, pouring kerosene on top, and then setting the kerosene alight in order to send flaming messages to our planetary neighbors.

Vittrow’s scheme never came to fruition, but for about 150 years it was the best idea around. It wasn’t until 1960 that another proposal for ET communication came along, one that continues to shape the exolinguistic field that it founded.  The proposal took the form of a book titled Lincos: Design of a Language for Cosmic Intercourse, and its publication marked the first artificial language constructed for the sole purpose of communicating with extraterrestrial life.

Lincos, a portmanteau of lingua cosmica, was the brainchild of the German mathematician Hans Freudenthal. Born in 1905, Freudenthal began his academic career as a lecturer at the University of Amsterdam in 1930, a position he held until the Nazi invasion of the Netherlands in 1940. After losing his job, Freudenthal kept a low profile for several years of the occupation. He was sent to the labor camp Havelte in 1944, but managed to escape a few months later to Amsterdam, where he would watch the Allied liberation in May of 1945. Shortly thereafter, Freudenthal was offered a full professorship in geometry at the University of Utrecht.

A fierce proponent of educational reform in the post-war years, Freudenthal vehemently opposed the introduction of “New Math,” a rigorously logic-based teaching methodology, into the Dutch curriculum. Freudenthal favored pedagogical methods that connected mathematic principles with daily life, something at which New Math failed dismally. It was the combination of these two interests—logic and applied math—which would ultimately provide Freudenthal with the intellectual fodder necessary to create Lincos, a language that used math to communicate both universal truths and the particulars of daily life on Earth.

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Despite its status as a milestone for the SETI community, Lincos never really garnered much attention from the general public. This is probably because the text is mostly comprised of dense, technical jargon and mathematical formulas that are all but unintelligible to the lay reader.

“It’s a groundbreaking work,” said Yvan Dutil, an astrophysicist with the University of Québec’s Télé-université, “but Freudenthal’s book is the most boring I have ever read. Logarithm tables are cool compared to it.”

In the introduction to Lincos, Freudenthal announced that his primary purpose “is to design a language that can be understood by a person not acquainted with any of our natural languages, or even their syntactic structures … The messages communicated by means of this language [containing] not only mathematics, but in principle the whole bulk of our knowledge.”

To this end, Freudenthal developed Lincos as a spoken language, rather than a written one—it’s made up of phonemes, not letters, and governed by phonetics, not spelling. The speech is itself made up of unmodulated radio waves of varying length and duration, encoded with a hodgepodge of symbols borrowed from mathematics, science, symbolic logic, and Latin. In their various combinations, these waves can be used to communicate anything from basic mathematical equations to explanations for abstract concepts like death and love.

The very first message sent in Lincos, Freudenthal wrote, should contain numerals that introduce the receiver to mathematics. This would consist of short, regular pulses or “peeps,” the number of pulses corresponding to a particular numeralone peep for 1, two peeps for 2, and so on.  The next step, he wrote, would be to transmit basic formulas, using symbols such as =, +, or > to demonstrate properties of human notation and mathematical knowledge (for example: . . . . . > . . . . to show that 5 is greater than 4). Each successive message would increase in complexity, moving from numerals and basic formulas to complex subjects like human behavior.

Despite its rigorous methodology and logical coherence, one of the primary criticisms of Lincos was that Freudenthal had failed to consider that extraterrestrials might not think like us at all, in which case our logic would be lost on them. Freudenthal acknowledges this limitation, writing that he must “suppose that the person who is to receive my messages is human or at least humanlike as to his mental state…[because] I should not know how to communicate with an individual who does not fulfill these requirements.”

According to Dutil, this also seems to be the general consensus of other SETI scientists. If there is intelligent life in the universe, some have argued, odds are it will in fact think like us—or will at least be familiar with our mathematics. According to this train of thought, if the civilization is capable of building a receiver for our message, this implies that they are capable of understanding the mathematics and science necessary to build such a machine. Another argument in favor of like-minded aliens was put forth by the renowned cognitive scientist Marvin Minsky, who noted in an essay dedicated to Freudenthal’s memory that aliens are subject to the “same ultimate constraints – limitations on space, time, and materials.”

On October 13, 1990, Freudenthal was found by school children on a bench in Utrecht, having succumbed to humanity’s time-constraint while taking his daily walk. He had died without finishing his lingua cosmica—the 1960 Lincos text was meant to be the first of two volumes, the latter to include means for sending messages on the subjects of “Matter,” “Life,” and “Earth.”

There’s no evidence that Freudenthal ever began work on this second volume, but the fact that Lincos is technically an uncompleted work has failed to temper its enduring legacy within the SETI community. In 1999, his mathematical language was given new life by Dutil and his colleague Stéphane Dumas when the two astrophysicists used Lincos as a starting point for a series of messages they sent out into the cosmos from a radio telescope in Ukraine. Known as the Evaptoria Messages, these transmissions were the third to ever be sent out to potential alien civilizations, and the first to draw from Freudenthal’s Lincos protocols.

“Lincos was the starting point of our language and to my knowledge, there are not many messages that have been sent using that approach,” said Dumas. ”Most messages sent to the stars are series of pictures describing simple ideas, similar to the Arecibo message in 1974.”

Unlike the Arecibo message, which was the first message intentionally sent into the cosmos for the purpose of communication, Dutil and Dumas’ goal was to send an encyclopedic message, one containing as much information about life on Earth as possible. The duo designed a simple character alphabet that would allow for the maximum amount of information to be transmitted during their limited use of the Ukrainian radar transmitter. In keeping with Freudenthal’s dictum that interstellar messages should begin with topics that would conceivably be known to any intelligence in the universe, the 1999 message began by teaching the recipient how to count, before moving on to more complex subjects such as physics and biology. The final message consisted of 23 pages (one page was 127x127 pixels) and was sent to its targets three times each to ensure sufficient redundancy.

Importantly, the message also included a formal request for a reply.

The targets for the message these messages were selected from SETI’s long list of potential solar systems that might harbor intelligent life. The candidates, all somewhere between 50 and 70 light-years away, were chosen based on a number of criteria, such as the age of the star and its position in the galaxy. The first message can be expected to arrive at its cosmic address (Hip4872 in Cassiopeia) sometime around 2035.

Page 1 of the 1999 Evaptoria Message (Yvan Dutil and Stéphane Dumas)

In more recent years, the SETI community has refined Lincos to develop more advanced options for interstellar communication. For example, the language CosmicOS was designed by MIT’s Paul Fitz as a computer program that could be run by extraterrestrials once they had received the message. Then there’s a second-generation lingua cosmica designed by the Dutch mathematician Alexander Ollongren (described by Dutil as “the only human to master Freudenthal”) which largely relies on constructive logic to compose the message.

While a standard language for interstellar communication doesn’t yet exist within the SETI community, CosmicOS and the second generation of Lincos neatly encapsulate the two ends of the spectrum: On one end is CosmicOS, which has the capability to transmit more information, but also has more logistical problems as a result; on the other is the new version of Lincos, with a smaller data package and a more limited amount of information that can be sent.

Yet according to Duntil and Dumas, these two disparate approaches to cosmic communications need not be mutually exclusive. In fact, they see them as two potential steps in a much larger program, where interstellar communication begin with a more simple message of greeting in one language and then proceeds to send increasingly complex messages in another. Yet regardless of the package, the duo agrees that any messages sent or received by extraterrestrial civilizations are going to be strongly rooted in mathematics.

“The creation of any language to communicate with an alien civilization is very difficult, because you need something called a metalanguage to make the bridge between the artificial language and the alien's language,” said Dumas. “The metalanguage par excellence is mathematics because it is the base of science, and any civilization that has built a device to listen to radio waves knows science.”

According to Dutil and Dumas, some more recent language designed for interstellar communication have incorporated more artistic elements such as music into the message—but at their core, most are still using Lincos as a starting point, at least in part.

Regardless of whether Lincos is totally abandoned in the future or continues to be a source of inspiration for our cosmic messages, Freudenthal’s tome will always be remembered among SETI scientists as a manual for uniting species light-years apart, species that will in all probability have little but mathematics in common. It was a Dutch mathematician’s attempt to make the alien familiar by rendering the most profound human emotions in mathematical equations.

Indeed, as Dumas was quick to point out, in many ways, Lincos was written more for Earthlings than ET.

“The creation of an interstellar language to communicate with an alien civilization is interesting, but in the end not very practical since the communication would occur over decades,” said Dumas. “The exercise of creating a message is more of a benefit to us than the alien because it shows how we want to portray ourselves. What do we want to give ET — the truth, or a beautiful image? Will the message contain our history of war, famine, and ecological disaster, or only the nice things? Ultimately, an interstellar message is a reflection of humankind to itself.”