Before talking to aliens, it would be helpful if we had some insight into what it is like to be one. Since we don’t, and won’t, we will have to do the next best thing — identify all our anthropocentric assumptions about intelligent life in the universe and then ruthlessly eradicate these from the messages we send them.

To that end, we need to ask ourselves: What common ground could there be between all forms of intelligence in he universe? What is the minimal definition of the term intelligence in this regard? And is there a medium for communication that is shared by all these intelligences?

Jules Verne implicitly had a go at some answers when he conjured up a scheme for communicating with moon dwellers, the “Selenites,” in From the Earth to the Moon:

Thus, a few days ago, a German geometrician proposed to send a scientific expedition to the steppes of Siberia. There, on those vast plains, they were to describe enormous geometric figures, drawn in characters of reflecting luminosity, among which was the proposition regarding the ‘square of the hypothenuse,’ commonly called the ‘Ass’s Bridge’ by the French. “Every intelligent being,” said the geometrician, “must understand the scientific meaning of that figure. The Selenites, do they exist, will respond by a similar figure; and, a communication being thus once established, it will be easy to form an alphabet which shall enable us to converse with the inhabitants of the moon.” So spoke the German geometrician; but his project was never put into practice, and up to the present day there is no bond in existence between the Earth and her satellite. (Found via the University of Zimbabwe)

Here a geometric proof of the Pythagorean theorem is proposed as something so fundamental that it must be one of the first discoveries made by a budding civilization’s mathematicians. The Greeks indeed discovered it first here on Earth, but still: How fundamental is it exactlyIn hyperbolic space, the angles of a triangle add up to less than 180 degrees. In elliptical space, they had up to more than 180 degrees — as is the case if you draw a triangle on a sphere, for example. We don’t currently know what kind of space the universe is made of. On a very small scale, the human scale, space certainly looks Euclidian, but that would also hold true in hyperbolic or elliptical universes. My own gut feeling is that space is hyperbolic. But aliens might know for sure.? The theorem only holds true in Euclidian space, which we think of as “normal” space, but not in hyperbolic or elliptical space. We’re biased that way, however. We’re instinctive flat-Earthers — we prefer to shoehorn the elliptical plane we call Earth into flat, Euclidian maps, replete with massive Greenlands. We exude pro-Euclidian sentiment in everything we do.

We shouldn’t expect aliens to know about this proclivity of ours. Actually, they probably wouldn’t even notice proofs transmitted at wavelengths suited specifically for our eyes — aliens have no reason to suspect we’d be broadcasting at those entirely arbitrary wavelengths. Or else they might be in a phase of their development where geometric proofs are unfashionable, not to be trusted, much as was the case for generations of our own mathematicians in the era between Descartes and Riemann — and they’d even be right in this caseIn Verne’s time, aliens might (correctly) have interpreted our depiction of the Pythagorean theorem across Siberia as a statement of our (unjustified) belief in a Euclidian universe; or else they might (incorrectly) have concluded that we think the theorem holds true on an elliptical plane (Siberia). Either way, they’d think we’re stupid..

We have on several occasions made real attempts to talk to aliens. In the early 70s we attached a plaque with an engraved diagrammatic message to the Pioneer 10 and 11 space probes, which we then sent on flyby missions to Jupiter and Saturn and on into outer space.

Pioneer 10 is travelling to Aldebaran, a giant aging star around 65 light years away. As of 2005, the probe is about 12 light hours from us — one 50,000th of the way there.

In the late 70s we launched the Voyager 1 and 2 probes on a similar, upgraded mission. They contain a more ambitious attempt at communication — a gold-plated phonograph record! With a supplied needle, no less.

Both attempts unintentionally reveal some less flattering aspects of humanity, though fortunately these should be way above aliens’ potential heads. For example, the naked woman on the Pioneer plaques has no genitalia. Apparently the plaque’s designer, astronomer Carl Sagan, left them out rather than risk rejection of the entire project. The fact that there were naked people at all on these plaques nevertheless led to angry letters accusing NASA of peddling smut to the stars. More embarrassing, at least to me, is that one of the two greetings on the Voyager records is by an ex-Nazi stormtrooper, Kurt Waldheim. How on Earth — literally — did we manage thatThe other greeting is by Jimmy Carter.?

I rather doubt aliens will ever “hear” the encoded sounds on the record. If they find a Voyager spacecraft they will conclude it was built by an intelligence, but in the absence of ears, atmosphere or human brain circuitry, the bits on that record will be as revealing to aliens as a jpeg of Monica Bellucci is to a blind personCue yet another reference to Thomas Nagel and his essay, What is it like to be a bat?. And how should aliens tell if they are seeing the plaque the right side up, given they have never met a human before? It’s just a load of Pollocks to them.

In 1974 we carefully aimed the Arecibo radio telescope’s transmitter at M13, a globular star cluster 25,000 lightyears away, and sent it a three minute message containing exactly 1,679 bits (around 0.2 kilobytes). The message, travelling at the speed of light, will unfortunately miss M13 completely, as the cluster will by then have moved out of the signal’s path, seeing as our galaxy rotates.

This problem aside, using radio was not an arbitrary choice. Radio transmissions offer a faster medium than plaques and a less anthropocentric medium than records or light. Radio is as fast as light, since both are just electromagnetic radiation made up of photons, but radio frequencies are far lower than light frequencies, so radio photons require much less energy to produce.

Which exact frequency to use for radio transmissions (and thus also for listening)? In this universe, one part of the radio spectrum — at around 1420 Megahertz — has far less background noise than other parts, so anybody who would want to maximize their signal-to-noise ratio would use it. We use it when we listen for aliens with SETI. So did we use it to send the Arecibo message? Not exactly:

It’s interesting to note that in 1974 the Arecibo message was transmitted at 2380 MHz, a frequency well above the “water hole” band. In Earth’s first “Active SETI” attempt we didn’t transmit at a well known and preferred frequency of either 1420 or 1665 MHz. Furthermore, 2380 MHz is the second harmonic of no particularly special frequency. The Arecibo transmitter was designed for S-band planetary radar experiments and SETI used it because it was available.

Luckily, it technically relatively easy for aliens to listen to many frequencies simultaneously, as this fuller discussion on making guesses about the medium makes clear.

The one thing the makers of the Arecibo message did get right, in my opinion, was to use the basic properties of whole numbers to encode it. Because the sequence of prime numbers is the same regardless of where you are in this universe, the prime factors of 1,679 — the number of bits sent in the message — will be 23 and 73 everywhere. Aligning the bits sequentially on a 23 x 79 grid produces the patterns that make up the message. That’s really clever, and hints at the kind of message I think we should be sending.

Do the patterns that comprise the Arecibo message make any sense to aliens? As there will not be any opportunity to start a dialogue, aliens won’t be able to ask for clarifications. I think mixing binary counting systems with graphical representations is therefore really just a way of not imparting any information at all. Aliens might think we look like the blobs representing binary representations of our DNA molecules. Maybe they look like the binary representations of our DNA molecules. Maybe our representative pinheaded human provides them with an unsolveable binary counting puzzle which they just can’t crack.

And why oh why do we have to count to 10 in our binary counting lesson at the start of the message? Haven’t we learned anything about anthropocentrism? Much better, I think, to drop using bases altogether when talking to aliens, and just focus on winking at them unambiguously. How? I have a plan.