# A message in a bottle to the stars

*7 min read*

*.*Updated: 07 Jul 2017, 09:21 AM IST

It's a pretty good assumption that an advanced alien civilization on some distant planet will also understand mathematics

It's a pretty good assumption that an advanced alien civilization on some distant planet will also understand mathematics

Years ago, a couple in Puerto Rico took me on a drive through the mountains on that lovely island. The twists and turns got my stomach heaving, so we stopped somewhere and the wife pulled an orange off a nearby tree. “Don’t eat it," she advised. “Just sniff the peel and you’ll feel better." I did, and I did.

Then she said: “Actually, when we get to where we’re taking you, I promise you’ll feel even better." Not long afterwards, I caught glimpses, above the trees ahead, of some curiously fragile-looking machinery, suspended in the air like it was part of some giant spider’s web. She was right. I was so curious about this odd sight that I forgot my shaky stomach. And when we finally stopped, we walked a short distance to an overlook. What I saw there, sprawling at my feet, took not just my nausea away, but my breath too.

This was the Arecibo Radio Telescope, a gigantic bowl that filled the entire valley. I do mean “entire"—the diameter of this monster is 305m, and at the time and for many years after, it was the largest such dish in the world. (In September 2016, a 500m telescope began operations in South-West China). It is used for radio observations of our universe, and has plenty of intriguing discoveries to its credit.

In 1982, for example, a University of California (Berkeley) team, including the astronomer Shrinivas Kulkarni, used Arecibo to find the first “millisecond pulsar" (called PSR B1937+21). A pulsar is a rotating star that emits a beam of radiation. On earth, we detect it only when the beam points towards us—think of a lighthouse and its rotating beam. The effect is that we observe the star’s brightness varying regularly, or in pulses (thus the name). Now a lighthouse’s beam might rotate once every 15 seconds, for example. But Kulkarni’s strange B1937+21 pulses 642 times a second. That is, it rotates once every 1.5 milliseconds, very rapidly indeed. Especially for something as massive as a star.

Still, while that’s fascinating, to me that’s hardly the most intriguing use that Arecibo has been put to.

Arecibo is also part of the effort to answer an ancient question: “Is there anyone out there?" — that is, the search for extraterrestrial intelligence, or SETI. Arecibo supplies data for the worldwide volunteer-based SETI@home project that has been running since 1999. While it hasn’t yet found conclusive evidence of an extraterrestrial intelligence, at least one astronomer, Seth Shostak, believes we will get such evidence sometime between 2020 and 2025. This is from how he calculates and interprets the Drake equation (about which, another time).

But think about this: Anyone who is out there might also be listening for a signal from us. After all, why should we be the only ones with our ears cocked? And if someone’s listening, we should give them something to listen to. Thus it was that in 1974, a team of astronauts used Arecibo to broadcast what’s now known as the “Arecibo message" into space. This produced an immediate and loud controversy, and several scientists objected. The history of mankind’s exploration on Earth, they argued, shows that whenever more technologically advanced civilizations have met others less so, the lesser ones have suffered. Why would the motivations and imperatives be any different in outer space, especially since there’s a compelling argument that an alien civilization will almost certainly be more advanced than we are? Thus why are we drawing attention to ourselves?

All that apart, perhaps you’re wondering: What was in that Arecibo message? Think this over for a moment. We want to send out a signal that says we exist and we’re a (somewhat) intelligent, sentient civilization. We hope it will eventually be intercepted by another such civilization. Actually, we’re just beaming a stream of data into space. Sure, we earthlings have devices—radios, cellphones, TVs, radio telescopes—that know how to receive and decode signals that waft through the air. We must assume an alien civilization has such devices too. So when they receive our signal, they will know it’s not just more random noise from the arcane rumblings of the universe.

What should go into such a message?

There are complications, which is why this is such a thought-provoking question. Obviously, aliens won’t understand English or Tagalog or Bhojpuri. So it’s no use sending something in one of those or in any other language spoken on this planet. What can we send out that we can be sure they will recognize and understand? Is there a language, or something, that we can be sure is universal?

In fact, there is. It’s called mathematics.

***

Consider this: At some point in our distant past, our ancestors hit upon the idea of counting. After all, there were things all around them—plants, rocks, animals, hills, stars—and they will have needed ways to refer to their number. “That clump of trees will be shadier than this one", you can imagine some early mother telling her children as they wandered the plains under a scorching sun, “because there are five trees there and only two here." For which, she and the kids both needed to understand five, and two, and that five is greater than two.

And once they had numbers, other things followed. “You picked up two oysters?" the intrepid mother asks her eldest. “Well, I’ve got three. That’s five altogether. One for each of us and one left over for the dog. All right, dinner time!" Addition and division, right there. Similarly, subtraction and multiplication.

Foundation laid; and rising from there is the entire edifice of mathematics as we know it today — Pascal’s triangle, prime numbers, infinite series, the Riemann hypothesis, irrational numbers, the Pythagoras theorem and Benford’s Law … and on and on.

How does all this relate to sending signals into space?

Well, every advanced civilization has likely been through the same process. That has been the experience of every civilization on this planet—whether in Greece or China or the Indus Valley, they had a need for numbers. They evolved their particular approach to them, and then grappled with more complex mathematical ideas. So it’s a pretty good assumption that an advanced alien civilization on some distant planet will understand mathematics as well.

Note that I don’t mean the symbols “1", “2", “3" and so forth. Our alien civilization almost certainly won’t know what these mean. But it almost certainly will know the concept of numbers because at some point in its history it will have had to start counting things. And once that happened, our intelligent aliens no doubt learned to add and subtract, divide and multiply their numbers—and eventually built the whole edifice of mathematics that we know too. It may look different, but the ideas at its core will be familiar to us too. They won’t call it “pi", for example, but they will undoubtedly know of the ratio between any circle’s circumference and its diameter, and the way it pops up all over the mathematical landscape.

Such was the thinking behind the Arecibo message: That any alien civilization would have mathematics.

In particular, the astronomer who crafted the message, Frank Drake, chose to use prime numbers. Primes are, in many ways, the building blocks and milestones of a number system. For example, any given number can be expressed as a product of primes. (95 = 5 x 19, 70 = 2 x 5 x 7, etc.,). Or take the still unproved Goldbach conjecture—every even number greater than 2 can be expressed as the sum of two primes. (56 = 19 + 37; 172 = 5 + 167, etc.,). Because primes are so fundamental, Drake argued that an intelligent alien civilization would know about them. (Maybe they will have proved Goldbach).

Drake encoded the message in the form of exactly 1,679 pulses, which he sent out again and again from Arecibo so that it would be clear it wasn’t random noise. “Why 1,679?" you wonder. Drake hopes the aliens will ask the same question, and then realize that 1679 is the product of two primes, 23 and 73 (1679 = 23 x 73). That might make them arrange the pulses in a 23 x 73 grid and voila! They will find crude images of the human body, the Arecibo telescope itself and our solar system, plus a few other bits of information Drake thought would be of universal interest

We haven’t detected any alien response to the Arecibo message yet, but that’s no surprise. It was aimed at a cluster of 300,000 stars called M13, and M13 is about 25,000 light years away. So if you’re around 50,000 years from now, remember to listen for a possible reply.

Until then, you might want to think about two questions that scientists too are grappling with. One, if you were asked to send out such a message today, how would you craft it? Two, should we send one out at all?

Once a computer scientist, Dilip D’Souza now lives in Mumbai and writes for his dinners.

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