The Drake Puzzle by Shane L. Larson Department of Astronomy, Adler Planetarium

“Our sun is one of 100 billion stars in our galaxy. Our galaxy is one of billions of galaxies populating the universe. It would be the height of presumption to think that we are the only living things in that enormous immensity.” ∼ Wernher von Braun

Introduction The Search for Extraterrestrial Intelligence (SETI) has long been of interest to humankind. The problem is how would we communicate with extraterrestrial biological entities (EBEs) if we met them?

It is said that in 1820, the famous German mathematician Karl Friedrich Gauss recommended that a giant right triangle of trees be planted in the Russian wilderness, an exercise that would demonstrate to EBEs that the inhabitants of Earth were civilized enough to understand geometry. It is also said that 20 years later, the Viennese astronomer Joseph von Littrow proposed digging a twenty-mile-long ditch in the Sahara, filling it with kerosene, and lighting it at night, again to communicate that there was intelligent life down here.

In the modern era, the American radio astronomer Frank Drake is generally credited with beginning the first serious efforts geared toward communication with possible extraterrestrial intelligences. In 1960, at the Green Bank radio astronomy facility in West Virginia, he began the first modern search for radio signals of extraterrestrial origin, called Project Ozma.

Communication without preamble In the years that followed Project Ozma, there was a great deal of debate as to whether or not we could actually decode a message if we received it, and even more to the point, whether or not an EBE could decode a message from us if it received one. So Frank picked up the challenge, and mailed to several scientists around the world a piece of paper that had only a string of 1’s and 0’s on it, in an unmarked envelope. No explanation, no requests, no instructions: just the number string. Every single person who received the number string extracted a message that Frank had encoded into it!

Drake’s experiment proved the idea that communication without preamble was a viable idea, and was the basis for the signal which the planet Earth sent out into the galaxy (towards a globular cluster in Hercules, some 24,000 light years away) from the Arecibo Radio Telescope, in Puerto Rico, in 1974.

The remarkable result of Drake’s experiment was that every person the puzzle was sent to was able to decode it. At first glance, it might appear that there is some type of binary numbering or lettering system in use, akin to that used in modern digital computers), but that would not be information that could readily be deciphered by and EBE, since it is highly unlikely that they have a written alphabet similar to ours.

Drake’s premise in constructing his message is that there are certain fundamental concepts that exist in mathematics, of which any civilization technical enough to receive radio information should be capable

Drake Puzzle Activity 1 of understanding. One such concept is the relationship of the area of a circle to the square of the radius (the proportionality constant being the number π). Another such concept, and the one Drake employed in his experiment, is the idea of prime numbers. Every number can be factored into a unique set of non-factorable numbers, which are called its prime factors. Drake imagined a message formulated as a grid of pixels that when properly displayed would make an image. By carefully choosing the grid size of his message, Drake created a quantity of characters for which there were precisely two prime factors. By arranging the number string in a grid of characters, the length of each side being one of the prime factors, an image was formed (color in squares with 1’s and leave 0’s blank, or vice versa).

The 1974 Arecibo Message The Arecibo message of 1974 was a string of 1’s and 0’s, 1679 in all, that was beamed toward the globular cluster M13 in Hercules. There are only two prime factors for this number of digits: 1679 = 23 × 73. This is the only way to multiply two numbers together and get 1679! If I take the entire string of digits, I can make a picture which is either 23 digits tall and 73 digits wide, or a picture which is 73 digits tall and 23 digits wide. Both cases are shown in Figure 1, where the 1’s have been shaded in as black squares and the 0’s have been left as open squares. There is a remarkable difference between the two! The image formed by the Arecibo Message in 1974 contained the molecular structure of several molecules essential to life, a picture of DNA, a picture of a human being, a picture of the solar system, and a picture of the Arecibo Telescope. Other information was encoded as well, like the first ten binary numbers, which were used to indicate the size of the various objects depicted in the message.

PART A: Decoding a Signal “Who needs TV?” you exclaim one day, and commandeer your satellite dish to search for extraterrestrial intelligence. Within several hours of starting your search, you run across the following interesting signal:

100000000000000000000000000000000000110000000001001100100011101100 000000011000000001010101010001000101000000001100000000101010101000 110011000000000110000000011101010100010001010000000011000000001010 110011101110101000000001100000000000000000000000000000000000110001 110101011101110010001100111000011000100010100100100010101000010100 001100010001110010010001010101101010000110001000101001001000111010 010101000011000111010101110111010100110011100001100000000000000000 0000000000000000001

Obviously, this message was meant to be decoded by you (a human who speaks English), so it is not necessarily the best thing to send to extraterrestrials. But the basic idea is there. The Arecibo Message was significantly more complex, and even after the picture was generated had to be puzzled out and deciphered. For a complete description of the Arecibo decipherment, visit the Wikipedia page on the topic: http://en.wikipedia.org/wiki/Arecibo message

PART B: Communicating Now it is your turn to communicate with the Cosmos.

⊲ Write your own pictorial message in the same spirit as the Drake Puzzle. Remember to make the message size the product of two prime numbers.

⊲ Write out your message both in picture form (on graph paper), and as a string of 1 and 0 that you could send out into the Cosmos through a radio telescope.

Drake Puzzle Activity 2 Figure 1: (a) The original Arecibo Message, represented as a 1679 digit long stream of 1’s and 0’s. (b) Arranging these digits in a 23 × 73 grid reveals nothing of interest, only apparently random dots. (c) Arranging these digits in a 73 × 23 grid suddenly reveals interesting pictures. Even in the grid of 1’s and 0’s, your eye can see patterns emerging, though the rendering in pixels makes the pattern much more apparent.

⊲ You’re going to have to pick someplace to send your signal. If you got to send one signal, and got to choose where to send it, what would you consider when choosing where to point your radio telescope when you hit send? The messages we’ve sent before have been targeted at stars that are similar to the Sun.

Solution to the puzzle may be found at: sciencejedi.com/science/drakePuzzle/.

Drake Puzzle Activity 3