by Shane L. Larson
Back in the Olden Days (and by that, I mean the 1980’s and 1990’s) information and knowledge were truly commodities. The sum of all human knowledge was not instantly available with the swipe of a finger from every backwater Irish pub or aisle at Walmart. Never-the-less, information was systematically collected (much to the regret of middle school teachers the world over) in encyclopedias.
I had a set of encyclopedias I had commandeered from the family, and kept on the bookshelf at the head of my bed, spending long hours (often late at night, with a flashlight) pouring over the pages, drinking it all in. It was a seminal time in my life, with volumes of information literally at my fingertips, spending every moment I had attempting to assimilate as much as I could.
This was the beginning of a long trajectory for me, one example of how the Universe stirs atoms together in such a way that they can think about the world around them. It is remarkable, really. A rock is also a collection of atoms that the Universe has stirred together, but if a rock contemplates the Cosmos, I have no strong notion of what its rocky thoughts might be. A platypus can think more than a rock, but I don’t know what a puddle of platypuses talk about over drinks on a Friday night. Humans, on the other hand, have a possibly unique habit of thought: we ask questions, and then we figure out the answers.
Of particular interest are questions about life and our own existence. What is the origin of life? Is there life elsewhere? Is there intelligent life (on this planet or others)? Could we talk with extraterrestrial intelligences? These are BIG THOUGHTS — heady questions that for the most part have no answers yet, no entry in our encyclopedias of knowledge.
I often imagine what it would be like to live in a galaxy brimming with life. Suppose we knew we weren’t the only intelligent beings in a vast and lonely Cosmos. How would we communicate with each other? The distances between the stars are vast, too far to be traversed in a single human lifetime (who knows about alien lifetimes!). Fortunately, there is another way to communicate — we call it “radio astronomy.” We can beam messages from Earth, out into the depths of space, and wait for a reply.In my reverie, I often wonder what can we send to our civilized alien friends? What can we, the human race, contribute to the Encyclopaedia Galactica, the composited knowledge of a million intelligent species in the Milky Way? One could imagine beaming the entire contents of Wikipedia into the vast darkness, a merging of one of our encyclopaedias with the common knowledge of the galaxy. All things being equal, that would probably be a waste of time because English is not the Universal Langauge (nor is any other language on Earth). Furthermore few, if any, of our aliens will understand the nuance and meaning of much of the cultural content in our encyclopaedias. What is a Centaurian going to do with an article about popsicles?
But as it turns out there is a language that, for reasons that are subtle and not well understood, describes everything. That language is called mathematics, and the Universal vocabulary built from it is called science. One of the prejudices we have about the nature of intelligent life is that to become technologically advanced, they will have to discover and understand the basic laws of Nature, just as the human race has. In order to understand and interpret the laws of Nature, particularly in the application to technology, will necessarily require an intimate appreciation of mathematics.
If we imagine using mathematics then, we can use a very few basic principles to construct a message that could be sent to the stars, and understood. One of the first concepts to make good on this idea is often attributed to the mathematician, Karl Friedrich Gauss. The proposed idea was to plant vast lines of trees in the shape and form of geometric elements that illustrated our understanding of the Pythagorean Theorem (a relationship between the lengths of the sides of a right triangle). In 1840, Joseph von Littrow suggested we dig enormous trenches in the Sahara desert, fill them with kerosene and set them on fire at night. The trenches would be large enough to be visible from nearby worlds like the Moon or Mars. People who think of these things are my heroes!A modern approach to using mathematics for communication with extraterrestrial civilizations was worked out by American astronomer, Frank Drake. Drake was interested in “communication without preamble,” and presumed that if one constructs a message with underlying mathematical principles, no preamble would be necessary to begin decoding a received message. A great debate had started after Drake’s 1962 Project Ozma, a radio observing project to detect radio signals from extraterrestrials. If aliens were beaming their encyclopaedia entries at us, and if we detected them, people doubted we would even be able to decode them. More to the point, if we were beaming our encyclopaedia entries into space, would an extraterrestrial intelligence be able to decode the message? This question interested Drake, so he constructed an anonymous challenge. He 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 Drake had encoded into it!
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 of understanding. One such concept is the relationship of the area of a circle to the square of the radius (they are related by the number, pi = 3.141592654…). 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. Factors are the numbers you have to multiply together to get another number. For instance, it has been 106 years since the Chicago Cubs have won a World Series (the last time being in 1908, against the Detroit Tigers); two “factors” of 106 are 2 and 53: 106 = 2 x 53. You use factors everyday. You’re preparing for the Cosmos: A Spacetime Odyssey premiere, and want pizza for 4 friends. Each person will eat 4 slices of pizza, so you need 16 slices. There are 8 slices per pizza, so you buy 2 pizzas: 16 = 2 x 8. A prime number is a number with only two factors: itself and the number 1. An excellent example is 5. There is no way to multiply two whole numbers together to get 5 other than 5 x 1.
So what was the message? It was a string of 1’s and 0’s. On the paper, it was written as 1’s and 0’s, and the astute reader should object to this — “Alien’s won’t read our alphabet! How will they know what is a 1 or a 0?” In the context of communicating with extraterrestrials, we’ll be sending radio signals. A series of written 1’s and 0’s can be sent as a series of signals are that are ON or OFF, LOUD or QUIET, UP or DOWN. All that matters is that however they aliens are reading out the radio signals, they see two distinct states.The remarkable result of Drake’s experiment was that every person the puzzle was sent to was able to decode it. At first glance, a string of 1’s and 0’s might appear as some type of binary numbering or lettering system, akin to that used in modern digital computers, but that would not be information that aliens could readily decipher, since it is highly unlikely that they have a written alphabet similar to ours. The key to Drake’s idea, is that the numbers represent the pixels in a picture.
Drake’s experiment proved the idea that communication without preamble was a viable idea, and was the basis for a signal which the planet Earth sent out into the galaxy (towards the globular cluster M13 in Hercules, some 24,000 light years away) from the Arecibo Radio Telescope, in Puerto Rico, in 1974.
So how was the message formulated? What bit of the Encyclopaedia of the human race did it contain? 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, he created a quantity of characters for which there were precisely two prime factors. 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 x 73. This is the only way to multiply two numbers together and get 1679!
Here is the full content of the original Arecibo Message:
0000001010101000000000000101000001010000000100100010001000 1001011001010101010101010100100100000000000000000000000000 0000000000011000000000000000000011010000000000000000000110 1000000000000000000101010000000000000000001111100000000000 0000000000000000000001100001110001100001100010000000000000 1100100001101000110001100001101011111011111011111011111000 0000000000000000000000010000000000000000010000000000000000 0000000000001000000000000000001111110000000000000111110000 0000000000000000000110000110000111000110001000000010000000 0010000110100001100011100110101111101111101111101111100000 0000000000000000000001000000110000000001000000000001100000 0000000000100000110000000000111111000001100000011111000000 0000110000000000000100000000100000000100000100000011000000 0100000001100001100000010000000000110001000011000000000000 0001100110000000000000110001000011000000000110000110000001 0000000100000010000000010000010000000110000000010001000000 0011000000001000100000000010000000100000100000001000000010 0000001000000000000110000000001100000000110000000001000111 0101100000000000100000001000000000000001000001111100000000 0000100001011101001011011000000100111001001111111011100001 1100000110111000000000101000001110110010000001010000011111 1001000000101000001100000010000011011000000000000000000000 0000000000000011100000100000000000000111010100010101010101 0011100000000010101010000000000000000101000000000000001111 1000000000000000011111111100000000000011100000001110000000 0011000000000001100000001101000000000101100000110011000000 0110011000010001010000010100010000100010010001001000100000 0001000101000100000000000010000100001000000000000100000000 0100000000000000100101000000000001111001111101001111000
By arranging the number string in a grid of characters, the length of each side being one of the prime factors, an image can be formed (color in squares with 1’s and leave 0’s blank, or vice versa). There are two ways to organize 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 below, 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! for 23 rows and 73 columns, the image looks like a random collection of dots, without an obvious organization to them.
But if you make 73 rows and 23 columns, it becomes far more clear that there is some kind of organization to the string of digits. Even in the printed numbers, your eye will pick up patterns, which are much easier to see when converted into a shaded grid.What does it all mean? Here is the information we encoded in the message, starting at the top (referring to the colorized version, for ease):
- Numbers from 1 to 10 (white pixels): this shows how numbers are represented throughout the rest of the message. In all places where a number is shown, the pixels are colored white
- Atoms (purple pixels): the atomic numbers (the number of protons, which uniquely identify each kind of atom) of hydrogen, carbon, nitrogen, oxygen, and phosphorus. These are the basic atoms needed for the biochemical description of life
- Sugars and bases (green pixels): the chemical formulae, using the atoms described above, that are the sugars and bases that make up the nucleotides, the building blocks of DNA.
- Double Helix (blue pixels): the DNA double helix; the number it winds around is the number of nucleotides in a strand of human DNA
- Human Figure (red pixels): the DNA terminates on the organism it represents, the human figure. On the left is a bar and number representing the average height of a human, and on the right is the total population of humans on Earth
- Solar System Map (yellow pixels): a map of the solar system from where the message came; the third planet is offset toward the figure, indicating this is the organism that sent the message
- Arecibo Telescope (purple pixels): a graphic of the telescope that sent the message, with a line and number underneath it telling how large it is
There is, of course, some debate as to whether or not even this message would be understandable by an alien intelligence. Maybe they decode the message upside down, and instead of a human balancing on two feet under a strand of DNA, they see a 4 tentacled alien swirling uncontrollably down into a cosmic maelstrom (maybe a black hole?). Perhaps extraterrestrials are intelligent and technologically advanced, but don’t have a sensory facility similar to vision. Will they even understand the concept of images? Perhaps, perhaps not; but they will understand prime numbers and hopefully realize there is something intelligent in the long string of radio pulses.
What is most important about the Arecibo Message, is that we are thinking about how to communicate with the rest of the Cosmos. Someday, if there is life elsewhere, we may become aware of each other, and when we do, we’ll want to think about how we can co-author a true Encyclopaedia Galactica. How can we exchange information, to know more about the Cosmos and our place within it?
This post is part of an ongoing series, celebrating the forthcoming science series, Cosmos: A Spacetime Odyssey by revisiting the themes of Carl Sagan’s classic series, Cosmos: A Personal Voyage. The introductory post of the series, with links to all other posts may be found here: http://wp.me/p19G0g-dE
This is a very useful post on the Arecibo message. Thank you! Best I have come across on the web.
Thanks! I’m glad you enjoyed it!
Hey! I have problems understanding the purple image near the top, below the white numbers 1 to 10.
From left to right, the numbers are supposed to be 1,6,7,8,15 right?
OK: 1,6,7 are straightforward. But how are the two right colums 8 and 15? If anyone can shed some light on this, thanks!