Tag Archives: Frank Drake

Dinosaurs in the Cosmos 2: Dinos without Radios

by Shane L. Larson

One of the things physicists and astronomers do very well is make simple estimates about the physical nature of the world around us. Part of this skill is (simple) math, and another part is knowing what physical quantities are important.  The most astonishing fact about this skill is that you and I do it every day, we just don’t realize it! Scientists have honed the skill — the place where science comes out is when those unconscious habits are used purposefully!  So how does it work? How is it that you and I are perfectly capable of describing complex physical phenomena, without necessarily resorting to equations we memorized in some long forgotten science class? To demonstrate, let’s consider sticking your hand (or your dog’s head) out the window of your car.

There is some serious physics behind dog ears in the wind, or flying your hand like an airplane. Despite that fact, you have some well defined and excellent intuition about what is important for this problem!

There is some serious physics behind dog ears in the wind, or flying your hand like an airplane. Despite that fact, you have some well defined and excellent intuition about what is important for this problem!

What affects how much force the wind presses on your hand (or your dog’s face) with?  With a little experimentation (something you probably did a lot as a kid, and have committed to memory but forgotten) you find there are three things:

  • how fast the car is driving. If the car is going faster, the force is stronger.
  • how you hold your hand (or, how big your hand is). If you hold your hand palm out, there is a bigger force than if you hold your hand finger tips out. The force is stronger if there is a bigger area being hit by the wind.
  • how thick the air is. Most of us don’t experience thick and thin air too often, at least not that we can tell the difference. But air is a fluid, like water, and water is much thicker than air. When you run your hand through water (a thick fluid) there is a much greater resistance than through air (a thin fluid).

That’s it — those are the three physical quantities that affect how much force you experience when you hold your hand/dog head out the window of your car. And you knew them, at least intuitively, whether you could explain it out loud or not! In a very similar way, the genesis of thinking about extraterrestrial life began with a few intuitive numbers that astronomer Frank Drake wrote down.

Frank Drake, circa 1962.

Frank Drake, circa 1962.

The serious scientific consideration of searching for extraterrestrial intelligences had started with a paper in the scientific journal Nature in 1959, by physicists Giuseppe Cocconi and Philip Morrison. This paper sparked Drake’s interest, leading up to his Project Ozma in 1960, the first human search for radio signals from an extraterrestrial civilization. By 1961, Drake decided to host a small scientific conference at the National Radio Astronomy Observatory, in Green Bank, West Virginia, where the Project Ozma search was carried out. Drake made a list of topics that should be discussed at the conference, dutifully writing down all the things that could affect how many communicative extraterrestrial civilizations there might be. When he was done, he realized he had created a Fermi problem estimate of the number of alien civilizations in the galaxy that we might communicate with — his list of topics were seven numbers that could be multiplied together.

A plaque showing the Drake Equation, hanging on the wall of the conference room where the equation was first presented. [NRAO].

A plaque showing the Drake Equation, hanging on the wall of the conference room where the equation was first presented. [NRAO].

He presented his seven number equation at the conference. It was promptly dubbed “The Drake Equation,” and has been used ever since as a baseline estimate for the kinds of discussions we are having now. A plaque of it now resides on the wall in the conference room where the meeting was held.

So what was Frank’s famous equation? Simply put, it is seven numbers — you multiply those seven numbers together, and you get the number of civilizations in the galaxy that could be communicated with, a number we denote as “N.”  It is written as:

          N = (R* x fp x ne) x FL x Fi x Fc x L

Of those numbers, the first three are matters of observational astronomy that can be verified and estimated from what we see of the Cosmos through our telescopes.  The last four numbers are quantities for which answers certainly exist, but whose values we are still uncertain about; it is playing with plausible values of these four numbers that illustrates our uncertainty about the Cosmos.

The stellar nursery, RCW 108, near the new emergent cluster of young stars (on the left), NGC 6193.

The stellar nursery, RCW 108, near the new emergent cluster of young stars (on the left), NGC 6193.

Let’s look at the first three numbers.  The first is R*, the rate at which stars are born in the galaxy.  The star formation rate is a simple way to start thinking about issues related to planets and life, because the number of planets must necessarily depend on the number of stars in the galaxy — you can’t have planets without parent stars for them to orbit!  For this number, astronomers think R* ~ 6/yr.

Young planetary systems form early on during the growth of a young star. [ESO image]

Young planetary systems form early on during the growth of a young star. [ESO image]

The second is fp, the fraction of stars that develop planetary systems. For a long time, we had no idea what this number was. For most of recorded history, no star other than the Sun was known to shepherd planets.  Then, in 1995 astronomers discovered planets around the star 51 Pegasi, a star very similar to the Sun about 51 lightyears away.  Today, we think planets may very well be common around most stars, and we are regularly discovering planets. As of the time of this writing (23 June 2014) there are 1797 planets known around other stars (visit the exoplanet catalogue here). To be conservative, let’s assume that not every star develops planets (though astronomers are beginning to think that a star without planets may be the exception, not the rule). We’ll take fp = 0.5.

Are there worlds like the Earth, orbiting other suns?

Are there worlds like the Earth, orbiting other suns?

The third number, ne, is the number of planets that could support life in a planetary system. Here, we don’t have a definitive value for this number, but any value we do use has some of our personal prejudices built into it since we have not had the opportunity to study an alien biology! One prejudice we have is that water plays an important role in the chemistry of life. Looking around the Sun, we find Venus, Earth and Mars are all at a distance from the Sun where liquid water could exist under the right conditions (this generic concept, the distance from a star where liquid water can exist on a planetary surface, is called “the habitable zone“). Venus has no liquid water, but Mars may harbor subsurface water. Based on what we know about our own planetary system then, let’s take ne = 2.

These numbers could change as we see more and more of the Cosmos, but probably not much.  So let’s multiply them all together and leave that number alone:

 R* x fp x ne = 6 x 0.5 x 2 = 6

For convenience, we now write the Drake Equation as:

N = (R* x fp x ne) x FL x Fi x Fc x L = 6FL x Fi x Fc x L

Now what about the last four numbers? These are numbers which have more uncertainty, and more speculation in them. They are absolutely numbers of importance when trying to figure out the number of civilizations in the galaxy, we just don’t have good ways to reliably estimate their values.

Prokaryotic cellular organisms were among the first forms of recognizable life to develop on the Earth.

Prokaryotic cellular organisms were among the first forms of recognizable life to develop on the Earth.

The first two are FL, the fraction of planets that develop life, and Fi, the fraction of planets with life that develop intelligent life.  These are complete unknowns; Earth is the only planet we know of with life!  Is it common for life to arise on other worlds? We know from the fossil record on Earth that simple life arose on Earth soon after its formation, in the form of single celled organisms — prokaryotic bacteria (cellular organisms with genetic material free floating in the cell, and not contained in a central nucleus), algae and the like. Given the simplicity of making the organic building blocks of life (chemical combinations called amino acids, used to build proteins), and given that self-replicating molecular systems are not uncommon, the early origin of life suggests that maybe life, in its simplest forms, may arise on planets quite often.  I’m an eternal optimist, so let’s assume FL = 1.  We’re just multiplying numbers together, so I can always go and change this number later.

If life arises, how often does that life become “intelligent?”  This is a harder question to answer, but again we can make an educated guess based on what we see on Earth. It is a fuzzy concept because you have to decide what you mean by “intelligent,” but there are many species on Earth we might consider intelligent — monkeys, dolphins, cats, even humans.  But there are many species that aren’t — oak trees, slime molds, or sea cucumbers.  How common is “intelligence?” Let’s assume Fi = 0.01 — a 1 in 100 chance.

What might life on other worlds look like? How do we define whether or not life is "intelligent?" In the Drake Equation context, we mean life capable of understanding and using science. [Image by David Aguilar]

What might life on other worlds look like? How do we define whether or not life is “intelligent?” In the Drake Equation context, we mean life capable of understanding and using science. [Image by David Aguilar]

The next number is Fc, the fraction of civilizations that can or want to communicate.  Here also, there are several extremes.  Consider humans — since the early 20th Century, we’ve been willy-nilly broadcasting our radio and television signals all over the place, blasting music videos of Eric Clapton and Chuck Berry out into the Cosmos (which I’ve written about before here).  We’ve even sent a few organized messages out, specifically with the intent of communicating with extraterrestrials; these have included radio signals, as well as physical messages.  On the another extreme, one could imagine a completely xenophobic civilization. Maybe they don’t want anyone to know of their existence, lest aliens invade and use them for food.  One could also imagine that a civilization never develops the technology to communicate. If Europe had not emerged from the Middle Ages in the Age of Enlightenment, perhaps we would have never had an Industrial Revolution; we’d all still be peasants, living off mushrooms and earthy root vegetables and not burdened by technology like smartphones or microwave ovens. Certainly the dinosaurs never developed radio communications, despite the intelligence we’d like to associate with marauding bands of velociraptors.  Let’s make a guess at this number (which we can always change) of Fc = 0.01.

We have no idea how easily civilizations rise, or how long they survive. All we can do is look at examples from Earth's history, such as the Indus Valley Civilization, which lasted for several millenia, then utterly vanished.

We have no idea how easily civilizations rise, or how long they survive. All we can do is look at examples from Earth’s history, such as the Indus Valley Civilization, which lasted for several millenia, then utterly vanished.

Now for the last number: the lifetime L of the civilization. There is enormous latitude in possible values for this number because we know absolutely nothing about it, and that is where this discussion gets interesting.  Suppose we take L to be the length of time modern humans have been on the planet.  We don’t know exactly how long that is, but our written history goes back only to about 3000 BCE, so we could take L to be the length of recorded human history, L = 5000 years.  By contrast, the dinosaurs lived on the planet for 170 million years before an asteroid obliterated them, so you could take L = 170 million.  Considering both of these cases we get:

 N = 6 x 1 x 0.01 x 0.01 x 5000 = 3

N = 6 x 1 x 0.01 x 0.01 x 170,000,000 = 102,000

That is quite a range in numbers — there could be more than 100,000 civilizations broadcasting radio; or there could be 3, with a very strong possibility that we are the only ones. The consequences of this calculation could be elating, or very depressing. Whatever the result is, the answer to this question will have profound consequences for our understanding of the Cosmos.

Which brings me back to where we started: dinosaurs and Fermi problems.  In many ways, the Drake equation is a Fermi problem.  What is different from many Fermi problems is that we don’t have a good handle on the last four numbers. But what if we didn’t care about all of these numbers?

What if all I wanted to know was "are there dinosaurs elsewhere?" [Images by S. Larson, at Eccles Dinosaur Park, Ogden, UT]

What if all I wanted to know was “are there dinosaurs elsewhere?” [Images by S. Larson, at Eccles Dinosaur Park, Ogden, UT]

What I love about the Drake equation is that it allows you to answer many related questions, by simply deciding what you think is important.  Let’s take the radical viewpoint that we don’t care about communicative civilizations; instead let’s simply ask how much life (of any sort) might there be in the galaxy?  Is the galaxy teeming with life, or is it a barren wasteland populated only by the descendants of some monkeys on a backwater forgotten world?

Suppose we don’t care about communication.  What if we only wanted to know if there were, say, dinosaurs?  We don’t keep the intelligent number or the communication number. That makes a modified Drake Equation that looks like this:

N = (R* x fp x ne) x FL x L = 6 x FL x L

Let’s keep our optimistic estimate of life developing on every planet possible, FL = 1. I’m interested in dinosaurs, and the dinos lived on the Earth for 170 million years before an asteroid whacked the Earth, erasing them utterly from the Cosmos; so I take L = 170 million years.  Multiplying this all together, I find

N = 6 x 1 x 170,000,000 = 1,020,000,000

There could be 1 BILLION worlds with advanced, but non-intelligent, lifeforms.  If you imagine those lifeforms to be something as complex as a dinosaur, then you might say it this way: there could a BILLION WORLDS with dinosaurs on them in the Milky Way!

That makes the little kid inside of me very happy. 🙂

PS: As an even more interesting exercise, suppose we treat L not as the lifetime of a civilization, but simply the length of time for which life exists on a planet, and again ignore the issue of intelligent and technologically able lifeforms.  Taking Earth as the role model, life on Earth arose soon after the planet formed, and while there have been MANY extinction events, life has never been eradicated on Earth, making L ~ 3.5 billion years. If I replace the 170 million years we used with the dinosaurs with 3.5 billion years, we get N ~ 21 BILLION worlds with life.  Go stare at the stars tonight, and think about that for a little while.

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This is the second of two parts; the first part, about Fermi problems, can be read here.

This particular piece was completed while in residence at the Aspen Center for Physics.

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Dinosaurs in the Cosmos 1: Enrico & Frank

by Shane L. Larson

shaneRockOne of the most profound consequences of the development of life on Earth is that the Cosmos has produced complex systems with the ability to question their own existence.  We are each of us a collection of atoms that the Universe has stirred together in such a way that we can contemplate the nature of the Cosmos itself. 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.  Humans, on the other hand, have been given a remarkable gift: we can ask questions, and then we can figure out the answers.  This game of questions and answers has a name.  We call it science.

Deep sea anglerfish (Monterey Bay Aquarium, E. Widder/ORCA).

Deep sea anglerfish (Monterey Bay Aquarium, E. Widder/ORCA).

There are many questions that we could use the atomic computing engine between our ears to consider, like: how can we grow enough food to feed 10 billion people? will a catastrophic shift in the San Andreas Fault change the geography of California? can I make a jetpack safe enough for sixth-graders to fly to school? anglerfish — what are they all about? why do some tissues develop cancer in the human body and others don’t?  Where did the Universe come from?

Questions about life and our own existence often dominate conversations in philosophy classrooms, research labs, and late nights around a campfire.  What is the origin of life?  Is there life elsewhere?  Is there intelligent life (on this planet or others)? These are BIG THOUGHTS — heady questions that have been asked for as long as we have been capable of asking them.  Some of them may have answers that can be figured out, and some of them may not.  Let’s think about one of these together — is there life elsewhere?  This is a question that could be answered by simply looking.  Except that looking for life elsewhere is difficult for two reasons: (1) Everywhere else is far away (as I’ve talked about before!) (2) We’re not even sure what life elsewhere might look like! We’re still discovering new life on Earth (like under the Antarctic ice, and even in the deep forests where humans have not tread before).

These points are hindrances to be sure, but that is the nature of this game. Our atomic computing engines are very good at facing down such adversity, and finding ways to answer our questions irrespective of the difficulties we face.  For big questions, it is often useful to make an estimate of what the answer could be before you embark on your quest for knowledge. This helps define the boundaries of your quest.  One of the defining traits of modern scientists is their ability to make quick, quantitative statements about extremely complex questions using only a few pieces of data that almost everyone agrees upon.  These kinds of problems often go by the name “back of the envelope calculations” because they are supposed to be simple enough as to fit on the back of an old bill envelope (though sometimes you may need a manila envelope).  They are often called Fermi Problems, after Enrico Fermi who was famous for this skill.

Enrico Fermi.

Enrico Fermi.

Enrico Fermi was born in 1901 in Rome; he rose to prominence in physics very quickly, completing his laurea (the equivalent of a Ph.D.) at the age of 21. He worked in Italy until 1938, when the Fascist regime passed the leggi razziali (“racial laws”), which threatened his wife Laura, who was Jewish. That same year, he was awarded the Nobel Prize in physics, and after acceptance in Stockholm, took his family to New York, where they applied to become residents of the United States. He famously worked on the world’s first nuclear reactor (“Chicago Pile-1”), and the Manhattan Project.

Fermi was, without a doubt, one of the giants of modern physics. When you first start studying physics, you are regaled with tales of the great minds of physics — their accomplishments as kids, their discoveries early in their careers, and the myriad ways they have transformed the way we view the world. As a young and aspiring physicist, it is incredibly intimidating and almost crippling; fortunately, I had many outstanding mentors. Each of them played a role in calming my doubts and fears; each of them helped me look at great scientists like Fermi and learn something about how to do science from their examples.

One of those things is Fermi problems. Fermi was famous for his ability to quickly estimate the answers to complicated problems. When his answers were checked against precise calculations, his results were amazingly close to the “real” answer! One of the most famous examples was Fermi’s estimate of the strength of the atomic explosion at the Trinity test. Fermi dropped handfuls of paper from a height of 6 feet before, during, and after the blast wave washed over the observation post. Based on the distance the paper spread as it fell, Fermi estimated the explosion to be the equivalent of 10,000 tons of TNT; the strength reported after the test had been fully analyzed was 20,000 tons of TNT.

The Trinity fireball, 16 milliseconds after the first human-made atomic explosion. Fermi was the first person to estimate the energy in the explosion.

The Trinity fireball, 16 milliseconds after the first human-made atomic explosion. Fermi was the first person to estimate the energy in the explosion.

Calculating the yield of an atomic bomb is definitely a big physics problem; it’s not the kind of thing most of us have to do in our lives. But all of us do Fermi problems every day. Every one of us. Things like: you’re going to watch curling with 4 other friends; how many pizzas should you order? how many bikes can fit in your garage with everything else? what time do you need to leave home to make it to work on time?

The classic problem that Fermi used to introduce this estimation concept is “how many piano tuners are there in your city?”  With Google, or the yellow pages (if you are a caveman), this question could easily be answered definitively.  But it can also be calculated by using some things you know or can estimate from your own personal experience.  Let’s try this together — I’ll do it for Logan, Utah, and you do it for wherever you happen to be right now.

The number of piano tuners in a given city is not general knowledge that most of us carry around. Despite its seemingly esoteric nature, it is a number that can easily be estimate to high accuracy using Fermi estimation methods!

The number of piano tuners in a given city is not general knowledge that most of us carry around. Despite its seemingly esoteric nature, it is a number that can easily be estimate to high accuracy using Fermi estimation methods!

The method is to ask a series of questions upon which the answer must depend, and that you may know the answers to. Questions like: how many people live in your city? how many households are there? how many households have pianos? How often do they tune pianos?  if you are a piano tuner, how many days a year do you work? how many tunings can you do in one day?  The answers to these questions don’t need to be 100% correct, nor do all of them have to be the same as someone else would guess.  All in all, the guessing and errors average out to give about the same answer for everyone.  This is a beautiful and elegant method of trying to understand the nature of the world by relying on the fact that your knowledge sometimes does better and sometimes does worse than reality, but overall combines to give something close to the truth.  In the figure below, I show the calculation for Logan, Utah. If I check the answer in my phone book, I find that I was pretty close!

Estimating the number of piano tuners in a city. Starting at the top, there is a simple series of numbers you need to estimate, most of which you probably know or can guess.

Estimating the number of piano tuners in a city. Starting at the top, there is a simple series of numbers you need to estimate, most of which you probably know or can guess. (Click to embiggenate)

The key methods to bear in mind in your quest to become a good Fermi problem estimator are:

  • Most problems seem unanswerable when posited, but usually can be broken down into simpler bits which you do know the answer to.
  • Rely on numbers you know the value of, or can estimate a reasonable value for.
  • Don’t worry about being precise!
  • Round relentlessly (“7 is about 10”)
  • Combine numbers sloppily (“15 x 6 is about 100”)
  • Use everyday experience as averages (“a human masses about 70 kg”)

This is a powerful and robust technique for answering questions. More to the point, you do this every day when you figure out how many cupcakes to make when the cousins are visiting, or when you buy rope to make a new tire swing, or when decide how long before the football game to start mowing the lawn to make sure you are done on time.  You could do it for all kinds of other things that may be important in your life and business, like: estimating how much pizza is consumed on a nearby college campus every day, or how many ball point pens are sold in your city each year, or how many car crashes there are in town each month.

Frank Drake.

Frank Drake.

For our purposes here, we are going to use this powerful technique to figure out how much life there might be elsewhere in the Cosmos.  One of the first people to think about this was astronomer Frank Drake. Drake was a radio astronomer, and made important discoveries regarding the nature of Jupiter’s magnetosphere, and in pulsar astrophysics. In the 1960’s he also began to think about how radio astronomy could be used to search for transmissions from extraterrestrial civilizations, initiating Project Ozma in 1960 to search for possibly intelligent transmissions from the nearby Sun-like stars, Tau Ceti and Epsilon Eridani.

When thinking about life in the Cosmos, and whether we are alone or members of a vast chorus of civilizations spanning the galaxy, Drake asked a specific (but plausibly unanswerable) question: how many civilizations might exist in the galaxy that we could communicate with?  The Fermi problem solution to this question is known as The Drake Equation.  We’ll examine the Drake equation and its implications next time.

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This is the first of two parts. The second part can be read here.

This particular piece was completed while in residence at the Aspen Center for Physics.

Cosmos 12: Encyclopaedia Galactica

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.

How I remember my room as a kid in elementary and middle school. I had a lot of space stuff around, my stuffed animal (a snake named Shorty, who I still have), and my headboard bookshelf full of the family encyclopedia set.

How I remember my room as a kid in elementary and middle school. I had a lot of space stuff around, my stuffed animal (a snake named Shorty, who I still have), and my headboard bookshelf full of the family encyclopedia set.

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.

A few of the radio telescopes that make up the Very Large Array (VLA) near Socorro, New Mexico. The VLA is one of the premiere radio astronomy observatories on planet Earth. [Image by S. Larson]

A few of the radio telescopes that make up the Very Large Array (VLA) near Socorro, New Mexico. The VLA is one of the premiere radio astronomy observatories on planet Earth. [Image by S. Larson]

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).  greenPopsicleFurthermore 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!

There are all kinds of ways to imagine talking to aliens. [Calvin & Hobbes, by Bill Watterson]

There are all kinds of ways to imagine talking to aliens. [Calvin & Hobbes, by Bill Watterson]

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?

Drake's original pictorial message, to test communication without preamble. [Image from D. Vakoch, in Mercury (March, 1999)]

Drake’s original pictorial message, to test communication without preamble. [Image from D. Vakoch, in Mercury (March, 1999)]

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.

A pulsing radio signal, showing how a message consisting of 1's (signal on) and 0's (signal off) can be encoded without writing the characters "1" or "0."  [Image by S. Larson]

A pulsing radio signal, showing how a message consisting of 1’s (signal on) and 0’s (signal off) can be encoded without writing the characters “1” or “0.” [Image by S. Larson]

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.

(L) The 300 m Arecibo Radio Telescope, built into the landscape of Puerto Rico. (R) The globular cluster in Hercules, M13, located 24,000 lightyears from Earth.

(L) The 300 m Arecibo Radio Telescope, built into the landscape of Puerto Rico. (R) The globular cluster in Hercules, M13, located 24,000 lightyears from Earth.

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.

(L) The Arecibo message string arranged horizontally into 23 rows, 73 columns wide. (R) The same message, shown as shaded squares; there is not much that seems obviously organized in the message.

(L) The Arecibo message string arranged horizontally into 23 rows, 73 columns wide. (R) The same message, shown as shaded squares; there is not much that seems obviously organized in the message.

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.

(L) The Arecibo Message string, arranged in 73 rows and 23 columns. Even in text, your eye can see patterns emerging. (C) The same message shown as a shaded grid, making the patterns more clear. (R) The same image colorized for discussion. [Images by S. Larson; R image from Wikimedia Commons]

(L) The Arecibo Message string, arranged in 73 rows and 23 columns. Even in text, your eye can see patterns emerging. (C) The same message shown as a shaded grid, making the patterns more clear. (R) The same image colorized for discussion. [Images by S. Larson; R image from Wikimedia Commons]

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?

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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