Lena_graphics, ValeryBrozhinsky/iStockphoto; composite by L. Steenblik Hwang
This is one in a series on careers in science, technology, engineering and mathematics made possible with generous support from Arconic Foundation.
This is the second in a three-part series on the search for extraterrestrial life.
On November 16, 1974, astronomers at the Arecibo radio telescope in Puerto Rico broadcast a powerful signal into outer space. Aiming their transmitter at a star cluster on the edge of our galaxy, they sent out a series of pings — 1,679 of them, to be exact. Why that number?
They knew 1,679 was unusual. It is the result of multiplying 23 by 73. Each is a prime number, a type divisible only by one and itself. The product of this equation would be unlikely to occur in nature. So the scientists hoped that if any aliens intercepted their broadcast, the number would show them that the pings were meant to be an intended signal. It might then help them decode the hidden message that those pings had contained (including pictures of DNA, the solar system and a stick figure).
Searching for aliens may sound like science fiction. Yet for many scientists, it has become serious business. Here we meet three who are using math in their quest to find other living beings in our universe. One is calculating the likelihood of finding life on other planets. Another is trying to figure out where best to beam a “hello” to E.T. The third is looking for a common language with extraterrestrials — and it will likely be numbers.
If we could talk to the aliens
Douglas Vakoch has spent a lot of time thinking about what he’d like to say to E.T. He is president of METI International in San Francisco, Calif. (METI stands for Messaging Extraterrestrial Intelligence.) His group is focused on broadcasting signals to outer space in the hope of contacting a civilization on some other world. Vakoch wants to use bright lights, such as lasers or perhaps a powerful radio telescope like the one at Arecibo (Air-eh-SEE-boh). But the big question: How could he write a message that aliens would understand?
“We don’t expect the extraterrestrials to be speaking English or German,” Vakoch explains. “So we look to mathematics as a universal language.”
The idea is simple. You need to understand math to build things. Any world advanced enough to have the technology to pick up our signals should also know how to work with numbers.
It’s not a new idea. Back in the 1820s, when astronomers still thought there might be little green men living on the moon, they suggested using geometry — the math of shapes — to communicate with them.
One scientist suggested planting trees or using mirrors to draw an enormous triangle in Siberia, a part of Russia. Another proposed digging a giant trench in the shape of a circle and filling it with kerosene. Then someone would light it on fire at night so that it would be visible from space. For these scientists, math was a way to show the aliens not only that we were here, but also that we were intelligent.
Vakoch’s plan is a little closer to what the Arecibo scientists tried in 1974. Back then, they used a binary system: two signals at slightly different frequencies. By sending out the signals in a series of bursts that form a pattern, scientists could create a kind of code, or draw pictures. The Arecibo team used its code to send a dense message. It included pictures.
Vakoch would start with something simpler: counting.
His first message would be seven signals at the same frequency: “ping-ping-ping-ping-ping-ping-ping.” Next, he’d send seven signals again but using two frequencies, like this: “ping-pong-pong-pong-pong-pong-ping.” He’d repeat that sequence four more times, then finish with seven “pings” again. If you draw that pattern on a piece of paper, you’ll see what the aliens will see if they decode his message: a box.
Next, Vakoch would add a third frequency to the code. By dropping in the third frequency at different places in the box, he could count numbers up to 25. By using a binary system — a way of representing numbers by combining zeros and ones — he could count into the millions. (The binary system is commonly used here on Earth. It can be found encoding the data in every computer.)
Once he introduced the code, Vakoch could then use it to send information. For instance, he might try to transmit the periodic table of the elements. It would list chemicals by their atomic numbers. This would show the aliens that we understand what the universe is made of. Another message might contain the Fibonacci sequence. This is a series of numbers that increase, with each successive number being the sum of the two before it. It’s a pattern that commonly appears both in nature and human art.
Even though he’s speaking in numbers, Vakoch wants to do more than count at the aliens. For him, math is just a tool to establish more meaningful communication. In the end, he says, “I want to know something about their culture, their society, their value system and what they see as beautiful.”
Story continues below image
Stay on target
So you want to talk to an alien. Just point your transmitter at the nearest star system and press “send,” right?
Wrong, says Philip Lubin. He’s a physicist at the University of California, Santa Barbara who works on directed-energy systems. These are powerful lasers that could be used to flash signals at other stars. While radio signals spread out as they travel across space, lasers are tightly focused. That means it’s important to aim them precisely. Being off by just a few degrees to either side could cause the signal to miss its target.
Big as a star is, hitting it with a laser is not easy. For one thing, when you look at a star in the sky, you’re seeing light that has been traveling through space for years — maybe thousands of years. “What you see is where the star was,” Lubin says. But its light was traveling to Earth, the star has moved. So you have to project your message into the direction where you think that star will be when your message is due to arrive.
And don’t forget, it will take years for the light from Lubin’s lasers to travel through space in the other direction. And that star is still moving. “It’s like taking a flashlight and trying to shine it at a spacecraft flying by,” he says. “If you want to shine your flashlight at it and have it hit it, you have to know something about the trajectory of the spacecraft.”
Astronomers use math to determine proper motion — a measurement of how objects in outer space change their apparent position in our sky. To do this, the scientists calculate the object’s angle relative to Earth. Next, they figure out how fast it’s moving and in what direction.
Many astronomical objects are so distant that those angles are measured in arcseconds or even smaller milli-arcseconds. Each are tiny amounts describing angles that are less than one degree in size. By calculating proper motion, Lubin can figure out where a star system will be when his signal arrives. “You have to figure out not only where the star is now, but where it will be in the future,” he emphasizes.
Is anybody out there?
For many scientists, trying to communicate with aliens is jumping the gun. They are asking more basic questions: Are we alone in the universe? What are the odds that life exists anywhere else? These scientists use math to figure out whether Earth is likely to be a lonely outpost in space, or one of many inhabited worlds in a universe teeming with life.
More than 50 years ago, astronomer Frank Drake devised an equation to estimate the number of extraterrestrial civilizations whose signals we might pick up from Earth. To get this number, he multiplied many factors. These included the rate at which new stars form, the number of stars with planets that host life and the number of life-bearing planets where that life would be intelligent. Just one problem: Almost all of the variables in this now-famous “Drake Equation” are still unknown.
“It’s not an equation that you can make predictions with,” says Avi Loeb. “It’s an equation that summarizes what we don’t know.” Loeb is a physicist at Harvard University in Cambridge, Mass. He decided to look at the search for extraterrestrial life from a different perspective. Instead of asking how much life exists in the universe, he wanted to know when in the history of the universe life would be most likely to develop?
For this, Loeb developed an equation of his own. It looks at different types of stars, the rate at which they form and how long they live. When he crunched the numbers, Loeb came up with a surprising conclusion: In the scale of cosmic time, the glory days when the universe is full of life might still be far ahead of us.
Many scientists had assumed that life most likely would occur in star systems similar to our own. After all, we know our sun can support life. If life exists elsewhere in the universe, sun-like stars are probably where we would find it, right?
Those sun-like stars usually burn out after some 6 billion years, Loeb knew. Yet there are stars that live longer. Some very small ones can survive for around 10 trillion years! And many of these small stars have planets. Might these planets also support life?
“If the answer is yes, then we know we [on Earth] are premature,” he says. Stars like our sun burn out quickly. So when our sun and its kin are gone, “the life that will remain is life around low-mass stars,” he argues. These are those tiny stars.
Unlike the Drake Equation, Loeb’s math contains only one unknown variable: whether low-mass stars can host life. He hopes other scientists will investigate that question in the decades ahead. “Once we know that, it can be folded into my equation,” he says.
Scientists in the search for extraterrestrial intelligence, or SETI, know they are unlikely to meet a Vulcan or Klingon in their lifetime. Still, they are excited to explore our universe for signs of life. Whether they’re figuring out the odds that we’re alone, or writing messages to aliens and beaming them out to other worlds, they couldn’t carry out this search without turning to numbers.
alien A non-native organism. (in astronomy) Life on or from a distant world.
angle The space (usually measured in degrees) between two intersecting lines or surfaces at or close to the point where they meet.
arcsecond A measure of some angle relative to a circle. A circle is divided into 360 equal-size wedges (or pie slices). Each of these is described as being 1 degree in size (something a school protractor for measuring angles can help you picture). Partial degrees are measured in other units: arcminutes (each equal to 1/60th of a degree) and arcseconds (each equal to 1/3600th of a degree).
astronomy The area of science that deals with celestial objects, space and the physical universe as a whole. People who work in this field are called astronomers.
atomic Having to do with atoms, the smallest possible unit that makes up a chemical element.
atomic number The number of protons in an atomic nucleus, which determines the type of atom and how it behaves.
binary Something having two integral parts. (in mathematics and computer science) A number system where values are represented using two symbols 1 (on) or 0 (off).
broadcast To cast — or send out — something over a relatively large distance. A farmer may broadcast seeds by flinging them by hand over a large area. A loudspeaker may send sounds out over a great distance. An electronic transmitter may emit electromagnetic signals over the air to a distant radio, television or other receiving device. And a newscaster can broadcast details of events to listeners across a large area, even the world.
chemical A substance formed from two or more atoms that unite (become bonded together) in a fixed proportion and structure. For example, water is a chemical made when two hydrogen atoms bond to one oxygen atom. Its chemical formula is H2O. Chemical can also be an adjective to describe properties of materials that are the result of various reactions between different compounds.
code (in computing) To use special language to write or revise a program that makes a computer do something.
cosmic An adjective that refers to the cosmos — the universe and everything within it.
culture (in social science) The sum total of typical behaviors and social practices of a related group of people (such as a tribe or nation). Their culture includes their beliefs, values, and the symbols that they accept and/or use. Culture is passed on from generation to generation through learning. Scientists once thought culture to be exclusive to humans. Now they recognize some other animals show signs of culture as well, including dolphins and primates.
decode To convert a hidden or secret message into a language that can be understood.
degree (in geometry) A unit of measurement for angles. Each degree equals one three-hundred-and-sixtieth of the circumference of a circle.
DNA (short for deoxyribonucleic acid) A long, double-stranded and spiral-shaped molecule inside most living cells that carries genetic instructions. It is built on a backbone of phosphorus, oxygen, and carbon atoms. In all living things, from plants and animals to microbes, these instructions tell cells which molecules to make.
Drake equation A mathematical statement created in 1961 by radio astronomer Frank Drake. It posits that science can estimate the number of technological civilizations in distant star systems by considering: how many civilizations in our Milky Way galaxy would have electromagnetic emissions that could be picked up on Earth, the rate at which new stars that are suitable for hosting intelligent life form, the share of those stars with planets, the number of planets per solar system having an environment that could support life, the share of those planets on which life actually developed, the share of those planets on which the life was intelligent, the share of civilizations that then developed a technology that could signal its existence into space, and how long such civilizations would issue those detectable signals.
element (in chemistry) Each of more than one hundred substances for which the smallest unit of each is a single atom. Examples include hydrogen, oxygen, carbon, lithium and uranium.
equation In mathematics, the statement that two quantities are equal. In geometry, equations are often used to determine the shape of a curve or surface.
E.T. (n.) An abbreviation made famous by the 1982 Universal Pictures movie, E.T. the Extra-Terrestrial. The main character was a charming space alien called E.T. His most famous line from the movie was “E.T. phone home.” E.T. has since come to be used as a colloquial term for any intelligent and potentially friendly space alien.
extraterrestrial Anything of or from regions beyond Earth.
factor Something that plays a role in a particular condition or event; a contributor.
Fibonacci sequence A pattern of numbers that frequently shows up in nature. Each successive number is equal to the addition of the two numbers before it, starting with 0 and 1. So it starts out: 0, 1, 1, 2, 3, 5, 8, 13, 21 — and then goes on from there.
frequency The number of times a specified periodic phenomenon occurs within a specified time interval. (In physics) The number of wavelengths that occurs over a particular interval of time.
galaxy A massive group of stars bound together by gravity. Galaxies, which each typically include between 10 million and 100 trillion stars, also include clouds of gas, dust and the remnants of exploded stars.
geometry The mathematical study of shapes, especially points, lines, planes, curves and surfaces.
intelligence The ability to collect and apply knowledge and skills.
laser A device that generates an intense beam of coherent light of a single color. Lasers are used in drilling and cutting, alignment and guidance, in data storage and in surgery.
mass A number that shows how much an object resists speeding up and slowing down — basically a measure of how much matter that object is made from.
milli A prefix for fractional units of measurement, here referring to thousandths in the international metric system.
moon The natural satellite of any planet.
periodic table of the elements A chart (and many variants) that chemists have developed to sort elements into groups with similar characteristics. Most of the different versions of this table that have been developed over the years tend to place the elements in ascending order of their mass.
physicist A scientist who studies the nature and properties of matter and energy.
planet A celestial object that orbits a star, is big enough for gravity to have squashed it into a roundish ball and has cleared other objects out of the way in its orbital neighborhood. To accomplish the third feat, the object must be big enough to have pulled neighboring objects into the planet itself or to have slung them around the planet and off into outer space. Astronomers of the International Astronomical Union (IAU) created this three-part scientific definition of a planet in August 2006 to determine Pluto’s status. Based on that definition, IAU ruled that Pluto did not qualify. The solar system now includes eight planets: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus and Neptune.
premature Too early; before something should occur. Premature births, for instance, are when babies are born weeks or months early — potentially before they are ready for life on their own, outside their mom’s protective womb.
prime number A whole number that is divisible only by itself and 1. For example, 2 and 3 are prime numbers but 4 (which is divisible by 2) is not.
proper motion A measure of the angular velocity of some object in distant space relative to Earth. This motion has two components: its speed of change and direction of change over time.
radio To send and receive radio waves; or the device that receives these transmissions.
science fiction A field of literary or filmed stories that take place against a backdrop of fantasy, usually based on speculations about how science and engineering will direct developments in the distant future. The plots in many of these stories focus on space travel, exaggerated changes attributed to evolution or life in (or on) alien worlds.
SETI An abbreviation for search for extraterrestrial intelligence, meaning life on other worlds.
Siberia A region in northern Asia, almost all of which falls within Russia. This land takes its name from the language of the Tatar people, where Siber means sleeping land. This region is vast. It has become famous for its long, harsh winters, where temperatures can fall to −68° Celsius (−90° Fahrenheit).
society An integrated group of people or animals that generally cooperate and support one another for the greater good of them all.
solar system The eight major planets and their moons in orbit around the sun, together with smaller bodies in the form of dwarf planets, asteroids, meteoroids and comets.
star The basic building block from which galaxies are made. Stars develop when gravity compacts clouds of gas. When they become dense enough to sustain nuclear-fusion reactions, stars will emit light and sometimes other forms of electromagnetic radiation. The sun is our closest star.
sun The star at the center of Earth’s solar system. It’s an average size star about 26,000 light-years from the center of the Milky Way galaxy. Also a term for any sunlike star.
technology The application of scientific knowledge for practical purposes, especially in industry — or the devices, processes and systems that result from those efforts.
telescope Usually a light-collecting instrument that makes distant objects appear nearer through the use of lenses or a combination of curved mirrors and lenses. Some, however, collect radio emissions (energy from a different portion of the electromagnetic spectrum) through a network of antennas.
trajectory The path taken by a projectile moving through space and time, or the direction that a trend is taking over time.
transmit (n. transmission) To send or pass along.
trillion A number representing a million million — or 1,000,000,000,000 — of something.
universe The entire cosmos: All things that exist throughout space and time. It has been expanding since its formation during an event known as the Big Bang, some 13.8 billion years ago (give or take a few hundred million years).
variable (in mathematics) A letter used in a mathematical expression that may take on different values.