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The Math of Love: Calculating the Odds of Finding Your Soulmate

The science of why there are roughly 871 special someones for you out there.

Since the dawn of recorded history, poets and philosophers have pondered the nature of love and, in recent times, so have scientists. But can the concrete lens of science really be applied to something as seemingly abstract and amorphous as amore? Joe Hanson, mastermind of the wonderful science-plus compendium It’s Okay To Be Smart, has a new online show in partnership with PBS and the latest episode explores what the search for extraterrestrial life can teach us about our odds of finding that much-romanticized human soulmate, using the Fermi paradox, the Drake equation, and a lesson in love from Carl Sagan — who, with his timelessly magnificent Golden Record love story, should know a thing or two about the wisdom of the heart.

Joe ends with a beautiful quote from Sagan’s 1985 debut novel, Contact:

For small creatures such as we the vastness is bearable only through love.


How to Save Science: Education, the Gender Gap, and the Next Generation of Creative Thinkers

“The skills of the 21st century need us to create scholars who can link the unlinkable.”

“What is crucial is not that technical ability, but it is imagination in all of its applications,” the great E. O. Wilson offered in his timeless advice to young scientists — a conviction shared by some of history’s greatest scientific minds. And yet it is rote memorization and the unimaginative application of technical skill that our dominant education system prioritizes — so it’s no wonder it is failing to produce the Edisons and Curies of our day. In Save Our Science: How to Inspire a New Generation of Scientists, materials scientist, inventor, and longtime Yale professor Ainissa Ramirez takes on a challenge Isaac Asimov presaged a quarter century ago, advocating for the value of science education and critiquing its present failures, with a hopeful and pragmatic eye toward improving its future. She writes in the introduction:

The 21st century requires a new kind of learner — not someone who can simply churn out answers by rote, as has been done in the past, but a student who can think expansively and solve problems resourcefully.

To do that, she argues, we need to replace the traditional academic skills of “reading, ’riting, and ’rithmetic” with creativity, curiosity, critical-thinking, and problem-solving. (Though, as psychology has recently revealed, problem-finding might be the more valuable skill.)

Ainissa Ramirez at TED 2012 (Photograph: James Duncan Davidson for TED)

She begins with the basics:

While the acronym STEM sounds very important, STEM answers just three questions: Why does something happen? How can we apply this knowledge in a practical way? How can we describe what is happening succinctly? Through the questions, STEM becomes a pathway to be curious, to create, and to think and figure things out.

Even for those of us who deem STEAM (wherein the A stands for “arts”) superior to STEM, Ramirez’s insights are razor-sharp and consistent with the oft-affirmed idea that creativity relies heavily upon connecting the seemingly disconnected and aligning the seemingly misaligned:

There are two schools of thought on defining creativity: divergent thinking, which is the formation of a creative idea resulting from generating lots of ideas, and a Janusian approach, which is the act of making links between two remote ideas. The latter takes its name from the two-faced Roman god of beginnings, Janus, who was associated with doorways and the idea of looking forward and backward at the same time. Janusian creativity hinges on the belief that the best ideas come from linking things that previously did not seem linkable. Henri Poincaré, a French mathematician, put it this way: ‘To create consists of making new combinations. … The most fertile will often be those formed of elements drawn from domains which are far apart.’

Another element inherent to the scientific process but hardly rewarded, if not punished, in education is the role of ignorance, or what the poet John Keats has eloquently and timelessly termed “negative capability” — the art of brushing up against the unknown and proceeding anyway. Ramirez writes:

My training as a scientist allows me to stare at an unknown and not run away, because I learned that this melding of uncertainty and curiosity is where innovation and creativity occur.

Yet these very qualities are missing from science education in the United States — and it shows. When the Programme for International Student Assessment (PISA) took their annual poll in 2006, the U.S. ranked 35th in math and 29th in science out of the 40 high-income, developed countries surveyed.

Average PISA scores versus expenditures for selected countries (Source: Organisation for Economic Co-operation and Development)

Ramirez offers a historical context: When American universities first took root in the colonial days, their primary role was to educate men for the clergy, so science, technology, and math were not a priority. But then Justin Smith Morrill, a little-known congressman from Vermont who had barely completed his high school education, came along in 1861 and quietly but purposefully sponsored legislation that forever changed American education, resulting in more than 70 new colleges and universities that included STEM subjects in their curricula. This catapulted enrollment rates from the mere 2% of the population who attended higher education prior to the Civil War and greatly increased diversity in academia, with the act’s second revision in 1890 extending education opportunities to women and African-Americans.

The growth of U.S. college enrollment from 1869 to 1994. (Source: S. B. Carter et al., Historical Statistics of the United States)

But what really propelled science education, Ramirez notes, was the competitive spirit of the Space Race:

The mixture of being outdone and humiliated motivated the U.S. to create NASA and bolster the National Science Foundation’s budget to support science research and education. Sputnik forced the U.S. to think about its science position and to look hard into a mirror — and the U.S. did not like what it saw. In 1956, before Sputnik, the National Science Foundation’s budget was a modest $15.9 million. In 1958, it tripled to $49.5 million, and it doubled again in 1959 to $132.9 million. The space race was on. We poured resources, infrastructure, and human capital into putting an American on the moon, and with that goal, STEM education became a top priority.

President John F. Kennedy addresses a crowd of 35,000 at Rice University in 1962, proclaiming again his desire to reach the moon with the words, ‘We set sail on this new sea because there is new knowledge to be gained.’ Credit: NASA / Public domain

Ramirez argues for returning to that spirit of science education as an investment in national progress:

The U.S. has a history of changing education to meet the nation’s needs. We need similar innovative forward-thinking legislation now, to prepare our children and our country for the 21st century. Looking at our history allows us to see that we have been here before and prevailed. Let’s meet this challenge, for it will, as Kennedy claimed, draw out the very best in all of us.

In confronting the problems that plague science education and the public’s relationship with scientific culture, Ramirez points to the fact that women account for only 26% of STEM bachelor’s degrees and explores the heart of the glaring gender problem:

[There is a] false presumption that girls are not as good as boys in science and math. This message absolutely pervades our national mindset. Even though girls and boys sit next to each other in class, fewer women choose STEM careers than men. This is the equivalent to a farmer sowing seeds and then harvesting only half of the fields.

The precipitous drop in girls’ enrollment in STEM classes. (Source: J. F. Latimer, What’s Happened To Our High Schools)

And yet it wasn’t always this way — a century ago, the physical sciences were as appropriate a pursuit for girls as they were for boys, with roughly equal enrollment numbers for each gender at the beginning of the 20th century. So what happened? Ramirez explains:

Several factors caused this decline: First, secondary schools began to offer courses in classics to promote their status and to help prepare girls for college entrance (classics were still needed for college admissions). Unfortunately, the introduction of classics reduced the science offerings. Second, practical learning (or vocational training like home economics) was emphasized at the end of the 19th century, which put another nail in [the] coffin of girls’ STEM access. Third, the role of science changed, particularly physics around the time World War II, when science was deemed a conduit to making weapons. These cultural mindsets pushed girls away from science. In the 1890s, 23 percent of girls were taking physics. By 1955, that number had dropped to less than 2 percent.

Today, we are slowly recovering from this decimation of girls in the sciences. Still, it is important to examine the messaging that rides alongside our efforts to rebuild. While there is discussion of different learning styles between boys and girls, it is important to recognize that they may be linked to this old legacy of prejudice that has morphed in form. Girls can do science and math just as well as boys. Period. In fact, the gender performance gap is narrowing in the U.S.; and in Great Britain, girls have outperformed boys in ‘male’ topics like math and economics. The relationship between girls and science has never been a question about their skill but more a reflection of society’s thinking about them.

In turning toward possible solutions, Ramirez calls out the faulty models of standardized testing, which fail to account for more dimensional definitions of intelligence. She writes:

There is a concept in physics that the observer of an experiment can change the results just by the act of observing (this is called, not surprisingly, the observer effect). For example, knowing the required pressure of your tires and observing that they are overinflated dictates that you let some air out, which changes the pressure slightly.

Although this theory is really for electrons and atoms, we also see it at work in schools. Schools are evaluated, by the federal and state governments, by tests. The students are evaluated by tests administered by the teachers. It is the process of testing that has changed the mission of the school from instilling a wide knowledge of the subject matter to acquiring a good score on the tests.

The United States is one of the most test-taking countries in the world, and the standard weapon is the multiple-choice question. Although multiple-choice tests are efficient in schools, they don’t inspire learning. In fact, they do just the opposite. This is hugely problematic in encouraging the skills needed for success in the 21st century. Standardized testing teaches skills that are counter to skills needed for the future, such as curiosity, problem solving, and having a healthy relationship with failure. Standardized tests draw up a fear of failure, since you seek a specific answer and you will be either right or wrong; they kick problem solving in the teeth, since you never need to show your work and never develop a habit of figuring things out; and they slam the doors to curiosity, since only a small selection of the possible answers is laid out before you. These kinds of tests produce thinkers who are unwilling to stretch and take risks and who cannot handle failure. They crush a sense of wonder.

Like Noam Chomsky, who has questioned why schools train for passing tests rather than for creative inquiry, and Sir Ken Robinson, who has eloquently advocated for changing the factory model of education, Ramirez urges:

While scientists passionately explore, reason, discover, synthesize, compare, contrast, and connect the dots, students drudgingly memorize, watch, and passively consume. Students are exercising the wrong muscle. An infusion of STEM taught in compelling ways will give students an opportunity to acquire these active learning skills.

Reminding us, as a wise woman recently did, that it’s only failure if you stop trying and that “failure” itself is integral to science and discovery, with fear of failure an enormous hindrance to both, Ramirez writes:

In STEM, failure is a fact of life. The whole process of discovery is trial and error. When you innovate, you fail your way to your answer. You make a series of choices that don’t work until you find the one that does. Discoveries are made one failure at a time. One of the basic tenets of design and engineering is that one must fail to succeed. There are whole books written on this topic. In civil engineering, every bridge we’ve traveled across was built upon failed attempts that taught us something (and cost many lives). It was all trial and error. Scientists fail all the time. We just brand it differently. We call it data.

She acknowledges our disheartening collective attitude towards math — which, as we’ve seen, is actually full of whimsy and playful fascination — and laments:

More broadly, as a society we tacitly acknowledge that its OK to be bad at math. … Our cultural attitude toward math creates an impossible job for math teachers, because their students arrive prepared to be bored and confused.

This isn’t just an anecdotal observation. Ramirez points out that math is one of the top three reasons why college students drop out of STEM majors — in fact, more than 60% of students who set out to major in STEM fail to graduate with a STEM degree, and the tendency is even more pronounced among women and minorities, who collectively constitute 70% of college enrollments but a mere 45% of STEM degrees. (And that’s today: When Ramirez herself graduated with a doctorate in engineering from Stanford, she was one of only ten African-American engineering doctorates that year in the entire country, and a handful of women.)

Ramirez goes on to propose a multitude of small changes and larger shifts that communities, educators, cities, institutions, and policy-makers could implement — from neighborhood maker-spaces to wifi hotspots on school buses to university science festivals to new curricula and testing methods — that would begin to bridge the gap between what science education currently is and what scientific culture could and should be. She concludes, echoing Alvin Toffler’s famous words that “the illiterate of the 21st century will not be those who cannot read and write, but those who cannot learn, unlearn, and relearn”:

The skills of the 21st century need us to create scholars who can link the unlinkable. … Nurturing curious, creative problem solvers who can master the art of figuring things out will make them ready for this unknown brave new world. And that is the best legacy we can possibly leave.

Save Our Science — which comes from TED Books on the heels of neuroscientist Tali Sharot’s The Science of Optimism, wire-walker Philippe Petit’s Cheating the Impossible, and the lovely illustrated six-word memoir anthology Things Don’t Have To Be Complicated — is excellent in its entirety and, at a mere $3, a must-read for anyone remotely interested in the future of scientific culture. (Which, as Richard Feynman is always there to remind us, should be everyone, since science is culture.)


Thomas Edison, Power-Napper: The Great Inventor on Sleep and Success

“Success is the product of the severest kind of mental and physical application.”

It took Thomas Edison superhuman feats of biology to fuel his astoundingly ambitious to-do list. He reportedly slept a mere three to four hours at night, “regarding sleep as a waste of time, ‘a heritage from our cave days,'” as James Maas tells us in his 1997 productivity bestseller Power Sleep (public library). In fact, Edison is often accused of having forever disrupted our internal clocks with his invention of the lightbulb — some researchers go as far as estimating that artificial light has stripped modern life of 1-2 hours of sleep per night. David K. Randall writes in Dreamland: Adventures in the Strange Science of Sleep, one of the best science books of 2012:

Thanks to Edison, sunset no longer meant the end of your social life; instead, it marked the beginning of it.


Yet all of the artificial light in use around the world before Edison developed his lightbulb amounted to the brightness of a match compared to the lights of Times Square.

The Incandescing Electric Lamp, one of Edison’s 1,093 inventions, was patented on October 30, 1883. His first functional incandescent electric lamp was successfully tested at his Menlo Park Lab on October 21, 1879, which marked the beginning of the electrical age.
Image: Henry Ford Foundation

Indeed, Edison had so much faith in the power of his invention to liberate people from the burden of sleep that he made some boldly outlandish causal inferences. In Sleep Thieves (public library), Stanley Coren quotes the inventor:

When I went through Switzerland in a motor-car, so that I could visit little towns and villages, I noted the effect of artificial light on the inhabitants. Where water power and electric light had been developed, everyone seemed normally intelligent. Where these appliances did not exist, and the natives went to bed with the chickens, staying there until daylight, they were far less intelligent.

So contemptuous was Edison’s attitude towards sleep that he wrote in 1921:

People will not only do what they like to do — they overdo it 100 per cent. Most people overeat 100 per cent, and oversleep 100 per cent, because they like it. That extra 100 per cent makes them unhealthy and inefficient. The person who sleeps eight or ten hours a night is never fully asleep and never fully awake — they have only different degrees of doze through the twenty-four hours. … For myself I never found need of more than four or five hours’ sleep in the twenty-four. I never dream. It’s real sleep. When by chance I have taken more I wake dull and indolent. We are always hearing people talk about ‘loss of sleep’ as a calamity. They better call it loss of time, vitality and opportunities. Just to satisfy my curiosity I have gone through files of the British Medical Journal and could not find a single case reported of anybody being hurt by loss of sleep. Insomnia is different entirely — but some people think they have insomnia if they can sleep only ten hours every night.

In hindsight, of course, his assertions were not only scientifically misguided but also rather hypocritical. We now know that sleep is essential to overcoming creative blocks, and it turns out, so did Edison. While he carried his lack of sleep as a kind of badge of honor, he had a duplicitous little secret: Power-napping. Not only were napping cots scattered throughout his property, from labs to libraries, but he was also frequently photographed sneaking his stealthy shut-eye in unusual locations.

Edison’s office, with napping cot
Image: Mike Roush
The cot in Edison’s library
Image: Holly Korus
Thomas Edison taking a midday nap under a tree in the Blue Ridge Mountains (1921)
Image: Bettman/Corbis via TIME
Thomas Edison sleeping at his West Orange, New Jersey laboratory (1924)
Image: Henry Ford Foundation
Thomas Edison napping at the Ford Edison Camp in Hagerstown, Maryland, with President Warren Harding (right) and automobile tire magnate Harvey Firestone reading the newspapers in the background (1921)
Image: Edison-Ford Winter Estates Museum / Brian Bennett
‘Tearing off a nap after 72 hours of continuous work’ (1912)
Image: National Museum of Education

Edison used napping to counterbalance the intensity of his work. Most days, he took one or two brief naps — on his famous cots, outdoors in the grass, and even on a chair or stool if no better option was available. Per multiple first-hand accounts, he always awoke from his naps reinvigorated rather than groggy, ready to devour the rest of the day with full alertness and zest. Frank Lewis Dyer and Thomas Martin write of the West Orange laboratory in Edison: His Life And Inventions (public library):

As one is about to pass out of the library attention is arrested by an incongruity in the form of a cot, which stands in an alcove near the door. Here Edison, throwing himself down, sometimes seeks a short rest during specially long working hours. Sleep is practically instantaneous and profound, and he awakes in immediate and full possession of his faculties, arising from the cot and going directly “back to the job” without a moment’s hesitation…

Edison’s diary, which he kept only briefly while on vacation in the summer of 1885 and which was eventually published in 1971, reveals an even more conflicted and ambivalent relationship with sleep. On Sunday, July 12, he writes playfully, but in evident circadian distress:

Image: The Thomas Edison Papers at Rutgers

Awakened at 5:15 a.m. My eyes were embarrassed by the sunbeams. Turned my back to them and tried to take another dip into oblivion. Succeeded. Awakened at 7 a.m. Thought of Mina, Daisy, and Mamma G. Put all 3 in my mental kaleidoscope to obtain a new combination a la Galton. Took Mina as a basis, tried to improve her beauty by discarding and adding certain features borrowed from Daisy and Mamma G. A sort of Raphaelized beauty, got into it too deep, mind flew away and I went to sleep again.

Awakened at 8:15 a.m. … Arose at 9 o’clock, came down stairs expecting twas too late for breakfast. Twasn’t.


Had dinner at 3 p.m. Ruins of a chicken, rice pudding.


The sun has left us on time, am going to read from the Encyclopedia Britannica to steady my nerves and go to bed early. I will shut my eyes and imagine a terraced abyss, each terrace occupied by a beautiful maiden. To the first I will deliver my mind and they will pass it down down to the uttermost depths of silence and oblivion. Went to bed worked my imagination for a supply of maidens, only saw Mina, Daisy and Mamma [G]. Scheme busted. Sleep.

Image: The Thomas Edison Papers at Rutgers

On July 14, contradicting his contention that he never dreams, Edison notes:

In evening went out on sea wall. Noticed a strange phosphorescent light in the west, probably caused by a baby moon just going down Chinaward, thought at first the Aurora Borealis had moved out west. Went to bed early dreamed of a demon with eyes four hundred feet apart.

Then, on July 19:

Slept as sound as a bug in a barrel of morphine.

Image: The Thomas Edison Papers at Rutgers

Only July 21, another poetic vignette:

Slept splendidly — evidently I was inoculated with insomnic bactilli when a baby. Arose early, went out to flirt with the flowers.

One thing that becomes apparent from Edison’s habits and cognitive dissonance about sleep is his extreme compulsion for productivity. In fact, Dyer and Martin cite an anecdote in which Edison tells his friend Milton Adams:

I have got so much to do and life is so short, I am going to hustle.

And hustle he did. Writing in 1885, Sarah Knowles Bolton marvels at Edison’s remarkable work ethic:

Five feet ten inches high, with boyish but earnest face, light gray eyes, his dark hair slightly gray falling over his forehead, his hat tipped to the back of his head, as he goes ardently to his work, which has averaged eighteen hours a day for ten years, he is indeed a pleasant man to see.

You perceive he is not the man to be daunted by obstacles. When one of his inventions failed — a printing machine — he took five men into the loft of his factory, declaring he would never come down till it worked satisfactorily. For two days, and nights and twelve hours — sixty hours in all — he worked continuously without sleep, until he had conquered the difficulty; and then he slept for thirty hours.

He often works all night, thinking best, he says, when the rest of the world sleeps.

In the same fantastic 1901 tome that gave us Amelia E. Barr’s 9 rules for success, Orison Swett Marden sets out to discover the secret to Edison’s success, camping out in the vicinity of the inventor’s New Jersey laboratory for three weeks awaiting a chance to interview him. When he finally does, he is particularly interested in the inventor’s “untiring energy and phenomenal endurance” and asks 53-year-old Edison a number of questions about his daily routine, including his relationship with sleep:

‘Do you have regular hours, Mr. Edison?’ I asked.

‘Oh,’ he said, ‘I do not work hard now. I come to the laboratory about eight o’clock every day and go home to tea at six, and then I study or work on some problem until eleven, which is my hour for bed.’

‘Fourteen or fifteen hours a day can scarcely be called loafing,’ I suggested.

‘Well,’ he replied, ‘for fifteen years I have worked on an average of twenty hours a day.’

When he was forty-seven years old, he estimated his true age at eighty-two, since working only eight hours a day would have taken till that time.

Mr. Edison has sometimes worked sixty consecutive hours upon one problem. Then after a long sleep, he was perfectly refreshed and ready for another.

Still, Edison used much of the time others invested in sleep not merely for mindless sleeplessness but for building his networked knowledge and combinatorial creativity:

‘I’ve known Edison since he was a boy of fourteen,’ said another friend; ‘and of my own knowledge I can say he never spent an idle day in his life. Often, when he should have been asleep, I have known him to sit up half the night reading. He did not take to novels or wild Western adventures, but read works on mechanics, chemistry, and electricity; and he mastered them too. But in addition to his reading, which he could only indulge in at odd hours, he carefully cultivated his wonderful powers of observation, till at length, when he was not actually asleep, it may be said he was learning all the time.’

Marden proceeds to inquire about Edison’s legendary work ethic, producing an anecdote you might recall from the timelessly fantastic How To Avoid Work and affirming the recurring theme of focused persistence as the key to success:

‘You lay down rather severe rules for one who wishes to succeed in life,’ I ventured, ‘working eighteen hours a day.’

‘Not at all,’ he said. ‘You do something all day long, don’t you? Every one does. If you get up at seven o’clock and go to bed at eleven, you have put in sixteen good hours, and it is certain with most men, that they have been doing something all the time. They have been either walking, or reading, or writing, or thinking. The only trouble is that they do it about a great many things and I do it about one. If they took the time in question and applied it in one direction, to one object, they would succeed. Success is sure to follow such application. The trouble lies in the fact that people do not have an object, one thing, to which they stick, letting all else go. Success is the product of the severest kind of mental and physical application.’

Complement with the science of internal time and how dreaming regulates depression.


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