Atlas, the hulking humanoid robot from Boston Dynamics, now does backflips. I’ll repeat that. It’s a hulking humanoid that does backflips.

Check out the video below, because it shows a hulking humanoid doing a backflip. And that’s after it leaps from platform to platform, as if such behavior were becoming of a bipedal robot.

To be clear: Humanoids aren’t supposed to be able to do this. It's extremely difficult to make a bipedal robot that can move effectively, much less kick off a tumbling routine. The beauty of four-legged robots is that they balance easily, both at rest and as they’re moving, but bipeds like Atlas have to balance a bulky upper body on just two legs. Accordingly, you could argue that roboticists can better spend their time on non-human forms that are easier to master.

But there’s a case to be made for Atlas and the other bipeds like Cassie (which walks more like a bird than a human). We live in a world built for humans, so there may be situations where you want to deploy a robot that works like a human. If you have to explore a contaminated nuclear facility, for instance, you’ll want something that can climb stairs and ladders, and turn valves. So a humanoid may be the way to go.

If anything gets there, it’ll be Atlas. Over the years, it’s grown not only more backflippy but lighter and more dextrous and less prone to fall on its face. Even if it does tumble, it can now get back up on its own. So it’s not hard to see a future when Atlas does indeed tread where fleshy humans dare not. Especially now that Boston Dynamics is part of the Japanese megacorporation SoftBank, which may have some cash to spend.

While Atlas doing backflips is full-tilt insane, humanoids still struggle. Manipulation, for one, poses a big obstacle, because good luck replicating the human hand. And battery life is a nightmare, what with all the balancing. But who knows, maybe one day humanoids will flip into our lives, or at the very least at the Olympics.

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Nothing in robotics is as unintentionally hilarious as watching a biped fall. But roboticists are making progress- like with this machine named Cassie.

In 1891, a New York doctor named William B. Coley injected a mixture of beef broth and Streptococcus bacteria into the arm of a 40-year-old Italian man with an inoperable neck tumor. The patient got terribly sick—developing a fever, chills, and vomiting. But a month later, his cancer had shrunk drastically. Coley would go on to repeat the procedure in more than a thousand patients, with wildly varying degrees of success, before the US Food and Drug Administration shut him down.

Coley’s experiments were the first forays into a field of cancer research known today as immunotherapy. Since his first experiments, the oncology world has mostly moved on to radiation and chemo treatments. But for more than a century, immunotherapy—which encompasses a range of treatments designed to supercharge or reprogram a patient’s immune system to kill cancer cells—has persisted, mostly around the margins of medicine. In the last few years, though, an explosion of tantalizing clinical results have reinvigorated the field and plunged investors and pharma execs into a spending spree.

Though he didn’t have the molecular tools to understand why it worked, Coley’s forced infections put the body’s immune system into overdrive, allowing it to take out cancer cells along the way. While the FDA doesn’t have a formal definition for more modern immunotherapies, in the last few years it has approved at least eight drugs that fit the bill, unleashing a flood of money to finance new clinical trials. (Patients had better come with floods of money too—prices can now routinely top six figures.)

But while the drugs are dramatically improving the odds of survival for some patients, much of the basic science is still poorly understood. And a growing number of researchers worry that the sprint to the clinic offers cancer patients more hype than hope.

When immunotherapy works, it really works. But not for every kind of cancer, and not for every patient—not even, it turns out, for the majority of them. “The reality is immunotherapy is incredibly valuable for the people who can actually benefit from it, but there are far more people out there who don’t benefit at all,” says Vinay Prasad, an Oregon Health and Science University oncologist.

Prasad has come to be regarded as a professional cancer care critic, thanks to his bellicose Twitter style and John Arnold Foundation-backed crusade against medical practices he says are based on belief, not scientific evidence. Using national cancer statistics and FDA approval records, Prasad recently estimated the portion of all patients dying from all types of cancer in America this year who might actually benefit from immunotherapy. The results were disappointing: not even 10 percent.

Now, that’s probably a bit of an understatement. Prasad was only looking at the most widely used class of immunotherapy drugs in a field that is rapidly expanding. Called checkpoint inhibitors, they work by disrupting the immune system’s natural mechanism for reining in T cells, blood-borne sentinels that bind and kill diseased cells throughout the body. The immune cells are turned off most of the time, thanks to proteins that latch on to a handful of receptors on their surface. But scientists designed antibodies to bind to those same receptors, knocking out the regulatory protein and keeping the cells permanently switched to attack mode.

The first checkpoint inhibitors just turned T cells on. But some of the newer ones can work more selectively, using the same principle to jam a signal that tumors use to evade T cells. So far, checkpoint inhibitors have shown near-miraculous results for a few rare, previously incurable cancers like Hodgkin’s lymphoma, renal cell carcinoma, and non-small cell lung cancer. The drugs are only approved to treat those conditions, leaving about two-thirds of terminal cancer patients without an approved immunotherapy option.

But Prasad says that isn’t stopping physicians from prescribing the drugs anyway.

“Hype has encouraged rampant off-label use of checkpoint inhibitors as a last-ditch effort,” he says—even for patients with tumors that show no evidence they’ll respond to the drugs. The antibodies are available off the shelf, but at a list price near $150,000 per year, it’s an investment Prasad says doctors shouldn’t encourage lightly. Especially when there’s no reliable way of predicting who will respond and who won’t. “This thwarts one of the goals of cancer care," says Prasad. "When you run out of helpful responses, how do you help a patient navigate what it means to die well?”

Merck and Bristol-Myers Squibb have dominated this first wave of immunotherapy, selling almost $9 billion worth of checkpoint inhibitors since they went on sale in 2015. Roche, AstraZeneca, Novartis, Eli Lilly, Abbvie, and Regeneron have all since jumped in the game, spending billions on acquiring biotech startups and beefing up in-house pipelines. And 800 clinical trials involving a checkpoint inhibitor are currently underway in the US, compared with about 200 in 2015. “This is not sustainable,” Genentech VP of cancer immunology Ira Mellman told the audience at last year’s annual meeting of the Society for Immunotherapy of Cancer. With so many trials, he said, the industry was throwing every checkpoint inhibitor combination at the wall just to see what would stick.

After more than a decade stretching out the promise of checkpoint inhibitors, patients—and businesses—were ready for something new. And this year, they got it: CAR T cell therapy. The immunotherapy involves extracting a patient’s T cells and genetically rewiring them so they can more efficiently home in on tumors in the body—training a foot soldier as an assassin that can slip behind enemy lines.

In September, the FDA cleared the first CAR-T therapy—a treatment for children with advanced leukemia, developed by Novartis—which made history as the first-ever gene therapy approved for market. A month later the agency approved another live cell treatment, developed by Kite Pharma, for a form of adult lymphoma. In trials for the lymphoma drug, 50 percent of patients saw their cancer disappear completely, and stay gone.

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Kite’s ascendance in particular is a stunning indicator of how much money CAR-T therapy has attracted, and how fast. The company staged a $128 million IPO in 2014—when it had only a single late-phase clinical trial to its name—and sold to Gilead Science in August for $11.9 billion. For some context, consider that when Pfizer bought cancer drugmaker Medivation for $14 billion last year—one of the biggest pharma deals of 2016—the company already had an FDA-approved blockbuster tumor-fighter on the market with $2 billion in annual sales, plus two late-stage candidates in the pipeline.

While Kite and Novartis were the only companies to actually launch products in 2017, more than 40 other pharma firms and startups are currently building pipelines. Chief rival Juno Therapeutics went public with a massive $265 million initial offering—the largest biotech IPO of 2014—before forming a $1 billion partnership with Celgene in 2015. In the last few years, at least half a dozen other companies have made similar up-front deals worth hundreds of millions.

These treatments will make up just a tiny slice of the $107 billion cancer drug market. Only about 600 people a year, for example, could benefit from Novartis’ flagship CAR-T therapy. But the company set the price for a full course of treatment at a whopping $475,000. So despite the small clientele, the potential payoff is huge—and the technology is attracting a lot of investor interest. “CAR-T venture financing is still a small piece of total venture funding in oncology, but given that these therapies are curative for a majority of patients that have received them in clinical trials, the investment would appear to be justified,” says Mandy Jackson, a managing editor for research firm Informa Pharma Intelligence.

CAR-T, with its combination of gene and cell therapies, may be the most radical anticancer treatment ever to arrive in clinics. But the bleeding edge of biology can be a dangerous place for patients.

Sometimes, the modified T cells go overboard, excreting huge quantities of molecules called cytokines that lead to severe fevers, low blood pressure, and difficulty breathing. In some patients it gets even worse. Sometimes the blood-brain barrier inexplicably breaks down—and the T cells and their cytokines get inside patients’ skulls. Last year, Juno pulled the plug on its lead clinical trial after five leukemia patients died from massive brain swelling. Other patients have died in CAR-T trials at the National Cancer Institute and the University of Pennsylvania.

Scientists don’t fully understand why some CAR-T patients experience cytokine storms and neurotoxicity and others come out cured. “It’s kind of like the equivalent of getting on a Wright Brother’s airplane as opposed to walking on a 747 today,” says Wendell Lim, a biophysical chemist and director of the UC San Francisco Center for Systems and Synthetic Biology. To go from bumping along at a few hundred feet to cruise control at Mach 0.85 will mean equipping T cells with cancer-sensing receptors that are more specific than the current offerings.

Take the two FDA-approved CAR-T cell therapies, he says. They both treat blood cancers in which immune responders called B cells become malignant and spread throughout the body. Doctors reprogram patients’ T cells to seek out a B cell receptor called CD-19. When they find it, they latch on and shoot it full of toxins. Thing is, the reprogrammed T cells can’t really tell the difference between cancerous B cells and normal ones. The therapy just takes them all out. Now, you can live without B cells if you receive antibody injections to compensate—so the treatment works out fine most of the time.

But solid tumors are trickier—they’re made up of a mix of cells with different genetic profiles. Scientists have to figure out which tumor cells matter to the growth of the cancer and which ones don’t. Then they have to design T cells with antigens that can target just those ones and nothing else. An ideal signature would involve two to three antigens that your assassin T cells can use to pinpoint the target with a bullet instead of a grenade.

Last year Lim launched a startup called Cell Design Labs to try to do just that, as well as creating a molecular on-off-switch to make treatments more controlled. Only if researchers can gain this type of precise command, says Lim, will CAR-T treatments become as safe and predictable as commercial airline flight.

The field has matured considerably since Coley first shot his dying patient full of a dangerous bacteria, crossed his fingers, and hoped for the best. Sure, the guy lived, even making a miraculous full recovery. But many after him didn’t. And that “fingers crossed” approach still lingers over immunotherapy today.

All these years later, the immune system remains a fickle ally in the war on cancer. Keeping the good guys from going double-agent is going to take a lot more science. But at least the revolution will be well-financed.

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The Big Show Journal is no ordinary gun magazine. The print periodical, which appears on newsstands nationwide six times a year, is also, according to its website, "America’s most interesting gun and knife magazine" and "America’s most accurate and complete gun and knife show calendar." Gun enthusiasts may dispute the former claim—but the latter is less subjective than you might think.

In fact, The Big Show Journal might be the closest thing researchers have to a comprehensive record of gun shows in the US.

"There’s no readily compiled, publicly available database of where and when gun shows occur," says UC Berkeley epidemiologist Ellicott Matthay, who recently found herself in want of such a database. That includes the internet. When Matthay used the Wayback Machine to scour archived web pages for the dates and locations of past shows, she found gaps in the historical record; events she knew had happened were nowhere to be found. So she turned to trade magazines instead. The Big Show Journal, true to its claim, proved more comprehensive than competing publications like Gun List Magazine and Gun and Knife Show Calendar.

Matthay needed that data to test a hypothesis about gun violence in America. Gun shows—of which the US sees about 4,000 per year—account for between 4 and 9 percent of firearm sales. As a public health researcher, Matthay knew that gun ownership increases the risk of suicide, homicide, and unintentional casualties in the home, and that firearms acquired from gun shows are disproportionately implicated in crimes. Matthay wanted to know if gun shows could lead to increased rates of gun violence, specifically in her home state of California. And the numbers she needed to find out were buried not in a government database, but in back issues of a big, glossy gun magazine.

But magazines are hard to mine for data. So Matthay set to work, scanning issues of The Big Show Journal published between 2005 and 2013 in the copy room at UC Berkeley's school of public health. She used optical character recognition software to convert the scans into alphanumeric data. Then she trained an algorithm to isolate the dates and locations of gun shows in California and neighboring Nevada, which shares the largest border with the state.

When Matthay was finished, she cross referenced her database with death records from the California Department of Public Health, along with ER and inpatient hospitalization records collected by the state. By comparing death and injury rates for the two weeks before and after each gun show, Matthay could see whether firearm casualties increased in nearby California areas in the wakes of California and Nevada gun shows.

Her hypothesis turned out to be half right: California gun shows did not appear to have a significant effect on local gun violence. But in regions near Nevada shows, rates of death and injury due to firearms spiked by 70 percent.

That staggering disparity could boil down to policy differences. California's gun laws are among the most stringent in the country. Nevada, in contrast, has some of the least restrictive—and no explicit regulations on gun shows. Data from the Bureau of Alcohol, Tobacco, Firearms and Explosives—which monitors where guns originate and where law enforcement recovers them—shows that firearms have a knack for flooding into states with tough gun laws from those without. (To cite just one example: Sixty percent of guns used to commit crimes in Chicago between 2009 and 2013 originated outside of Illinois.) A state's gun laws, it seems, can be undermined by those of its neighbors.

But that kind of inter-state analysis isn’t always possible. Many states—Nevada among them—don't require documentation of private gun sales.

"If a gun originated in Pennsylvania, changed hands between private parties at a Nevada gun show, and resulted in a firearm death or injury in California, even if we were to trace it, we'd have no way of knowing it was ever in Nevada," Matthay says. What's more, ATF only tracks the provenance of guns recovered from crime scenes. But not all crimes involving guns result in injury or death. Conversely, not all firearm casualties—particularly unintended injuries—are logged as crimes.

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So researchers like Matthay have to use trickier methods to understand the impact of firearms. "The biggest challenge, when it comes to understanding gun violence, is money—but the second biggest is data," says Frederick Rivara, an epidemiologist at the University of Washington and an expert on gun violence. The NRA's efforts to stymie gun research are extensive, palpable, and well documented: When a car kills somebody in the US, the details of the incident go into a massive government database. No such database exists for gun deaths. If you want to study firearms in this country—how they move, the way they're used, how often they murder and maim—you have to get creative. See: scanning old gun magazines by hand.

But with limited data comes limited information. Matthay's study didn't trace any guns, so it's unclear whether California's post-show spike in gun violence is tied to an inundation of Nevada firearms. (It could be due to an influx of ammunition, for example.) Neither did the study examine associations with firearm casualties in Nevada. (“We could do that,” Matthay says, for Nevada and neighbor states like Oregon and Arizona, “but we would need additional funding.”) Likewise, there's no telling if the link between gun shows and gun violence is causal. A randomized controlled trial—the gold standard of evidence in medical and epidemiological circles—could help isolate the signal. But researchers can't exactly go around exposing random populations to gun shows. "That would not be ethical," Matthay says, not to mention unfeasible.

Still, the study does paint a more nuanced picture of the relationship between gun shows and gun violence. By accounting for deaths and injuries ATF's data overlooks, Matthay's research points not only to the effectiveness of California's gun laws, but the pitfalls of porous borders—two valuable insights that policy makers can use to inform laws at the state and federal levels.

"That's our job as investigators—to see if those laws help or not and determine whether they should be more widespread, to reduce the total gun violence," Rivara says.

With the help of Congress, researchers like Matthay could do that job much more effectively. Until then, they'll make do with the data they have.

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When Rebecca Goldin spoke to a recent class of incoming freshmen at George Mason University, she relayed a disheartening statistic: According to a recent study, 36 percent of college students don’t significantly improve in critical thinking during their four-year tenure. “These students had trouble distinguishing fact from opinion, and cause from correlation,” Goldin explained.

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She went on to offer some advice: “Take more math and science than is required. And take it seriously.” Why? Because “I can think of no better tool than quantitative thinking to process the information that is thrown at me.” Take, for example, the study she had cited. A first glance, it might seem to suggest that a third of college graduates are lazy or ignorant, or that higher education is a waste. But if you look closer, Goldin told her bright-eyed audience, you’ll find a different message: “Turns out, this third of students isn’t taking any science.”

Goldin, a professor of mathematical sciences at George Mason, has made it her life’s work to improve quantitative literacy. In addition to her research and teaching duties, she volunteers as a coach at math clubs for elementary- and middle-school students. In 2004, she became the research director of George Mason’s Statistical Assessment Service, which aimed “to correct scientific misunderstanding in the media resulting from bad science, politics or a simple lack of information or knowledge.” The project has since morphed into STATS (run by the nonprofit Sense About Science USA and the American Statistical Association), with Goldin as its director. Its mission has evolved too: It is now less of a media watchdog and focuses more on education. Goldin and her team run statistics workshops for journalists and have advised reporters at publications including FiveThirtyEight, ProPublica and The Wall Street Journal.

When Quanta first reached out to Goldin, she worried that her dual “hats”—those of a mathematician and a public servant—were too “radically different” to reconcile in one interview. In conversation, however, it quickly became apparent that the bridge between these two selves is Goldin’s conviction that mathematical reasoning and study is not only widely useful, but also pleasurable. Her enthusiasm for logic—whether she’s discussing the manipulation of manifolds in high-dimensional spaces or the meaning of statistical significance—is infectious. “I love, love, love what I do,” she said. It’s easy to believe her—and to want some of that delight for oneself.

Quanta Magazine spoke with Goldin about finding beauty in abstract thought, how STATS is arming journalists with statistical savvy, and why mathematical literacy is empowering. An edited and condensed version of the conversation follows.

Where does your passion for mathematics and quantitative thought come from?

As a young person I never thought I liked math. I absolutely loved number sequences and other curious things that, in retrospect, were very mathematical. At the dinner table, my dad, who is a physicist, would pull out some weird puzzle or riddle that sometimes only took a minute to solve, and other times I’d be like, “Huh, I have no idea how that one works!” But there was an overall framework of joy around solving it.

When did you recognize you could apply that excitement about puzzles to pursuing math professionally?

Actually very late in the game. I was always very strong in math, and I did a lot of math in high school. This gave me the false sense that I knew what math was about: I felt like every next step was a little bit more of the same, just more advanced. It was very clear in my mind that I didn’t want to be a mathematician.

But when I went to college at Harvard, I took a course in topology, which is the study of spaces. It wasn’t like anything I’d seen before. It wasn’t calculus; it wasn’t complex calculations. The questions were really complicated and different and interesting in a way I had never expected. And it was just kind of like I fell in love.

You study primarily symplectic and algebraic geometry. How do you describe what you do to people who aren’t mathematicians?

One way I might describe it is to say that I study symmetries of mathematical objects. This comes about when you’re interested in things like our universe, where the Earth is rotating, and it’s also rotating around the sun, and the sun is in a larger system that is rotating. All those rotations are symmetries. There are a lot of other ways symmetries come up, and they can get really, really complicated. So we use neat mathematical objects to think about them, called groups. This is useful because if you’re trying to solve equations, and you know you have symmetries, you can essentially find a way mathematically to get rid of those symmetries and make your equations simpler.

What motivates you to study these complex symmetries?

I just think they’re really beautiful. A lot of mathematics ultimately is artistic rather than useful. Sometimes you see a picture that’s got a lot of symmetry in it, like an M.C. Escher sketch, and it’s like, “Wow, that’s just so amazing!” But when you study mathematics, you start to “see” things in higher dimensions. You’re not necessarily visualizing them in the same way that you could with a sculpture or piece of art. But you start to feel like this whole system of objects that you’re looking at, and the symmetries it has, are really just beautiful. There’s no other good word.

How did you get involved with STATS?

When I arrived as a professor at George Mason, I knew I wanted to do more than research and mathematics. I love teaching, but I felt like I wanted to do something for the world that was not part of the ivory tower of just solving problems that I thought were really curious and interesting.

When I first joined what became STATS, it was a little bit more “gotcha” work: looking at how the media talks about science and mathematics and pointing out when someone has gotten it wrong. As we’ve evolved, I’ve become more and more interested in how journalists think about quantitative issues and how they process them. We found pretty early in our work that there was this huge gap of knowledge and education: Journalists were writing about things that had quantitative content, but they often didn’t absorb what they were writing about, and didn’t understand it, and didn’t have any way to do better because they were often on really tight timelines with limited resources.

So how has your work at STATS changed?

Our mission at STATS has changed to focus on offering journalists two things. One is to be available to answer quantitative questions. They could be as simple as “I don’t know how to calculate this percentage,” or they could be pretty sophisticated things, like “I’ve got this data, and I want to apply this model to it, and I just want to make sure that I’m handling the outliers correctly.” The other really cool thing that we do is, we go to individual news agencies and offer workshops on things like confidence intervals, statistical significance, p values, and all this highly technical language.

Someone once described to me the advice he gives to journalists. He says, “You should always have a statistician in your back pocket.” That’s what we hope to be.

What are the most common pitfalls of reporting on statistics?

A favorite one is distinguishing between causation and correlation. People say, “Oh, that’s obvious. Of course there’s a difference between those two things.” But when you get into examples that target our belief system, it’s really hard to disassociate them. Part of the problem, I think, is that scientists themselves always want to know more than they can with the tools they have. And they don’t always make clear that the questions they’re answering aren’t necessarily the ones you might think they’re answering.

What do you mean?

Like, you might be interested in knowing whether taking hormones is helpful or harmful to women who are postmenopausal. So you start out with a question that’s really well-defined: Does it help or hurt? But you can’t necessarily answer that question. What you can answer is the question of whether women who take hormones whom you enroll in your study — those specific women — have an increase or decrease in, say, heart disease rates or breast cancer rates or stroke rates compared to a control group or to the general population. But that may not answer your initial question, which is: “Is that going to be the case for me? Or people like me? Or the population as a whole?”

What do you hope STATS will achieve?

Partly our goal is to help change the culture of journalism so that people recognize the importance of using quantitative arguments and thinking about quantitative issues before they come to conclusions. That way, they’re coming to conclusions that are supported by science rather than using a study to further their own agenda — which is something scientists do too; they may push a certain interpretation of something. We want to arm journalists with a certain amount of rigor in their thinking so they can challenge a scientist who might say, “Well, you just don’t understand my sophisticated statistic.” There’s a lot of value in giving reporters the tools to develop their sense of quantitative skepticism so that they’re not just bullied.

You argue that statistical literacy gives citizens a kind of power. What do you mean?

What I mean is that if we don’t have the ability to process quantitative information, we can often make decisions that are more based on our beliefs and our fears than based on reality. On an individual level, if we have the ability to think quantitatively, we can make better decisions about our own health, about our own choices with regard to risk, about our own lifestyles. It’s very empowering to not be scared or bullied into doing things one way or another.

On a collective level, the impact of being educated in general is huge. Think about what democracy would be if most of us couldn’t read. We aspire to a literate society because it allows for public engagement, and I think this is also true for quantitative literacy. The more we can get people to understand how to view the world in a quantitative way, the more successful we can be at getting past biases and beliefs and prejudices.

You’ve also said that getting people to understand statistics requires more than reciting numbers. Why do you think storytelling is important for conveying statistical concepts?

As human beings, we live in stories. It doesn’t matter how quantitative you are, we’re all influenced by stories. They become like statistics in our mind. So if you report the statistics without the story, you don’t get nearly the level of interest or emotion or willingness to engage with the ideas.

How has the media’s use of data changed in the 13 years you’ve been with STATS?

With the internet, we see a tremendous growth in data produced by search engines. Journalists are becoming much more adept at collecting these kinds of data and using them in media articles. I think that the current president is also causing a lot of reflection on what we mean by facts, and in that sense journalists maybe think of it as more important in general to get the facts right.

That’s interesting. So you think the public’s awareness of “fake” news and “alternative” facts is motivating journalists to be more rigorous about fact checking?

I do think it’s very motivating. Of course sometimes information gets spun. But ultimately a very small percentage of journalists do that. I think 95 percent of both journalists and scientists are really working hard to get it right.

I’m surprised you’re not more jaded about the media.

Ha! This is maybe more a life view. I think there are people who are pessimistic about humankind and people who are optimistic.

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You also volunteer with math clubs for kids. What ideas about math and math culture do you try to get across?

I try to bring in problems that are really different and fun and curious and weird. For example, I’ve done an activity with kids where I’ve brought in a bunch of ribbons, and I had them learn a little bit about a field called knot theory. There are two things I’m trying to get across to them. One is that math in school is not the whole story—there’s this whole other world that is logical but also beautiful and creative. The second message is a certain emotional framework that I have to offer: that math is a joyous experience.

Original story reprinted with permission from Quanta Magazine, an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences.

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Suppose aliens land on our planet and want to learn our current scientific knowledge. I would start with the 40-year-old documentary Powers of Ten. Granted, it’s a bit out of date, but this short film, written and directed by the famous designer couple Charles and Ray Eames, captures in less than 10 minutes a comprehensive view of the cosmos.

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The script is simple and elegant. When the film begins, we see a couple picnicking in a Chicago park. Then the camera zooms out. Every 10 seconds the field of vision gains a power of 10—from 10 meters across, to 100, to 1,000 and onward. Slowly the big picture reveals itself to us. We see the city, the continent, Earth, the solar system, neighboring stars, the Milky Way, all the way to the largest structures of the universe. Then in the second half of the film, the camera zooms in and delves into the smallest structures, uncovering more and more microscopic details. We travel into a human hand and discover cells, the double helix of the DNA molecule, atoms, nuclei and finally the elementary quarks vibrating inside a proton.

The movie captures the astonishing beauty of the macrocosm and microcosm, and it provides the perfect cliffhanger endings for conveying the challenges of fundamental science. As our then-8-year-old son asked when he first saw it, “How does it continue?” Exactly! Comprehending the next sequence is the aim of scientists who are pushing the frontiers of our understanding of the largest and smallest structures of the universe. Finally, I could explain what Daddy does at work!

Powers of Ten also teaches us that, while we traverse the various scales of length, time and energy, we also travel through different realms of knowledge. Psychology studies human behavior, evolutionary biology examines ecosystems, astrophysics investigates planets and stars, and cosmology concentrates on the universe as a whole. Similarly, moving inward, we navigate the subjects of biology, biochemistry, and atomic, nuclear and particle physics. It is as if the scientific disciplines are formed in strata, like the geological layers on display in the Grand Canyon.

Moving from one layer to another, we see examples of emergence and reductionism, these two overarching organizing principles of modern science. Zooming out, we see new patterns “emerge” from the complex behavior of individual building blocks. Biochemical reactions give rise to sentient beings. Individual organisms gather into ecosystems. Hundreds of billions of stars come together to make majestic swirls of galaxies.

As we reverse and take a microscopic view, we see reductionism at work. Complicated patterns dissolve into underlying simple bits. Life reduces to the reactions among DNA, RNA, proteins and other organic molecules. The complexity of chemistry flattens into the elegant beauty of the quantum mechanical atom. And, finally, the Standard Model of particle physics captures all known components of matter and radiation in just four forces and 17 elementary particles.

Which of these two scientific principles, reductionism or emergence, is more powerful? Traditional particle physicists would argue for reductionism; condensed-matter physicists, who study complex materials, for emergence. As articulated by the Nobel laureate (and particle physicist) David Gross: Where in nature do you find beauty, and where do you find garbage?

Take a look at the complexity of reality around us. Traditionally, particle physicists explain nature using a handful of particles and their interactions. But condensed matter physicists ask: What about an everyday glass of water? Describing its surface ripples in terms of the motions of the roughly 10²⁴ individual water molecules—let alone their elementary particles—would be foolish. Instead of the impenetrable complexities at small scales (the “garbage”) faced by traditional particle physicists, condensed matter physicists use the emergent laws, the “beauty” of hydrodynamics and thermodynamics. In fact, when we take the number of molecules to infinity (the equivalent of maximal garbage from a reductionist point of view), these laws of nature become crisp mathematical statements.

While many scientists praise the phenomenally successful reductionist approach of the past centuries, John Wheeler, the influential Princeton University physicist whose work touched on topics from nuclear physics to black holes, expressed an interesting alternative. “Every law of physics, pushed to the extreme, will be found to be statistical and approximate, not mathematically perfect and precise,” he said. Wheeler pointed out an important feature of emergent laws: Their approximate nature allows for a certain flexibility that can accommodate future evolution.

In many ways, thermodynamics is the gold standard of an emergent law, describing the collective behavior of a large number of particles, irrespective of many microscopic details. It captures an astonishingly wide class of phenomena in succinct mathematical formulas. The laws hold in great universality—indeed, they were discovered before the atomic basis of matter was even established. And there are no loopholes. For example, the second law of thermodynamics states that a system’s entropy—a measure of the amount of hidden microscopic information—will always grow in time.

Modern physics provides a precise language to capture the way things scale: the so-called renormalization group. This mathematical formalism allows us to go systematically from the small to the large. The essential step is taking averages. For example, instead of looking at the behavior of individual atoms that make up matter, we can take little cubes, say 10 atoms wide on each side, and take these cubes as our new building blocks. One can then repeat this averaging procedure. It is as if for each physical system one makes an individual Powers of Ten movie.

Renormalization theory describes in detail how the properties of a physical system change if one increases the length scale on which the observations are made. A famous example is the electric charge of particles that can increase or decrease depending on quantum interactions. A sociological example is understanding the behavior of groups of various sizes starting from individual behavior. Is there wisdom in crowds, or do the masses behave less responsibly?

Most interesting are the two endpoints of the renormalization process: the infinite large and infinite small. Here things will typically simplify because either all details are washed away, or the environment disappears. We see something like this with the two cliffhanger endings in Powers of Ten. Both the largest and the smallest structures of the universe are astonishingly simple. It is here that we find the two “standard models,” of particle physics and cosmology.

Remarkably, modern insights about the most formidable challenge in theoretical physics—the push to develop a quantum theory of gravity—employ both the reductionist and emergent perspectives. Traditional approaches to quantum gravity, such as perturbative string theory, try to find a fully consistent microscopic description of all particles and forces. Such a “final theory” necessarily includes a theory of gravitons, the elementary particles of the gravitational field. For example, in string theory, the graviton is formed from a string that vibrates in a particular way. One of the early successes of string theory was a scheme to compute the behavior of such gravitons.

However, this is only a partial answer. Einstein taught us that gravity has a much wider scope: It addresses the structure of space and time. In a quantum-mechanical description, space and time would lose their meaning at ultrashort distances and time scales, raising the question of what replaces those fundamental concepts.

A complementary approach to combining gravity and quantum theory started with the groundbreaking ideas of Jacob Bekenstein and Stephen Hawking on the information content of black holes in the 1970s, and came into being with the seminal work of Juan Maldacena in the late 1990s. In this formulation, quantum space-time, including all the particles and forces in it, emerges from a completely different “holographic” description. The holographic system is quantum mechanical, but doesn’t have any explicit form of gravity in it. Furthermore, it typically has fewer spatial dimensions. The system is, however, governed by a number that measures how large the system is. If one increases that number, the approximation to a classical gravitational system becomes more precise. In the end, space and time, together with Einstein’s equations of general relativity, emerge out of the holographic system. The process is akin to the way that the laws of thermodynamics emerge out of the motions of individual molecules.

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In some sense, this exercise is exactly the opposite of what Einstein tried to achieve. His aim was to build all of the laws of nature out of the dynamics of space and time, reducing physics to pure geometry. For him, space-time was the natural “ground level” in the infinite hierarchy of scientific objects—the bottom of the Grand Canyon. The present point of view thinks of space-time not as a starting point, but as an end point, as a natural structure that emerges out of the complexity of quantum information, much like the thermodynamics that rules our glass of water. Perhaps, in retrospect, it was not an accident that the two physical laws that Einstein liked best, thermodynamics and general relativity, have a common origin as emergent phenomena.

In some ways, this surprising marriage of emergence and reductionism allows one to enjoy the best of both worlds. For physicists, beauty is found at both ends of the spectrum.