Knocking on Heaven's Door: How Physics and Scientific Thinking Illuminate the Universe and the Modern World - Lisa Randall (2011)



This book has presented glimpses of how the human mind can explore to the outer limits of the cosmos as well as into the internal structure of matter. In both pursuits, the late Harvard professor Sidney Coleman was considered one of the wisest physicists around. The story students told was that when Sidney applied for a postdoctoral fellowship after finishing graduate school, all except one of his letters of recommendation described him as the smartest physicist they had known—apart from Richard Feynman. The remaining letter was from Richard Feynman, who wrote that Sidney was the best physicist around—though he wasn’t counting himself.

At Sidney’s sixtieth birthday Festschrift celebration—a conference organized in his honor—many of the most notable physicists of his generation spoke. Howard Georgi, Sidney’s Harvard colleague for many years and a fine particle physicist himself, observed that what struck him in watching the succession of talks by these very successful theoretical physicists was how differently they all think.

He was right. Each speaker had a particular way of approaching science and had made significant contributions through his (indeed they were all male) distinctive skills. Some were visual, some were mathematically gifted, and some simply had a prodigious capacity to absorb and evaluate information. Both top-down and bottom-up styles were represented among those present, whose accomplishments ranged from understanding the strong nuclear force in the interior of matter to the mathematics that could be derived using string theory as a tool.

Pushkin was right when he wrote, “Inspiration is needed in geometry, just as much as in poetry.” Creativity is essential to particle physics, cosmology, and to mathematics, and to other fields of science, just as it is to its more widely acknowledged beneficiaries—the arts and humanities. Science epitomizes the extra richness that can enhance creative endeavors that take place in constrained settings. The inspiration and imagination involved are easily overlooked amid the logical rules. However, math and technology were themselves discovered and formulated by people who were thinking creatively about how to synthesize ideas—and by those who accidentally came upon an interesting result and had the creative alertness to recognize its value.

In the past few years, I’ve been fortunate to have had a variety of opportunities to meet and work with creative people in different walks of life, and it’s interesting to reflect on what they share. Scientists, writers, artists, and musicians might seem very different on the surface, but the nature of skills, talents, and temperaments is not always as distinctive as you might expect. I’ll now round up our story of science and scientific thinking with some of the qualities I’ve found most striking.


Neither scientists nor artists are likely to be thinking about creativity per se when they do something significant. Few (if any) successful people sit down at their desks and decide, “I will be creative today.” Instead, they are focused on a problem. And when I say focused, I mean single-mindedly, can’t-help-but-think-about-it, intently-concentrated-on-their-work focused.

We usually see the end product of creative endeavors without witnessing the enormous dedication and technical expertise that underlie them. When I saw the 2008 film Man on Wire, which celebrated Philippe Petit’s 1974 high-wire walk a quarter of a mile up in the air between the twin towers of the World Trade Center—a feat that at the time captured the attention of most New Yorkers like myself, but also many others around the world—I appreciated his sense of adventure and play and skill. But Philippe doesn’t just bolt a tightrope into two walls and wiggle it around. The choreographer Elizabeth Streb showed me the inch-thick book with the many drawings and calculations he did before he installed a wire in her studio. Only then did I understand the preparation and focus that guaranteed the stability of his enterprise. Philippe was a “self-taught engineer,” as he playfully described himself. Only after careful study and application of known laws of physics to understanding his materials’ mechanical properties was he prepared to walk his tightrope. Of course until he actually did it, Philippe couldn’t be absolutely sure he had taken everything into account—merely everything he could anticipate, which, not surprisingly, was enough.

If you find this level of absorption hard to believe, look around. People are frequently transfixed by their activities—whether of small or great significance. Your neighbor does crossword puzzles, your friends sit mesmerized watching sports on TV, someone on the subway is so absorbed in a book she misses her stop—not to mention the countless hours you might spend playing video games.

Those who are preoccupied by research are in the fortunate situation where what they do for a living coincides with what they love—or at the very least can’t bear to neglect. Professionals in this category generally have the comforting idea (albeit possibly illusory) that what they do might have lasting significance. Scientists like to think we are part of a bigger mission to determine truths about the world. We might not have time for a crossword puzzle on a particular day but we will very likely want more time to spend on a research project—especially one connected to a bigger picture and larger goal. The actual act might involve the same sort of absorption as engaging in a game or even watching sports on TV.70 But a scientist is likely to continue thinking about research when driving a car or falling asleep at night. The ability to stay committed to the project for days or months or years is certainly connected to the belief that the search is important—even if only a few might understand it (at least at first)—and even if the trajectory might ultimately prove to be wrong.

Lately it has become fashionable to question innate creativity and talent and attribute success solely to early exposure and practice. In a New York Times column, David Brooks summarized a couple of recent books on the subject this way: “What Mozart had, we now believe, was the same thing Tiger Woods had—the ability to focus for long periods of time and a father intent on improving his skills.”71 Picasso was another example he used. Picasso was the son of a classical artist and in his privileged environment was already making brilliant paintings as a child. Bill Gates too had exceptional opportunities. In his recent book, Outliers,72 Malcolm Gladwell tells how Bill Gates’s Seattle high school was one of the few to have a computer club, and how Gates subsequently had the opportunity to use the computers at the University of Washington for hours on end. Gladwell goes on to suggest that Gates’s opportunities were more important to his success than his drive and talent.

Indeed, focusing and practice at an early stage so that the methods and techniques become hard wired is unquestionably part of many creative backgrounds. If you have a difficult problem to solve, you want to spend as little time as possible on the basics. Once skills (or math or knowledge) become second nature, you can call them up much more easily when you need them. Such embedded skills often continue operating in the background—even before they push good ideas into your conscious mind. More than one person has solved a problem while asleep. Larry Page told me that the seed idea for Google came to him in a dream—but that was only after he had been absorbed by the problem for months. People often attribute insights to “intuition” without recognizing how much lead time of detailed studies lies behind the moment of revelation.

So Brooks and Gladwell undoubtedly are correct in some respects. Though skill and talent matter, they won’t get you very far without the honing of skills and intensity that comes with dedication and practice. But opportunities at a young age and systematic preparation are not the whole story. This description neglects the fact that the ability to focus and practice so intently is a skill in itself. The exceptional people who learn from what they did before and who can hold the accumulated lessons in their heads are far more likely to benefit from study and repetition. This tenacity allows for concentration and focus that will eventually pay off—in scientific research or any other creative pursuit.

The name of Calvin Klein’s original perfume, “Obsession,” was no accident: he became successful because (in his own words) he was obsessed. Even if golf pros perfect their swing over countless repeated attempts, I don’t believe everyone can hit a ball a thousand times without becoming exceedingly bored or frustrated. My climbing friend, Kai Zinn, who works on difficult routes—hard 5.13s for those in the know—remembers the details and moves much better than I do. When he does a route ten times, he therefore benefits far more. This in turn makes him much more likely to persevere. I’ll get bored and move on and remain a midlevel climber while Kai, who knows how to learn efficiently from repetition, will continually improve. Georges-Louis Leclerc, the eighteenth-century naturalist, mathematician, and author, succinctly summarized this ability: “Genius is only a greater aptitude for patience.” Though I’ll add that it’s also rooted in impatience with lack of improvement.


Practice, technical training, and drive are essential to scientific research. But they are not all that is required. Autistics—not to mention some academics and far too many bureaucrats—frequently demonstrate high-level technical skills yet lack creativity and imagination. All it takes is a trip to the movies these days to witness the limitations of drive and technical achievements without the support of these other qualities. Scenes in which animated creatures fight other animated creatures in hard-to-follow sequences might be impressive accomplishments in themselves, but they rarely possess the creative energy needed to fully engage many of us—even with the light and noise, I frequently fall asleep.

For me, the most absorbing films are those that address big questions and real ideas but embody them in small examples that we can appreciate and comprehend. The movie Casablanca might be about patriotism and love and war and loyalty but even though Rick warns Ilsa that “it doesn’t take much to see that the problems of three little people don’t amount to a hill of beans in this crazy world,” those three people are the reason I’m captivated by the movie (plus, of course, Peter Lorre and Claude Rains).

In science, too, the right questions often come from having both the big and the small pictures in mind. There are grand questions that we all want to answer, and there are small problems that we believe to be tractable. Identifying the big questions is rarely sufficient, since it’s often the solutions to the smaller ones that lead to progress. A grain of sand can indeed reveal an entire world, as the title of the Salt Lake City conference on scale (referred to in Chapter 3)—and the line of poetry by William Blake it refers to—remind us, and as Galileo understood so early on.

An almost indispensable skill for any creative person is the ability to pose the right questions. Creative people identify promising, exciting, and, most important, accessible routes to progress—and eventually formulate the questions correctly. The best science frequently combines an awareness of broad and significant problems with focus on an apparently small issue or detail that someone very much wants to solve or understand. Sometimes these little problems or inconsistencies turn out to be the clues to big advances.

Darwin’s revolutionary ideas grew in part out of minute observations of birds and plants. The precession of the perihelion of Mercury wasn’t a mistaken measurement—it was an indication that Newton’s laws of physics were limited. This measurement turned out to be one of the confirmations of Einstein’s gravity theory. The cracks and discrepancies that might seem too small or obscure for some can be the portal to new concepts and ideas for those who look at the problem the right way.

Einstein didn’t even initially set out to understand gravity. He was trying to understand the implications of the theory of electromagnetism that had only recently been developed. He focused on aspects that were peculiar or even inconsistent with what everyone thought were the symmetries of space and time and ended up revolutionizing the way we think. Einstein believed it should all make sense, and he had the breadth of vision and persistence to extract how that was possible.

More recent research illustrates this interplay too. Understanding why certain interactions shouldn’t occur in supersymmetric theories might seem like a detail to some. My colleague David B. Kaplan was mocked when he talked about such problems in Europe in the 1980s. But this problem turned out to be a rich source of new insights into supersymmetry and supersymmetry breaking, leading to new ideas that experimenters at the LHC are now prepared to test.

I’m a firm believer that the universe is consistent and any deviation implies something interesting yet to be discovered. After I made this point at a Creativity Foundation presentation in Washington, D.C., a blogger nicely interpreted this as my having high standards. But really, belief in the consistency of the universe is probably the principal driving force for many scientists when figuring out which questions to study.

Many of the creative people I know also have the ability to hold a number of questions and ideas in their heads at the same time. Anyone can look things up using Google, but unless you can put facts and ideas together in interesting ways, you aren’t likely to find anything new. It is precisely the slightly jarring juxtaposition of ideas coming from different directions that often leads to new connections or insights or poetry (which was what the term creativity originally applied to).

A lot of people prefer to work linearly. But this means that once they are stuck or find that the path is uncertain, their pursuit is over. Like many writers and artists, scientists make progress in patches. It’s not always a linear process. We might understand some pieces of a puzzle, but temporarily set aside others we don’t yet understand, hoping to fill in these gaps later on. Only a few understand everything about a theory from a single continuous reading. We have to believe that we will eventually piece it all together so that we can afford to skip over something and then return, armed with more knowledge or a broader context. Papers or results might initially appear to be incomprehensible, but we’ll keep reading anyway. When we find something we don’t understand, we’ll skip over it, get to the end, puzzle it out our own way, and then later on return to where we were mystified. We have to be absorbed enough to continue—working through what does and does not make sense.

Thomas Edison famously noted that, “Genius is one percent inspiration, ninety-nine percent perspiration.” And—as Louis Pasteur once said—“In the fields of observation, chance favors the prepared mind.” Dedicated scientists sometimes thereby find the answers they are looking for. But they might also find solutions to problems apart from the original target of investigation. Alexander Fleming didn’t intend to find a cure for infectious diseases. He noticed a fungus had killed colonies of Staphylococci he’d been investigating and recognized its potential therapeutic benefits—though it took a decade and the involvement of others before penicillin was developed into a powerful world-changing medicine.

Subsidiary benefits often arise from a reserve of a broad base of questions. When Raman Sundrum and I worked on supersymmetry, we ended up finding a warped extra dimension that could solve the hierarchy problem. Afterward, by staring hard at the equations and putting them in a broader context, we also found that an infinite warped dimension of space could exist without contradicting any known observations or law of physics. We had been studying particle physics—a different topic altogether. But we had both the big and small pictures in mind. We were aware of the big questions about the nature of space even when concentrating on the more phenomenological issues such as understanding the hierarchy of mass scales in the Standard Model.

Another important feature of this particular work was that neither Raman nor I was a relativity expert, so we arrived at our research with open minds. Neither we (nor anyone else) would have conjectured that Einstein’s theory of gravity permits an invisible infinite dimension unless the equations had shown us that it was possible. We doggedly pursued the consequences of our equations, unaware that an infinite extra dimension was supposed to be impossible.

Even so, we weren’t immediately convinced we were right. And Raman and I hadn’t dived into the radical idea of extra dimensions blindly. It was only after we and many others had tried employing more conventional ideas that it made sense to leave our spacetime box. Although an extra dimension is an exotic and novel suggestion, Einstein’s theory of relativity still applies. Therefore, we had the equations and mathematical methods to understand what would happen in our hypothetical universe.

People subsequently used the results from this research assuming extra dimensions as launching points to discover new physical ideas that might apply in a universe with no such extra dimensions at all. By thinking about the problem in an orthogonal way (here, literally orthogonal), physicists recognized possibilities they had previously been entirely unaware of. It helped to think outside the box of three-dimensional space.

Anyone facing new ground has no choice but to live with the uncertainty that exists before a problem is completely solved. Even when starting from a nice solid platform of existing knowledge, someone investigating a new phenomenon inevitably encounters unknowns and the uncertainty that accompanies them—though admittedly with less risk to life and limb than a tightrope walker. Space adventurers, but artists and scientists, too, try to “boldly go where no one has gone before.” But the boldness isn’t random or haphazard and it doesn’t ignore earlier achievements, even when the new territory involves new ideas or anticipates crazy-seeming experiments that appear to be unrealistic at first. Investigators do their best to be prepared. That’s what rules, equations, and instincts about consistency are good for. These are the harnesses that protect us when traversing new domains.

In my colleague Marc Kamionkowski’s words, it’s “OK to be ambitious and futuristic.” But the trick is still to determine realistic goals. An award-winning business student present at the Creativity Foundation event I participated in remarked that the recent successful economic growth that had escalated into an economic bubble stemmed in part from creativity. But he noted too that the lack of restraint also caused the bubble to burst.

Some of the most groundbreaking research of the past exemplifies the contradictory impulses of confidence and caution. The science writer Gary Taubes once said to me that academics are at the same time the most confident and the most insecure people he knows. That very contradiction drives them—the belief that they are moving forward coupled with the rigorous standards they apply to make sure they are right. Creative people have to believe that they are uniquely placed to make a contribution—while all the time keeping in mind the many reasons that others might have already thought of and dismissed similar ideas.

Scientists who were very adventuresome in their ideas could also be very cautious when presenting them. Two of the most influential, Isaac Newton and Charles Darwin, waited quite a while before sharing their great ideas with the outside world. Charles Darwin’s research spanned many years, and he published the Origin of Species only after completing extensive observational research. Newton’s Principia presented a theory of gravity that was well over a decade in development. He waited to publish until he had completed a satisfactory proof that bodies of arbitrary spatial extent (not just pointlike objects) obey an inverse square law. The proof of this law, which says gravity decreases as the square of the distance from the center of an object, led Newton to develop the mathematics of calculus.

It sometimes takes a new formulation of a problem to see it the right way and to redefine the boundaries so you can find a solution where, on the surface, none appears possible. Perseverance and faith often make a big difference to the outcome—not religious faith but faith that a solution exists. Successful scientists—and creative people of all kinds—refuse to get stuck in dead ends. If we can’t solve a problem one way, we’ll seek an alternative route. If we reach a roadblock, we’ll dig a tunnel, find another direction, or fly over and get the lay of the land. Here’s where imagination and superficially crazy ideas come in. We have to believe in the reality of an answer in order to continue, and to trust that ultimately the world has a consistent internal logic that we might eventually discover. If we think about something from the right perspective, we can often find connections that we would otherwise miss.


FIGURE 81 ] The nine-dots problem asks how to connect all the dots using only four segments without lifting your pen.

The expression “thinking outside the box” doesn’t come from getting outside your work cubicle (as I once thought might be the case), but from the nine-dots problem, which asks how to connect nine dots with four lines without lifting your pen (see Figure 81). No solution to the ninedots problem exists if you have to keep your pen inside the confines of the square, but no one told you that was a requirement. Going “outside the box” yields the solution (see Figure 82). At this point you might realize you can reformulate the problem in a number of other ways too. If you use thick dots, you can use three lines. If you fold the paper (or use a really thick line, as a young girl apparently suggested to the problem’s creator), you can use just one line.


FIGURE 82 ] Possible creative solutions to the nine-dots problem include “thinking outside the box,” folding the paper so the dots align, or using a very thick pen.

These solutions aren’t cheating. They would be only if you have additional constraints. Education unfortunately sometimes encourages students not only to learn how to resolve problems, but also to second-guess the teacher’s intention—narrowing the range of correct answers and potentially also the students’ minds. In The Quark and the Jaguar,73 Murray Gell-Mann cites Washington University physics professor Alexander Calandra’s “Barometer Story,”74 in which he tells of a teacher who wasn’t sure he should give a student credit. The teacher had asked his students how they might use a barometer to determine the height of a building. This particular student answered that you could attach a string to the barometer, lower it to the ground, and find out how long the string was. When he was told to use physics, he suggested measuring the time it took for it to fall from the top of the building, or measuring the shadow at a known time of day. The student also volunteered the nonphysics solution of offering the superintendent the barometer in exchange for being told the height of the building. These answers might not have been what the teacher was looking for. But the student astutely—and humorously—recognized that the teacher’s constraints weren’t part of the problem.

When other physicists and I started thinking about extra dimensions of space in the 1990s, we not only went outside the box, we went outside three-dimensional space itself. We thought of a world in which the very stage in which we solved the problems was bigger than we had originally assumed. In doing so, we found potential solutions to problems that had plagued particle physicists for years.

Even so, research doesn’t arise in a vacuum. It is enriched by the many ideas and insights that others have thought of before. Good scientists listen to one another. Sometimes we find the right problem or solution just by very carefully listening to, observing, or reading someone else’s work. Often we collaborate to bring in different people’s talents, and also to keep ourselves honest.

Even if everyone wants to be the first to solve an important problem, scientists still learn from and share with one another and work on common topics. Occasionally other scientists say things that contain the clues to interesting problems or solutions—even unwittingly. Scientists might have their own inspiration, but they will often also exchange ideas, work out the consequences, and make adjustments or start again if the original idea doesn’t work. Imagining new ideas and keeping some while shooting others down is our bread and butter. That’s how we advance. It’s not bad. It’s progress.

One of the most important roles I can play as an adviser to graduate students is to be alert to their good ideas, even when they haven’t yet learned how to express them—and to listen when students find loopholes in my suggestions. This back-and-forth is perhaps one of the best ways to teach—or at least foster—creativity.

Competition plays an important role as well—in science as well as in most any other creative endeavor. In a discussion of creativity, the artist Jeff Koons simply told those of us in the room that when he was young, his sister did art—and he realized that he could do it better. A young filmmaker explained how competition encourages him and his colleagues to absorb each other’s techniques and ideas and thereby refine and develop their own. The chef David Chang expressed a similar thought a little more bluntly. His reaction after going to a new restaurant is, “That’s delicious. Why didn’t I think of that?”

Newton waited to publish until his results were complete. But he might also have been wary of his competitor Robert Hooke, who knew about the inverse square law as well—but lacked the calculus to support it. Nonetheless, Newton’s publication seems to have been prompted in part by a question relayed to him about Hooke’s overlapping research. Darwin, too, was clearly motivated to present his results by the knowledge that Alfred Russel Wallace was working on similar evolutionary ideas—and was likely to steal his thunder if he remained silent much longer. Both Darwin and Newton wanted to have their stories straight before presenting their revolutionary results, and developed them until they were extremely confident they were correct—or at least until they thought they might be scooped.

The universe repeatedly reveals itself to be cleverer than we are. Equations or observations open up ideas that no one would have dreamed of—and only creative open-minded inquiries will unearth such hidden phenomena in the future. Without incontrovertible evidence, no scientist would have invented quantum mechanics, and I suspect that anticipating the precise structure of DNA and the myriad phenomena that make up life would have been pretty nearly impossible unless we were faced with the phenomena or equations that told us what was there. The Higgs mechanism is ingenious, as are the inner workings of the atom and the behavior of the particles that underlie everything we see.

Research is an organic process. We don’t necessarily always know where we are headed, but experiments and theory serve as valuable guides. Preparation and skill, concentration and perseverance, asking the right questions, and cautiously trusting our imaginations will all help us in our search for understanding. So will open minds, conversations with others, wanting to do better than our predecessors or peers, and believing there are answers. No matter what the motivation, and independently of the particular skills that might come into play, scientists will continue to investigate inward and outward—and look forward to learning about the other ingenious mechanisms the universe has in store.