Nobel laureate Eugene Wigner once wrote that mathematics has the uncanny ability to describe the universe around us.
That’s the spirit behind the new book “The Big Bang of Numbers: How to Build the Universe Using Only Math,” written by Manil Suri, professor of mathematics at the University of Maryland, Baltimore County.
“Usually math is thought of as something that we invent, perhaps, to explain things around us. I’m kind of reversing this perspective and saying that math is the true driver of the universe and the universe itself is a model of the mathematical principles,” he told Marketplace’s Kimberly Adams in a recent interview.
The following is an excerpt from Suri’s new book.
On Monday, September 13, 2013, the New York Times published my opinion piece “How to Fall in Love with Math.” I awoke to find my email inbox overflowing with messages, not just from acquaintances but also from a bewildering number of strangers. Many more responses poured in online on the Times website—some enthusiastic about math, some scathing, all impassioned—clearly, I’d struck a nerve. By mid-afternoon, the number of posts had reached 360, and the paper closed the comments section. The article quickly climbed to the top of the Times’s most-emailed list and remained there for much of the next day.
The aim of my piece was to challenge the popular notion that mathematics is synonymous with calculation. Starting with arithmetic and proceeding through algebra and beyond, the message drummed into our heads as students is that we do math to “get the right answer.” The drill of multiplication tables, the drudgery of long division, the quadratic formula and its memorization—these are the dreary memories many of us carry around from school as a result.
But what if we liberated ourselves from the stress of finding “the right answer”? What would math look like if delinked from this calculation-driven motivation? What, if anything, would remain of the subject?
The answer is ideas. That’s what mathematics is truly about, the realm where it really comes alive. Ideas that engage and intrigue us as humans, that help us understand the universe. Ideas about the perfection of numbers, the nature of space and geometry, the spontaneous formation of patterns, the origins of randomness and infinity. The neat thing is that such ideas can be enjoyed without needing any special mathematical knowledge or being a computation whiz.
This is what I’d observed over the past decade and a half, during which, in addition to my day job as a mathematics professor, I’d been pursuing a dual career as a novelist. The juxtaposition put me in frequent contact with artists, writers, composers, journalists, and I was struck by the curiosity they expressed about math. Some had been good at it, but lost contact with the subject once they chose their career path; others had encountered difficulties learning it and viewed it as an unfulfilled intellectual challenge. Often, I was asked to give a talk not on my writing but about mathematics. “Something really exotic,” a few would add, their eyes shiny with daring, as if venturing into an Indian restaurant and asking for the menu’s hottest curry.
So I began talking about the mysteries of infinity (a topic that’s spicy, but not overwhelmingly so), which eventually developed into an animated PowerPoint talk. I’d go to dinner at people’s houses and once the plates had been cleared, ask if they’d like to see the show. (You know you’ve become a math evangelist when you carry such presentations on a flash drive in your wallet.) These activities got headier, more addictive. I started seeing myself as Florence Nightingale, administering math to the mathless; Johnny Appleseed, scattering math seeds like fairy dust everywhere I went. Some of my targets may have regarded me more like the Ancient Mariner and themselves as the cornered wedding guest. A few had to be rescued by their parents.
My novels (on India, not math) were doing well, so I was able to infiltrate even more venues where nonmathematicians congregated. My coolest coup was at the 2006 Berlin International Literature Festival, where a class of eleventh graders who thought they’d hear me speak about my second novel got my infinity talk instead. They seemed to like it—or at least sat through attentively, without fidgeting (the fact they were German may have had something to do with this).
By 2013, I’d begun to get a sense of the limits of such outreach efforts. So when my New York Times op-ed took off, I wondered if I’d finally hit it big. Nothing I’d ever written had ever gone “viral”—in fact, I wasn’t even sure what numbers earned that characterization. By Thursday, my piece had climbed into the weekly top-ten list; by Friday, it had inched up a few slots more. Over the weekend, I watched obsessively as it crept into the top three, then nudged its way into second place. What I barely noticed was that the pope had chosen that very week to make some startlingly progressive statements about gays, abortion, and birth control. Just as I was about to claim my rightful pinnacle of victory, he appeared behind me from nowhere, bounding up the list in twos and threes. Quads flexing, cassock billowing, he made one final spectacular jump, to leapfrog clear over me and land in my number one spot.
Now, you may wonder if I developed a lingering grudge against the pope, if I’ve written this book to vindicate myself in an imagined mano a mano with him. Let me assure you that’s not the case. I’ve completely forgiven him and will even be mailing him an autographed copy of the finished book at the Vatican to show no hard feelings remain.
However, his surprise appearance did have a crucial effect: it focused my attention on religion. In the popularity contest with mathematics, religion had handily won—as it almost surely would each time. What did it offer that math didn’t? What lesson could one take away for math to draw people in, to compete in the attention economy we live in?
There’s no shortage of answers to this question, but I was reminded of a quote I’d seen years earlier that had cut me to the quick. It was attributed to Rob Fixmer, a former editor of the New York Times, who was attempting to explain why math got so little media attention:
Mathematics has no emotional impact. What physicists do challenges people’s notions of origins and creations. Math doesn’t challenge any fundamental beliefs or what it means to be human.
My immediate reaction was indignation—how could anyone malign something I loved this way? In time, I realized this might be an opinion many shared. Also, though the quote had compared math with physics, the same could be said while comparing math to religion. After all, both physics and religion seek to address the Big Questions—albeit from opposing perspectives: Where does everything come from? Why is the universe the way it is? How do we fit in? The two camps have been duking it out over the answers for centuries, begetting even more attention for themselves.
Math doesn’t seem to have a dog to enter in this fight. The subject is abstract, agnostic—ready to describe and analyze phenomena, without having a position of its own to stake. That’s the image perceived by most, anyway. Without such blockbuster spectacles as Genesis or the big bang, no wonder math has difficulty competing in the engagement sweepstakes.
But I’m here to tell you this picture of math is inaccurate. Math does have a compelling “origins” story, one that creates its basic building blocks out of nothing. With a little inventiveness, this narrative can be extended to show how with these building blocks—called numbers—the entire universe could plausibly be constructed. Big Questions do indeed get addressed along the way, with answers that come not from God or science but mathematics.
As I watched my article begin its descent on the NYT list, I realized that, as follow-up, I should write precisely the above kind of narrative. One that would flesh out my article’s central assertion about math being more about ideas than calculation (which meant I’d need to severely limit formulas and equations!). Something that would not only convey the aesthetic pleasure of the subject but also reveal the deeper connections we—and our cosmos—have with it.
The book you (and, God willing, the pope) are about to read emerged from that day’s realization. Its premise is this. I’m going to put you, the reader, in the driver’s seat and have you take on the task of creating the universe using only numbers, and the mathematics you formulate from them. We’ll launch this adventure in the next chapter with the above-mentioned “origins” blast—math’s very own creation spectacle!
Sitting at the controls of this thought experiment, you’ll soon find yourself devising arithmetic, then geometry, then algebra, then physics—all in response to the needs of your universe-in-progress. (This will incidentally answer the question “Why does algebra exist in the world?” asked by untold legions of unhappy schoolchildren.) The perspective you’ll get is unusual, even radical: math as the life force of the universe, a top-down driving power that fashions everything that exists. This turns on its head the traditional way mathematics is understood. Rather than regarding it as something we devise to explain preexisting real-life phenomena (given to us by God or physics), we will view mathematics as the fundamental source of creation, with reality trying to follow its dictates as best it can.
Such a view is actually not new—it has precedents traceable all the way back to the ancient Greeks, particularly Plato. What differentiates us from Plato is that we don’t assume all of mathematics already exists in some idealized form somewhere, waiting to be discovered, as he did. Rather, we invent math—from scratch, and through active, energetic exploration. Math that will create the universe, rather than explain something already in place.
There are several advantages to this reverse, hands-on approach. For one, it will enable you to get a firsthand taste of the playful nature of mathematics. This is something mathematicians often rhapsodize about but outsiders can find hard to access. Sitting in the driver’s seat, you’ll see how even simple arithmetic operations like addition and multiplication are, at heart, games. You’ll be able to experiment with such games and ideas creatively, as if playing with an abstract set of toy building blocks or Lego bricks. Each time the inevitable question—“What good is this, anyway?”—comes up, the answer will be right there. After all, the components of the universe will, quite literally, be arising from your play!
Contrast this with the alternative, of starting with real-life phenomena and demonstrating how math can be used to approximately model them. Such efforts (as I’ve noticed in my own outreach) can come across as a “good for you” vitamin, with playfulness often smothered under the weight of technical elaboration. Using play and exploration to bring out the usefulness of math, as we do here, makes the connection feel more natural, effortless. The fact that we can embed math in a single continuous narrative helps show how its different areas are linked.
Another advantage of our approach is that it allows us a fresh look at the “unreasonable effectiveness of mathematics” in describing the universe (as Nobel laureate Eugene Wigner put it). This is a riddle that’s central to the subject—how can something so abstract be so uncannily adept at explaining the reality we live in? Clearly, if we demonstrate that the mathematics in our thought experiment leads inevitably to the creation of everything in our universe (and only our universe, rather than some different one!) then we’ve come a long way toward changing “unreasonable” to “very reasonable” effectiveness.
Let me be up-front: our thought experiment won’t quite achieve this kind of slam dunk. Trying to build everything just with math is, to put it mildly, a tad ambitious. However, proceeding step by step, we’ll find out what other ingredients might be minimally needed, while getting to appreciate just how deeply numbers are hardwired into our experience. In particular, our flipped perspective will lead us to an insightful new interpretation of how Nature fits in. We’ll view her as a building contractor, who has the task of turning our design for the universe into tangible reality. By casting her in this role, we’ll be able to better understand why she doesn’t follow our mathematical instructions to the letter, what role randomness plays.
Our explorations will also reveal that the universe we live in isn’t the only one possible. That’s because such basics commonly taken for granted—like size, distance, space—arise innately from mathematics. Consequently, you can make them strikingly different in any universe you create by defining them in alternative mathematical ways. For instance, we’ll use the very physical art of crocheting to figure out the different fabrics possible for the universe’s geometry. (It turns out that we don’t quite know which is the correct one even for our own universe!) Expect to have your “fundamental beliefs” challenged as we explore such variations, thereby checking off one of the boxes in Fixmer’s quote.
Another critical question raised in the quote was whether math has “emotional impact.” It’s true that mathematics, much more than art or music, is experienced more intellectually than viscerally. However, comprehension is often followed by a eureka moment, which is part of the emotional punch math packs. That’s what our thought experiment is set up to deliver—whether through games that suddenly open up to reveal a deeper truth, or through “eye candy” fractals that transform into essential drivers of the universe when you engage with the math behind them. Look for such experiences particularly in the section on patterns, where we attempt to make the Mona Lisa prettier through a mathematical makeover.
We’ve adopted our top-down version of mathematics because it works so well in our exposition. But could this reflect reality? Could math truly be what guides our universe? We debate both sides of this ahead, but the section on physics contains evidence supporting our viewpoint. You’ll see how mathematics actually determines physical principles like Newton’s law of gravitation (and even a very basic idea used in general relativity), rather than just being a language used to explain them.
The penultimate section, on infinity, transports our thought experiment to a more expansive, philosophical realm. While previous sections bring out how mathematics informs such essential qualities as randomness, symmetry, and beauty, we now explore what it tells us about even deeper questions. Does knowledge have boundaries? Is omniscience possible? Can one list successive instants of time? The concept of infinity is essential for delving into such issues. Even though it’s something that can only be envisaged, never physically attained, infinity is inextricably tied up with setting down the universe’s blueprints; much of the reality around us involves the push and pull of the finite versus the infinite. Be on the lookout for a fictional interplanetary battle through which we’ll steer our thought experiment to unlock infinity’s secrets.
In the final section, we get down to the task of physically building our universe from the designs we’ve created. Iteration, where one state in time evolves to another, is the key mathematical process that facilitates construction. We explore how elementary rules of iteration can lead to complex, self-arising phenomena—fractal patterns, stripes on a zebra, “herd intelligence” in ants. Such emergence (as the spontaneous generation of complexity is called) could plausibly create life itself.
The issue of creation, of course, is also in the domain of religious philosophy, whose relationship to science we comment on at several points in the text. One of the most essential questions both ask is this: Why do we exist? Is it a result of randomness or intent?
This is the final enigma we address. Mathematics will reveal the answer at the end of our thought experiment.
The most stringent test of our ideas would be if we scrubbed our minds clean of all knowledge of both math and our universe, and started from a blank slate. We’re going to do nothing of the sort. Which means that, consciously or unconsciously, such knowledge might seep in to inform everything we create. Will this damage the integrity of our experiment?
It won’t. Many mathematical concepts can indeed be deduced quite naturally from the universe’s components (e.g., a sphere from the universe’s round objects, the Golden Ratio from sunflower seeds and pine cones). Although we’ll often point out such links to familiarize you with a new concept, our charge will be to also find an independent path to develop the concept, one that ignores connections with the physical universe, and uses only the math we’ve created. In other words, our first guideline will be to always strive to maintain our top-down philosophy, by composing a narrative in which math drives the universe, rather than the universe providing us the math.
As far as prior knowledge of math goes, our second rule will be that we can’t use a mathematical concept before we’ve developed it. For instance, we can’t arrange numbers along a straight line if we haven’t created lines yet. This will ensure we’re actually constructing all the math we need as we go along.
Since we’re following the math, we can expect (as mentioned earlier) for it to lead us to several alternative universes. We’ll look into some of these variations, since they can provide interesting insights into our own reality. However, when a choice arises on how to proceed with our thought experiment, our guideline will be to pick the path most likely to lead us back to our own universe, since that’s the one we want to build.
Finally, let’s note that thought experiments have a particularly rich tradition in physics and philosophy, where they typically explore rather focused questions or concepts (“What does quantum superposition have to say about the health of Schrödinger’s cat?”). We can afford to be more relaxed, since our thought experiment is just the vehicle—the true purpose of our journey is the understanding and appreciation of math. Consequently, we’ll take some liberties—step outside our experiment at will, get Nature and the numbers to roam around as characters, have the pope materialize from time to time to offer commentary, and let a Greek chorus of physicists do the same.
As you’ve no doubt surmised, I’m aiming this book not only at novices but also at math enthusiasts. This includes inquiring high schoolers, teachers and parents, seasoned STEM readers, all the way up to hardened math professionals. If you’ve ever tried to get anyone excited about math, I promise you’ll find new strategies within these pages.
However, a word of warning—some people’s experiences with mathematics may have convinced them they can never find its ideas engaging. (“So—good for you, you’re moved by the pure beauty of math. Please, take a cookie and congratulate yourself” is how one reader of my NYT article put it. Others were less generous.) We can all be resistant to the charms of different endeavors; my biggest blind spot—a problem, since I grew up in India—happens to be cricket (unlike everyone around me, I was always loath to watch it). So, try keeping an open mind as you embark on this book, with the perspective that you can enjoy math under the right circumstances. (I’ll meanwhile think about giving another shot to cricket.)
Next, for novices, relax. Some of you might find it liberating to read about mathematical ideas for the first time without the nagging worry: Is this going to be on the test? Experience this math appreciation at your own pace—you can always come back to topics that you decide to just skim. Remember, even though the formulas I’ve used are both elementary and minimal in number, the ideas expressed can run rather deep.
Do read the footnotes, since they’re interesting (that’s why I added them!). Endnotes, which contain references, technical qualifications, and proofs, but also some engaging elaborations, can sometimes be more mathematically challenging to read. I’ll alert you only to the most essential ones as we go along. That said, if you’re a mathematician and feel something’s missing, chances are it’s addressed in one of the unflagged endnotes, so do check them.
You’ll notice I’ve organized this book in “days,” as in Genesis. It’s a metaphor I couldn’t resist, once I realized our mathematical creation would have exactly seven stages. Although these stages don’t correspond to what God creates in the Bible (light on Day 1, sky on Day 2, etc.), both progressions suggest how naturally each creation might lead to the next—in our case, arithmetic giving rise to geometry, geometry to algebra, and so on. Math becomes more of a story, not just like Genesis, but also like the narrative of how everything gets built up from the big bang in physics. And who doesn’t love a story, as they say.
This brings me to my final note. Both religion and science might have, for each reader, their own place. Despite any apparent irreverence, my aim isn’t to supplant or disrespect either. Rather, it’s to take you on a thought experiment that introduces another worldview, one fashioned around mathematics. It’s an offering that even the pope, my most treasured potential reader, shouldn’t have a problem with.
This is a good spot to make clear that Pope Francis (who’s been the pope while I’ve been writing this book) has not participated in this work in any way beyond his chance entanglement with me on the NYT “most emailed” list. The comments, actions, and thoughts I attribute to him ahead are fictional, though details about his educational background are correct.
