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What Math Can Tell Us About the Nature of the Universe

Manil Suri on the Less-Logical Side of Mathematical Knowledge

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?

What would math look like if delinked from this calculation-driven motivation?

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 non-mathematicians 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 my new book, The Big Bang of Numbers, 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.

Without such blockbuster spectacles as Genesis or the big bang, no wonder math has difficulty competing in the engagement sweepstakes.

As I watched my article begin its descent on the NYT list, I realized that, as follow-up, I needed to 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 premise that grew out of that day’s realization was this. I’d put readers (including, God willing, the pope) in the driver’s seat and have them take on the task of creating the universe using only numbers, and any mathematics formulated from them. We’d launch this adventure with the above-mentioned “origins” blast—math’s very own creation spectacle!

Sitting at the controls of this thought experiment, you’d find yourself devising arithmetic, then geometry, then algebra, then physics—all in response to the needs of your universe-in-progress. (This would incidentally answer the question “Why does algebra exist in the world?” asked by untold legions of unhappy schoolchildren.) The perspective you’d get would be 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’d 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 would differentiate us from Plato is that we wouldn’t assume all of mathematics already exists in some idealized form somewhere, waiting to be discovered, as he did. Rather, we’d invent math—from scratch, and through active, energetic exploration. Math that would create the universe, rather than explain something already in place.

I soon saw the benefit of such a reverse, hands-on approach: it affords a firsthand taste of the playful nature of mathematics. This is something mathematicians often rhapsodize about, but outsiders can find hard to access. The driver’s seat is the perfect spot from which to see how even simple arithmetic operations like addition and multiplication are, at heart, games.

One can 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 is right there. After all, the components of the universe would, 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 math’s usefulness makes the connection feel more natural, effortless.

Another advantage of this approach is that it facilitates 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’re able to show 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: such a slam dunk isn’t achievable. Trying to build everything just with math is, to put it mildly, a tad ambitious. However, proceeding step by step, we can find out what other ingredients might be minimally needed, while getting to appreciate just how deeply numbers are hardwired into our experience.

Exploring creation from this perspective also leads to the realization that the universe we live in isn’t the only one that could have been 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. Surely this challenges “fundamental beliefs”—checking off one of Fixmer’s boxes.

Perhaps the most critical question in Fixmer’s quote is 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 I needed my thought experiment to deliver. Maybe through games that suddenly opened up to reveal a deeper truth, or “eye candy” fractals that transformed into essential drivers of the universe when readers engaged with the math behind them.

Mathematics held the key to questions about omniscience, about the limits of knowledge, about the nature of time.

As I tried to address such issues, a deeper question began to intrigue me. I’d chosen my top-down approach because it worked so well in an expositional sense, but could this reflect reality? Could math really be what guides our universe? Was the idea more than a convenient premise for my book, something I truly believed?

Certainly, rules that govern nature, once I started examining them from this perspective, offered supporting evidence. For instance, the familiar inverse-square law of gravity comes from purely geometrical considerations – mathematics actually gives rise to the law, rather than just being a language to state or describe it. The same is true about a core principle that underlies general relativity. Could reality indeed be based on mathematical blueprints? Was nature best viewed as a contractor of sorts, who manifests the universe from such blueprints, if a bit capriciously?

The further I progressed into the book, the more profound math’s role in the universe seemed to become. I was able to see how mathematics informs such essential qualities as randomness, symmetry, and beauty. The many different ways that infinity, a quintessentially mathematical concept, impacts our life, even though we never encounter it in reality. Mathematics held the key to questions about omniscience, about the limits of knowledge, about the nature of time. It even shed light on how life might have been created through a process of “emergence”—the name given to the spontaneous generation of complexity from elementary rules.

Through it all, I could see the biggest of the Big Questions always looming up ahead, one that both religion and science have built entire careers around, trying to address. Why do we exist? Is it a result of randomness or intent?

Mathematics, I felt, had to have its own unique answer to this. Something that would speak to the core of our existence, while also tying together its own complicity in our being.

Indeed it did, as I found towards the end of writing The Big Bang of Numbers. The answer came from the very essence of mathematics, but was not what I had expected.

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Excerpted and adapted from The Big Bang of Numbers: How to Build the Universe Using Only Math by Manil Suri. Copyright © 2022. Available from W.W. Norton & Company.

Manil Suri
Manil Suri
Manil Suri is a distinguished mathematics professor at the University of Maryland, Baltimore County. He is the author of three internationally acclaimed novels, including The Death of Vishnu, which have been cumulatively translated into twenty-seven languages. He is a former contributing opinion writer at the New York Times, for which he has written several widely read pieces on mathematics. His work has also appeared in the New Yorker, the Wall Street Journal, the Washington Post, Granta, and other publications. He lives with his husband in Silver Spring, Maryland. https://www.manilsuri.com/





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