Science Friday - Poetry of Science, The Power of Calculus. March 29, 2019, Part 2

Episode Date: March 29, 2019

April is National Poetry Month, a time of readings, outreach programs, and enthusiastic celebration of the craft. And for a special Science Friday celebration, we’ll be looking at where science and poetry meet. Tracy K. Smith, the current U.S. poet laureate, wrote the 2011 book Life On Mars, which touches on dark matter, the nature of the universe, and the Hubble Telescope—all as an elegy for her deceased engineer father, Floyd. Rafael Campo, a physician, poet, and editor for the Journal of the American Medical Association’s poetry section, writes poems about illness, the body, and the narratives each patient brings to medical settings. The two talk to Ira about where science fits into their work—and how poetry can inform science and scientists. Read some of the poems, and a syllabus of science-related works suggested by SciFri listeners, here. Calculus underpins many of the greatest ideas about how the universe works: Newton's Laws, Maxwell's Equations, quantum theory. It's been used to develop ubiquitous technologies, like GPS. It was even used to model the battle between HIV and the human immune system, which helped researchers fine tune triple-drug therapies to combat the virus. In his book Infinite Powers: How Calculus Reveals the Secrets of the Universe, mathematician Steven Strogatz takes readers on a journey around the world, detailing the bright ideas that contributed to modern calculus and citing the many ways those mathematical ideas have changed the world. Learn more here. Subscribe to this podcast. Plus, to stay updated on all things science, sign up for Science Friday's newsletters.

This is Science Friday. I'm Ira Flato. Later in the hour, mathematician Stephen Strogatz is here to talk about infinite powers, his new book about calculus. And trust me, this is the book he wish you had during high school math class. He might actually like calculus after this. But first, it was the poet T.S. Eliot, who wrote that April is the cruelest month. And as March wraps up and the new month begins, we want to take you, we want to take some time this spring. to consider poetry. Yes, poetry. April is National Poetry Month after all, and it's a time of reading, outreach, and celebration in the literary community.

And plenty of those poems meditate at least somewhat on questions of science. The late Mary Oliver famously incorporated observations of biology and ecology in her work, while other poets have looked

to astrophysics or even anthropomorphized the entire discipline. As Edgar Allan Poe does, in one sonnet, science, true daughter of time, thou art. Wish I were better at reading poetry, but they have to wait for someone better. And I have two of those people on the program right now. Two poets join us today to help celebrate the intersection of poetry and science.

First, the current U.S. Poet Laureate, Tracy K. Smith. She's the author most recently of Wade in the Water. And her previous book, The Pulitzer Prize-winning Life on Mars, touches on dark matter, the Hubble Space Telescope, and the vastness of the universe. Welcome, Tracy. Thank you. And Raphael Campo is a poet and physician.

He's an associate professor of medicine in Harvard Medical School, editor of the Journal of the American Medical Association's poetry section, and his most recent book is Comfort Measures Only, New and Selected Poems. Welcome, Dr. Campo to Science Friday. Thanks so much. I'm glad to be here. Nice to have you. And for our listeners, some further reading, you can check out excerpts from our guests

and some listener suggestions on our website at ScienceFriety.com slash poetry. And if you have a favorite poem about science, give us a call. You make the call 844-724-8255, 845, 844-724-8255, or you can tweet us at SciFri. Let me begin with you, Tracy. You're a poet who sometimes works science into your work, like in your book, Life on Mars. Your poems speculate on the nature of the universe, characterized dark, matter. They bring us into the room where the Hubble Space Telescope was built. Where did the roots for that book come from? Well, some of my initial questions that drew me to science and what I really

understand is also science fiction in that book came from wanting to ask questions like, who are we, what do we belong to, what are the effects that we have upon others? And those questions can live in terms of nationhood or private realms, but they also can exist in terms of us as a species. So I began trying to imagine this thing that we belong to and to use it as a way of seeing ourselves differently, maybe the future that we're paving the way for as well. Now, your father worked on the Hubble telescope.

Did he not? He did, yeah. That must have had some influence. You know, it's really funny. I know it did, and I know that it informs the shape of my imagination, but it wasn't until late in the process of writing that book that I remembered that that was a job that he had held when I was in elementary school. It was when the poems in that book shifted toward elegy after his unexpected death, that space became a backdrop for exploring questions of grief and maybe even a fantasy of the afterlife. And then this voice said, oh, right, my dad worked on the Hubble. And suddenly everything became more private than I thought that it was.

The universe became something that my father was connected to in a different way. So it was a personal story for you then. Yeah. Can you read us a little excerpt from your life on Mars? Sure. I'll read you one of the poems that is thinking maybe in terms of science fiction. It's called The Universe is a House Party. The universe is expanding.

Look, postcards and panties, bottles with lipstick on the rim, orphan socks, and napkins dried into knots. Quickly, wordlessly, all of it whisked into file with radio waves from a generation ago, drifting to the edge of what doesn't end, like the air inside. a balloon. Is it bright? Will our eyes crimp shut? Is it molten, atomic, a conflagration of suns? It sounds like the kind of party your neighbors forget to invite you to, base throbbing through walls and everyone thudding around drunk on the roof. We grind lenses to an impossible strength, point them toward the future, and dream of beings will welcome with indefatigable

hospitality. How marvelous you've come. We won't flinch at the pinprick mouths, the nubbin limbs, will rise, grassal, robust, mi-casa is su casa, never more sincere. Seeing us, they'll know exactly what we mean. Of course it's ours. If it's end, if it's anyone's, it's ours. That is such a hopeful vision of aliens. Well, I don't know. I think we come off poorly in that poem. The last line for me is a way of saying, oh, right,

but somehow we claim dominion over this infinite space, which probably doesn't speak too well to our nature as humans. Rafael, you're the editor of the Journal of the American Medical Association poetry section. I bet you it's news to a lot of people that Jem even has a poetry section. Well, it's actually been part of the journal for quite some time, and it's just an incredible forum for physicians who are encountering patients at points in their lives where, you know, we need poetry. We need a context for making sense of human suffering and the human condition. So poetry actually has a really, I think, important role for physicians and other care

providers. And many of your poems are about the body, hospital settings, and your patients. I guess they're a natural draw for you. Yeah, you know, I started really writing poetry quite some time ago. It was always, in some sense, related to healing, this notion of repair, being the child of immigrant parents, and hearing the poems of my homeland as a way of connecting across that wound in a sense. And so poetry, yeah, has always been, has always had that association for me. And so I am really interested in how poetry can help us become more located in our physical bodies, how it can help us be more present in the experiences of pain and suffering that we encounter. And so, so yes, for a long time, that's been a real attraction for me.

Can you read us one of your poems? Sure. This is a poem called The Mental Status Exam. What is the color of the mind? Beneath the cranium, it's pinkish gray with flecks of white mixed in. What is the mind's motif? Depends on what you mean. It's either sex or it's a box, release, or pessimism.

Remember these three things. Ball, sorrow, red. count backward from 100 down by sevens. What is the color of the mind? It's said that love can conquer all. Interpret, please. And who's the president? What year is it?

The mind is timeless, dizzy, unscrupulous. The mind is sometimes only dimly lit. Just two more silly questions. Can you sing for us? Do you remember those three things? Wow. What did you think of that, Tracy? Oh, wow.

I think it's so beautiful because those huge questions of being are peppered with these small questions, and it's easy to imagine anybody getting lost between those two scales. A body or a mind in distress would probably be even more befuddled by that simple. request to remember these three things. I love the way that poem makes me think about the different contexts and versions of ourselves that we juggle just in being alive. Raphael, what can your colleagues or other physicians get out of your poetry or just poetry in general? You know, I think it's a number of things, really. I mean, I think, you know, one is empathy.

We talk a lot about empathy, but I think we often don't really have a sense of what it actually is. And to my mind, poetry really is a way of enacting empathy or performing empathy. We enter into the experience of another person. We become immersed in another's voice. And that's critically important for doctors who are struggling, I think, often with distancing, which actually used to be explicitly part of our training. We were taught detached concern that we needed this sort of scientific objectivity to be able to, you know, make rational decisions about, you know, next steps in patients' care. And it turns out, actually, that empathy can actually help us listen better. There's some science behind this, that poetry, teaching poetry and other arts

and humanities to medical students not only helps us listen better, I think, but also improves patients' perceptions of our care. And then also, I think, it provides this larger context for us. You know, we are dealing with people, you know, at the most difficult points in their lives, at the most difficult moments in their lives, and sometimes also the most joyous, the most ecstatic moments in their lives. And so I think we need to be able to see our patients, not as just their problemless, you know, not as just their, you know, what's the potassium level, how many lymph nodes are positive on the CT scan, all important data, of course, but we also need to be able to say, you know, where is this person at in the story, in the narrative of this illness? What are the social determinants of disease, as we sometimes call them in medicine? But, you know, what is that context? How is this person living with diabetes or with whatever the health condition might be? So poetry, I think, can, can really help us locate ourselves in relation to some of those larger questions, as Tracy was

saying. And then also, I think, one last thing perhaps is how it locates us in our physical bodies again. I'm particularly interested in the rhythms of the body. I spend all day listening to the iambic beat of the heart through my stethoscope. And so poetry, I think, especially for doctors, can remind us that. We live in physical human bodies. Rafael Campo and Tracy Smith. We're going to come back and talk lots more with them. Our number 844-8255. We'll be right back after this break.

Hey there, Ira here. You know, I've been looking back at the first quarter of 2019, and I've got to say that some of my favorite conversations on Science Friday have happened in the last three months. As you know, space is always one of my favorite topics. So we were eager to bring NASA administrator Jim Bridenstein on the show to answer your questions. We also discussed how exercise could reshape our hearts,

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I'm Ira Flato. Next week starts National Poetry Month, so we're celebrating poetry that has its roots in science. With my guests, U.S. Poet Laureate Tracy K. Smith, author of Wade in the Water and Life on Mars, Raphael Campo, a poet and physician at Harvard Med School, an editor of the poetry section in the Journal of the American Medical Association. Our number 844-8255, let's continue our discussion. Tracy, you said in other interviews that poems are machines and that, quote, poetry is a kind of science you can practice.

Tell us about that. Well, you know, poetry is a subjective art form because poets and readers bring different values and preferences to the practice of it. But it's also a discipline. And whatever your formal principles are, they are principles. And those guidelines and those technical aspects of this imaginative art give a kind of rigor and structure to the more expansive and speculative aspects of poetic exploration or inquiry. I think you need both, and they look different from person to person. I find that when I'm writing poems that lead me into a place where I really have little

to go on, form can help push me forward into the material. It requires my thoughts to follow a different path than they might. follow in, you know, in conversation. And that's useful. And poems also, you know, research is a part of the process for many, many poems as well. Raphael, it seems that Tracy is sort of equating science and poetry as a scientist yourself. Do you find that the equivalence? Oh, yes, absolutely. I agree entirely with what Tracy is saying that there is a discipline, a discipline of the body in poetry. I think that, you know, it's not this sort of simply visceral, you know, quality that attracts me to poetry. And I think attracts other physicians to the art of poetry.

But it also is that kind of rigor, that muscularity, that sense of, you know, that the mind shapes the sounds on the page and the shape of the words on the page, the shape of the lines on the page. And so it is this wonderful juxtaposition of the physical, of the innate rhythms of our body and the work of our minds. And in fact, that's a bit about what that poem I read is about, you know, that there's a kind of formal structure. It's a sonnet. It's about love in some sense, and it has the baggage of a sonnet. But it's also about, you know, just the beating of the heart and how the mind, perhaps in some sense, is the same. seat of what we understand is love, but also love resides in our physical bodies, in our hearts. Tracy, can I get you to read another poem for it?

Sure. I'll read you a poem from Wade in the Water that is, it's driven by a metaphor. I think it's a poem about the planet. It's called The World is Your Beautiful Younger Sister. seeing her as seldom as you do, it doesn't change. The ire, the shame, the fists you must remember to smooth flat, just thinking what they did, what they promised, then took those men who offered to pay, to keep, the clan of them lording it over the others like high school boys and their kid brothers.

men with interests to protect and mute marble wives, men who let her beam into their faces, watching her shoulders rise, her astonishing new breasts, making her believe it was she who gave permission. They plundered her youth, then moved on, those awful, awful men, the ones whose wealth

is a kind of filth. Wow, that's very powerful. Thanks. I like poems that allow me to articulate my sense of a problem, but that also drag me into it in a way that I think is only honest. You know, like our lives and our choices are kind of like the men in that poem. And I think it's important to think about that sometimes. And Raphael, I'll give you a chance to read us another poem, please.

Oh, thanks. This is a poem called Incidental Finding. The sun through green leaf's flesh recalls the X-ray. Inner structures seen but imprecisely, branching veins and something like planned avenues, all leading to the source of what we never cease to seek. Too few, too momentarily alike, these chance encounters with the truth.

The X-ray that permitted me to see both into you and through the glowing silhouette of your soft tissues like the swaddling soul still diagnoses it. A mass, the radiologist in me, could not help noting first, and then your failing heart terribly large. That's terrific. Thank you, ma'am. Tracy, what is your research process like?

What do you immerse yourself in to start building your images? Well, if it's a poem that's rooted in something real, an event, or, you know, a phenomenon in the world, I'll try and learn as much as I can about that so that my questions have something to push against, you know, real terms, sometimes even a real vocabulary. And I also might develop a sense of who is, involved in this thing. Is it a conflict or something other than that? And that is sometimes enough to get me started.

My imagination begins to move and my questions can, we'll find their way into language. And then I have to go back and learn more sometimes. And what's exciting to me is that I don't learn everything at the beginning and then write the poem as a way of demonstrating what I've discovered. the act of writing the poem is a kind of discovery process, so that by the end of the poem, I've learned something that I didn't know. And that's true, even when I'm writing a poem about private experience that doesn't really warrant research, looking at that through the lens of metaphor,

thinking in terms of the music of the language, and allowing that to put pressure upon the actual changes what I find within it. Raphael, how important is the accuracy of your poetry? You know, accuracy is an interesting concept, I think, you know, hearing Tracy read her poems and just the utter precision of the imagery is just extraordinary. And so, you know, I think of accuracy in some sense in that way, that, you know, how closely can we look at an image? how clearly can we see a detail.

But I also think that metaphor can transport us through that close-looking process into a deeper understanding, perhaps, of what we see. And so I'm really interested in that kind of tension, too, that, yes, our poems ought to be precisely observed, precisely felt. perhaps they also, as I was saying before, mimic or express the rhythms of the body in some sense, the rhythms of our imagination. But then they also can transcend those kinds of observations. And again, through metaphor, I think, really take us to another place and transcend what we can perhaps more simply see through or perceive through our senses. And I'm just, again, fascinated by this way that our bodies can translate crude sensory data into this more nuanced, complex knowing. Tracy, as April and National Poetry Month kicks off, how would you encourage the rest of us to celebrate?

Oh, I think reading poetry is something that should be done every day, but especially in National Poetry Month. I always tell my students and people who want to become writers, look how slim books of poetry are. They're so slim. You could sit down and read one over breakfast or over lunch, and it can really change your way of looking at yourself and other people. And so it's worth doing that. So pick up a book of poetry this month and spend some time with it. Raphael could be therapeutic, it sounds like. Yes, absolutely.

I say to all those scientists out there listening to us, yes, poetry can be therapeutic. I think for us, it can give us that larger context that we were talking about. And for our patients, I think it can really be really be a way of reclaiming a kind of authority over the story of the illness that in medicine, unfortunately, at times is kind of appropriated by doctors. And we, you know, take it and translate it into the medical record. And, you know, we're checking all our boxes. And the poet, the patient's.

story sometimes gets marginalized and there are many instances I think in which we silence our patients and so yes poetry can be a way of speaking that experience and reclaiming that authority all right so that's how we're going to kick off

national poetry month on Science Friday I want to thank both of my guests U.S. Poet Laureate Tracy K. Smith author of Wade in the Water and Life on Mars. Ralph Raphael Campo poet and physician at Harvard Med School editor of the poetry section

in the Journal of the American Medical Association. Thank you both and happy National Poetry Month to both of you. Thanks. Happy National Poetry Month to you too. For the rest of the hour, we're going to be talking about well, maybe something that you don't find very poetic but my next guest certainly does. And I'm talking about integrals, derivatives, infinite series.

You're getting the hint here, bringing back any memories? I'm talking about calculus. calculus class pleasant memories i hope well for me not so much i really struggled with calculus 101 you know maybe you did too but strangely it was not until i got beyond the basics and into what you do with calculus what calculus can do to appreciate how the world is ordered mathematically that i actually began to appreciate its power and beauty elegance as my math teacher would say So I realized years ago how fascinating calculus could be, but not until I began reading a new book, Infinite Power, by my guest mathematician Stephen Stroggatz, did I appreciate its place in history and how it contributed to that history. Stroggatz has his own definition of calculus, taking us back to ancient Greece, the Middle East, and the letter-writing intrigue in the 17th century Europe.

He describes how calculus underpins pretty much everything we're. we know about the universe, motion, gravitation, electrical magnetism, quantum theory. He says we all at all take calculus. He's even a connection to the Beatles in there. We'll get back to that rock group in a minute. Stephen Stroggatz is Professor of Mathematics at Cornell, an author of Infinite Powers, how calculus reveals the secrets of the universe. We have an excerpt up on our website, ScienceFriday.com slash calculus.

Welcome back to Science Friday, Stephen. Thanks very much, Ira. It's great to be with you. This is really a great, you know, if you can say as a page Turner about a book about mathematics, this was a great feat. Well, thanks very much. That's wonderful to hear. So tell us why you write a book about calculus. Oh, I've been in love with this subject since I was a teenager, and I feel like it's just something beautiful that I would love to share with other people. I feel like it's a gift, especially because, as you mentioned, it sometimes gets a bad rap as being a, hard to understand or it's where some people feel like they hit the wall in their math education.

So it has a bit of a rough reputation and, you know, it makes me sad because you mentioned poetry. Yes, it's absolutely the poetry of the universe. And I would like people to get that and see, not just, you know, not just lofty stuff like that, but that it's really affecting everything we do in our everyday lives from when we turn on our microwave ovens to, you know, using our GPS to find our way home at night. that's calculus. And you frame the pillars of calculus as derivatives, breaking things down,

and integrals, building things back up, sort of a mathematical yin-yang here. Yeah, you could look at it that way. I mean, people who have taken calculus will know those words, jargon, derivatives, and integrals. But I would actually say it a little differently. I would say what's really going on,

the heart and soul of calculus, is the spirit of problem-solving, that you take a really hard problem and break it into smaller pieces. Now, anyone who's ever solved problems knows that's a good strategy, breaking a hard problem into easier, smaller problems. But what's so interesting and almost, you know,

kind of maniacal about calculus is it never stops. It chops a problem again and again and again infinitely often into infinitesimal bits, and that's a mind-bending idea. That's the great intellectual breakthrough of calculus, this strategic use of infinity to chop problems into their tiniest conceivable parts where they become much easier, and then you solve those and then put them back together.

And you were writing that calculus, those tiny little breaking it down into those tiny little bits goes way back further than we think that the Europeans invented. It goes back to the Greeks. Yes, it does. So you often hear it said that calculus was invented in the 1600s, but I would say that this definition of calculus I'm giving, this strategic use of infinity and infinitesimal. We can see it clearly happening in the work of Archimedes around 250 BC. He lived in Syracuse on the island of Sicily, and he gave us all those formulas that kids memorized for the SATs, you know, like the area of a circle is pi R squared, where R is the radius, and pie is that an amazing number that we just celebrated a few weeks ago. So formulas like that are for the surface area of a sphere, the volume of a sphere, all of that is, it's taught in general. geometry class, but it's really beyond geometry, because geometry before Archimedes could not handle

smoothly curved shapes like circles and spheres as far as finding, as far as measuring them, finding their area or their circumference or their volume. You won't find the formula, say, the formula, pi R squared. That's not in Euclid's geometry. That had to wait for Archimedes and his incredibly ingenious use of infinity to find that formula. I'm Ira Flato. This is Science Friday. from WNYC Studios. And then it was adopted. Years later, it took, what, over a thousand years to come back? I put it closer to 2000 years.

Two millennia, as you call it in the book. It's really two millennia. I mean, if you ask, who's the person who was most ahead of his or her time, I think it would be hard to beat Archimedes. He had the ideas of calculus. Like I say, 250 BC, he was going strong. and then you don't really see it with the same level of virtuosity until Isaac Newton in the 1660s. So that's to have to do the subtraction here, but something like 1900 years.

And you write that one of Archimedes' letters actually brought a tear to your eye. Well, that could just be me, but... We'll talk about it after the break, because we've got to take a break. I don't want to let you get away. We're not talking about it. Okay, okay. We'll read a little bit from your book. Talking with Steven Stroggatz, a professor of mathematics,

at Cornell University, an author of Infinite Powers, how calculus reveals the secrets of the universe. As I say, we have an excerpt from the book, ScienceFriady.com slash calculus. We'll be back with more talk with Stevens, so stay with us after the break. This is Science Friday. I'm Ira Flato, talking with mathematics professor Stephen Strogett's,

and his new book, Infinite Powers. It's all about calculus, how calculus reveals the secrets of the universe. And as I said at the opening, if you had trouble with calculus like I did, this is an eye-opener. You will really like reading and following up because I have spent the rest of my life trying to figure out calculus. I think I've gotten there. Stephen, let's bring you back to Archimedes' letters. You write, there's a sense of loneliness in Archimedes. He writes, I can't do everything.

I'm going to die at some point. So I want future generations to know what I know. I just find this very beautiful. You feel like you're talking to him? Well, I do. And there's especially a poignant letter that he wrote to another mathematician named Eretocthenes, who was one of the few people in the world who could understand what Archimedes was doing.

Eratosthenes is someone we might have heard about in school as the person who figured out a way to measure the circumference of the earth, you know, that we now know to be around 24,000 miles. He figured that out. But so anyway, he was a really first-rate mathematician himself, and Archimedes sent him this letter describing a certain method that he had used to find the answers to these incredibly hard geometry problems that nobody had been able to do ever for, you know, for centuries. And as he describes the method, he does two things that kind of choke me up.

I have to admit, which is one, he admits that they're, it's like he exposes the soft underbelly of his method. He shares his private intuition. And most people in math are scared to do that. to show their soft side. But he shows eratosthenes that there are some things about his method that aren't completely rigorous. They might be a little unsound, but they give him the right answers. And then he goes on to say that he hopes that future generations will be able to use the method to find theorems that have not yet fallen to our share, which is a strange expression.

But I think what he's trying to say is there are things that I haven't figured out. The theorems haven't fallen to my share. I haven't gotten them. But maybe somebody somewhere in the future, you know, like sending a message in a bottle out into the vast oceans of time, somewhere in the future, someone will learn what I've done and they'll be able to solve these problems. And I just think, you know, here's this person who's one of the all-time great geniuses of the human race, and yet he feels the finiteness of his life against the infinitude of mathematics. Interesting. You mentioned about how calculus was sort of the roots of it were sort of lost for two millennia and then brought back in Europe.

But what was the key insight that Leibniz and Newton had that led to what we think of today as calculus? Well, so there's this big 2,000-year interlude where algebra is being developed in the Middle East, in Arabic countries, and, you know, in Baghdad and in Cairo. And eventually it makes its way back to Europe in the, say, around 1,200. 1300, and once you get algebra fusing with old-time classical geometry of the Greeks in the work of people like Fermat and Descartes, that's what really sets the stage for Newton and Leibniz then in the second half of the 1600s, where they're addressing old, still unsolved problems about curves, how to find tangent lines to curves and things like that that might not seem of much

practical interest. But still, they're of great interest in geometry, and Newton and Leibniz both figure out how to do that, not only finding tangent lines, but also areas under all kinds of exotic curves. And it all sounds a little bit pointless maybe until you realize that, as we do now, that you can draw a graph of any relationship between, let's say, you know, the level of virus in a person's blood who's suffering from HIV. You can draw that as a curve on a graph. And so you can take something as disembodied as a curve and use it to represent a life and death thing like the viral load in an HIV patient. And so with this enhanced understanding of how things change

through graphical representations of that on these graphs that we nowadays draw X versus Y, Newton begins to figure out the laws of the universe. We hear about Newton's laws of motion and laws of gravity, but ever since we've been drawing those same graphs and analyzing them using the techniques developed now 350 years ago. And let's get into that viral load, because you talk about how calculus was key to determining the drug regimen,

that cocktail of drugs that HIV patients must take. Absolutely. So, I mean, if we fast forward now to the 1980s, and we've got the AIDS epidemic, people are dying, there's no hope, it seems there's nothing to do to, certainly a cure is nowhere in sight, not even anything to make it a chronic illness. And it was a terrible epidemic, terrible plague, really. But once a new kind of drug became available called protease inhibitors in the 1990s, mathematicians working in collaboration with immunologists and doctors were able to figure out the answer to what had been a big mystery about HIV,

which was just to remind people, you know, what would happen is someone who get infected with the virus, they'd be sick for a little while, then they'd feel, you know, like they're kind of getting better. And then they really wouldn't show many symptoms for about 10 years. during that time, you know, was unclear what's going on is the virus lying dormant in the body, you know, hiding out the way chicken pox can do or what. So there was a question. Should you give the patients the available treatment as soon as possible after they're infected, the trouble with that idea being that they might become resistant to it,

and then you'd have nothing to help them once they really got full-blown AIDS, or should you not treat them until they do show AIDS and then try to hit them with the drugs? and so it all depended on whether you thought the virus was lying dormant in the body or not. And what Dr. David Ho, the clinician and Alan Perilsen, a mathematical immunologist, realized through the application of calculus to the data that David Ho was collecting with his collaborators, was that actually HIV was not hibernating during those 10 years in a patient's body. It was in an unbelievably pitched all-out raging battle with the person's immune system such that every day, about somewhere between a billion and 10 billion new virus particles were being produced by the virus and being cleared out by the body's immune system. And this is going on every second of every day for 10 years until the body eventually would get exhausted. And so then, you know, and then AIDS would sit in.

So the big insight was that if you gave one drug in the face of this very rapidly evolving virus, it wouldn't be enough. It would develop resistance. Two drugs also, the math showed, wouldn't be good enough. But three drugs would make it so difficult for HIV to do the three simultaneous mutations needed to escape the triple combination therapy that it would give patients hope. And of course, that has turned out to be true. So nowadays, HIV for people who can afford or have access to the treatment has become a chronic illness rather than a near certain death sentence. I don't think anybody ever heard that story before reading it in your book, you know? Well, if you're on the inside, people know.

I mean, those of us that do mathematical biology have revered Alan Perilsen for the work he did. And also another team did it. Martin Novak and his student, Sebastian Bonhofer, did it simultaneously. obviously. So it's out there, but, you know, it's been so overshadowed by the success of the clinicians. And maybe I should say, just to be very clear, I hope it's been clear already, but to really drill it in, calculus didn't solve HIV on its own, certainly. I mean, this was very much a team effort with doctors and immunologists, but it did play an important supporting role. Yeah, and you write through your book, how under the radar calculus flies.

in all different aspects of our life? Well, it does. I mean, it's interesting you use the word radar because that's a perfect example. You know, I mean, radar was key to the British being able to fend off the Nazis in World War II during the Battle of Britain. And radar was at that time a state-of-the-art technology.

The idea that you could beam these radio waves off of airplanes and then reinterpret the signals as they bounced back to figure out where the planes were and how far away they were, how fast they're moving and all that, that was an outgrowth of calculus from work on, you know, the ideas that led to radio and television and what today we're using as wireless communication for cell phones. All of that came out of work in the late 1800s by Maxwell, the great Scottish physicist who first put together the laws of electricity and magnetism in the form

of calculus equations that we call today Maxwell's differential equations. Those equations are predictions predicted that electricity and magnetism could propagate as invisible energy at the speed of light, and that's what radar is doing. And you also talk about the role of infinity in the success of calculus. It's one of your main thesis. It is, it is. That's why I call the book Infinite Powers, that infinity is this key concept that's very spooky for many people. I mean, my wife gets upset if I start talking about infinity. That gives me a headache. I don't want to hear about that. You know, when people start to talk. about bottomless pits and a lot of our worst nightmares are about infinity, but it's this interesting beast, you know, that if you can tame it, it's a tremendously powerful tool for making sense of hard problems by, as I say, chopping them into infinitely many tiny parts,

which they tend to, the tiny parts, I mean, to give you a visual of what I'm talking about, why infinity would be helpful, if you think about, say, something like a circle, which is round, obviously, but if you imagine looking at the edge of a circle, the rim, under a microscope, and start zooming in, what looked curve will start to look increasingly straight. And that's nice because straight things are easier than curved things. And so you can kind of think of a circle as almost being like a polygon, you know, in other words, like take a square, then a hexagon, then an octagon, more and more sides. As you take more and more sides and make each side smaller and smaller, it starts to look like a circle. And that idea that a circle, that a circle

is well approximated by something almost having infinitely many infinitesimal sides. That turned out to be the key to understanding circles and other curved objects. And you say that was one of the key reasons of how calculus got started was that the geometry people knew that you could easily take base and height and whatever uncalculate a rectangle or a square, but a circle is smooth. It's got waves, it's a circle. Can we take that same idea? and figure out how to work with curved objects?

It was a big insight. It's sort of a fantastic creative conception. I want to emphasize that point that people sometimes think of math as very black or white and cut and dried. But it takes tremendous creativity, like poetry, like music, like any kind of art, to see something that is smooth and curved and imagine it as being made up of lots of little flat, straight pieces. And today, that's a very practical idea because think of when your kids watch a movie like Shrek or Toy Story, and there are these animated characters running around on screen. When you see Shrek's big bulging belly or his little trumpety ears,

those are made up of millions of polygons. Computer animators use Archimedes' old idea of breaking curved things into lots of tiny, flat, jewel-like polygons. So it's absolutely practical. practical these ideas. We're using them all the time today. Amira Flater. This is Science Friday from WNYC Studios. Talking with Stephen Strogatz, author of Infinite Powers, how calculus reveals the secrets of the universe. And I actually think that Oscars have gone to those mathematicians who've created these polygons,

the ideas of smoothing out, you know, creating the animation figures. That's true. Right. There have been, you know, in the old days, they would use millions of polygons per movie. I think When the movie Avatar was made that was all completely computer generated, they were in the billions of polygons. Is there something about calculus that you don't know that you'd like to know more about? I mean, you write about everything in this book. Well, that's the question I was not expecting.

I mean, I'm stuck with that. I can't say no. I mean, of course, there are things in calculus. I don't know. And calculus has gone on. I should say, it's sort of like the gateway to all of modern math. You know, we've talked about its applications in the universe and in the real world, but for mathematicians, calculus is just the first step.

That's why it's a course we teach in freshman year to all of modern math. And so that includes subjects with names that sound like they're part of calculus, differential geometry, integral equations, analytic number theory. Those are all calculus words. And they all have to do with our now understanding that math is this giant way, of ideas all interconnected, rather than a lot of people think of math as a tower. You know, you have to build up and go higher and higher, but it's really not a tower. It's a web, and we now know that through calculus.

Now, I can't get away with that. I teased at the top of the program about the connection of this little band from Liverpool called the Beatles and calculus. Fill us in on that. Well, all right. So after x-rays were discovered, it was known at first. you could use x-rays to look for broken bones, or you could use them on teeth. So for hard structures in the body like bones and teeth, x-rays were great. But if you tried to look at a person's brain, like to look for a brain tumor or a hemorrhage or a blood clot,

x-rays were really no good because the brain would just look like a big cloudy mass, just gray nothingness. So when it was proposed in the 1960s by a couple of, there was one engineer who came up with the idea and one physicist, that maybe if instead of just shooting x-rays from a single direction, if you did many different directions of firing the x-rays and then use calculus to help you figure out how to recombine the information obtained from all those different directional shots, maybe you could see brain tumors, maybe you could see blood clots. And this is what we nowadays call cat scanning.

And the interesting thing about it in connection with the Beatles is that one of the first companies to take a leap on this wacky idea was a company called EMI, which was electric and music industries, or maybe it's electronic. Anyway, EMI in England had all this money lying around because they happened to sign the Beatles. And so they were flush with money, and they took a stab on this crazy idea of CAT scanning, which later won a Nobel Prize and revolutionized medicine. And we have the Beatle albums to thank for revolution. Thank you, Beatles, yes.

Thank you. Thank you. Thank you. Thank you. Thank you. You know, and as your book says, there's so many connections that calculus is connected to so many different things. And to me, as someone who loves the history of science, I love the applications of calculus because I learned that in college, and I really appreciated calculus like I couldn't before.

But the history that you have in the book, how far back thinking about calculus, going back to the Greeks, and then the hiatus who went through, I just love that of understanding how. how really, you know, people are involved in it, and the great figures you have, Descartes and all these other people in there. I want to thank you very much for taking time to write that book and for taking time to be with us today, Stephen. Well, thank you, Ira. I guess we're probably out of time, but I just want to inject one last point,

which is that there are several women in the story, too. We've only talked about men so far, but women mathematicians started to become recognized and important players by the 1800s, and so if you want to hear what half of humanity did to contribute to this. They're in there, too. Great point. Great point. I'm glad you brought it up. Stephen Struggatz, Professor of Mathematics of Cornell, author of Infinite Powers, Hell Calculus, Reveals, Reveals the Secrets of the Universe. Excerp on our website, ScienceFriiday.com slash calculus. Good luck with the book, Stephen.

Thank you, Ira. BJ Lehman, compose our theme music, and if you missed any part of the show, you want to hear it again, podcast, subscriptions, all kinds of stuff. And, you know, smart speaker will play the latest episode of our podcast, Ask it to play Science Friday, whatever you want. So every day now is Science Friday. Have a great weekend. Happy National Poetry Month.

I'm Ira Flato in New York.