Searching for Order in the Universe

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Original Air Date: 
August 08, 2020

When things don't go the way they're supposed to — viruses, star systems, presidents, even fish — we're often desperate to explain the chaos. In this episode, we search for order in the universe.


Eels are philosophically and scientifically slippery — they're still some of the most mysterious creatures on the planet. Journalist Patrik Svensson has been obsessed with them, and wound up writing a surprise bestseller — “The Book of Eels.”


Lulu Miller's book “Why Fish Don’t Exist” — which examines ichthyologist David Starr Jordan — is a meditation on the shadow side of scientific classification, and the dangers of trying too hard to impose order on chaos.


Putting aside the question of whether there's any validity to it, the ancient science of astrology has a lot in common with contemporary data science. In fact, data scientist Alexander Boxer calls astrology humanity’s very first set of algorithms.

Math of the universe

For centuries, people have considered mathematics the purest form of knowledge — and our best bet for deciphering the universe's hidden order. Steve spoke with two people who love math: physicist James Gates and science writer Margaret Wertheim.

Show Details 📻
August 08, 2020
April 24, 2021
January 22, 2022
January 28, 2023
January 27, 2024
Full Transcript 📄

Anne Strainchamps (00:00):

It's To The Best of Our Knowledge. I'm Anne Strainchamps.

New Speaker (00:23):

Sometimes the most profound questions come out of the simplest experiences.

Patrik Svensson (00:33):

I have very strong memories from my childhood: fishing for eels with my father.

Anne Strainchamps (00:41):

This is Patrik Svensson.

Patrik Svensson (00:45):

I think I started when I was six or seven years old. It was always just me and my father down by a small stream close to where my father grew up on a farm. We went fishing for eels on a summer night. It was a very special place. A lot of green grass, willow trees, the bats flying through the moonlight. It was what me and my father did. We fished for eels. It was something that combined us.

Patrik Svensson (01:37):

I would always watch my mother prepare the eels. She chopped them up and she put salt and pepper on them and then she fried them with butter in the pan. When she put them in the pan, they started moving. Those small pieces of eel started to wriggle and shake. I always found it fascinating and a bit scary, too. It made me think about what's really the difference between life and death. Where is the exact border between? It's the mystery, of course.

Anne Strainchamps (02:35):

Eels are philosophically and scientifically slippery. They're fish that can survive for several hours on land, that can live for 85 years, that don't have sex until the last year of their life. Even after centuries of study, eels are still some of the most mysterious creatures on the planet. Journalist Patrik Svensson has been obsessed with them for a long time and he wound up writing a surprise international best seller: The Book of Eels. Steve Paulson reached him at his home in Malmo, Sweden.

Patrik Svensson (03:17):

People, for many, many hundreds of years, have trying to understand the eel. It's become such a big issue in natural science that the term, the eel question, was a question that was especially hard mystery to solve. The eel question has been different things over the years. From the beginning it was, "What is the eel? Is it a fish? Or something else?" Then it has a lot to do with sexuality of the fish. Does it have sexual differences? Are there males and females?

Steve Paulson (03:57):

Isn't part of the mystery that for centuries no one could actually find the sexual organs?

Patrik Svensson (04:03):


Steve Paulson (04:03):

They couldn't tell whether there was a male eel or a female eel.

Patrik Svensson (04:07):

No human being has ever seen eels breed. To explain how they do it was an extremely hard question.

Steve Paulson (04:17):

Wait. To this day no person has ever seen eels mate?

Patrik Svensson (04:22):

Exactly. No one has ever seen it because all eels breed in the Sargasso Sea and only there. They won't breed in an aquarium or in confinement, but only the Sargasso Sea. No one has ever seen it happen.

Steve Paulson (04:39):

Just so I understand this, you're saying that the eels that we might see in a river or a pond in America, or in Europe, all of those come from the Sargasso Sea?

Patrik Svensson (04:50):

Exactly. It's both the American eel and the European eel. That's two different species but they are very much alike and both of them breed in the Sargasso Sea and only there.

Steve Paulson (05:00):

I know this controversy about where eels come from goes way back. Aristotle had this crazy idea that somehow they were born out of mud.

Patrik Svensson (05:11):

Yes. He studied the eel and he was trying to explain how do they breed, but he couldn't find any sexual organs. There's an explanation for that. The eel doesn't evolve their sexual organs until they're on the way to the Sargasso Sea in just the last year of its life.

Steve Paulson (05:32):

You're saying that some eels live more than half a century. They might've lived 50 years before they develop sexual organs.

Patrik Svensson (05:40):

Yes, exactly. That's why people like Aristotle studied the eel, dissecting them, trying to find the sexual organs. Didn't find any, of course, and came to the conclusion that eels don't breed at all. He thought that the eel just came to life out of nothing from the mud in the rivers and the seas.

Steve Paulson (06:04):

The young Sigmund Freud spent his summer trying to crack the eel mystery. Wasn't he hunting for some evidence of testicles?

Patrik Svensson (06:15):

Yes, and that's an amazing story I think, and it's quite a funny story if you see it that way. Sigmund Freud, he was 19 years old and he was studying natural science. He wanted to solve the eel question. At that time... this is in the 1870s... they had found an eel with eggs inside: a female eel with eggs. So to solve the eel question, they had to find a male eel with testicles. So Sigmund Freud, he went to [inaudible 00:06:46] to find the eel testicle. That was like the holy grail of natural science at the time. Every morning he went out to the harbor and picked up a big basket of freshly caught eels and then he went to his lab and he cut eels open for a whole day looking for the eel testicle. Of course he didn't find one. Not one testicle did he find. I think it's very funny to at least think about. This is the man who laid the basis for the modern psychological therapy and the man who developed the theories about penis envy and castration [crosstalk 00:07:30].

Steve Paulson (07:30):

Sexual impression, yeah.

Patrik Svensson (07:32):

Yeah. He started his scientific career with trying to explain the sexuality of a fish, and he failed.

Steve Paulson (07:40):

We should talk some about the basic mystery of the eel, because people have eventually found out that they go through these four completely different life stages. Can you tell us what these different stages are?

Patrik Svensson (07:53):

Yes. They're born in the Sargasso Sea as a small larva. They have the shape as a willow leaf and it's drifting with the ocean current. The European eel is bound to Europe and the American eel to the west. When they reach land they develop into what we call the glass eel. They have the same shape as an eel but they are totally transparent. When they find their way up in the rivers and streams, they go through their... another metamorphosis and they became yellow eel. Then they live for a very long time as a yellow eels in fresh water: up to 85 years.

Patrik Svensson (08:44):

Around 15 to 30 years, they suddenly leave the fresh water, swim out in the ocean again, and return to the Sargasso Sea. At the same time, they transform again and become what we call the silver eel. This is a very strange creature. They stop eating completely, for the whole travel back to the Sargasso Sea. This can take over a year. Instead, they develop their sexual organs. Their eyes change. The way they swim change. All they do is swim to the Sargasso Sea: to the place where they once came from.

Steve Paulson (09:22):

We've talked about some of the scientists who were obsessed with the eel question, and there was one in particular, a Danish scientist, who actually kind of cracked the mystery: a guy named Johannes Schmidt, who spent years and years studying eels trying to figure this out. Tell me about him. What did he do?

Patrik Svensson (09:40):

This was in the beginning of the 20th century. This Johannes Schmidt, he went out in the ocean with a boat and he was going to find the birthplace of the eel. And he had a method and that method was to catch this small larvas of the eel and measurement. The place where they were the tiniest, then therefore newly hatched, that has to be the birthplace. The problem, of course, is that these eel larva is very small and the Atlantic Ocean is very, very big. You know, the first World War broke out. It was very dangerous to sail around looking for eel larvas on the Atlantic Ocean, but he just kept on going. Actually, he sailed around the Atlantic for 18 years before he found the larva that was newly hatched and he could say that this is the place: "This is where the eel breeds." That was the Sargasso Sea.

Patrik Svensson (10:39):

That says something also about science but also something about this human urge to understand. What makes a man sail around the Atlantic Ocean for 18 years looking for eel larva, just to know where the eel is born? There wasn't any prestige in it. There was no money in it. It was just this curiosity. He had to find out.

Steve Paulson (11:06):

Right. And there's still so much that we don't know. I'm still trying to wrap my head around how time figures in the life cycle of the eel. They might be in a European or an American pond for 50 years, then something triggers them and they think, "Okay, time to go back to the Sargasso Sea and to reproduce." It's a very fluid sense of time, all of this.

Patrik Svensson (11:32):

You know, if the eel can't travel back to the Sargasso Sea it also never goes through the last metamorphosis and it doesn't become sexually mature and it doesn't become a silver eel. Then it seems like it can live almost forever in that stage. In a way, it's like the eel can put a stop to its own aging, and some eels travel back to the Sargasso Sea after just five, six, or seven years. Some eels travel back to the Sargasso Sea when they are 60 years old.

Steve Paulson (12:08):

It kind of raises the question of what home is.

Patrik Svensson (12:11):


Steve Paulson (12:12):

Is home where you originally came from? Or is home where you are living for 50 years?

Patrik Svensson (12:17):

Exactly. There's a famous eel in Sweden. It's an eel that lived in a well on a small farm in Sweden. According to the story, it was a boy that catched the eels in the 1850s and put it in the well, and there it stayed. They actually... Just a couple of years ago, a TV team went to this well and they found the eel. It was very small but it had enormous eyes.

Steve Paulson (12:50):

Was it still living?

Patrik Svensson (12:51):

It was still living. If the story's true, it has lived for over 150 years in complete darkness alone in a well. You have to imagine that life. You have to imagine what that really feels like. Of course, the eel doesn't feel time like we do. It doesn't count seconds and minutes. But there has to be some experience of that.

Anne Strainchamps (13:17):

That's Patrik Svensson talking with Steve Paulson from his home in Malmo, Sweden, about The Book of Eels. It won his country's top literary award. Their full length conversation ran in Nautilus Magazine and you can read it on our website at I'm Anne Strainchamps. It's To The Best of Our Knowledge from Wisconsin Public Radio and PRX.

Anne Strainchamps (14:00):

A lot of science is driven by the search for some kind of underlying order in the laws of universe or the patterns of the stars or even in fish, and people can be remarkably persistent about trying to find it. Take the case of David Starr Jordan, the first president of Stanford University and the foremost ichthyologist of his time. He was credited with discovering nearly a fifth of the fish known to humans. And then, on Wednesday, April 18, 1906, at 5:12 AM the San Francisco Earthquake struck. Much of the city was destroyed including Jordan's vast collection of fish specimens.

Speaker 5 (15:16):

"Imagine seeing 30 years of your life undone in one instant. Imagine whatever it is you do all day, whatever it is you care about, whatever you foolishly pick and prod at each day hoping against all signs that suggest otherwise that it matters... Imagine finding all the progress you have made on that endeavor smashed and eviscerated at your feet. Those words go here. Fish were everywhere. Glass was strewn all over the floor, flounders bashed further flat by fallen stone, eels severed by shelves, blowfish popped by shards of glass. There was a pungent smell of ethanol and corpse. But far worse than any of the carnal damage was the existential. For many of those specimens left in tact, hundreds of them, nearly a thousand, their precious name tags had scattered all over the laboratory floor. In those 47 seconds, Genesis had been reversed. His meticulously named fish had become a confusion of unknown again."

Anne Strainchamps (16:32):

Lulu Miller tells this story in her book, Why Fish Don't Exist. It's a meditation on the shadow side of scientific classification and on the dangers of trying too hard to impose order on chaos. Lulu's the former host of the NPR podcast Invisiblia and she knows a great character when she meets one. David Starr Jordan was irresistible: a brilliant scientist able to bounce back even after an earthquake destroyed his life's work. But he was also a man so obsessed with categorization and natural hierarchy that he became a proselytizer for eugenics and the, quote unquote, cleansing of the gene pool. Shannon Henry Kleiber asked Lulu what first captivated her about him and the answer, a visit to a San Francisco museum.

Lulu Miller (17:23):

The tour guide just kind of off-handedly told the story. He pulled out... it was actually... a hammerhead shark. He pulled it out of the tanks where it was being stored and there was a labeled tied to its eye tube, sown through the skin, and there was a label with its species name there. He told us the story about how the 1906 earthquake in San Francisco destroyed a whole lot of the fish collector and that the curator in charge of things afterwards invented this technique of tying labels directly to the specimen. It was a small but I remember standing there thinking, "That's so human that an earthquake would wreck your order and scatter the names everywhere and your response would be, 'I'm going to invent a way to get back at you, chaos.'" In that moment it just struck me as the silliest thing, to believe that you could outsmart all of chaos itself.

Shannon Henry Kleiber (18:22):

Wow. That earthquake, the 1906 San Francisco earthquake, 3,000 people were killed. It was 7.9 on the Richter scale. What was gained and lost that day for David Starr Jordan?

Lulu Miller (18:34):

That's a really interesting way to ask it: what was gained and lost. What was lost were decades of work and meticulous ordering. There were possibly even species that were lost to science because there were a few in there that hadn't yet been identified. But I think what was gained was shortly thereafter he was so desperate to keep going and fight back against the chaos that kept invading his life that he invented this new technique of sowing a specimen label directly to the creature itself. I think in a weird way any time this guy is hit with tragedy or destruction it's almost always a moment of innovation.

Shannon Henry Kleiber (19:19):

You had pinned an idea on him: an idea of hope and inspiration. And then you got to know him better, as people do when you research. You're a biographer and a reporter and a detective, really in a lot of ways, in his story. Did he fulfill this idea of hope for you? Or did he teach you something different?

Lulu Miller (19:41):

He's so complicated. In certain ways he did. He showed me a very different way to react to the sense that as a human your chances are pretty doomed. He kind of showed me that blind confidence really can get you results. I think I went into it thinking that hubris, as the Greeks instruct, as my dad kind of instructed me growing up, was always dangerous and would ultimately lead to humiliation. I think he shows the real potential, for better or for worse, that hubris can do you some concrete good. But there was also... turned out to be a profoundly set of troubling things about him. There was some pretty intense [bothness 00:20:28] in there. Is that too vague? Is that okay?

Shannon Henry Kleiber (20:31):

No, I can totally picture you in these manuscript rooms and reading these books that you find... The Philosophy of Despair black book that you describe so well... and all these different documents and letters and thinking, "I understand him. I'm seeing this." And then there's a discovery and it's beautiful in some ways, and then there's another discovery and you're disappointed and I felt bad for you.

Lulu Miller (20:53):

Yeah. It's what made it fun, though, because it's history. This guy is dead. But he was so vibrant. He was like this muscly snake that just kept moving in my hands. And he's full of charm. In certain ways, studying him actually felt really similar to making a radio piece where you have a ton of tape and then you're whittling it down to these gems where someone's really funny or emotional or dark. He's vibrant. He is the full spectrum. He's charm, he's hilarious, he's dark, real dark. He's an incredible character. He is hero and villain all in one.

Shannon Henry Kleiber (21:30):

So what was the most surprising thing to you?

Lulu Miller (21:35):

I think for me, hands down, it was... His life becomes intertwined with the eugenics movement and going into this I had no idea about our country's role in the eugenics movements. I remember those early days of researching it and learning about just how we were a main player in the eugenics movement. This thing we ultimately come to define our national identity in opposition to, we were actually crucial to getting the eugenics movement going.

Shannon Henry Kleiber (22:08):

The story you're writing about, the historical part, is very messy and unexpected and surprising and not easily tied up. And then you go into your story, which is also... like so many of us... messy and not easily explained. It matches in a way.

Lulu Miller (22:23):

Yeah, it does. I've always had almost like a parable-shaped hole in my heart, growing up with a very atheist father and then both of my parents were professors, so ambiguity really reigned in our home. Like, nothing means anything, or if it means something it could many things. There was just no moral instruction and I think I've always had, actually, a craving for more. I think a lot of people grow up with moral instruction they come to find messed up and then they want more ambiguity, but I'm one of these weirdos who actually wants more dogma. I don't know why I turned out this way, but I do, and that's part of what has always drawn me to storytelling. But as I've slowly, clumsily, tried to become a better reporter and learned the art of reporting and realizing that story can actually be very dangerous in reporting, the sense of story, a clear moral, I have tried to ignore my cravings for moral clarity and black and white and really study the bothness.

Shannon Henry Kleiber (23:27):

The way you brings things up, these different stories and characters, it is about curiosity and you kind of go these different directions. Did it make you more curious as you worked on this?

Lulu Miller (23:40):

Yeah, it totally did. The world as we know it is far less known than we think it is. It's so easy to think that we have a handle of everything now, that science knows, that we have it all mostly figured out. Maybe there's one new little bacteria that will be discovered but basically we've got it down and how it works, and we're so far from that. We're so deep, at all times, in the midst of these revolutions and paradigms shifts and we're not done. We haven't arrived anywhere. We're at a clumsy, approximate, best guest of our understanding of the world and there is so much more waiting in the wings.

Shannon Henry Kleiber (24:20):

Even just the title, Why Fish Don't Exist... We think, "Fish. I know what a fish is." But what does the title mean? Fish don't exist, it turns out.

Lulu Miller (24:30):

I have a question for you. After reading it, do you think fish exist? Answer honestly.

Shannon Henry Kleiber (24:39):

I think fish exist in a way that might not be the way we thought they did.

Lulu Miller (24:46):

Yeah. I like that. To me, it is an example that just intersected with David's story in a really cool way because he was a fish collector, an ichthyologist, a person who studied the supposedly existent creature of fish. There has been a profound revolution in scientific circles of people who think about how to classify animals that pretty convincingly calls into question the existence of fish as a kind of creature. It challenges the category of fish. Maybe that just sounds fussy, sematic distinction. "Who cares if your day job isn't a taxonomist?" But for me, when you really think about what that means, and if you can do the mental scrunching required to let the category go, then some pretty profound things open up.

Anne Strainchamps (25:46):

Lulu Miller is the former host of the NPR podcast Invisiblia and she was talking with Shannon Henry Kleiber about her new book, Why Fish Don't Exist.

Anne Strainchamps (26:01):

That urge to look for some kind of order in the midst of chaos and uncertainty, the belief that there might be a code hidden in the tree of life or the movement of the stars, that's been with us for a long time and still is. Let me put it this way; do you ever check your horoscope? And putting aside the question of whether there's any validity to it, the ancient science of astrology actually has a lot in common with contemporary data science. In fact, data scientist Alexander Boxer calls astrology humanity's very first set of algorithms. He makes the case in his book, A Scheme of Heaven: The History of Astrology and the Search for Our Destiny in Data.

Anne Strainchamps (26:49):

So Alexander, you are a data scientist. I love the way you describe astrology. You call it storytelling with numerical data, which is something we're still doing. That just really hit home thing about astrologers as maybe the world's first data scientists.

Alexander Boxer (27:07):

So, like all my science colleagues, I don't believe in astrology. I guess I'll put that out just right on the table at the beginning, but I'm curious about it. Science builds from one generation to the other. I thought astrology is just this fascinating topic to try to tease apart the question of how do we know what we know. I really wanted to look at these really interesting questions that astrology asks and put aside my biases and say, "Can we explore this the best we can using modern methods and modern techniques and really situate it and fill a hole in the history of science?"

Anne Strainchamps (27:40):

I'm just trying to imagine what would happen if you gave a talk at Google. Imagine telling a room full of data scientists that they're standing on the shoulders of ancient astrologers.

Alexander Boxer (27:52):

Much of this is, again, motivated by... You look at the apps. You look at what people are doing with data today. All of a sudden we are very seriously asking our algorithms to predict and tell us things about ourselves that previously people would've thought crazy and the only people who ever would've dreamed of asking these questions, these very personal questions, about what sort of person am I going to be, what sort of job am I suited for, who am I going to vote for, what are my food preferences... I think there's a bigger question that astrology rubs up against, which is that in the ancient world people were very interested in numbers and they were interested in a strict hierarchy of the sciences and how you know what you know. The role of mathematics and science was something that people thought a lot about in particular because numbers were these pure and eternal entities, but the idea that they could be used to describe in a meaningful way the physical world, which is full of change and full of corruption and decay, was something that ancient thinkers were very careful about, and astrologers never were. Astrologers always represented this very optimistic sense that, "Let's just make algorithms to describe these things as best we can."

Anne Strainchamps (29:00):

There's some photographs in your book of ancient objects that are in the British Museum, including some Assyrian tablets... there's some from like 650 BC... that seem to show at least there are some astrological records or forecasts.

Alexander Boxer (29:17):

Yes. The Babylonians were taking nightly records of the positions of the planets going back to about the year 700 BC. It lasted for many hundreds of years. It's probably the longest continually running scientific research program ever undertaken, and these are the records that end up filtering through the Greek world in order to make the theories of the heavens that come down to us and came down to the scientific revolution.

Anne Strainchamps (29:44):

So those early astrologers, the Babylonians, they weren't charting people's sun signs or anything, but they were making some predictions.

Alexander Boxer (29:54):

They were interested in the ups and downs of kingdoms and politics. In particular, they're looking at eclipses, and eclipses could be bad news depending on where you saw them in the sky. In fact, there's a very famous lunar eclipse that is observed shortly before Alexander completes his conquest of Persia and takes Babylon.

Anne Strainchamps (30:16):

You mean they actually predicted Alexander the Great's victory?

Alexander Boxer (30:20):

I do not mean to suggest that they do, however, there's a fun tablet that actually talks about a lunar eclipse that would be seen in that specific month. It gives a vague and ominous warning that "You need to be wary of the intruders from the west," and the original tablet and Alexander's victory are separated by about 300 years. It's a fun thing of astrology where with a vague enough prediction and enough of them you get to pick and choose and scratch your head and say, "Isn't that extraordinary."

Anne Strainchamps (30:50):

The one thing most of us know about astrology is our sun sign. Actually, what's yours?

Alexander Boxer (30:59):

I'm a Taurus, although if I wish I could be... I'm technically a Taurus-Gemini cusp. I have even more personality traits I can pick and choose from.

Anne Strainchamps (31:07):

I am pure Gemini all the way and every description of Gemini always fits me.

Alexander Boxer (31:14):

I think that was another question I was interested in, is, "How far back do these traits go?" It's actually in Roman times where you find the first descriptions of these traits. I'd say they're much more specific than they are today. Also, astrology back then was much more complex. Previously, to make a horoscope, you really needed to know the precise minute, if not hour, of somebody's birth and their locations. And you would plot where the planets were in according to the, what are called, houses of heaven, which are sort of different sectors of the sky. It made an ancient horoscope much more sophisticated and much more complicated.

Alexander Boxer (31:53):

It also made me wonder, "Why just think of yourself as one of 12? How unique would an ancient horoscope be?" I came up with the number. It's something... About 45 million is really, I think an ancient term, how many possible birth horoscopes there could be.

Anne Strainchamps (32:10):

You're saying if you put in all the possible dates and all the possible times and zodiac signs and then you calculated how many possible different horoscopes could there be, there are only 45 million?

Alexander Boxer (32:22):

Right, which seems like a lot, but of course if you consider that there are seven billion people on the planet obviously not everyone can get their own unique horoscope, but you can see why you could never print, let's say, predictions for 45 million different horoscopes in a newspaper.

Anne Strainchamps (32:36):

You actually have an astrological twin, am I right?

Alexander Boxer (32:40):

One of my good friends... and we didn't meet until high school, but it turned out that we were born in the exact same city, exact same day, in the exact same hospital within eight minutes of each other. Of course, yes, in many ways our lives have been very similar but...

Anne Strainchamps (32:58):

Really? Are you similar?

Alexander Boxer (32:59):

We are very similar. We didn't meet until high school. We both then went on to study physics and we've both been involved in math and science outreach over the years. And then what was crazy is that friend proceeded me in writing a popular science book and she wrote that a couple of years before I wrote this book, so now we're both published authors. But at the end of the day [crosstalk 00:33:20].

Anne Strainchamps (33:20):

Wait, are you just going to dismiss all of this as coincidence? Or do you think in fact...

Alexander Boxer (33:24):

I am going to dismiss it as coincidence not because I'm not curious about it, but what can you... From a numbers point of view, what can you really say about two people? In fact, if you asked me, I could give you an even longer list of all the ways our lives have been very different. I think astrology, maybe in its best sense, kind of gets us to think about our connections to the wider universe and maybe how special each moment is. So here's, I thought, a really fun way to think about how unique... At given moment, where the planets are and their relations to each other and their relations to how we see them on the Earth are quite unique and do not repeat ever exactly, but at least viewed in this way it takes a very long time for these things to cycle through.

Anne Strainchamps (34:15):

That's data scientist Alexander Boxer. His book is called A Scheme of Heaven: The History of Astrology and the Search for Our Destiny in Data.

Anne Strainchamps (34:28):

All of this makes me wonder, is thinking mathematically encoded in our DNA?

James Gates Jr. (34:34):

Humans, I believe, are actually intrinsically mathematical. Here I'll relate a personal family story. My son started spontaneously adding at two and a half years old. It wasn't anything that we had taught him to do, it was just sort of he hung around and... He was actually playing with ducks in a tub at the time. He demonstrated to me that you take two ducks and throw them in the tub and you have two ducks. You take two more ducks and put them in front of dad's face, say, "Two ducks." And dad says, "Yes, two ducks." And he throws those two in. Then he says, "Four all ducks." It's clear that addition is going on here.

James Gates Jr. (35:06):

We as a civilization, in my opinion, do not celebrate that kind of activity in young people. Even before they get to school you can do this very simple thing. We actually threw him a party.

Anne Strainchamps (35:20):

How to think like a mathematician, next. I'm Anne Strainchamps. It's To The Best of Our Knowledge from Wisconsin Public Radio and PRX.

Anne Strainchamps (35:36):

For centuries, people have considered mathematics the purest form of knowledge and our best bet for deciphering the hidden order of the universe. Some of the earliest mathematicians, the Pythagoreans in ancient Greece, even started a religion based on numbers. Do we really live in a mathematical universe? Steve Paulson has been doing a series of conversations at the New York Academy of Sciences about the nature of reality. In one of many mind-bending evenings, he talked with two people who love math: physicist James Gates and science writer Margaret Wertheim.

Steve Paulson (36:12):

I know each of you has a deep affinity for mathematics. It seems to be personal. I want to dig into that. Jim, let me start with you. Why is mathematics such an interesting way to see the world?

James Gates Jr. (36:25):

It appears that among all the languages that humans have ever developed, this is the only one that is sufficient to the task of describing what you call reality because for a scientist when we talk about reality we mean taking our experience of observing and then asking, "Are there things out there that do not depend on our emotional state?" I think that's the most fundamental definition of objective reality that a scientist can give you.

Steve Paulson (36:52):

You want to divorce it from the personal.

James Gates Jr. (36:54):

It's like going into people's homes and asking, "How does the house work when they're not at home?" That's what science is all about.

Steve Paulson (37:03):

Margaret, let me turn to you. Why mathematics? Why are you so obsessed with mathematics?

Margaret Wertheim (37:08):

Werner Herzog has something very interesting to say that I think is pertinent here. I know Werner quite well and he likes to say, "There are two kinds of truth. There's the account's truth and there's the ecstatic truth." Werner, of course on the ecstatic truth, and I think mathematics is on the side of ecstatic truth. Particularly, modern mathematics is really an ecstatic exercise. It's like some sort of brilliant dream. I think of mathematics as being the language of pattern and form.

Steve Paulson (37:40):

I'm curious about how far this goes back for each you: your fascination with mathematics. Can you remember back to your childhood? Was there a moment when it suddenly hit you: "This stuff is really interesting"?

James Gates Jr. (37:52):

In my case it actually goes back to before I was born because it turns out that my grandfather could neither read nor write but he could do arithmetic. My father never finished high school but I remember as a child watching him study trigonometry and some calculus. Mathematics is kind of the family business for me and my kids. I have two twins that are STEM people.

James Gates Jr. (38:16):

But the time when it sort of personally dawned on me that mathematics was something rather extraordinary was when I was 15. When I was four I decided I was going to be a scientist, so I'm 11 years into this process by the time I'm 15 years old. One day my physics teacher performed an experiment. The thing that you have to understand is for me mathematics was always an element of my imagination. It was like reading science fiction or going to the movies. To me, mathematics existed inside of my head and I was peculiarly aware of that. But one day in a physics class my physics teacher showed me an experiment. You just roll a ball down an inclined plane and you measure the distance versus the time, and you can write an equation which describes that. That's the closest and only thing I have seen in life that looks like magic. It's like we're all at Hogwarts, right? You learn to conjure. The conjuring is with the tools of mathematics, not with the tools of Latin as you would see in a Harry Potter movie. This actually burst upon my consciousness, 15 or 16 years old, and I've never recovered.

Steve Paulson (39:28):

Margaret, I'm wondering how much this resonates with you and going back to your childhood. Was math a part of your imagination?

Margaret Wertheim (39:36):

I was very lucky in that in primary school I had a couple of teachers who were very, very good math teachers. Mr. Marshal gave us a lesson about circles and instead of just telling us about pi and saying, "The circumference of a circle is 2PiR," he had us drawing circles on graph paper and measuring the diameter verus the circumference. The idea was that we were to discover pi for ourselves. I spent night drawing circles on graph paper and I realized there was this very special number that determined this relationship and I had this sort of blinding revelation. I remember the world lit up and it was like, "Oh my god, there's this thing called pi and it's in the heart of... Every time I see a circle in the hubcap of a car, in the pearls my mother wore, in the shape of the sun of the moon," and there was this magical number. Ever since then I've been obsessed with what is the meaning of the mathematical relationships that we find in nature.

Steve Paulson (40:44):

I'm fascinated by this because I do not think in mathematics like either of you do. I'm sort of trying to put myself into your minds. Do you think about different kinds of things? Do you sort of order the world in a different way? Jim?

James Gates Jr. (41:00):

It's a bit like you're asking me, "How would you see the world if I was blind?" I can't do that. For people like me, mathematics is intimately part of who we are even down to the emotional level. It's not just an engagement at the rational level where it's a useful tool for balancing checkbooks, say. But when you engage math at this level, what you find is it is as beautiful as any form of art that humanity has ever constructed. In fact, for me, it is indistinguishable from art at some level. But it has this other useful property: it allows me to build apps. It's the only form of art that I know that does that.

Steve Paulson (41:45):

One of the questions we're trying to get at here is... Mathematics, these elegant formulas, is that ultimate reality? Is that sort of as deep as it goes? Jim, I sort of get the sense that you think yes, that is the deepest kind of reality.

James Gates Jr. (42:01):


Steve Paulson (42:01):

No. Okay.

James Gates Jr. (42:04):

And I'm not being a contrarian, but literally no. It's not necessarily the case that mathematics is the ultimate expression of reality. It may be the case that it is the ultimate expression of reality that humans can understand. I believe that any rational being observing the universe will be driven to a mathematics that will be universally recognizable, but as to whether mathematics is reality itself? That's a bridge too far for me to take.

Steve Paulson (42:32):

There's an aesthetic dimension to all of these questions as well. A lot of people have talked about the beauty of math, the beauty of the laws of nature. I'm wondering how far we can take that. Particularly, I'm interested in your take, Margaret, because you work in art.

Margaret Wertheim (42:49):

Yes. I do some projects at the intersection of mathematics and art. Personally, I find mathematics extremely beautiful, but beauty is a very multi-[inaudible 00:43:01] concept. At least when we talk about mathematics in the world, which a lot of physicists talk about, they seem to automatically now equate the concept of beauty with symmetry. Symmetry has become a kind of obsession, a beautiful obsession, but modern physics and mathematics. I do my art projects with my twin sister who, after high school, I went to university and studied physics and math, she went to art school. She's really into math and science but sometimes I show her things that I think are really beautiful, incredibly super-symmetric things about mathematics, and she just looks at them and says, "That's boring." So the notion that beauty is universal, which is something that keeps being uttered in physics books, is just nonsense.

James Gates Jr. (43:50):

The kind of beauty that people like me find in mathematics... There's a story I like to tell people to try to pass along an understanding of what we're dealing with. It goes as follows. Imagine a planet on which there's no sound at all, but there are beings of our ability that occupy this planet. You can imagine a small group of them learning how to score music, because after all on our planet we not only listen to music, we have musical scores. On this planet let's imagine that's the only way that music exists, but on our planet we also know that people who score music will tell you that they can, in their mind's ear, hear the composition. So what would forbid these aliens who know how to score from experiencing that way to access music? That small group would talk about the beauty of this symbolic representation system. That's kind of what happens to those of us who engage in mathematics.

Margaret Wertheim (44:54):

I'm so thrilled that you've brought up this planet of aliens who can't hear but can only relate to music as a score, Jim. I think you're right: that music is a fantastic parallel for thinking about mathematics in the world because if you think about music you can write down music and score it but most musicians throughout history did not write down scores. There have been plenty of great musicians who didn't read music: people like Jimi Hendrix and apparently Michael Jackson said he didn't read music. But yet, they do it. I want to make this claim about mathematics that you can learn mathematics symbolically, like you and I did, at university by studying equations and textbooks, but you can also learn a lot of mathematics by doing it.

Margaret Wertheim (45:47):

But this actually has really wider philosophical consequences, because I believe that what this means is that when we find mathematics incarnated in the material world... like, say, coral reefs, which coral organisms embody non-euclidean hyperbolic geometry. I want to make the claim that the corals and the sea slugs actually are doing non-euclidean geometry and that constitutes a form of knowing. I want to ask the question, does a sea slug or a coral, which are completely non-conscious beings, do they know hyperbolic geometry? And I want to say, "Yes, they do."

James Gates Jr. (46:30):

I often like to say dogs were the first one to learn how to learn Newton's second law. Why?

Margaret Wertheim (46:37):

Because they can catch.

James Gates Jr. (46:38):

Because they can catch, exactly. Seriously. You go to the park and there are lots of smart dogs out there. The owners are tossing sticks and balls and they're catching. At some level that's the doing of mathematics. You don't have to go to sea slugs. However, something new has been added to the human experience. It's called a computer. I like to think of a computer as an instrument on which math is played. I think those of us who are scientists are kind of stuck in a rut and I also think that mathematicians are stuck in rut because I think that computers are going to powerfully impact the way humans interact with mathematics in the future.

James Gates Jr. (47:14):

Let me relay a story. Some years ago I was in a meeting with Eric [Schmidt 00:47:18] and he looked over at me and he said, "Jim, in maybe 20 years or so Google will be able to have artificial intelligence that do what you do." My response, "Not unless the artificial intelligence can dream," because the...

Margaret Wertheim (47:37):

Do androids dream of electric sheep?

James Gates Jr. (47:39):

Exactly. Do androids dream of electric sheep? A question that has been asked in science fiction for several decades, right?

Steve Paulson (47:45):

So why do you need that capacity to tap into your unconscious to be able to do what you do?

James Gates Jr. (47:52):

I have, in physics, what I call my hero maximus. His name is Albert Einstein. Once he made this very interesting statement that puzzled me for decades. The statement was, "Imagination is more important than knowledge." For me, this was a puzzlement because imagination meant for me reading comic books, going to the movies and watching space adventures. Knowledge was how we got to the moon. I was born in 1950, so I watched the space age, the race to the moon. So how could it be that this frivolous activity was more important than the technology that ultimately provides a level of comfort for our species that's greater than has ever existed in our history? How could the play be more important?

James Gates Jr. (48:40):

After several decades... and I literally mean decades of thinking about this... I came to the following conclusion. Knowledge is like a finite ball and it has an edge beyond which we don't know the answers. This is true now. Come back in, say, 15 years from now. That ball will be bigger. How did it get there? How do you get this new, larger ball? The only thing that I've concluded is right at the edge, where you're trying to get it to grow, we make up answers. We literally make up answers and that is part of the creative process just like writing a story.

Steve Paulson (49:15):

And you're saying computers will never be able to do that?

James Gates Jr. (49:17):

I have difficulty understanding how they're going to be able to do it, but if Eric was right then I'm replaceable.

Margaret Wertheim (49:27):

Do you know how that's... I love your story about the ball getting bigger, Jim. You know Einsteins famous quote, "Imagination is more important than knowledge"? Most people don't know how it goes on. It goes, "Imagination is more important than knowledge. Knowledge is finite. Imagination encircles the world," which is...

James Gates Jr. (49:45):

It's imagination that's driving the growth of that ball, which supports our increased technology. That's why he got it right.

Anne Strainchamps (50:01):

Margaret Wertheim and Jim Gates talking with Steve Paulson at the New York Academy of Sciences. Wertheim is a science writer and director of the Institute for Figuring. Gates is a physicist at Brown University and co-author of Proving Einstein Right. That conversation was part of collaboration with the [Newer 00:50:21] Foundation and the New York Academy of Sciences. You'll find a link to the video of the full conversation on our website at

Anne Strainchamps (50:35):

Whether your life is orderly or chaotic or, preferably, some of both, we're glad you could listen today. To The Best of Our Knowledge is produced in Madison, Wisconsin, at Wisconsin Public Radio by Shannon Henry Kleiber, Charles Monroe-Kane, Angelo Bautista, and Mark Riechers. Our sound designer and technical director is Joe Hardtke. Our executive producer is Steve Paulson. And I'm Anne Strainchamps. Stay awhile and join us next time.

Speaker 11 (51:05):


Last modified: 
January 26, 2024