Science Friday - The Center Of The Milky Way, Rats At Play, And Geometry. Sept 13, 2019, Part 2

Episode Date: September 13, 2019

The Greek mathematician Euclid imagined an ordered and methodical universe, but his vision struggled to catch on for centuries, until Renaissance painters and French monarchs found a way connect the ancient science of geometry to the real world. Science historian Amir Alexander joins Ira to share the story of geometry’s rising global influence in his new book Proof!: How The World Became Geometrical.  Plus, a million years ago, the black hole at the center of our galaxy burped. Now, scientists are exploring what the resulting bubbles might say about our kinship with other galaxies. And here on Earth, neuroscientists say they can learn a lot by observing brains at play—particularly those of rats playing hide and seek. 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 Plato. A bit later in the hour playing hide-and-seek with rats. We have a video of this. You have to see this. This is really cool. How do you teach them to do that? And we'll talk about, of course, what neuroscientists can learn by studying the brain at play. But first, a journey to the center of our galaxy, the Milky Way. There is a lot going on at the center of most galaxies. You start with a hungry, massive, or supermassive black hole.

You add some gas and dust, and you get jets of plasma, x-rays, other great bursts of energy. And yes, our galaxy in the Milky Way has a big black hole at the center, and it's emitting at small bursts of energy a few times a day. But researchers writing in the journal Nature this week say they have evidence of at least one big feeding frenzy over one million years ago, a pair of bubbles towering above and below the galactic, Center, kind of mysterious. Here to explain more about why this is exciting news for space science

is Dr. Farhedsaday, an astrophysicist at Northwestern University's Center for Interdisciplinary Exploration and Research in Astrophysics. He's also co-author of the research on this. Welcome to Science Friday.

Thank you for having me, here. Can you give us a picture of what's going on at the center of the galaxy? Take us on a tour, if you will. Sure. We're about 25,000 light years away from the center of the Milky Way. And the Milky Way Center is really an interesting region. There is obviously a massive black hole at the center of the galaxy. And then you have a very large concentration of stars in there.

And these stars are orbiting around the black hole, the supermassive black hole. and they have these crazy orbits that you don't find them elsewhere. So just to compare the number of stars that we have in our solar neighborhood compared to the galactic center, you find that usually the closest star is about a few light years away from us. But at the galactic center is about something like 100 times smaller, the average distance between stars. So it's a very crowded region of the sky. and these stars in Iraq with each other.

And so it's really the metropolis of the galaxy. And we're sort of more or less in the rural area of the Milky Way galaxy way out there, 25,000 like years away. So we've got a lot of crazy stars bunching together toward the middle of the... That's right, that's right. The concentration of stars peaking right around where the black hole is. And so we now have these giant bubbles, from what I understand it? What do you mean by bubbles? Well, it's just a lobe of material that is actually covering over 1,000 light years around the center of the galaxy.

So it's just, this material is hot and we think it's expanding. There is, in fact, x-ray emitting gas. inside this sort of bubble of gas that is actually pushing and making the material basically expand. So that's what we mean by a bubble of gas, just the material that is basically produced by some, by an outflow or a wind from the center of the galaxy. And that's what this bubble is telling us, that there must have been. an outflow, a really caught past activity in the nucleus of a galaxy about a few million years ago, and we actually see this. And that's what this is about. Do we know why it might

have suddenly started a few million years ago? It might have kicked it off? Well, I think we think that it could be due to an outburst from the supermassive black hole. So this kind of event happens quite often in external galaxies and supermassive black holes elsewhere. And we see actually structures like this in other galaxies. So either the supermassive black hole produced this sort of a wind, powerful wind that is actually eventually led to this sort of a large-scale structure around the center of the galaxy. Or could be just a large number of massive stars, all basically blowing up at the same time, and then they produce an outflow.

So there are two ideas, and people are debating about these two different possibilities. But a lot of people think that it's actually the black hole that was active a few million years ago and produced this giant bubble of material. Is the center of our galaxy, that black hole and the stars around it, is it typical of other galaxies or different than other galaxies? I think it's very typical. Any mature galaxy has a supermassive black hole at its center,

and we actually see a lot of galaxies also showing these beautiful, beautiful structures on the same sort of scale size as what the bubble that we see in our own galactic center. And so the event is usually considered to be due to either an active black hole or could be due to bursts of stars, basically, producing these bubbles. Now, I know there is another bubble, or there are other bubbles we've seen in the Milky Way, even bigger ones than these called the Fermi bubbles. That's right, that's right. So that makes it, yeah, quite interesting because the Fermi bubble is a much larger scale structure

than even the bubble that we're talking about. The bubble we're talking about, maybe a little bit more than a thousand light years across. The one that we see the Fermi bubble is about something like 28,000 light years. I mean, it's just tremendous. It's really the giant, the elephant, the most, the elephant in the Milky Way galaxy. You can't find anything else.

and that is producing gamma rays. And in fact, what's really interesting is that these features that we see closer in to the black hole could be the base of the Fermi bubble. And that's one of the ideas that maybe, and it could be basically feeding the Fermi bubble. Maybe there are ways that you can actually have multiple events that are constantly pushing the gas out into a much, much larger region of the galaxy. So it is, I think we don't really know for sure that this is how they're connected to each other, but I think both are relic of past activities in our galactic center.

So it's very likely that the two are really causally connected in a way. Now, I know you've been studying the center of our Milky Way for, what, 30 years, something like that? Well, what makes you so excited? What is there so exciting? Tell us, share us. It is an exciting region. I mean, I never had a plan to really just study the same region. I mean, the universe is huge.

I mean, you can do so many different things, so it's not. But I think one discovery leads to another discovery, and at the same time, you really want to understand what's going on. So understanding something takes much more time than really even discovering something. So in order to really figure out what's going on, and there's always fantastic instrumentation coming up with different telescopes. and you look at the same object basically in a different view,

and you really get a big picture of what's going on from different angles. So I didn't really study just one wavelength band, but I did different things and different structures. But it is really interesting. You have a supermassive black hole. You have the highest concentration of stars orbiting around the black hole and further away,

and you see these sort of a torus of gas cloud orbiting, orbiting around the black hole and we think that some of the gas is actually being captured by the black hole. And so you learned a lot about the different structures and how the interplay between these different components of the Milky Way galaxy. And it's so close by. It's only about 25,000 like years away from us compared to the next sort of distant galaxy, which is 100 times further away. Now I'm going to ask you this question because I think I know the answer, but I'm going to ask it anyhow, because this year we saw the first ever picture of a black hole's event horizon. Are we not ours?

And that's what I'm going to ask about. Are we going to be able to turn that same instrument to the black hole at the center of our Milky Way and get a look at the end? How much would you like to do that? Well, one of the main sort of motivation for building E.HT, the Event Horizon Telescope, was actually to look at the black hole at the center of our own galaxy, and of course, M-A-D-7. And I was actually disappointed when I didn't see the image of the black hole

coming from our own galactic center. So there are two objects that they were proposed to be observed with the event Herodian Telescope, and certainly they have been doing a lot of work on the black hole at the center of the galaxy, and we haven't really got the result. And I think I can say why we haven't been able to get a good image so far. The black hole at the center of a galaxy is relatively active. I mean, it does a flare, as you mentioned earlier, a few times a day,

and these flares basically fluctuates the emission that comes from the black hole. So it makes it very difficult to image. to image this. It doesn't want to stand still as witches. Yeah, that's exactly right. You can't take its picture. Yeah, you have to really wait until it becomes really quiet. And then you have a better opportunity.

I think that's one of the main reason. Whereas M87, that black hole is actually active, but the activity is not on an hourly time scale. It's at a much longer time scale, and we can actually image those galaxies further away in some ways better because they're quiet. Whereas here, Galaxy Center is happening in a way. And a lot of people are really interested.

Yeah. Well, we'll have you back on when we get that photo. It comes back from the drugstore. We'll have you on to talk about it. Thank you very much, Dr. Zaday for taking time to be with us today. Dr. Farhead Zaday, professor of physics and astronomy at Northwestern University's Center for interdisciplinary exploration and research in astrophysics. We're going to take a break, and when we come back,

does your pet like to play games? And how can you tell if it's having fun? We want to hear your stories about animals playing. You can give us a call 844724-8255, 844724825, or leave us a voice comment on Science Friday Voxpop app. We're going to talk about how you can train a rat to play hide-and-seek. You've got to see this video. It's up on our website.

We'll talk about how to see it. really cool. Stay with us. We'll be right back after this break. This is Science Friday. I'm Ira Plato. One of the most popular things about the internet is spending hours, days, maybe even years, watching videos of animals at play. You know how many videos of animals there are and you have watched? Just amazing. You've got the classic cat playing with a box genre, but you can also watch a dog playing jenga. Seriously, Google it. And you can type in pretty much any combination of animals and the word playing, and you find adorable little videos like a baby deer, roughhousing with a lemur.

Incredible stuff out there. So why am I telling you this? Well, because my next guest, a neuroscientist, actually gets inspiration for his work by watching those home videos, ideas about how to study animals, interacting, and playing with other animals and humans. And in his latest work out this week in the journal Science, he describes playing hide and seek with rats. Yes, we have that for you. My question for you, our audience is, what games do you play with your pets? And how do you know when your pet is having fun? Here's what you told us on Science Friday Vox Pop app.

So I have a little Boston Terrier named Pablo, and this dog loves fetch. When he sees the ball, his eyes dilate. He's obsessive. Every 10 or 12 throws, I have to hide the ball just so he can catch his breath. And I'm assuming he's having fun while doing it, because as long as you're willing to keep throwing the ball, he's willing to fetch it. When I do a partial water change in my aquarium, the Harleco-Nerasboras, there are three of them, will swim alternately up into the stream going against the current of the incoming water, and then they'll stop and get washed back down into the tank, and then they'll come back up again kind of in rotation. It sure does look like they're playing. I have fun with my cat when she brings me toys and looks at me, like she really, really wants me to throw them, and I throw them, and she gets all excited and bolts after it. Like, well, we call her NASCAR, NASCAR, NASCAT. NASCAR.

Sound familiar to you. Do you play with your pet? So that was Kevin from Nevada. It's Steve from Pennsylvania. Tamara from Colorado. Tell us your stories. Science Friday Voxpop app, or give us a call 844-7-27. 8255, 844724-8255, or you can tweet us at SciFRI.

Juan Ignacio Nacho Sanguinetti is a neuroscientist at the Humboldt University of Berlin, and one of the authors on that research published in science. And we have a link to that and videos. You want to see the video, rat hide and seek and what animals are playing? Well, it's up there on our website, sciencefriiday.com slash animal games. Science Friday.com slash animal games. Welcome to Science Friday, Dr. Sanguinetti. Thank you. Thank you, Ira.

It's a pleasure talking to you. Were you really inspired to study animal play by the videos on the internet? Well, so in the lab, we've been looking into play behavior for a couple of years. A few years ago, our lab published research about tickling rats and how rats vocalize and create this job. boy laughters when they are tickled by a human experimenter. So we've been looking for different ways of study, play, behavior in animals. And it is true that anybody who's had a pet before knows that you can play different things with your animals.

As some of your audience has described, Fetch is a classic game you play with a dog. And if you teach a dog how to play Fetch, then you'll need to hide from him because he will come with the ball to you, like all the time. So we've been looking into different place, and luckily YouTube is a treasure trope of animal behavior. The fact that anybody has a cell phone and a camera and their cell phone allows us to see so many different animals and so many different animal behaviors just by going into YouTube, you know? I want to get right to the rats playing the game. You mentioned that you could tickle them. They make certain sounds.

We have a sample of these sounds modified so humans can hear them. Wow. What was that, Dr. Sanguinetti? What were we hearing there? That is a rat being tickled and having this joy vocalizations, which are these vocalizations in the ultrasound range, so humans can hear them and that are associated with positive emotions, with playful behaviors and playful encounter between rats. And that was part of the things that we found in our study when we tried to put now rats to play a more sophisticated form of play. the game known as Hide and Seek, a very old game, a game that is shared by many different cultures in the world. You know, I didn't really, until I looked at the video, it's up on our website at Science Friday.com slash Animal Games.

I could not believe that anybody could play hide and seek with a rat until I saw this. It's amazing. How did you get the rat to learn how to play this? So the first thing to point out is that you cannot grab any random rat. in the lab and teach it how to play Highland Seek. As you know, like old dogs don't learn new tricks. So you have to use rats that are very young, for example, because we know that play is something that animals do more when they're young

and do less when they are adults, right? So the first thing you need to do is to really abituate the rats both to the experimenter and to the room where it's going to play. And then slowly but surely you can teach, the rat how to play the game. For example, in the game of Sikh, what we did, we had a starting box where the animal was placed to start the game. And then what Anika Reinholt, who was a master student running these experiments did, she would get far away from the rat, and then the rat would come close, and whenever the rat came close, she would tickle the rat and play with the rat

and made the rat chase around her hand. And in some way, given the rat a social reward. And then what she would do was to increase slowly the complexity and start hiding better and better from the rat until the point where we were able to close the starting box and then open the box remotely, and the rat would have to search in this 30-square-meter room for Anika. So the reward for the rat is not a pellet of food? It's getting tickled? Yes, exactly. There is no food reward, no water reward. It's just the social interaction with the experimenter. And we know that social interaction is a very rewarding thing.

Like when you deal with children, they like to be to be cuddled, they like to be played with. So this is the same for our pets and for our rats in our study. And so that's what you're really studying then is the social interaction feature. What do we learn about humans from that? Well, it's very important to study social interactions. we're still trying to figure out the social brain and how the brain conducts social interactions between animals.

So the play is one critical example of a type of interaction. There is this thing called social play when an animal plays with another animal. And from studying these kind of things, we will get closer to understanding social interactions in human and how the brain controls social interactions in humans. And humans are an incredible case of social interaction.

They are basically a species that has this incredible social network, right? We've evolved to have like this big families, these big groups, and to have this big social networks around us. So to navigate those social networks, we need a brain that allows us to go from one place to another and to understand the people around us and how they behave what the other people can do and what you can do with them. So this is a very important topic to understand our brain

and how our brain involved. A lot of reaction from asking people how they play with their animals. I have a Claire who writes, I play Find It with my dogos. You hide the treats throughout the house while they wait into the bathroom. Afterwards, you let them out and say, find it. They then search, sniff for the treats.

we had to be more obvious with the treats after we got a beagle to give the lab a chance. So I had a couple of dogs. Let me go for a reaction to Melissa in State College PA. Hi, Melissa. Hi, Iris. It's pleasure to talk to you. Thank you. Go ahead.

Okay. I was saying earlier that my definition of play for an animal is when they initiate it, then you know they're into it, or when they return to it voluntarily, like a dog bringing you a ball is saying, play with me. Play with me now. It's not very ambiguous. Or when you're playing tug-of-war,

the animal will tug if you let go, and they hand it back to you. So that's one, those are two clues. And the other is the body tension. If it's a stiff tension and the defensive, they're not having fun. But if it's a bouncy tension, they're full of, well, bounce,

then I think they're playing. Yeah, I've seen that with dogs I play with also. It's the same kind of thing. Because you can really tell one, when an animal is playing, can't you? Yeah, I think those things that the audience member mentioned are critical things. For example, we know that rats, when they are in this playful state, she said something about this bouncy nature.

So we described a type of behavior that rats do when they're playing that is called in German Freudensprung, which is translates into joy jumps, which is the rats are jumping in place, basically with their four legs. So this is one kind of way to tell when the animal has some positive response. The other thing that the audience member mentioned, which is very interesting, is the willingness to continue the game, to continue playing. And that is something that we found in our paper. That is that we found that rats not only cared about the social reward at the end of the game, but that sometimes they would even try to evade this reward so that they could.

could continue playing. So sometimes if the rat was hiding and the experimenter would find the rat and would try to introduce this social reward, the rat would leave and hide somewhere else again. So they would really try to extend the game.

Did you ever try to trick the rat? Like play a joke on the rat? No. So that is something that I've been thinking about for many years since I'm also an amateur, improviser and comedian, but is how to try to surprise a rat into something that would be funny.

So I've been thinking very unprofessionally, but many years about how to... So my idea of a joke for a rat is that... So you train the rat to always run a maze, a normal maze, where the objective is to find cheese. let's say, right? Right. So then you train the rat and the rat is focused. It gets into the maze.

It smells cheese and tries to find it. And then again and again and again. Until at some point, what you do is to, you do the same thing. But then suddenly all the walls are made out of cheese. So then I imagine myself in the position of the rat just running around, like trying to find the cheese. And then that moment when you realize, ah, you know, that eureka moment. And so that's what I envision myself. But this is, of course, just my fantasy into one day trying to understand some of the basis of humor and surprise.

Well, you say you're into the theater, you're into doing improv. Do you think you could have an act with your rat on stage, you know, doing hide and seek? People would love to see that, I'll bet you. No, no, but I'm going to tell you something. I know some improvisers in New York that have shows for dogs. So they pretend to be dogs and dogs are the audience. So it's not that far away that you could try to do performance with animals themselves. But it's a very interesting topic because how one plays a role and how animals play roles in their natural lives in the animal kingdom,

whether they're in the role of a prey or a predator accidentally, or if they're in other kind of social situations, that there is a relationship of status and hierarchy. These are very interesting questions that neuroscience is starting to tackle. You're about 30 years too late for Ed Sullivan. You could have done it. I'm Ira Plato. This is Science Friday from WNYC Studios.

You know, you have to be of a certain age. You remember Ed Sullivan's show. No, no, no. I got it. I didn't know if I was allowed to laugh. Oh, wait. I never laugh on this show. You'll know it.

So where do you go from here? What else can you do? Do you want to teach the rat to do other things or another game or something else to further study it? Or you just keep following this maze, so to speak? So there are several things. The first thing that we like to point out is that we think this paradigm of playing with the rats and playing hide-and-seek with the rats allows us to probe some of the rat's cognitive capabilities. Like we want to figure out

when the rat is making decisions and when the rat is choosing to hide in a certain location or in another location or for example where is the rat choosing to search for the experimenter so these are very interesting it's a very interesting paradigm to tackle questions like decision making

motivation when is the rat motivated truly to play for example so that on one hand and on the other hand of course we're still looking for inspiration and games to try to teach animals to use those games as a way to, in a very naturalistic way, probe for understanding the brain at play. Right. Well, you know, we've talked a lot about birds recently and how intelligent birds are. I have a tweet coming from Skip who says,

I lived for a time with a crow named Hugin. If I was on the phone too long, she would go to the modular plug at the baseboard and unplug the phone. Now, birds would seem, we've talked about birds recently, how smart they are. You say you're looking for other animals to play with? How about a bird?

Think about working with birds. Crows are also known to play. In fact, I will challenge the audience to go to YouTube and try to find videos of crows playing in the snow. There are some videos where crows use the snow on a windshield of a car, to slide down and then they would just go up and slide down again.

And they also use roofs for things like this. So crows are very interesting animals indeed. But you're sticking with your rats for now? Or are you branching out? We will see. We will see. I still have to decide what my future holds in neuroscience. I just finished my PhD here and I'm trying to find new topics.

So I'm very excited about that. So improv is not a day job yet. I can't fall back to your improv career. No, no, no, no, no. I have a serious science career with a side of improv addiction. But it must help you think creatively, I would think, you know. Oh, absolutely, absolutely. I think like it's a very creative endeavor,

and I treat it in some ways in a very similar way as I do all my other. work because I do take it seriously and I think it's incredibly interesting and it's a very, very interesting way of also figuring out things about the brain, I think. Because it's in a way the social brain, the human brain gone wild. It's taking all the skills that we have to navigate social situations and using them in make-believe social situations. And starting in a set from nothing and just looking at your partner and going into a story is unbelievable. And humans can do that.

Yes, we wish you great luck, Dr. Sanguinetti. Juan Ignacio Nacho Sanguinetti Neuroscientist at the Humboldt University of Berlin. Thanks for joining us. We have a link to his paper, and I'll tell you the video of the rats playing hide and seek. We'll make your day, ScienceFriety.com slash animal games. We're going to take a break.

We'll go right back after this break. This is Science Friday. I'm Ira Plato. How well do you recall your high school geometry? I loved high school geometry. Mr. Cavallero was a great, great math teacher. You know, given Isosceles triangle A, B, C, whereas A.B. is equal to side BD, then angle A is also equal to angle C. Of course you remember that. It's not something your math teacher invented. It's a proof written down in 300 B.C. by the Greek mathematician Euclid. of Alexandria. You know that. He's also the founder of geometry. Yet Euclid's pie in the sky vision of an ordered and methodical universe ruled by geometric equations. It struggled to catch on for centuries until Renaissance painters and French monarchs found a way to connect the ancient science of geometry to the real world. And the story of how geometry went from a philosophical concept to a system for designing cities to a staple of high school mathematics is carefully laid out like a geometrical proof in the new book, Proof, How the World Became Geometrical, written by my next guest,

Science Historian, Amir Alexander. Welcome to Science Friday. Thank you so much for having me on. I've been a listener for many years, so it's great to be on. Yeah, you know, I never really realized the great history of geometry. I knew the math. I love the math. And you said, in your book that geometry was only discovered once in the course of human history? What does that mean? Well, that means that they were actually, there were very, there are different great mathematical traditions in the ancient world. There were traditions in Babylon. They developed forms of algebra in Egypt. They used math for measurement. But there were only one, there were only in one place. Did anyone have the idea that mathematics was not just a tool for counting, measuring,

or, you know, looking at astronomical observations, but actually simply a way of finding absolute truth. Mathematics can lead us to something that is absolutely irrevocably, irrefutably true. And that happened in the Greek world, in one of the Greek cities that dotted shores of the Mediterranean in the 5th century in the 5th century BC. And we don't know, we don't know when exactly it happened, right, and what exactly that first proof was. But we do know that it was the very first time.

It was the only time that that was discovered. And that, as I argue in my book, it really changed the world in the profound way. And you say that Euclid was the one who actually, I'm going to quote you, Euclid is likely the most influential mathematician who ever lived. I mean, there have been a lot of mathematicians. That is true, but I think there's a good argument to be made that there was no one more influential than Euclid, because what Euclid did was really remarkable.

He took those already existing proof that were sort of a disjointed array of different theorems about lines and angles and circles and so on, things that we know from geometry today. And he turned them into not just a single, like a set of different truth. He turned them into a whole world, a geometrical, a pure, abstract, geometrical world

in which you start out with a set of postulates, and then you deduce step, biological step, you deduce absolute necessary truths that are absolutely incontestable. And not only that, but they're all dependent on each other. And first-level proofs are then the basis for a higher-level proofs, or then the basis of higher-level proofs. And all of these truths that are incontestable are interrelated.

It was sort of as I think Plato was a great admire. Plato lived before Euclid, but he saw what the project was. And he saw it as an absolute beautiful world of absolute interconnected, truth that there was nothing like it. That's where truth was. The world around us, as the Greeks thought, was chaotic, was changing, was transitory, was unreliable. But geometry, that gave you. a world of absolute, incontestable truths.

But you also say that the Greek geometers were not looking for any practical applications of geometry, but for truth, for the sake of truth, and then along comes Euclid and changes that whole thing. Well, Euclid did not change that. He was also, he was also, he created a world, an entire world of truths, of interconnected truth, something that is the closest thing to, you know, Plato always thought that the real, you that there is a world of the forms in which all the perfect, the perfect truth all reside, all reside that is better and more pure and more beautiful than our fob,

that our very corrupt and transitory world. Euclid claimed the closest to actually creating that world, making it real, an interconnected, interconnected, of absolute, of absolute truth, all interconnected, everything has its place, everything has its perfect relationships to other truth, everything is perfectly known, and everything is also hierarchical, because it starts from those general statements postulate, and then it goes step by step by step by step to higher and higher levels. But you also say that while they were all interested philosophically in these truths,

it was the artists that brought math back down to earth, right? Exactly right, exactly right. Yes, what happened was that first that the Greeks, they were very impressed with Euclid's accomplishment, but they didn't believe it described the real world. Our world is messy, too messy, changing, transitory. It's nothing like that perfect world, the world of geometry. And that was also the case in the Middle Ages when the church thought that the world is corrupt, it is fallen, right? And it can't be described by those perfect truth.

And what happened, and that happened in a particular place, at a particular time, in Florence, around in the first half of the 15th, the 14th century, the 1400s, a group of men that we know that we know well, they took those concepts of geometry and showed that geometry is not just up in the sky, it's not just up there in the abstraction, geometry pervades our world, that the world space, the space that we live in itself is geometrical. And they invented the science, the science of perspective. So that and that was that that was really that was really that was really that was really that was really a turning point. Tell us about, yeah, tell us, I want to get into that. Tell us how that was discovered.

You describe a really fascinating scene using a mirror and a whole punch. You describe it how this whole fascinating idea came about. Yes, that was, yes, the experiment, the famous experiment that the demonstrated the principles of linear perspective. That was accomplished by the Florentine Philippa Brunelleschi, who is also famous

for building that beautiful giant dome over the Duomo in Florence. But years before he built the dome, he conducted experiments in perspective. And he took,

he stood before in front and the front gate of the Duomo, the Cathedral of Florence, looking at that octagonal structure, that famous

extagonal baptistry of St. John in Florence, just across the square, about maybe 100 feet apart. And in his hand, he created, he had a painting. He had a painting. And the painting was not one of what you'd expect, like a Madonna and child or the traditional thing. The painting was, in fact, a picture of what he was seeing in his real, in his actual life. That is, he was a picture of the baptistry of St. John. And he looked through a hole from the back of the painting,

and in front of the painting, in the direction of the baptistery, he held a mirror. And because he drew the painting according to the geometrical principles of perspective, what he could see in the painting, in the mirror was also a three-dimensional picture of the baptistery. And then he could remove the mirror and looked at the baptistery, and his hope, what he was trying to accomplish was it would look exactly the same.

Why exactly the same? Because on a flat surface, he had managed to create an image of the, a three-dimensional image of the baptistry. So it was really a turning point, not because this was just a nice trick for a nice trick for painters, which it also was a practical thing,

but because he showed that you can actually recreate the geometry of space itself, that space itself is structured by geometrical principles and that every point in space can be defined, can be defined geometrically. And that was really the first time that was done. Geometry brought down from the sky, and now suddenly people started looking. It's all around us.

It's in the geometry of space. Where else is geometry? He sort of did the first virtual reality experiment. I guess so, yeah, yeah, yeah. But I want to move on to that next point that you make, which you say is very important because geometry then became a symbol of power, right? It did indeed. Because think about it. I mean, like, what did ukule do?

The ukule created a world that was perfect. It was all every single thing in that world. had its precise place. It was exactly true. It has an exact proper relationship to other things, and it was perfectly hierarchical, right? And if our world is in fact like that, well, that tells us something about space, that tells us some things about science, all true, but it also, it also tells us some things about ourselves and what kind of world and what kind of order human beings should be, should be living in. And the people, those who first, those who first realized the enormous political power of geometry

were the kings of France. And they adopted, they tried to create what you could really call Euclid's Kingdom, an orderly monarchy that is perfectly ordered in which everything is its exact proper place. It is true. It is irrevocable and it is hierarchical. And it is undeniable.

I mean, who could argue against? Who could try to overthrow a king that rules not just because he has a big army. He rules because he is an expression of the eternal laws of geometry, the deepest order of the universe. So you create Versailles, which is the symbol of that. Exactly. Versailles, it was a long process. It started quite humbly by a French king called Charlie Eight, who went to Pehu went at the head of the Great Army. He went to Italy and brought back a few gardeners, geometrical gardeners from Italy.

And over 200 years, the French kings identified the monarchy closer and closer with geometrical order and especially, especially with their geometrical gardens. And no garden, no garden was as spectacular, as powerful as the geometrical gardens of Versailles. Very interesting. I'm Ira Plato. This is Science Friday from WNYC Studios. talking about geometry with the Amir Alexander, author of proof how the world became geometrical. And of course, keeping them with this theme of power, if you weren't going to build a garden, you could build a whole city, right? That was geometrically sound.

Indeed, indeed. So when you go to Versailles, which is a great garden, but also a capital of a great nation, France, you learn by you walk those geometrical path, those straight. lines all leading uphill to the royal palace and you learn that the rule of the King of France is based on those geometrical principles because you see them all around you. It is, it tells you, it tells you that that the deep order of the world points at the King's Palace. But they're also, but like you said, it's not just garden, it is cities as well and there are many, there are quite a few examples of cities that were designed according to geometrical principles, But none is more, I think, more famous, perhaps even more beautiful and more astounding than our very own capital of Washington, D.C., which was designed by a Frenchman, a Frenchman who grew up in the gardens of Louis X15th and Louis XVIth and New Versailles well.

L'Anne Fawn. Yeah, L'Enfant. Yeah, Pierre-Sharle-Len-Fan. And he brought the principles, the geometrical principles of Versailles to America. But the Lafahe, of course, America is not a monarchy. I mean, it was everything but, of course, it was created as a rebuke to all monarchy. But he in Washington, D.C., he managed to use the geometrical principles that he had learned at Versailles and present them as a geometrical order as a geometrical, a republican geometrical order.

And that really what Washington, D.C. is. It is in a way the Constitution, the streets of the city are the constitution set geometrically. You see, I mean, if you look, for example, if you stand on the mall looking up at the houses of Congress and Capitol Hill, that is Versailles. That is Versailles. Palace on the hill, all roads lead to it, those straight geometrical roads pointing at the palace, telling you that this is the fixed eternal unchanging order looking up at the palace. In this case, the palace of the people. But in Washington, D.C., unlike in Versailles, that is not the end of the story,

because there's also other centers of power. So you have what Linfant called the President's Palace, and we know as the White House. He wanted it far grander than it actually is. He wanted it something on the same scale as the, as, the House of Congress. But again, a palace, a great house on the hill with a garden at a right angle to the mall, leading up to it. And again, if you look at it alone, it also reflects Versailles.

But in Washington, D.C., those are two poles of power. Those are two interconnect, they intersect at right angles, it was now in Washington Monument, and they are connected by Pennsylvania Avenue in a balance in this intricate balance of rivalry and cooperation, two centers of power. Instead of one, which would be at Versailles and the King, we have a balance of power. This is just fascinating, Amir. I mean, reading the book about geometry and then seeing how it is applied to gardens and cities, who would have thunk this is how, you know, geometry branched out.

I want to thank you for taking time to be with us. It's a fascinating book. It's called Proof. the world became geometrical, Amir Alexander, author of the new book. He teaches the history of science at UCLA. Good luck with the book. It's a great read. Thank you for taking time to be with us today. Thank you so much for inviting me. And we want to hear your voice on Science Friday. We have a new app to help you do that. It's called Science Friday Vox Pop, and it lets you easily record and share your voice comments with us. And this week we are asking you,

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That's about all the time we have today. If you missed any part of the program, you can hear it again. to our podcast or ask you smart speakers to play Science Friday. So, you know, every day of the week is now Science Friday. Have it great. You'll see. Ooh, there's a moon. It's a full moon.

A harvest new moon. Full moon. Harvest full moon on Friday the 13th. Digest that for a while. We'll talk about it maybe next week. Have a great weekend. I'm Ira Flato in New York.