TRANSCRIPT
Good afternoon everyone. Welcome and thank you for joining us this afternoon. I'm Kristy Gardner, Assistant Professor of Computer Science at Amherst College, and it is a tremendous honor to introduce today's speaker, Ingrid Daubechies, the James B. Duke distinguished professor of Mathematics and Electrical and Computer Engineering at Duke University. Professor Daubechies's illustrious career has included many groundbreaking contributions to theoretical and applied mathematics. Her pioneering research in Wavelet theory has transformed the fields of signal processing, data compression and image analysis, and has revolutionized the landscape of modern technology, making it possible for us to send photos from our cell phones, helping geologists analyze data from seismograms, and enhancing neuroscientists' ability to read MRI images of brain activity, to note just a few applications of her work.
Professor Daubechies's mathematical and scientific contributions have received international recognition at the highest levels. She has received the National Academy of Sciences Award in Mathematics, the Gauss Prize and a MacArthur Genius Grant, among many other accolades. And recently she became the first woman to win the highly prestigious Wolf Prize in Mathematics. Through her example and advocacy, Professor Daubechies has expanded the possibilities for women in STEM fields. Her unparalleled intellect and unswerving dedication to the pursuit of knowledge have driven her trailblazing work. But Professor Daubechies often points to the integral role played by creativity and an appreciation for the aesthetic beauty of mathematical structures.
Today she will discuss a project that specifically illustrates this, a collaborative initiative at the intersection of art and mathematics, for a talk entitled Mathemalchemy: How Intrepid Souls Created an Installation Celebrating, the Joy, Creativity, and Beauty of Mathematics. Please join me in welcoming Professor Ingrid Daubechies.
Oh, thank you so much, Kristy. So yeah, how intrepid souls create an installation. So how did it all start? Well, first of all, what is Mathemalchemy? So here you see it. It's a traveling exhibit that this was its first venue in a gallery at National Academy. It then went to Juniata College. It was at Boston University here. It was at the BT Museum of Natural Science in Vancouver. And so you could actually see it through the mouth of the whale here. It's at Northern Kentucky University, and it opened just three days ago at the Museum of Mathematics in Manhattan in New York City. So it'll be there until October 27th, and you can go visit there. It's not so far.
So how did it start? So for those of you who've gone to Joint Math Meetings, which is an annual meeting held by the mathematical societies of the US, there's always in the exhibit space, not only many booksellers and so on, but also a space for mathematical art. And this is where artists with a mathematical band or mathematicians, who like to make beautiful but mathematics-inspired objects, expose. And it's a juried exhibit and it has beautiful things. It has long fascinated me. These are three examples of art that has been exposed there by George Hart, Carolyn Yackel and Edmund Harris respectively at different JMMs. But it is beautiful, it's very well-made, and it's clear that it's delightful for mathematicians to observe.
So in the summer of '19, I happened to at an art exhibit on Cape Cod, I saw this work, which is called Time to Break Free. I had long thought, could it be possible to integrate many of these beautiful objects to have a collaborative thing that would tell stories instead of just present objects? And this artist is not a mathematician, but she was telling an incredible story. You see this quilt, it has broken away from its chain here, and it's being inspired by this steampunk machine and out step the figures that were just appliqué on the quilt, and they are 3D figures and step confidently into the world. I said, "Wow, what an imagination in just making this happen and constructing this installation." So I did what I had never done before and haven't done since. I looked her up on Facebook and I sent her a message by Messenger. I mean, I think I've done it only to my children otherwise.
And lo and behold, she answered. And she later told me that she never does this either. So we were just incredibly lucky. And she is a textile artist, and she always, from the beginning that she worked in quilting, had wanted to go beyond the traditional limits. Here are some pictures of early works of hers. See the first work she submitted to a jury already was making things thicker. The skirt of the lady was bulging out. She made irregular boundaries. She played also with light. I don't have that here. And with this quilt, she actually was in the very peculiar situation that she had submitted into an exhibit. And it was within the limits of what they had given, what works could do. And the jury decided to disqualify it because they said it's not a quilt. Well, it's not a quilt, but it satisfied all the criteria. I mean, it's a little bit like the movie Babe. Nobody said that the thing hurting the sheep had to be a dog, but she got the prize of the public.
So on the one hand was very much appreciated, on the other hand. And that's when she made time to break free because she said, "I want to be brilliant." And so she had completely just a few months before I called her and she told me maybe, I said, "Are you interested in working with mathematicians?" And she said, "Well," she said, "Math? I don't know." I said, "Well, please give us a chance." And so I started sending her and for the next three months, and actually ever since the fall of 2019, we'd speak once a week. I mean, on Zoom. Then it was still Skype. We hadn't discovered Zoom yet. So I sent her books on crafting and mathematics and some books that had quite a bit of math in it. And she told me later that she, for the next three months, she spent two hours a day looking through these books and absorbing material.
And whenever we talked the next time she would show me things. And also, yes, I introduced her to work by people who made high quality crafted work. Because this was a museum quality artist. I wanted to convince her that in this collaboration I was proposing there were people who had the skills that she would want. And so I introduced her to the work of these three who all became part. Daina Taimiņa, Carolyn Yackel, Susan Goldstein all became part of Mathemalchemy. And she would always have sketches made after we talked. She was very visual and she would sketch and show me things and she made. And you see, we talked about things that never made it, the Kakeya Conjecture, which never made it into the quilt. But very early on she wanted to have three figures; a little girl, a teenager, an adult. And you see the adult, remember the adult, the adult there is very stiff, very standing like that.
I mean, we'll see how she evolves. So she made a 3D little maquette with these elements that we were discussing because we were going to go to the JMM and talk in a special session on art and mathematics. And we wanted to have something concrete to show, even if the whole thing was going to be completely different because the collaborative was going to design things. You need to show something to give an idea. And we met in Denver in the Denver airport because we had not met before, and we made a joint presentation to that session. And I told people, I said, "Look, the idea is to make something collaborative, something that's more than different objects next to each other. And if you're interested, come to..." I was organizing a party, an evening party in a hotel room later in the week. And I said, "Come to the party and we'll discuss how."
And to that party, enough people showed up. I mean, we had in fact, 14 people showed up and with a couple of people from Duke who couldn't make it there, we already had a group. And then there were people who said, "You know, but this friend of mine really would really be interested and just was not that this JMM. Could they?" And they would augment. It's a different craft. They would augment the mathematical directions and the different art directions. And so we rounded out and we became this group of 24. And so we call ourselves the Mathemalchemists. In the beginning, the name Mathemalchemy was just a placeholder because it was going to be an alchemy of all kinds of crafts, all kinds of ideas, all kinds of mathematical directions. But then we adopted it and it became the title for the piece.
So I said, "Well, if we have a team, then I promise you I will find funding." And we already had a little bit of funding because Dorothy Buck, one of the early Mathemalchemists had in her grant that she got from the Leverhulme Trust, there was some money for art, and they encouraged that, art of knot theory. So we have a nautical scene in our work, and I found more money at the Simons Foundation. We were going to do this in workshops. We were going to have one workshop where we would get together, really hash out ideas, make a large-scale, full life-size, but flimsy model. And then we were going to go home and fabricate. And it's on three or four workshops. And of course the first workshop the third week of March 2020, I mean, so it didn't happen. We had everything booked and so on and everything shut down.
And at that time, every other meeting that existed was being canceled or postponed. And we decided we were not going to do that. We held our meeting anyway on Zoom. So that's the weekend I learned Zoom and I learned breakout rooms and everything because we needed it right away. And so over the next few months, we met on Zoom several times a week. We had the whole group met once a week and we had subgroups that met several times in the workshop. We talked about the ideas, we said we need stories, we need subgroups. We set up a certain framework. And then in smaller groups, people met and reported back every time. And we hammered out concept stories and components in these several meetings a week. And Dominique's perception of mathematicians started to change. And so that's higher sketch of what the mathematician was after a month of this process. Instead of that stiff person, is flowing very natural.
And so there was a lot of Zoom. At the end of that Dominique said, "Well, enough ideas. There's so many ideas already." She made a larger scale maquette of which we have, that still exists and that's now at Duke University. And then we fabricated because she said, "It's time to start making things." And so in the fall of 2020, everybody was sitting in their own places and teaching by Zoom and isolated. And we started fabricating and then showing things to each other. One thing was that we needed Dominique's thought of color and harmony of color and so on. And she first thought she would teach us about the color wheel and hue and saturation and the temperature of color and so on. It was an absolute disaster. I mean, only the people who already were making art, and even they kind of can intuition.
But so she decided this was not going to go. She went to Home Depot and she got little strips of the right colors and she said, "I'll just send you the codes." And I went to Home Depot and the codes in Canada where she lives and those in the US do not correspond. So she went back to her Home Depot, she got five of each thing that she wanted. She cut it into little bits and she sent us all an envelope with all the colors. And so, because of course since we were on Zoom, you can't judge the color from what you see in your screen, but you can judge whether a color is similar to another color if both are being shown. And that's how we worked. So whenever components had to be chosen, they said, "Look, I'm taking this and that's that color from your strips," and so on.
And so that way all the colors did harmonize. So we had to think, I mean we had to invent new solutions to work. And so I want to show you very quickly how many different materials there are before I take you on a tiny little tour around Mathemalchemy. So I'm going to show you many objects, many scenes, many and so on, and every time highlighting what technique is used and also giving you pictures of all the people who worked on it. I won't name them every time, but that way you see that most things involved more than one person. We actually used the mail a lot and we would be worrying about did that box get lost, and so on. One box took two months and we duplicated all that material because we thought it would never arrive.
But so there was 3D printing, there was beading, there were ceramics, crochet, cross stitching, laser cutting, metal welding, needle felting, origami, painting of many different things. Polymer clay, quilting, sewing, stained-glass, tamari balls, weaving, wire banding, woodwork in many guises, and light. So all these things are within Mathemalchemy, all these different techniques. So not only are there many media and many crafting techniques, there's also a whole lot of different layers. Many, many, many, many math concepts, but also different layers and some jokes. So there was an article that appeared about the Mathemalchemy and its making in the notices last year. So if you go back, if you search "Mathemalchemy notices AMS" you will find it. And they asked us to have a map of the things since people wouldn't have seen it.
And the conceit of part of the article is a walk by two of the quilters in it are Baker Arnold and are Harriet Conway from Conway's Curio Shop. And they walk around the island and they have a discussion and in which in their world, which we call through the looking glass world, is a world where kids are told that art is real hard, math is easy, but artist is. And so Harriet says, "My story is full of math," which Conway's office would have been full of math, "But art is really hard for me." And anyway, they have this discussion and we're going to follow them in this world. So that's one layer in Mathemalchemy. So Mathemalchemy really is like a wonderland where many quilters live and go through their business. And in that wonderland, there are many objects and many customs that have a mathematical content. And so you first see the stories and then you start seeing all the stuff.
So we follow Arnold and Harriet on their walk, and we start at the Mandelbrot Bakery. So if you go to website, mathemalchemy.org, then you can click on the menu and explore alchemy and you can do the stories. And so you see all these choices. And if you click on bakery, then one of the first things you'll see is you go down and you actually will see a movie. No, this is not it. And actually maybe I can show, I'm on internet anyway, so if I go to mathemalchemy.org, here on menu, I go to stories. You see that yellow thing that we just saw? And so here's the bakery. If I click on bakery and you scroll down and you see a little movie, and that's the movie we're going to see. You have others that have movies too, but let's watch this movie.
So we have little movies about many of these scenes, and that was the bakery movie. So we've seen, so here you have Arnold, the baker. So the different scenes in Mathemalchemy have different themes. The pie-shaped cookie was an early idea because that's a design I had made many years ago for Pi Day. And when I talked to the others about it, they said, "Oh, let's have that in Mathemalchemy." Actually, whenever somebody came up with something and described it and somebody else said, "Oh, that's cool," and somebody else said, "Maybe one of the first two, it could be a third person and I know how to make it," and it went. Until Dominique said, "Stop. We have enough. We start making." When I said the pie, people talked about tiling and then symmetries and symmetry groups and dynamical systems, fractals, dynamical systems. I mean, all of these are related.
And so we then set, and there's also the baker's map in dynamical system, the baker's transformation. And there was an earlier thing about mixing systems, which is what the baker's map shows, which was due to Arnold, Vladimir Arnold. And so that's why our baker is a cat and he's called Arnold. And Arnold is famous for having worked with Moser and Kolmogorov for KAM theory. And so that's why his assistant is a mouse. Cat gets a mouse of course, and he's called Moser. And the flour they have, you don't see it here, that they use in the bakeries, KAM flour. And so lots of jokes.
Arnold is baking these pie-shaped cookies. We got lots of requests about where can we get such a pie-shaped. I mean the thing is, I had one that was 3D printed, but you've got lots of responsibility if you give it to other people because a 3D printed thing is hard to keep clean and if bacteria start growing and so on and so on. So we actually now have cookie cutters that are in stainless steel. And if you go to the web page, it'll tell you how to get them. I didn't bring any because we used them for a fundraiser. I didn't feel it was cool to go to a commencement and start fundraising for a different, so usually I'm shameless, but that's beyond my... But we have a little video that I made this year for Pi Day that uses the cookie cutters.
Actually, can we put the light down? Because it's hard to see. And now you're going to see something cool. You see, because the shaped tiles. So I get this one, but now you don't have to punch them out. The remainder is already the right shape. It's too colorable and so on. I had to wait until my grandson was in bed because it was too hard to do it together with him. Okay, and here you see the cookies that we baked, I mean, and ate. My grandson took them to his school and they were much enjoyed. On the wall of the bakery, there's a wallpaper and what should a wallpaper illustrate but the wallpaper groups, of course? All the different ways in which you can take a shape and move it around and make something repeating by a lattice, by having mirrorings and so on. But there are 17 wallpaper groups. I'm only showing nine here.
That's because this is knit. Actually, it took two months to knit. Not continuously of course, but knitting is something that lends itself very well to left-right symmetry and to translation and even to up-and-down symmetry. Because knitting is really lines that yarn that goes up and down like that. But it does not lend itself to rotations. And so what happens? Well, these nine are the ones that you can knit well. Then there are three that involve 90-degree rotations, and those are on those three little mats, two on the terrace. And then those are cross-stitched, the tiniest cross-stitches I've ever sewn in my life. And I never will sew such tiny ones again. It took forever as well. But the symmetry of the craft leant itself to the symmetry of what we wanted to do. And then you have some that have 60-degree and a 120-degree rotations and those you can do with applique.
And so that's the wall hanging in the curio shop has those patterns on it, those five remaining patterns. So this shows one of the principles we would be exhaustive in all the different, if we had groups or a family of things, then we would show them all but in many different places and adapt it. So Conway's Curio Shop was actually one of the first things that was made physically because photographs of it featured on the memorial that was held for Conway, who we lost in the pandemic. And so we got the permission of his family to call it Conway's Curios. And it's illustrated, a big decoration in it is the Harris Spiral, which is a spiral that is similar to the Golden Spiral, but slightly different. And it has fractal properties. Okay, we are on our walk, we've seen downtown, we've seen the bakery and terrace, and now we are walking and we follow tortoise.
That's the tortoise. And Tess is going on a walk. And it turned out we discovered later, and I'll tell you when that comes up, that in fact she does this every day. She likes to walk this walk. She meditates on it. And this is Zeno's path. And Zeno's path was designed so that it had sections with 14 pavers every time. And the pavers would become smaller by a factor of two. And since the path has the same width, the section of the path becomes, well, like in Zeno's Paradox. And so it illustrates convergence. And the shell of Tess, so Tess's body is knitted and stuffed with wool and her shell is in ceramics. And of course we wanted to make something nice. And so it is decorated with a more or less hyperbolic tiling with heptagons. Heptagons are of course important because they're the first polygon you can draw with a straight edge and a compass.
And so Tess has a kite. Now from the beginning, Tess was going to take her lunch with her. It's on her list of things to do. Eat lunch. And so in the beginning she was going to have a backpack, but that was going to obscure this beautiful shell. So no backpack. And then we said, "Well, she'll have a cart and she'll have a harness with which she pulls the cart." And then there were too many of us who said, "But that will hurt. I mean, her poor little neck." And somebody else said, Henry said incredibly, he says, "You realize this is knitted, it's stuffed with... I mean, it isn't alive." No, no, no, no. So we had these incredible conversations. And so then somebody said she could have a kite, and of course there was a solution. And so she has a kite because then the kite could be a tetrahedral kite with a Sierpinski structure. And of course, I mean. And so her lunch hangs from the kite.
Okay, playground next. On the playground there are two chipmunks. And the two chipmunks have received as a task from school to explore the special properties of numbers. And they're holding numbers in cuneiform because we wanted to show that mathematics is universal in all cultures at all times. And one has 12 and one has 13. And what they have to do is they have to lay out as many acorns as their number says and see whether when they lay it out in short numbers, in short lines, it comes out evenly. Of course, 12 does it evenly except when you do five like here. And then there's remainder. The remainders are circled in these little bracelets that they crocheted themselves.
But 13, of course, there's always a remainder. And originally in the very first design, I wanted to make a joke and because the primes are always the stars, and I wanted the kid that had 12 to be jubilant because it had so many dividers. And the one with 13, no divisors at all. But then it was pointed out to be rightly so, that we didn't want to show kids being sad about things they discovered in mathematics. So in fact, they both discovered that their number is special and they are jubilant. The cryptography quilt. Dominique from the start had said, "Could we please, because I'm a quilt maker, could we please have one quilt?" And then several of the other mathemalchemists were mathematicians interested in cryptography. And so I said, "Let cryptography be the subject of the quilt." And so you have around there messages everywhere to decode.
Not difficult actually, but around the center medallion, there are five scenes that have to do with scenes in the installation. For instance, on the top right next to the medallion, you have a recipe for Mandelbrot, which are not only the name of Benoit Mandelbrot, of the fractals, but also Mandelbrots are little biscotti with almonds in them. So that's the name of the bakery. And then the outer thing are many, many things that have to do with cryptography. Actually the top left shows how the 4-7 Hamming code, how you generate code words, seven length code words from four bit messages. And the bottom right shows how you correct a mistake in a Hamming word. But you also have an illustration of RSA here with the squirrel and chipmunk sending information. And there's other way, I mean DNA encodes information, fingerprints encode information, even electric plug encodes information.
The white side tells you which of the two wires has a current and which is a neutral and so on, and hidden messages. And it's beautifully made. It's exquisitely quilted if you go and see it. I mean, Dominique is a fantastic quilter. I mean she quilts, it's not done by hand, but I cannot even with a very sophisticated machine, do what she does. It's incredible. And there's another little quilt that comes to the side because when it was exposed at the National Academy of Sciences Gallery, it was the annual meeting and one of the foreign members being inducted was called Gilles Brassard. And he is, together with Charlie Bennett, the father of the earliest quantum cryptographic protocol. And he said, "Oh, this is fantastic, but there's no quantum cryptography." And because he and Dominique were both Quebecois, they were chatting a lot together and she said, "I still have enough fabrics, we can have a little one that's trying to insert itself."
And so we made a picture of the protocol and it became the cover of the IEEE Bits magazine, the magazine of the Information Theory Society. But okay, on the other side, if you have a quilt that stands like that in the air, then there's another side to it. And that was one of the last things to gel. And we decided to make it a tribute to women mathematicians. And just because completely serendipitously, we hadn't intended that. We just asked whoever wants to come, comes. And of the 24 people we have, well, we have four dudes. I mean, so we had such an overwhelming number of women that we decided, and it was unanimously adopted to have a tribute to women mathematicians. And of course we had lost Maryam Mirzakhani not long beforehand, but we wanted to in keeping with her own modest nature, not just have a tribute to her, but to other women of mathematicians as well.
So we took things from the movie that probably you've all seen, where she's working on these large sheets and making drawings. We took snapshots of that and made some of these doodles into her portion of that great doodle page. But we have also, so this is from Maryam Mirzakhani. These we got from Caroline Series. These are from a notebook of Sofia Kovalevskaya, who apparently when she made mistakes would scratch it out and then start doodling. The top in the middle is drawings from a paper by Gladys West. There was a paper in the notices not long ago about her as well. She's an African-American mathematician who, like the people in Hidden Figures, although she's not in that book, couldn't get a job in academia and worked for the Navy in her case and analyzed and modeled in great detail images of the earth that came from satellite. And her model of the earth and deviations from the sphere are still used in GPS computations today.
So Alicia Boole Stott, again, somebody who was published in a Notes article who was not trained as a mathematician, she picked up, she was one of the daughters of Boole, but there was no money to educate the daughters. And so she learned the geometry from her brothers and she developed an uncanny insight in 4D geometry. And so even though she never finished high school, she actually got an honorary degree of university in Netherlands because she started working and she collaborated later with Koch Center. So I mean, all over the map, professional mathematicians, amateur mathematicians. So these are there. And the border itself, just like the floor of the bakery, is a tiling by identical but non-regular pentagons that was discovered by Marjorie Rice, another amateur mathematician who sent her stuff to Martin Gardner because she had discovered things that he had not described. And he sent it on to a Doris Schattschneider, who then wrote a lot about it.
And okay, we go on in the park, the squirrels actually have their annual picnic, and what they do every year is they go through ritual, which is the sieving of the primes below 100. And so they have this frame from one to 100. Well, one is [inaudible 00:37:27] of course, and then sieves come in, twos, and then sieve comes in that veils all the numbers that are multiples of two and so on. And so you see two, three and five have been done. The sieve for seven is being brought in. You see that 21 is veiled, as is 42, as is 63, so multiples of seven. And actually what Tassos, which is the familiar form of Eratosthenes, who of course is associated with the sieve, and who was the librarian of the great library in Alexandria. So Tassos is the librarian in Mathemalchemy, and he's kind of squirrel-splaining that the sieve for 11 that is coming next.
And there is really not necessary because if you only go to 100, then everything that's multiple of 11 will already have been sieved out. And he explains this every year. And every year there's a dedicated listener who is... Now, if you look from above, then next to where that scene is, are these pavers. And in fact, they are showing a sieving of the primes in the Gaussian integers. I mean, zero is here. You take the units one I minus one minus I out, here zero and the units are gone. But also all the multiples of one plus I and one minus I, because those are the same ones. And then here, all the multiples of two plus I. And next, the multiples of two minus I. And the next paver looks the same because the next prime of which you remove the multiples already within this horizon doesn't make a difference.
So we have here the primes for elementary school kids, well, middle or high school. And t
hen you can go to college math with the Gaussian integers. Oh, sorry, okay. The herons having in Nautilus Bay, because I told you we had a nautical scene. We had to have a nautical scene because of the Leverhulme Trust. And so we had lots of knots. So the herons are fishing and they are fishing all these knots. These are in fact theta knots. So they're knots which have extra branches in them that connect things that normally is. So they're multiple connected, but you can then there's a theorem that you can always cover them with normal knots, and that's illustrated.
And on deck of the boat you have cylinders and double cones and buoys that are really spheres. And the cylinders are cylinders that have the same height as diameter. They illustrate an observation that Archimedes already made, that when you take a sphere and you take that kind of short cylinder with the same height as diameter and double cone with the same two bases and the same height as the cylinder, that the volume of the double cone plus the volume of the sphere is the volume of the cylinder. And this is something that he was very proud of. And we know from the ancient literature that he asked for this to be marked on his tombstone. People visited centuries after his death his tombstone and saw it there. The tombstone no longer exists, but we have this witness to it.
So it's something that you can very nicely prove just using Pythagoras theorem. And we have that illustrated somewhere in Mathemalchemy, of course. That's actually that little proof. I mean, if you cut at a different height, then you have the two circles of the sphere and of the cone are the two, have us radiate the two sides of that rectangular triangle. And the Herons are singing a shanty. Because do you remember in '21 that everybody went crazy over the Wellerman shanty? So of course, one of us had to write a lyrics, very mathematical lyrics about the knots in nautical bay. And we made our own shanty.
(Singing).
So we had a lot of fun, as you can see, when we did Mathemalchemy. So this was just a first blitz tour. You'll have to go visit in Momath until 27th or October or on the website because there's so many scenes I haven't even talked about. The Integral Hill, for instance. Integral Hill consists of two things. It has these vertical columns, like basalt columns, those are the Riemann Cliffs and has these horizontal terraces, which are the Laubach Terraces, and so on. And even in the things that we did discuss, there's so much more detail. So I encourage you to go visit if you can. We've just toured a magical world. The silhouettes live in a different world. Silhouettes are outside. They're there because not all viewers can identify themselves with a squirrel or a chipmunk or an octopus. I mean, I have no problem with that.
But so there are these human figures. We don't know whether they are living in another world or dreaming or actually dreaming this world, this magical world. I mean, we leave that in the middle. I mean, the viewer can decide, but they got a back story, actually. This little girl inspired a comic book. At the second venue where we went, one of the faculty at Juniata College is Jay Hosler, who's a biologist, but he's also a prize-winning science comic book writer. And his son has just started grad school in mathematics. And first he was going to draw one panel and then a four-panel little comic and so on. And now we have a 36-page comic book. And it's great because it gives a back story to that little girl. She lives in a parallel world where her mother, who's the adult mathematician, is trying to bring the two worlds closer and trying to understand.
And through an accident, Emmy gets dropped in this world that is then trying to go home. And Emmy, of course, is named after Emmy Noether. And so this comic book, we were delighted and of course we adopted it and we have it on our homepage, but then people wanted to translate it. And we now have translations into five languages. Volunteers. I mean in Dutch, French, Italian, Spanish, and Swedish. I mean, I've never even met the Swedish translators, the others I have. And there are three more new works in Chinese, in Thai and in German. And we welcome more translations. We now have a protocol. People want to translate, get a whole protocol for doing it so that it's not too much work for them and that we can. So that's what I wanted to tell you about. We are a curious collaboration. We are curious in many more ways than one. And we hope you'll come visit and you can find out more on Mathemalchemy.org. Thank you.
Thank you so much for this wonderful talk. I think we have time for some questions. We have some microphones around.
Ingrid, thank you so much. It was an absolutely really fantastic story of collaboration and fun, really endless fun. And I just wanted to mention for those that are here, since we're at Amherst College, that one of your first collaborators, Susan Goldstein, is an Amherst graduate.
Oh, I didn't know that.
In fact, she was my Honors student years ago.
I see. Wow.
And so we're very proud of her and glad to see that she's part of this.
She's wonderful.
Absolutely.
Thanks.
I will ask a question.
Yes.
What is your favorite component in the exhibit?
It's so hard to say because I love all of it. It's actually been a very significant experience in my life to have done this and to have had this collaboration with all these people. And I like very much the bakery, but that's because I wrote that story. But I like the other stories too, actually. It's more fun to discover stories that you haven't originated because those you discover. I liked the balls, the arches of the two balls. I didn't talk about those. But the balls are, there's one big ball that they have in common. And then from then on the balls become smaller and smaller. And the second ball in each arch has the same dimensions, but one of them decreases geometrically from then on. And so of course it converges, we know that. But the nice thing is that if you put circles that have a geometric increase next to each other, and we have this as an activity for kids, it's very clear that the tops form a triangle and that it's going to finish.
You can say it's going to finish there because I see the triangle. And so you then can say, "Well," and the next ones, the ones that are too small for us to have made them, you can draw them. And you see they become smaller and smaller. So it's very easy for kids to accept that there will be infinitely many and that the sum of all those numbers is still going to be finite because you start from the triangle and the other ones decay. Like I wanted to the harmonic series, but then we had to have over 1,000 balls for that length. I mean, there was no way we were going to make 1,000. So it decays only like N to the 2th. It decays a bit slower, N to the two-thirds in the denominator. And we chose that power so that we would only make about 100 balls.
And so when you put them next to each other, you can see that there is an Asymptote. And so again, they can accept that it will become smaller and smaller and smaller and never really disappear. And so you say, "Well, what does that mean about this arch?" I mean, of course after 100 it goes into the water. I mean Nautical Bay, so that's why you don't see them anymore. But if you could see under the water, which you can't, then it would go through the floor and through the basement and through the earth and out of the solar system, and it makes it very vivid. So these are kids way beyond before converging and diverging series, but what I liked is that I learned to make the t balls. I had learned to learn to make temari balls, and now I'm making them.
And I have all the leftovers of Mathemalchemy. I have tons and tons and tons of threads. And so I'm making tons and tons and tons more of actually on the trip here this morning I was finishing a temari ball. So what's my favorite? It's hard to say. I liked the whole experience enormously. And it really helped us all so much during the pandemic because we formed the community. I mean, we celebrated new babies, we mourned people, we lost. My husband said, "I always know when you have a Mathemalchemy Zoom," he says, "You sound so cheerful." So yes.
Thank you for that. As someone who studied humanities, I look at people who study math like godlike sort of, and always impressed. I'm curious how you went about when you started the project deciding, "Okay, this is going to be my approach to win an artist over," what kind of books, how did you come up with that kind of list?
So because I've always been interested in mathematics and these beautiful objects, I had a collection of some books, and then I discovered some more. And I thought she would be interested in books where the mathematicians showed the beautiful pictures of the things they make and explained how they make and then linked to the mathematics. Even if she didn't get the mathematics, she was getting attuned to what they cared for and the symmetries and so on. And she really, I mean, Dominique in an interview once she was asked how had working on Mathemalchemy changed her view of mathematics. She says completely. She says, "It has nothing in common with what I thought mathematics was. I mean, not only has my view of what they care about changed, but my appreciation for mathematics." On the other hand, she had to get used to our culture of discussing with each other.
After the first two meetings, she actually called me privately. She says, "These people are not going to accept me as the artistic director of this project. I mean, they're constantly saying, 'No, not like that, like this'." And I said, "But that's the way we talk." I mean, we constantly argue and so on. And at some point the consensus emerges. We say no, I mean, because we tell each other about our different points of view. And we may do that in a way that seems aggressive to somebody who's not, but we don't mean it aggressively. We are used to the fact that everybody comes up for truth and we find common truth. And in mathematics, truth is easy. I mean, things are true or not. So the fact that we would discuss that, and you can see it this way and you say, "That's not how I see it." And then you'd think, say, "Oh, that's interesting." So it was a different way, but she got used to it and she now likes it. So yes.
Wavelets or image processing or any aspects of your own research come into this?
Well, I resisted for a long time because I felt so much that this was a collaborative thing and I didn't want it to be about me or my work. But then in the end they said, "Look, it will look strange if there's nothing there." And so we have a mural. Let me find that mural. So behind the lighthouse. So something that's hard to see is a mural that was painted by... So is it in the lighthouse? Yes, the mural. Okay, so this is on walls and so on. So the story in Toward Looking Glass is that Octopi, the artist, is really, she has the magical property of being able to flip between three and two dimensions. And so she saw this blank wall and she flipped it to two dimensions to go paint it. And so she's painting, and of course she has eight arms, so she can do many, many things because it has to do with fluids and so on.
She's painting the wave equation and the Navier-Stokes equation as graffiti. She's also dripping paint, and that's making swirls in the water. And she actually had a candle that just is extinguished, and the smoke, random. Her mouth stick is making [inaudible 00:55:09]. Here, this is actually a profile of a wavelet she had. So I constructed one that it was a bit more less regular than the one that's typically used for taps. And she incorporated that there. And you see here her tag, so this is not a pulp, so her tag is Octo and Pi walking like that. So Octopi. And [foreign language 00:55:40], well, that's [foreign language 00:55:42]. The thing is not a pipe. In Magritte's painting, it's painting of a pipe. Well, this is a painting of her tag. But there's an extra layer to it in French, which is the language that Magritte used because that was his mother tongue.
There are two words for octopus. It's pieuvre and poulpe. Pieuvre is a thing swimming in the sea and poulpe is the thing on your plate. And so she's also saying, "I'm very much alive. Thank you. I am not a food." And so all this here, well, this is the back of Conway's store, Curios. And Conway would have loved that Octonians, it's a Fano plane drawing, but it's also mnemonic for the multiplication in the Octonians. And he loved the Octonians. So yes, I mean, so I like this mural very much as well. But yes.
I was curious what drew you into mathematics in the first year?
Well, I've always been interested ever since I can remember in how things work and why things are the way they are. And so I actually, I only pretend to be a mathematician. My degrees are in physics, but they haven't caught me out yet. And so I remember when I was little, we had a little tiger hanging in our car from the rearview mirror. And one evening when we were driving in the street that had neon lighting, this little tiger was completely bleached. I said, "What happened to our tiger?" My father said, "Well, it's because the light is orange. And so white objects will look orange because it's the only light that they can reflect. And this tiger reflects the same thing as white objects. And so it looks to you as if it's bleached, but it's not. Everything looks orange now." And well, my father usually was right, but I remembered that I went to check the next morning and to see whether it really was still orange, and it was.
Then a few years later, again on a neon lit street. And I knew in the meantime about filters. I mean, how a colored filter changes color because it holds back some of the light. And so we have a colored green filter on our window shield, and I look at the neon light and I see it's much fainter, but what I see is still the same orange. I say, "How is that possible?" And that's because neon light is almost monochromatic. There are actually two lines very close to each other, so it's not a mix of a whole lot of things, some of which get held back. And so through colored filter, you see something else. Because the filter was not holding back that orange, a little bit of the orange came through, and that's what you saw. There was nothing else that could come through. So then my father had to explain monochromatic light to me.
So I always wanted to know. I would observe and it would not fit with what I knew, and I would ask why. So I also very quickly observed that mathematics is how you get a hold of how to explain things. I mean, yes, there are facts that are physical facts, but if you want to start working with things, when I was little, I was told if I couldn't sleep to count, to count up. And you know how at a certain stage kids love counting higher, but I thought it was boring. So what I'd count was by multiplying by factors of two. Of course, I mean, you have to work much harder in your memory because the numbers get big so quickly.
So I just liked figuring things out and asked myself questions and find answers, and mathematics is how we do that. I mean, people talk. There's this famous paper saying the unreasonable effectiveness of mathematics. And when people say that, I say, "As compared to what?" Because there's nothing else. I mean, mathematics is what we found, what we humans put together. We named, we saw systematic similarities of patterns of reasoning, and we named them so that we can start reasoning with them. We can hold them with our little brains and we can work with them. And that's what mathematics is. As soon as you're starting doing that, you're doing mathematics. And if you like doing that, then mathematics is a reasonable thing too. So that's how I like mathematics.
Probably good to end there. Let's thank Ingrid one more time.
