if you have a question, please use the microphone on either side of the stage to make sure your questions are concise and in question form. after questions, eugenia cheng will sign copies of her latest book, "beyond infinity". books will also be available for sale at that time and then you should come back. april is packed. with the seattle institute of the hot-- biology panel on institute of health and paul talking with 100 ways to reverse global warming and richard youngs exploration of artificial and emotional intelligence. you can find all of our programming at townhall seattle.org. finally, i would like to thank the members in our audience tonight pick your contributions allow us not only to create dynamic programming like this, but to make sure it's assessable to everyone in our city. members, thank you. this is your townhall and we are grateful to be a part of this with you and now it's my pleasure to introduce to you our speaker this evening. eugenia cheng is a scientist in residence at the school of art institute of chicago and an honorary fellow of the university of sheffield. her popular youtube videos these bastards when everything from the perfect glass of wine to the best way to share cake and has been viewed over a million times her latest youtube video has been viewed over 8 million times. in 2015 she joined stephen colbert on the late show to explore thmathemical wonders puff pastry. please join me igivi her a warm townhall welcome to eugenia cheng. [applause]. >> thank you very much and thank you for the wonderful introduction. think you, townhall seattle portland me back to talk about this book. i had a wonderful time when i came to talk about my previous book a couple of years ago, so thank you for joining us to talk about "beyond infinity". i was once called in to arbitrate a dispute between my four year old nephew and his best friend about whether infinity was a number or not his best friend said infinity is not a number because my daddy said so in my daddy is a scientist and he knows everything. my nephew sensibly focused on proving his daddy did not know everything, by reeling off my faxes daddy didn't know. [laughter] >> i love the fact that infinity is something children talk about and that adults cannot answer and for me that's a wonderful place to explore what goes on in the world, what goes on in our mind and to explore and nurture curiosity in children and it's amazing and wonderful to me that it took mathematicians thousands of years to pin down a way of talking about infinity that was still make a sense when you scrutinize it with logic. unfortunately, there are many arguments in the world these days i do not make sense even when you don't scrutinize them with logic, but certainly when you do scrutinize them with logic and the whole point of math is to construct arguments that hold up under logicso that'shat will ve a look at today. there are infinitely many things i would li tsay about infinity, so i have to pick some and i'm going to talk about loops, paradoxes, that infinitely big and i would like to touch on what infinity is. talk about dimensions and finish by talking about the infinitely small aircraft loops are of my favorite things and they are how i think i have encountered infinity because i grew up in a house that had a chimney in the middle with a fireplace in the idea was all the other rooms went around the fireplace and were heated by the fireplace and the thing is that my sister and i like to to chase each other around the fireplace and because it was in a loop we could basically chase each other infinitely far around the house. it was as if we had an infinite house. we could then also change directions and crash on the other side, but loops are way we get access to infinity even though our world is finite and one of my favorite computer programs, in fact my all time favorite computer program is when i wrote when i was five. my mother taught me to program computers when i was five and i was very good at it and i never got any better, so i still program like a 5-year old and i was so enthralled by my favorite program that i never got bored of it and i'm not easily bored and it has not downside because that means i'm never got any better a programming because i could always do the same program over and over. it was programmed in basics, which dates me. then you had to run and you get this and i could do this over and over again and i did do this ernd or agaibecause now we have an infinite loop. i think this is-- along with chasing assist-- my sister around my house was my first appearance of infinity in a loop. what is infinity? well, my friend is a basque translator and she tells me in basque infinity is the same word is 11, which kind of indicates that beyond 10 at midas will be infinity and this idea is borne out by my friend sally who one day was doing a stock of her homemade jam and she said she had three jars from 2013, 10 from 2014 and and not from 2015. somehow beyond to 10 is a lot and in my work and higher dimensional category in fact higher is anything higher than three, selling higher dimensional theory it goes 12-- one, two, three lot and after three midas will do infinity, so it tends-- it depends on what you do with members and what you can as big. another way we can get a loop is if we sing around and we probably all know this one, so i would like to try to see if we can see it together. now, maybe if we start over here , everyone over here can go first and then everyone over here can go second and everyone over here can go third admin force and we will see how we do. lets a start about here. ♪ row, row, row your boat. ♪ row, row, row your boat. ♪ ♪ row, row, row your boat. ♪ >> and we can go on forever. there was an-- an incident involving my nephew when we were walking him home and it was raining and he was screaming and the only thing that stopped him from screaming is if we sang row, row, row your boat in a round and here's the depiction of what we just did. so, singing row, row, row your boat and then the next people start here in the next people start here in the next people start here, but i am happy you spontaneously carried on and did not stop at the end, which means when you got to the end, which is here you started again and yellow people also started again and the green people started again and orange people also started again and then we kind of going and made this loop. if you look at the four lines in each section, they are the same for, they just rotate around this group of people, so this loop is the infinite loop of row, row, row your boat. we could keep going on forever because it's a loop we can go around as many times as we like, so it's another way we access infinity. let's talk about paradoxes now because if we think about what infinity is that we are not careful about it we run into issues and the issues-- there are two things you can do anyone into a problem or two can either away from it or go something looks interesting here and i think i will investigate why this paradox seems to be happening and if you are mathematicians than you tend to investigate why the paradoxes there rather than run away from it, so here's what i really like which is called hobart's hotel in you imagine your head you have an infinite hotel. your infinite hotel has rooms one, two, three, four, five, six , seven, eight all the way on forever of course this is not possible in real life, but the great thing about matt is that it's not real life, so some people think that's a terrible thing, but i like it because it means you can do things that aren't actually possible in real life. in real life there are restrictions, but in math the only restriction is logic so you can do things like have an infinite hotel took you can have a full hotel and see what happens when one new guest arrives and then you go well, how about i move the person in room two into room one interim to remove the person room to into three and the person room three to four and so on and i never run out of rooms to move into because it goes on forever and that means room one is now empty and i can with extra person in room one. you cannot do this in a finite hotel, but it would have changed -- anyway, so burt paradox was only from a couple hundred years ago. the net goes back up hundred thousand years and it's about motion and how we understand motion, so one said achilles can never be courses in a race. i'm going to challenge you to erase. i just went a little head start, not too big and the point is by the time-- sort of starts at this blackline here and by the time achilles has arrived at this blackline the horse has gone forward a little bit and maybe there by the time achilles is there the horses somewhere further and by the time achilles is there the horse has gone somewhere further, so that means it's always going to be headed achilles because achilles will never beat the horses, but that doesn't seem quite right because probably the tortoise will be being by achilles and there's a wonderful video on youtube where there is an actual race with a bunny against a tortoise and it's perfect because the bunny is like this and the tortoises like this and then the bunnies like to wonder what's in there and eventually everyone is screaming at the bunny to go that way in the bunny never does in the tortoise eventually went and is brilliant. i love it. the next paradox says you can't eat all of your chocolate cake because you eat half of it and then you have to eat half of what's left in you eat half of what's left in the new eat half of what's left and it would be of what's left left, so you never finish your chocolate cake and yet i do finish my chocolate cake. the last one is that nothing is moving because if you take a photo and we all wave around when someone takes a photo in the photo no one will be moving because it only captures one instance and in that instance no one is moving so how is it we are moving and these are things that where some form of logic has violated what we understand about the world and some people say that means math is dom and other people say we should explore math further to see we-- how we can resolve this. here's the solution to all this came 2000 years later and that's what calculus is about. you might think calculus is the thing invented to torture people. people say i was okay with math until calculus. a lot of people say i have-- i was okay with math until times tables. math is dealt with infinity and although you may think infinity is far away from this world actually condering infy and talking out how to think about it is what led to the development of calculus, which controls everything that moves continuously in the world around us, so everything that uses electricity, anything that has a curve and it, the curve of the piano, the way the strings work, everything is controlled by calculus. without that understanding infinity where we wouldn't have any of these technological developments, so there is a use for an infinity. i read that weary of a talking about how useful math is because i don't like to think it's the big selling point. it would be like saying i would like you to meet my friend, they are very useful. [laughter] >> math is useful, but also the fact that it's fascinating, not the fact it's useful. it's great it's useful as well. here's a picture of me eating the nose cookies. i made chocolate chip cookie dough in the first cookie dough is one 10th of the whole dough in the next one is one 10th of what's left in the next one is one 10th of what's left and do so on. that end ones i have eaten. so, now i will talk about infinitely big things to bit. what is infinity? is it a number? well, let's think about this big number. what is a million look like? i think about this and i think i have never seen a million of anything, but there is a great children's book called 1 million -- how million-- how many jellybeans. i don't want to spoil it for the last page is a picture a million jellybeans and it's really cool because yet unfolded because it's really big. here's 10, here's a hundred, here's0000. couldn't make a million dots becamy computer gave up because it said i didn't have enough memory. infinity is bigger than all numbers. it's bigger than how many people there are on earth and its more than how many animals or germs or cells or molecules or atoms. we don't have an infinite number of things on earth, but this doesn't tell us what infinity is. it only tells us what infinity isn't in which we like to say it's taller than everyone we know. what is infinity? well, we can also think about-- i said there aren't infinitely many things on earth, but how about infinity in a circle. i was helping some first-graders with symmetry and we did a triangle and a square and hexagon and so on. we did a hexagon and one said and hexagon has eight sides-- because octagon stands for octopus and eventually gave them a circle and wonder this line in one of them through this and then these lines. hundreds of them and the other one went there's millions of them and the other one went you could spend your whole life trying them and you would not finish and then the other one colored in the tests are called and said i've drawn them all now and i went home going at what just happened? but, there are infinitely lines of lines on a circle. we had many infinite things as long as they are not physical things. internee is also a way of winning arguments because someone might say i'm right times 10, i'm right times a million, i'm right times infinity, but what if one says i'm right times to infinity. is a bigger? let's think about this. what happens if you think infinity plus one equals infinity because infinity is the biggest thing? well, we could then subtract infinity from both sides of the equation and we would get one equals zero, which is not so great. we could then do infinity plus two equals infinity and then we would get two uals zero and if we keep going we will get everything equals zero and we could even suggest that to infinity is infinity plus infinity and that is also infinity and we subtract infinity from both sides and we get infinity. now everything equals zero. now, we are in the zero world. that's okay. is a perfectly valid mathematical world, just not the one we live in. it's like the world of candy and i was little because i was allergic to food coloring, so i couldn't have candy, so however much candy that people gave me i never had candy, very sad world to live in. infinity is not an ordinary number. if you cause a contradiction then you end up in the zero world, so you can say it in the is a ordinary number, but only if you are in the zero world. so what is it? it's not the real number. the real numbers are the ones that fit on this line. in between them are all the real numbers, but maybe there's another kind of thing it is an math petitions have developed this called a cardinal number and it's just the number of things there are in something, so you find some very well defined some kind of familiar object and you go, like this. this is how we tell a child what 10 is, the number of fingers we have. we can do infinity like that. infinity is how many numbers there are. we had to be a bit careful about that. it's how many whole members there are in the reason is that this is only the first infinity because they are far more infinity's beyond because there are gg members. look athat possibly mean? well, let's think about this. the first infinity is how many guests fit in hilbert's hotel. so, remember we could fit a new guest and like that, but they still fit in the hotel, so that seems to tell us that infinity plus one is still the same number of infinity because we still fit it in the same hotel, but it kind of depends. it depends whether you care about the hassle you have caused the people. imagine you checked into a hotel and they said excuse me, you need to move rooms. if you care about the hassle, one plus infinity is not the same as infinity plus one because one plus infinity means one guest arrives first and then infinity. in that case you just print the first guest in room one and infinity guest starts room to a known has to move. infinity plus one means you put the infinity guest in first and a new guest arrives at which point you move everyone up a room, so you have called everyone hassle and that is different. if you are doing that kind of thing than infinity plus one is bigger than infinity and this is what i think shakespeare means because in the painting of the shrew he said if this be not to look for have no more to say, but did for well-- bid farewell forever and a day which he evidently thought was longer than forever. he didn't say a day and forever. that's longer because you have to wait for the whole of forever and then another day after that. there is a bigger infinity and the whole number. there's a bigger infinity and the number of people in hilbert's hotel ended this is how me decimal numbers there are there are a lot of decimal numbers and some go on forever. one that goes on forever but repeats itself so kind of doesn't count whereas the square root of two goes on forever never repeats itself, which is because it's called an irrational number which means it's not a fraction. one over three is a fraction. pie is another decimal number that is very famous that goes on forever never repeats itself, so it's irrational and if you count all those ones and you put them in the one with the rational ones those are tl nuhe reaers and there are so many irrational numbers that there's actually more of th in another way of saying that is if you have hilbert hotel where all of the room numbers were decimal numbers that go on forever, think about how long it would take to get your teeth, but you wouldn't be able to evacuate that into a normal hotel if there was a fire. there's no way to do it. that tells us that there are more irrational numbers than rational numbers and the irrational numbers are called because it's a bigger infinity is called an uncountable infinity because counting is one, two, three, four, five. if you can count something you can put it in hilbert's hotel and if you can't it's called uncountable and by the way there are also more irrational people than rational people. [laughter] >> now, there's quite a lot to take in so i would like to have a musical interlude now. one of my favorite songs, the infinite shiny-- shining heaven. i like to think he knew about this infinity as well because he said uncountable angels, so he clearly thinks that's the next order of infinity up from the whole number, so i will now lets you ponder these things a bit and we will think about the fact that infinity inspires many people including poets and musicians. ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ [applause]. [applause]. >> going to talk about dimensions now. dimensions are one of my favorite things because i think it high dimensions all the time and i think actually we have all been thinking of infinite dimensions all our lives about-- without realizing that. he realized he had been speaking all his life that relates that. so, let's think about how many dimensions there are in the world. there are really only three dimensions, or are there? does four dimensional space exist? einstein main four dimensional space very famous because he included time and if we include time and we understand how gravity works in a better way, so space-time is a famous four dimensional space. you can think of it like this, if you meet up with someone somewhere then you need to tell them where the three-dimensional space to meet up, but you also need to tell them when it has if you go at a different time you won't see them because you are in a different spot in time. another way to think about is to escape from two-dimensional space, you need to use the third dimension, so in order to climb onto this stage, which is escaping from the two-dimensional space of the four i had to climb up steps or if someone tried to hem me in with the offense and if i could find their dimension i could escape. if a someone locked me in a cell i would be enclosed in three dimensions, but i could escape by traveling in time. i could time travel to yesterday when i wasn't blocked and i could walk out and come back to today and i would be five. there are plenty of fictional stories books and movies where people do that and i like that as a way of thinking about the fourth dimension. music, which could be considered to be a fourth dimension because you sort of escape from where you are when you listen to music and so if you are stuck in a cramped train with nowhere and you listen to music than it takes you away from that and maybe you forget you are there. it's not clear if you genuinely escape, but thoughts about what it forthcoming-- dimension could be your cares of four dimensional q, so how is this a four dimensional cube? think about a three dimensional cube for a second. three-dimensional cube is made by taking a pair of two-dimensional square's anointing them up, so if we take a pair of three dimensional cubes and join them up, that's a four dimensional cube and there are four pairs of parallel three dimensional faces. there's one pair, there's another pair. here's another pair and here is another pair of cubes inside of it. does that really exist? not clear. it does exist in our brain. that's another thing i love about math because we are limited only by what we can do in our brain took them-- the world is much more limiting. another type of dimension is if we think about when we go to the doctrine theake r vil statistics. my blood pressure and pulse are quite good. i never way quite as little as i want to. they can take your weight, your high, your blood pressure which is to numbers right there, your pulse, your age and that's already six things. if you tried that on a crap you would need a six dimensional graph. @six dimensional states right there. i was about to say my and then this popped up. let's talk about criteria instead. every time you evaluate something, you're thinking about different dimensions. you can think about what restaurant you want to go to for dinner. so, you can think about-- you can evaluate restaurants according to where they are, what kind of food they had and what the services like. .. and then another is how it is rotang then another for how far back my arm is and also the rotation in my upper arm. you meet this sometimes trying to put sunscreen on your back. there's a microphone back there but you reach down to here and get stuck so then you have to do this and move your arm all the way over to here and hopefully those points are close enough together you don't end up with a strip of sunburn across your back. it's not whether it is near here in three-dimensional space but it's no good if you are having to do that in order to move one little piece inside. a. of that is quite been what we could compare the different ways of getting to the place that we are going. maybe we could go by train or go by plane. but then we could compare the waves of comparing. so n we compare the way of comparing and we care that spending money or do we care about spending time and then we can compare the way of comparing and then that way of comparing those. we could do this for something like comparing books as well. sometimes people get into arguments and often the arguments are a bit pointless because all they are doing is using different criteria to compare the same thing. so you might say i like the book because it has a good plot and someone else says it has better characters and then this one would have better plots and that's one would have different characters. is it better to have a better plot or better characters and then you could say i like suspense because i like thinking about human behavior. they can compare the way of comparing and on it goes and you never have to stop. the thing is the more dimensions that you use the more nuance you have in the way that you think about the world, so i think if we all thought more dimensional all the time then all those arguments would become more nuancnuance instead just shoutig matches but maybe i'm just being an optimist. maybe the last cookie one over infinity is that zero that doesn't make any sense if one divided by infinity is zero then you could multiply and then what would happen? so there are ways of defining it to be one divided by zero although it doesn't make sense. so, you have to move into a different world and this is the thing about math, sometimes people think it's about getting the right answer but really it is about exploring possible answers and what mathematicians do in research is they dream up different worlds in which they make sense and then they explore what else has to be true in that world and what it looks like in order to make this make sense. and so, in the world where one over zero is infinity, you have to loosen up your space because it isn't like normal spacing for me that could be for things. thinking about what the world would have to look like to create an answer is relevant to my life because i could then think about what the world would have to look like in order for nobody to be afraid of mathematics, for example. that is currently a dream world i could look towards it by thinking of it as an imaginary world in my head personal. fact tools are a way you can think of where you have something that is the same as itself in the scale so you could limit and it would still keep looking like it's also here is one you take out the triangles and then from each of the remaining you keep doing that so it is like a loop you keep doing the same thing so now we take down each and i keep going and i couldn't get any further because my computer gave up. but you could do this also with a tree so i could start with a branching tree and then i'm going to make a branch like that come out of each branch. and now i will make one like this come out of each of those branches and goes and goes and goes and that might be the end. there is one more level. you can draw your own. so i will draw something resembling a gasket now and i think it is rather fun. when you draw it yourself is something i like about drawing it myself rather than the computer to do it. so you draw a circle, then you draw three circles inside the circle touching each other and then you fill in the biggest space you could find and then you keep going. so that instruction you find the biggest space buchanan and you fill it in with circles. it's quite therapeutic and meditative and the interesting thing is it looks like the biggest space. you fill everything in and then your sense of scale changes in your head and then it starts looking like a huge space that you can then fill in and you keep going like that forever and then you have something that is quite actual. although it is quite wonky i like the effect of having drawn in by hand. if you look this up on the internet, there are load of beautiful pictures. but now this space seems enormous maybe you can come in and keep going in a moment. another way that you can get this is by pointin planting twom at each other and taking photographs or staring down the middle because now that goes on forever and the reflections get infinitely small. here is a picture of me taking a picture of me forever. it's called the draft affect where they also get infinitely small and that's why it is a fun thing to do. you might have noticed this whole talk has gone in a loop. the thing i love about math is that it refers to itself because it is abstract you can build more which is why there is always more to discover. you can't build a new bird out of birds they don't work like that. you can build a sculpture of a bird out of sculptors of birds because they are abstract enough to do that. math is abstract enough to do that and i think that art is abstract enough to do that so they cannot refer to itself and it can also refer to othe othert and so to close the loop, i would like to show you a poem translated which demonstrates the way that these references make a kind of infinite self reference that takes on forever. so this refers to a painting of the fall but actually refers to another and it refers to the growth so i'm going to read you this. is that a tiny almost invisible figure falling into the sea. how it takes place when someone else is eating or opening a window or just walking along an, everything turns away, walks away practically to the disaster. the pain of someone's life never touches someone else to. if he falls it will hit on the roof and those power lines. if we were to join in everyone's suffering, life would be impossible. but i'm waiting and i'm going to help. i will collect the pieces of the broken wings and give them shelter when he falls away i fell. thank you. [applause] are there any questions? if you have questions we ask that you come up to the microphone on either side of this page. >> it sounds like you work with kids. that's one of the reasons i love teaching children is because they are much less afraid of math. with all the children you get them looking nervous. this little boy got really upset and said that there ar were noty member senate and it's interesting because most people are kind of put off by this. they are not members but this little boy wanted to give out numbers. it's what we should feel sad for everybody that has something bas have happened to them in the world. we can pick one person and help them and that would be okay. why do you think that we applied on the wonderful piece of music and ideas? the numbers that go on forever without repeating how do you have a certainty that they go on with forever without repeating. >> that is a great question and something that we do teach. if you follow that logic if were a fraction theitwere a fractiond repeat itself as also if it repeated itself, you could express it as a fraction because you could keep repeating parts antake the repeatingparts and ue fraction. so if you can prove it isn't a fraction then it would never repeat itself. any more questions? we will be having a book signing in the lobby. please join me in getting a round of applause. [applause]

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