Hall seattle and we are set up in the cafc right over here and our special guest tonight is you know howard, theyve been set up in the library showing off really cool mask games and im so excited to welcome you to tonights very special math theme doubleheader with Eugenia Cheng and Amir Alexander. This event is presented by townhall as sort of our big homecoming festival. Im hoping many of you might be returning for the first time after a couple of years while weve been remodeling the space and for a lot of you this might be your first time at town hall. This is the type of things we exist to do. Im excitedto present these fantastic authors tonight. We love all our lecture programs, all the political costs, all of the art programming that we do but i am especially fascinated by mass, mathematical approaches to thinking. Im a reformed college math student so having a chance to present Eugenia Cheng who we posted and a couple of times and Amir Alexander as a doubleheader was a great opportunity for this special homecoming festival so im pleased to see everything here tonight. The format is a little unusual. Youve been to other townhall talks because its a doubleheader. Were going to open with a solo presentation from Eugenia Cheng and take a short break while we switch the presentations over and Amir Alexander will give his talk after which we will have a joint un day. Keep questions in mind from both talks. There is this thematic residence where Eugenia Cheng talks about mathematical thinking in its dynamic and we take this broader historical view of these sort of historical developments of mathematical thinking with Amir Alexanders talk so hopefully there will be residences but both of them will be happy to answer questions and after all that you can pick up a copy of either book at the book table and we will have book signings afterwards and our bar and cafc will be open afterwards if youd like to break play some of those great xeno games. We are a member supported organization, membership is a great show of support and all the programs we do but now to introduce eugenia and after a few wordsabout xeno, id like to welcome julie newmar to the microphone. [applause] i am the executivedirector of zeno and zeno is a seattlebased nonprofit. Our vision is a word world where everyone knows they can do math. We achieve this through programming for families ages 3 to 5 with a focus on families of color and low income communities. Our work is all about making math fun and playful because we know that there is no such thing as life lived without math and believe that a strong Math Foundation is key to a life of opportunity and success. Were excited to be a Community Partner townhall for tonights lecture. Doctor Eugenia Cheng is a scientist in residence at the school of the Art Institute of chicago. She one tenure in pure mathematics at the university of sheffield uk and is honorary visiting fellow at the university of london. She has previously taught at universities of cambridge, chicago and nice and holds a phd in pure mathematics from the university of cambridge. Alongside her research and category theory and undergraduate teaching are goal is to rid the world of math phobia. Her first popular book how to bake pie was praised by the New York TimesNational Geographic and Scientific American and she was interviewed around the world including on the bbc, npr and the late show with stephen colbert. Her book beyond infinity was shortlisted for the Royal Society inside Investment Society book prize. Eugenia was an early pioneer of math on youtube and her videos have been viewed over 15 million times to date. She is now columnist for the wall street journal, concert pianist and founder of the leaders. Join me in welcoming doctor Eugenia Cheng. [applause] thank you very much. Thank you to the townhall for inviting me back here to speak on my next book. Its always very affirming to be invited back somewhere again and this is the first time ive been invited here so that tripoli affirming and its wonderful to be in seattle. The sun is outside every time i speak of the townhall so thank you for joining us for a mass evening where im going to talk about my next book the art of logic in an illogical world. And the point about that illogical world is that it can sometimes seem like were drowning in the world. The world is awash with devices miss and conflict and the fake news,victimhood, expectation, privilege, blame, bigotry and minuscule attention spans. And it can seem that we will never agree with each other ever again and were doomed to be stuck in echo chambers and just yelling backwards and forwards into nowhere and is all hope lost is the question . I say no, all hope is not lost. It can seem like that sometimes and this book arose from my teaching art students and in that fall semester of 2016 somethings happened. Various things on both sides of the atlantic and the morningafter the election i did what many people did. I cried, i drank and i thought what can i do thats productive because i truly believe in doing something rather than sitting around complaining and i also believe in looking at your own combination of abilities and trying to use them in the best way you can to do something to help the world in a way that you see fit and i thought what can i do as a pure mathematician in this situation and i realized what id been doing with my students all semester was using the principles of mathematical thinking to find greater clarity in those divisive problems and i felt i could share that more broadly with everyone who wants to find that clarity. Some people of course are interested in finding clarity but i believe there are people who do want to understand whats going on and understanding whats going on on all sides of the argument is the first step. Im not saying it will solve all the problems but if we dont understand it we cant talk about it and thats why i wrote the book and it grew out of discussions i had had with my art students where i teach abstract mathematics. Itsnot remedial mathematics, its not the things theyve from forgotten from high school. Its how to use mathematics as a way of thinking. And [laughter] theres somebody here with a question, wheres the computer . Does this work . Its on. Thank you. Perhaps, could the volume be turneddown . You see how loud i speak. At least when iminterested. When im not interested i dont speak very loud. Well, ill just keep going i suppose until we can findwhat my next slide is. I teach art students and art students are very interesting students. They are not mathematicians at all and its my dream job because i really want to share what i feel about mathematics with more people and there are so many myths about math that its just about numbers and equations, that its not for everybody, that some people are math people and other math people and i said if you dont do your tables you can be a mathematician, things like that are myths im trying to dispel so teaching art students is a wonderful place for me to find out more about what people put off math and what can as it were put them back on math and i really believe and im sure if there are any educated in the room youll all agree that its really important to tell into what most motivates your students in order to motivate them and what youre teaching rather than trying to impose your motivation on them and what motivates my students is social and political justice and thats why this book came out. My students in sheffield and what most motivates them is food and thats why my first book was about math and food. It still doesnt should i get close to it . Should i go and stand over there . Could give the rest of the talk without my slides but i like my slides. Okay, thats going to be very complicated because i have a lot of transitions but i guess well try it. Mathematics is not just i think about numbers and equations and not about getting the right answer and its not just about solving problems even. I believe its a framework for agreeing on things and what counts is good information and in the current world i think thats what we need and theres tons of information everywhere, information is no longer at a premium so whats more important is a way to decide what counts as good information and pure mathematics as one framework based on logic. So i believe there have been an oldfashioned traditional view of what pure mathematics is but pure mathematics applied to applied mathematics and applied mathematics is useful for science but science isnt useful for engineering and medicine which is useful for cutting numerical quantitative parts of the human world and that is true and i used to believe that was the extent of how my research would be useful because my research is so abstract but this narrow view enables people to declare that people can be glad that this exists but they can say im not ever going to go into that field so i dont need to do it myself whereas i believe pure mathematics is about how to think and that therefore it is about the entire human world. At least the parts of the human world that think and sometimes these days it seems like him of the human world doesnt think very much. Anyway, i am going to talk about first of all analogies and what role they play in mathematics and the interconnectedness of things. Then ill talk about how abstract math allows us to feel relationships we didnt see before and that we can use those abstract relationships to pivot in different situations so we can understand more things than we previously did and finally i will talk about how to get them with what i believe is intelligence. First of all, analogies. Another thing we can say is that pure mathematics is a theory of analogies and heres what i mean by that. Supposing we have two apples and two bananas, then we can say theres something they have in common and if we forget the details about them being apples and bananas we go they are both two things and this is fundamentally how we come up with the idea of numbers in the first place. Numbers are an abstraction from sets of objects that have something in common and if you teach children how to count, you just have to wait until they make that abstraction leap and you cant do it for them, they just have to see whats going on and every time we make another abstraction leap in the process of math education some people dont quite make it and there are various students with that and one of those is it can seem pointless if its not well motivated and another is you have to wait until you do it, nobodycan do it for you. Theother thing is there are different ways to do it. This is not a completely Automatic Process so if for example we wanted to oh. This is very exciting. But if instead of saying two things we said what this had in common was two fruits that would also be true and thats also an abstraction but in that case we would not be able to include for example two chairs in that situation. That is not an example of two fruits so in that example we have to go up one level further to two things in which case we can encompass those examples and one going to argue is that although abstraction teams to take us further away from real life it actually enables us to bring in far more examples than we could before so heres a more mathematical example where if we say, if we look at one 2 and 2 three, they are both examples of a b people often say i was fine with math until the numbers becameletters. Im going to show you what the point is of numbers becoming letters so we can look at one times to 2c and theyre both examples of a times be but now, this is supposed to work. A b and eight times be, thank you very much. [applause] thank you. So a b, a times b are all examples of a dumping be and that is a further level of abstraction and these levels are bottom levels of what you might do in Elementary School and this level is what happens when you start to meet algebra and this level is what happens if you go to be a math major in university and you take abstract algebra, maybe group theory and none of these levels is rightor wrong, thats not the point. People think math is all about right and wrong and its not, its about what light your shedding on any particular situation and one of the things my phd advisor taught me was the aim is to find the most abstract approach, the aim is to find a good level of abstraction for what youre trying to do and what happens in normal life typically is we talk about things being analogous to each other that we dont focus on what is making them analogous and that ambiguity that we leave leaves open the possibility of disagreement based on using Different Levels of abstraction so that were not making clear whereas in math where very specific about which level were using so that we remove that particular ambiguity so heres an example of how that ambiguity comesin. Its down. If we talk about straight marriage and samesex marriage, some people say oh no, its terrible and whats really going on is this, people are using Different Levels of abstraction. If you think marriage is about an unrelated man and woman, samesex marriage is not part of that picture some of us believe its actually really about two unrelated adults in which case sex marriage is part of that and people disagree because theyre using Different Levels of abstraction and the next thing that happens because were not being precise about which level were using, the people that disagree about upperlevel can hallucinate that weve gone farther than we have and they get upset and they say next and we know will be allowing any two adults even if they arent unrelated. Ive redacted in case there were children in the audience because then we could go up further and just have say three humans or we could say to living creatures or we could say to creatures. And the point is that just because some of us have decided we want to go to here does not automatically mean we have shot all the way up to the top but when were not being precise about what level of abstraction were using it can open art of those arguments about saying this is the same and this isnt the same so im not saying this approach off that problem but it gives us an opportunity to have a slightly clearer and more sensible argumentabout it. The next thing i wanted to talk about is how things can be seen as being interconnected. Heres my favorite diagram of interconnectedness and itis an abstraction of the London Underground system. We forgotten many details about where things are and its not geographically accurate but its useful for seeing how stations are connected by which lines but because its not geographically accurate you can end up with slightly hapless tourists trying to take the train from Leicester Square to common garden only even though there two minutes walk away. Here is the geographically accurate picture was which is a different abstraction and its not better or worse, its probably less useful if youre trying to take the train somewhere but its interesting seeing where everything is so the point is these are two different abstractions that eliminate aspects of thesituation. This is what math does, it abstracts to see what we can learn from it. Heres an abstraction that i find quite interesting. I think this is what often happens when relationships break down that maybe one person, ill call them alex, eels disrespected and when alex disrespected alex is unable to show love and sam eels unloved as a result of which sam is unable to show respect so alex feels disrespected and we have a vicious circle that can escalate. I can further abstract these are the kind of action arrows and these arrows are feelings and this doesnt solve the problem but it makes a start because we can think about how we could break these, at least one of these arrows because you only have to break one to break the circle and you can say is it easier to break an action arrow or a feelings arrow, maybe we can control our feelings but maybe we could decide not to act on them so perhaps even when alex feels disrespected they could concentrate on still showing love regardless of that and then the situation wont spiral out of control so we reduce it to these two action arrows and we could argue about who should take responsibility for breaking the arrows and one possible theory is whoever is more mature should be the arrow so we have this vicious circle and this vicious circle at an abstract level is very similar to even more tragic things. For example the situation of Police Violence which one could try to say happens like this but police threatened by black people so they defend themselves against black people which makes black people threatened by the police and so the police feel threatened by them. Im not saying this is what happens, its an overview of what happens but its been shown even when black people dont do anything to defend themselves and do everything they are supposed to do, theres still violence against them. We can say should we break the actionarrows or the feelings arrows and we might argue maybe the police, why do they feel threatened . Theyre the police and theyre trained to feel less threatened. Its been shown they feel less threatened by white people and black people but we can teach them to take action differently ratherthan escalating things and we could say who should take responsibility . People yell and say black people should just obey the law. But i would argue that its really the police who have the power in this situation though i think they should be the ones taking responsibility for changing it and if they dont it doesnt help the situation but maybe we can find more clarity about what is going on and this is something i thinkabstraction and help us with. Another way i use interconnectedness is when there are many factors contradictory to the same thing. There will be a grievous united incident when they needed to kick something off of a flight because it was overbooked and he didnt want to leave so they called security and dragged him off and he injured on the way out and there were arguments on the internet saying youshould just do what you told and you wont get injured. It really is that simple and never someone on the internet says it really is that simple usually isnt that simple. Its like if someone says fact, it usually means they donthave an argument to back themselves