I hope everyone in the room has a chance to visit tuesdays at the library showing off cool games and activities. I am so excited to welcome you to the doubleheader. Im hoping many of you might be returning after a couple of years while weve been remodeling this space and for many more you dismiss this type of thing that we exist to do. We love all of our programs and political talks with the arts programming a great opportunity for the special homecoming festival so i am so pleased to see everyone here tonight and thanks especially to our partners. The format is unusual if youve been to other talks because it is a doubleheader. We are going to open with a presentation from david could then take a switch debate could break while we switch over after rich peoplrich before they joina so keep questions in mind from both talks. There is a beautiful residence tonight where we talk about mathematical thinking in its urgent present political dynamic and then we take a broad historical view of the mathematical thinking so hopefully there will be some residences but they will be happy to answer questions and after that you can pick up a copy of either book at the book table and we will have book signings afterwards and the caee is open afterwards he would like to stick around and play some of those great games. The last thing i will say is we are a member of the organization. Now i would like to welcome julie up to the microphone. [applause] im the executive director of the seattlebased nonprofit. A world where everyone knows they can do math. Our work is about making math fun and playful because we know that there is no such thing as a life lived without math and believe a Strong Foundation is the key to the life opportunity and success. We are excited to be a Community Partner for tonights lectures. Doctor eugene is a scientist in residence at the school of Art Institute in chicago. Tenure in mathematics at the uk and is now the honorary visiting fellow at the City University of london. Previously taught at the universities of cambridge, chicago and holds a phd in mathematics from the university of cambridge. Alongside her research in category theory and undergraduate teaching her aim is to rid the world of math phobia. The popular math book how to bake pie was please praised by w York Times National geographic and the scientific americans and was interviewed her comfortable concluding on the bbc, npr and the police show stephen cole there. An early pioneer of mass on youtube please join me in welcoming doctor cheyn. [applause] thank you very much. Thank you for inviting me back here to speak on my latest book. Its very affirming to be welcomed back somewhere. Its wonderful to be at seattle when i speak at the town hall. Im going to talk about my book the art of logic and we were driving in the current world where it is awash with divisiveness and conflict victimhood from exploitation, privilege, shouting and miniscule Attention Spans and we will never agree with each other again we are doomed to be stuck in the chamber and just yelling back for my teaching art students at the Art Institute in the fall semester of 2016 some things happened, various things on both sides of the atlantic and the morning after, i did what many people did. I got depressed, i cried, i drank, and i thought what can i do that is productive because they truly believe in doing something rather than sitting around complaining and i also believe in looking at your own combination of abilities and using them in the best way you can to do something to help the world in a way you see fit and i thought what can i do as a mathematician in this political situation and i realized that i have been doing with my students all semester is using the principle of mathematical thinking to find clarity and i felt that i could share that with everyone who wants to find their clarity. Some people are not interested 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 that it would solve all the problems that even if they dont understand if we consult all the problems and that is why i wrote this book and it grew out of the discussions i had with my students where i teach abstract mathematics. Its not the things that they forgot from high school. Its how to think and use mathematics as a way of thinki thinking. [laughter] [inaudible] where is the computer, should this work lack . Thank you. Ken the volume be turned down . I will keep going until we can find the next slide. It is my dream job because i want to share what i feel with more people and there are so many myths about math but its about numbers and equations some people are math people and some people are not. If you cant do your timetable you cant be a good mathematician things like that so teaching art students is a really wonderful place for me to find out more. I really believe you will all agree that its really important to tap into what motivates your students to motivate them into what you are teaching rather than impose your motivation on top of them and i realized what motivated my students as questions of social and political injustice and that is why my book came out like this. What motivated them was food and that is why my first book was about math and food. Should i get closer to it . Should i stand over there . I could give the rest of my talk without the slides but i like my slide. Thats going to be very complicated because i have a lot of transitions but we will try. Its not just about numbers and equations were getting the right answer and its not just about solving problems. I believe it is a framework for agreeing on things and every academic discipline has a framework for assessing what counts as good information and in the current world i think that is what we really need an education. It is a premium so it is a way of deciding what counts as good information and pure mathematics has one particular framework based on logic. [laughter] i believe that there has been a traditional view of what the pure mathematics is. It applies to applied mathematics. It is useful for science and the sciences anscience has been user engineering and medicine which is then useful for the numerical quantitative parts of the human world. I used to believe that with the extensive but the thing is this enables people to declare they dont need math. People could say im not going into any of those fields. But i believe pure mathematics is how to think and therefore it is about the entire human world at least part of think and these days it seems part of the human world doesnt think very much. So i am going to talk about first of all analogies and what role they play in mathematics and the interconnected somethings then i will talk about how abstract math allows us to seal relationships we maybe didnt see before and we can use those to pivot between different situations so we can understand more things than we previously did and finally i will talk about how to fit in with what i believe is intelligence. First of all, and allergies. Another thing we can say is pure mathematics is a serious and allergies and what i mean by that is supposedly of two apples and two bananas we can say there is something they have in common and if we forget the details about them being apples and bananas they are both two things and this is fundamentally healthy, put the numbers in the first place they are not abstractions from the objects that have something in common and if you tell children how to count you just have to wait until they make that abstraction we. You can do it for them they just have to sort of see what is going on and anytime we make another leap in the process of education some people dont quite make it. There are various reasons for that. One can seem pointless and another you have to wait until you can do it. Nobody can do it for you. The other thing is there are different ways. Its not a completely Automatic Process so if for example very exciting. [laughter] if instead of saying two things they said what they had in common that would also be true and that is an abstraction however in this case we would not be able to include for example two chairs in that situation. That is not an example so in that case we have to go up one level further in which case we can encompass those examples. It seems to take us further away from real life and enables us to bring in far more examples than we could before so heres a mathematical example where if we look at one plus two and two plus three there are examples of a d. And people often say to me i was fine with math until the numbers became letters. [laughter] im going to show you the plaintiff numbers becoming letters. We could loo could have one timd a two times three but now a d. And a times b. P6 and its what you might do in Elementary School and what might happen when you start to use algebra or. None of the levels are right or wrong. It was like you are shedding on a particular situation. What happened in moral life as we talk about things being analogous to each other that we dont focus on what is making them and ill address and we leave those in the cases of disagreement. Heres an example how the ambiguity comes in. If we talk about straight marriage and samesex marriage some people say theres no difference really between them so what is going on as people start using Different Levels of abstraction. So if you think that its about an unrelated men and women then it isnt part of the. Some of us believe that its actually really about unrelated adults in which it is part of the. People disagree because they are using Different Levels of abstraction and we are not being precise about the level we are using. Even if they are not unrelated it wasnt just in case there were children from the audience because then we could go up further and say to living creatures. It doesnt automatically mean we have to go all the way to the top but we arent being precise about the level of your using. It gives us an opportunity to have a more sensible argument about it so the next thing i want to talk about is how things can be seen as being interconnected. Heres my favorite diagram of interconnectedness and its an abstraction. Weve forgotten many details about where things are because it isnt geographically accurate you can end up with different taking the train from its probably less useful if you are trying to take the train somewhere but its quite interesting seeing where everything is. Here is an abstraction that i find quite interesting and i think this is what often happens when the relationships break down that maybe one person feels disrespected and when alex feels disrespected shes unable to show love and when he feels unloved as a result sam is unable to show respect said he feels disrespected. I can further abstract entities are action errors and feelings. We can think about how we can break these euros because you only have to break one to break the circle. We could argue about who to take responsibly for breaking the era and one possible theory is whoever is more mature we have this vicious circle and. It is an overview of what happened. Should we break the action we could argue may be the police, why do they feel threatened they coultheycould be less preventedk and white people so they could also maybe train them i would argue the police have the power in the situation maybe we can find more clarity about what is going on here. Another way that i use the interconnectedness to help me is many contributing to the same way. It means they usually dont have an argument and i read an editorial that said you know whose fault this is, its your fault because you sometimes miss flights and thats why the overbooked flights. Lets think about this, shall we. And also because one might say that is a reasonable reason for someone to get to work. Simply forgetting most of the information, ignoring it isnt a very good way of simplifying it. It becomes relative to your brain. [laughter] one day i think that abstract math can help us is because it gives us ways to understand the interconnected systems as a single unit so that if we understand that this is a single unit, then we dont have to be afraid of it. It is still very complicated i like to think it is like those vacuum cleaner bags where you suck all the air out and it makes it easier to move around and put under the bed and things like that. Heres another one i drew about why i gain weight. I used to be larger the first thing is even rocket science. Ive taken more energy but its also because of my metabolism and if i eat stupidly and exercise too much, already it is because we eat too much or too little and also i exercised too much and exercise too little. Also, my metabolism is controlled by my genetics and also sleep and i eat too much because i like food. Also because i emotionally eat and both of those were caused by my genetics and my upbringing and different social pressures to eat so the social norms and time pressure causes me to get emotional stress and life happens and they are spending tons of money trying to get us to eat more. It doesnt want anything but how do they make money plus when i do gain weight, then i start eating too little and getting stressed so this is simple. Its not that simple, it is the simple but understanding this helps me see the vicious cycles and which links i can try to break which doesnt mean everyone should try to do that that is what i want to do so i did draw a diagram. I got tired of people saying it is just the fault of the people that voted for thirdparty heres something that is a piece of mathematics that may seem a bit irrelevant. We can remember one, two, three, five, six, ten, 15 and 30. Its not that interesting. When we step into the Straight Line it like to say this is why i do not tidy the papers on my desk. [laughter] they draw a kind of family chuck d. Of those relationships and at the top like a great grandparent if any of you came to hear me talk about this, i did show that spent it with to get a little bit further. Ten and 15 and 30, 5 to ten. Like any family tree we dont draw grandparent relationships because we can do to stem from two levels of children so 3,000 to six and 15 and one goes into two, three and five so now we see that its really a cube which is more interesting than a bunch of numbers in a Straight Line and if we think like a mathematician i think why did that happen. Other numbers, do other numbers make a cube . Maybe you can see that its because the three numbers are prime numbers and that gives us three dimensions to the cube so at this level they are products of two and 33. If i draw it like this i get the actual prime factor. I have two, three and a seven and then the products of two things were three things at the top. The middle diagram is analogous to the previous one but every site had been replaced by seven and when we go to the level of abstraction it isnt actually the same diagram and so abstraction shows us something that is the same about the situation and im going to show you how but first i want to stress something about this diagram which is that sex is less than seven. That might not sound very profound with six is less than seven and yet it is higher than seven in this hierarchy and whenever you have two different hierarchies that disagree on the same thing that can be a source of antagonism for example if somebody is older at work but more junior than someone else that can be a cause of antagonism. Now i want to show the point of going to this level of abstraction because they can not be anything they dont even have to be numbers. For example it could be three types of privilege such as rich, white and male so then we have here people with two of those types of privilege and people with one type of privilege and then at the bottom people with none of those privileges and if i go back into the missing words, rich white men and attendees at the bottom to people with none of those. The first thing i would like to stress whenever i talk about this everybody has a tendency to identify themselves as not rich. [laughter] while it is true many people are richer than a press theres also people that are less rich than all of us so it depends on how we want to see ourselves. This diagram shows the direct loss of one type of privilege along those arrows and i think this is important to remember because sometimes people get very upset about the privilege and to say things like that that rich black sports guy shows White Privilege doesnt exist but that isnt what White Privilege means. It means if everything about you stay thstayed the same but you d along one of these arrows then we would expect you to be worthy of society. It doesnt mean that all white people are better off than what people in society. And Something Else to learn from this just like in the previous theme where sex is less than seven, we can compare the people at this level, there are no errors at this level because there is no direct loss of a privilege that we can consider how they are doing in terms of absolute privilege and i think that the rich white women are probably doing better than those that are doing better than the poor white and it was the money. The same along this level but if we compare between the levels i think the rich nonwhite non men are doing better for example rich people like to say they are problem free are doing better than poor white men who are may be unemployed or homeless were really struggling so it is not a cube. This has helped me to understand particularly by some white men are so angry about their privilege because they are told they have two types of privilege but they dont feel the manifestations of that and they see people that are considered to have less privilege doing better in society and its more productive to understand this than to simply get angry with them in return. Mathematical thinking helps me understand that. So i would like to talk about how we can use this abstract thinking to help us understand different situations because in these situations the men were analogous and occupied the position in the diagram and we can look at another more analogous situation for example structural power is analogous to the structural power that white people have over black people which is analogous to the structural power over poor people and im not saying all have power over all female people but it is viewed in infection whereas if we look at people this is analogous because the structure goes the other way up and this gives us a sense where the that is different from if we think that counts as success. But we can say there is a sense that it is the same because both cases are people being portable thorribleto other people but als different. If it is more useful to think about them this is another thing if hockney. Something might be knocked out the talk but then it ends up in another for example in this diagram but if i focus my attention on this portion we could restrict the context and have an analogous with the take three other types of privilege among women involving those privileges at the bottom and this helps me understand some parts of the feminist movement because if they consider themselves underprivileged relative to men they will not understand how privileged they are. It means your gender identity matches with your assigned to adverse. We are all more privileged than somebody else and we can understand what its like to be in different parts of the diagram. I also acknowledge that asian people are among the privileged so i can pivot between these situations one where i am lower down and one where i am higher up to understand the experiences of different people and how i like to be treated when im feeling lower down. Im not so rich that i never need to work again. They work because i want to make the world a better place but im doing fine. Some people are really struggling they may be working hard and still be unable to make ends meet or have jobs that dont pay them enough or they have problems like homelessness into so we are all less rich than someone and more rich than someone else. Here is how they are less privileged but more privileged relative to the nonwhite women so everyone can do that pivot. I used these to hel use these te with other people which brings me to the conclusion that mathematics helps me with empathy and it might not be something that you put the same sentencin thesame sentence witht least not in a positive way. [laughter] but i think that this is an important part of mathematical thing in. And i would like to conclude by talking about what i think intelligence is and how this can help us be intelligent. I think that intelligence involves being reasonable but also being helpful. It means that you are able to be reasoned with. Some people hold the view where no evidence, logic or reasoning whatever change their mind and that is in fact unreasonable. So i think it means you have a framework for deciding why you believe the things you believe in a framework for deciding when it is time to stop believing them so you will change your mind. Part of that involves using logic. You dont just use logic but with some kind of technique to build your logic up because if you say for example that i think it should be between a man and a woman, that isnt illogical its just you havent actually gotten anywhere. It isnt illogical but you havent used any steps to develop your argument and that is what it is about. Being helpful is important because it isnt going to help anybody. And this is my opinion but i think being helpful involves not just using techniques but also engaging in motion and understanding the emotions of other people because if we keep yelling logic of people it wont help and we need to engage and empathize to understand why people disagree with us and access a form of discussion that involves making human connection. We noticed teaching mathematics. If we dont understand why a student thinks what they think then we will never persuade th them. I believe in the theory of stupidity which says it is a two dimensional theory and its how you benefit herself. If you are at the top left, you hurt yourself and would see imm not sure which one i found first. If you hurt other people while benefiting yourself then you are a bandit. On the top left your benefiting other people while hurting yourself and he calls the unfortunate. We might think of it as a matter i used to think was a good thing to be and many have been taught by society we should sacrifice ourselves for the good of other people and thats one of the reasons i kept working in a job that was making me miserable because i thought i was doing something good for society but then you see what about the bottom lefthand corner thats where you hurt other people and yourself at the same time and that is stupid. [laughter] it goes on to say an equal number shows the same portion with any group of people whether it is professor, students, children, convicted criminals come and he says its always more people than you are expecting even when you take that into account and this is what he said, people tha could t themselves and other people at the same time so this is where you benefit yourself and other people at the same time and he says this is intelligence and i agree that is what intelligence is. I dont think it has anything to do with the grade you get with a number of degrees you have or how much money you earn or how much money or how many people do have power over in your company. I think its about how and to what extent you are able to benefit yourself and others at the same time and i think that abstract mathematics can help us with this and it can help us understand the feelings of other people by giving those pivots and that empathy can also help us understand other peoples logics. I conclude abstract mathematics can help us create this circle and go out into the world and be intelligent, and i hope that we will all want to do that. Thank you very much. [applause] thank you all so much. That was fantastic and hyped up. Im going to welcome julie back onto the stage who will introduce amir alexander. [applause] i really enjoyed the conversation. As a quick announcement, if you think this can happe that can hh early math for kids we would love to have you october 23. Amir alexander is an author his first book geometrical landscape discusses the relationship between the 17th century english exploration of the americas and the Early Exploration by english mathematicians. His other books include heroes, martyrs and the rise of mathematics and infinitesimal how a dangerous mathematical theory shaped the modern world. Hes also contributed pieces to the New York Times science in the book review section, the Los Angeles Times oped and shes been interviewed on npr all things considered. He currently resides in los angeles where he teaches history at ucla. Please join me in welcoming amir alexander. [applause] thank you for a fascinating presentation, and one of the advantages, you worked out all of the technical bugs now so im told this works now. Virginia argued and i was not entirely convinced of the mathematical thinking that it really is useful and helpful so i will start with a person who completely disagreed with Eugenia Cheng was this man here. Shes a very prominent mathematician in the 19th century. And in 1842 he was invited to speak at the British Society for the advancement in the Industrial City of manchester and as he wrote his brother after he came back, h she stood there before all of those british men of science and told them it is the glorious science to be of no use and in particular mathematics. He said mathematics he declared his the only purpose of mathematics is the honor of the human spirit, that it really has nothing useful in it and he said that is a great thing. Now, the fact is completely useless. The fact is he didnt make a lot and the people he was talking to were the people making money from all of those innovations they thought were based on math and here he comes with his funny accents to tell them that mathematics is completely useless. He didnt make many converts among his audience. However, the view of the mathematics is in fact useless in that as a british mathematician said it is time to be justified. It is a view that was quite privileged among the mathematicians at that time and in fact ever since. He thought of course mathematics confused for various things like to describe the laws of motion, to make airplanes fly, cell phones work and create skyscrapers and send things to mars. We can add to what Eugenia Cheng said in that it also teaches you how to think properly and think in a productive way that all of that they said was not interesting. Real math is useless and pointless and there is some truth you can see what somebody means. After all, who ever actually used the method for the area, how useful is that . How useful are the different incidents that have different values. Its an amazing theory but how useful it really is it . What use does anybody make of it and the Language Program i will say when the media will be useful. A behemoth. Weve been waiting for more than 2,000 years is still so it isnt so clear that perhaps the mathematical thinking has its value and teaching but its far from clear that the actual mathematics is in fact useful in itself i would like to offer here a different kind of perspective. Mathematics is fundamentally the science of order. That is if there is something that was the deepest order in the universe, something that deep down is absolutely true cannot be wrong and orders everything in the universe, something that is unshakable and somehow true, im necessarily true if we can prove that, then that is what mathematics is and that has enormous implications because that means what we say about mathematics, the kind of order mathematics is that our world is different depending on what kind of mathematics we have described and what we think proper and true mathematics is also the human world is different. If we think mathematics is one way or another way, the whole world whether natural also social, political, religious philosophical, everything changes if we think that the deepest order of things, but one that includes everything that goes down to the very root of creation is different and that is mathematics. Today i would like to talk about the mathematics that has a particularly long and illustrious history, and it is the shape that because it told us about the particular kind of order in the world of shaped not just their understanding of the natural word, but also changed our understanding of the relationship of each other, our institutions, our political institutions. And our social relationships. That is the great science of geometry. Geometry matters a great deal and to show how it matters, let me tell you a great story about a famous person from the past. Some of you watch the Netflix Series on first i believe verse i. Okay maybe me. Its a nice series. It has louis the 14th. It was nothing like this one. There is no relationship or connection. Its a very modern kind of democratic guy. 1661 and he was the king already for 18 years, so since he was a child, 5yearsold but only a few months he was a real king. Immediately he declared he would rule by himself. He wouldnt have a minister anymore, he would rule personally by himself and usher in the great and glorious age. August 171661, he came to visit the estate of his own superintendent of finance has. That is this gentleman over he here. He just finished building a beautiful estate. You can see it here with the beautiful gardens and became descended and descended at the entrance to the chateau over here, and he was led by his host through the rooms decorated by the famous people by the greatest artist of the day, and after that, preceded down to the garden. It was beautiful, symmetrical and then down past the pond and where they were presented with a. After that, there was a grand entertainment and after that, they were served with a lavish dinner including the 5,000 soldiers of the royal house to accompany the king and just when they thought everything was over they have fireworks shoot up from the chateau and then descend on a garden like a midnight sun. It was a grand entertainment. He turned to his mother. Shouldnt we discourage people of all of the . He was a man of his word, someone who gave to an audience and in another room he asked. They put him under arrest and then he spent the rest of his life in a prison cell. The question is why did they react so strongly. It could never express anything but love and admiration and loyalty. What was it about what raised the kings wrath. The clue is what happened to this it was nice while it lasted. So she says okay, now he summons his gardener and tells him what you did there now you do for me but you did it on a scale that is ten times or more greater than anything you saw. You will create a garden like that that will make everyone forget what you forget that garden. Enough, if you have been to the garden of verses the scale of the place is far above any garden that had ever been before