Transcripts For CSPAN2 Eugenia Cheng The Art Of Logic In An Illogical World And Amir... 20240713

Math doubleheader with Eugenia Cheng and Amir Alexander. Many of you might be returning for the first time after a couple of years and for many more of you, this might be your first timeever townhall. This is the first, exactly the type of thing we exist to do. Im pleasedto present these two fantastic authors. We love our lecture programs, all the political thoughts, all of the art you hear but i am especially fascinated by a mathematical approach to thinking about the world. Im a reformed college math student having a chance to present Eugenia Cheng and Amir Alexander on a doubleheader is, was a great opportunity for this special homecoming festival im pleased to see everyone here tonight and thanks especially to our partners so the format is unusual tonight if youve been to other townhall because it is a doubleheader. Opening with a solo presentation from Eugenia Cheng, then we will take a short break while we switch the presentations over to Amir Alexander who will get his talk after which we will have a joint q a to keep questions in mind from both talks. There is this beautiful. [bleep] dee residence tonight where eugenius talk focuses on mathematical thinking and its urgent present political dynamic and then we take this broader historical view of the sort of Historical Development of mathematical thinking with Amir Alexanders talk so hopefully there will be residences, both of them will be welcomed so you can pick up a copy of either book at the table and we will have signings afterwards and the bar will be afterwards open if you want to play great zeno games. The firstthing ill say about townhall is we are a member supported organization. But now to introduce eugenia, the first of our two speakers and to say a few more words about zeno, i would like to welcome julie marl. [applause] thank you. I am the executive director of zeno zeno is a seattlebased nonprofit. Our vision of the world is one Everybody 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 no such thing as a life lived without math. And believe that a strong Math Foundation is key to a life of opportunity and success area were so excited to be sa Community Partner to townhall for tonights lecture. So doctor Eugenia Cheng is a scientist in residence at the school ofthe Art Institute of chicago. She one tenure in pure mathematics at the university of sheffield and is honorary visiting fellow at the university of london. She was previously taught at universities of cambridge, chicago denise holds a phd in pure mathematics from the university of cambridge. E. Alongside her research and category theory and her undergraduate teaching or aim is to rid the world of math phobia. Her first popular math book how to bake a pie was raised by the New York Times National 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 eybeyond infinity was shortlisted for the Royal Society Investment Science book prize 2017. Eugenia was an early pioneer of math on youtube and her videos have been viewed over 18 million times today. Eugenia is also math columnist for the wall street journal , a concert pianist and founder of the leader to, join me in welcoming doctor Eugenia Cheng. [applause] thank you very much. Thank you to the townhall for inviting me to speak on my latest book. Its affirming to be invited back somewhere again and this is the third time ive been invited here so that strictly affirming and its wonderful to be inseattle and the sun doesnt shine every time i speak at a townhall. Thank you for joining us this evening for a massive evening where im going to talk about my latest book, the art of logic in an illogical world and the point about that illogical world is this. It can sometimes seem like we are drowning in the current world. Where the world is awash with divisiveness and conflict and fake news, victimhood, explication, privilege, blame, bigotry, shouting and minuscule attention spans. And it can seem that we will never agree with each other ever again and we are doomed to be stuck in an chambers and just yelling backwards and forwards into nowhere and is all hope lost . Thats the question and i say no, all hope is not lost. It can seem like that sometimes and this arose from my teaching at the Art Institute and in that fall semester of 2016, some things happened, various things on both sides of the atlantic. The morning after the election i did what many people did. I got depressed, i cried, i drank and i thought thats 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 commendation 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 political situation and i realize what ive been doing with my students all semester was using the principles of mathematical thinking to find greater clarity in their divisive arguments and i felt that i could share that more broadly with everyone who wants to find that clarity. Some people of course are interested in finding any clarity in their arguments but i believe there are people who do want to understand whats going on an 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 solve the problem and thats why i wrote this book and it grew out of the discussions i hahad had with my heart students i teach abstract mathematics, not remedial mathematics. Its not the things that theyve forgotten from high school, its how to use mathematics as a way of thinking and so theres someone here who has a question. Does this, should this work . Its on. Thank you. Perhaps the volume be turned down . At least when im interested. Whenim not interested i speak a little less loud. Well, ill just keep going i suppose until we can findwhat my next line is. I teach art students and the students at the Art Institute are interesting students. They are not mathematicians at all and its my dream job because i want to share what i feel about mathematics with eemore people and there are so many myths about math that its just about numbers and equations that some people are math people and some people arent math people and if you cant do a science table you cant be a good mathematician and things like that are myths that im trying to dispel so teaching art students is a wonderful place for me to find out more about what of people have math in their class and what can put them back on math and i really believe and im sure if there are any educated in the room you will all agree that its really important. It happened to what motivates your students in order to motivate them and what youre teaching rather than trying to impose your motivation on some of them and i realized alwhat motivates my students is the presence of social and political justice and thats why this came out like this. I students , the thing that motivated the most was about food and thats why my first book was about math and food. So it still doesnt as i get closer to it. Should i go and stand over there . I could give the rest of the talk without my slidesthat i like my slides. Okay, thats going to be complicated because i have a lot of transitions but i guess we will try it. Its not just about numbers and its not just about getting the right answer and some are just about solving problems even. I believe in a framework for agreeing on things and every academic discipline as a framework for assessing what should count as good information and in the current world i think thats what we need eafrom education because theres tons of information everywhere. Information is no longer at a premium so whats more important is a way of deciding what counts as good informationand pure mathematics as one particular framework based on logic. So i believe that there has been an oldfashioned traditional view of what pure mathematicsis but pure mathematics applies to apply mathematics. And applied mathematics is useful for science but science is then useful for engineering and medicine is then useful for the numerical quantitative parts of the human world and its true and i used believe that was the extent of how my research would ever be useful because my research is so very abstract but the thing is this narrow view enables people to declare that they dont need math. People, math can exist but they say i am not going to go into any of those fields so im not going to do it emmyself whereas i believe your mathematics is about how to think that therefore it is t about the entire human world. At least the parts of the human world that bank and sometimes these days, it seems like some of the human world doesnt think very much. So anyway, i am going to talk about personal analogies and what role they play in mathematics and the interconnectedness of things. And i will talk about how abstract math enables us to see relationships we maybe didnt see before and that we can use those abstract relationships to pit between different situations so that we can understand more things and we previously did finally , i will talk about how to end with what i believe is intelligence read so first of all, analogies. Another thing that we can say is that your mathematics is a theory of analogies and heres what i mean by that. That supposing we have two apples and two bananas and we can say oh, theres something they have in common and if we forget the details about them being apples and we say they are both two things this is fundamentallyhow we come up with the idea of numbers in the first place. Numbers are an abstract that the projects that have something in common and if you teach children how to count, i love helping children count and if youre trying to teach them how to count you have to wait until they make that affect move and you cant do it for them, they just have to sort of see whats going on and every time we make another abstraction lead in the process of math education, some people dont quite make it and there are various reasons for that and i think one is it can seem pointless if its not well motivated and another is cyou have to wait until you can do it. Nobody can do it for you. So the other thing is there are different ways to do it. Theres not a completely Automatic Process so if for example we wanted to this is very exciting. If instead of saying 2 things we send what these have in common with b 2 groups, that would be an abstraction but in that case we would not be able to include or example 2 chairs in that situation. That is not an example of 2 fruits we have to go up one level further to 2 things in which case we can encompass those examples and what im going to argue, one of the things im going to argue is that abstraction seems to take us further away from real life enables us to bring in far more examples and we could before so heres a more mathematical example where if we say, if we look at one 2 and 2 3 they are both examples of a the people often say to me i was fine with math until the numbers became letters. Im going to show you what the point is of numbers becoming letters. We can also say look at one times to 2c and they are examples of eight times the now, a b and eight times the , oh. Thank you very much. Thank you. So a b and eight times the are examples of a something b that is against further level of abstraction and these levels of abstraction are bottom levels of what you might do in Elementary School when youre doing arithmetic upand this is what happens when you startmeet algebra and nothen this level is part of what happens if you go to be a math major in university and uk abstract algebra , maybe group theory. Its about finding operations and none of these levels are right or wrong, thats not the point that sometimes people think math is all about what like your shedding on a particular situation and one of the things my phd advisor Martin Hyland taught me was that jamison to find the most abstract possible approach, the aim is to find a good level of abstraction for what you are trying to do. And what happens in normal life typically is that we talk about things being analogous to each other but we dont focus on what is making them analogous and that ambiguity that we leave leaves open the possibility of disagreements just based on using Different Levels of abstraction where not making clear whereas in math we are very explicit about which level were using so that we remove that particular ambiguity. So y. Heres an example of how that ambiguity comes in. On its own. So if we talk about straight marriage and samesex marriage people say theres no difference really between those some people say its terrible and so whats really going on is that people are using Different Levels of abstraction so if you think that marriage is about an unrelated man and woman and indeed samesex marriage is not part of that picture, however some of us believe that its actually really about two unrelated adults in which samesex 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 where using so people who disagree about the upperlevel can hallucinate er that weve gone further than we have and they get upset and say the next thing we know we will be allowing any 2 adults even if they are unrelated. Ive redacted whats going on but in case there were children in the audience was then we can go up further and have lets say 2 humans read or we could say 2 living creatures. For we could say to creatures. And the point is that just because some of us have decided that we want to go to hear is not automatically mean we have to shot all the way up to the top but when were not being precise about what level of abstraction where using it can open us up to those arguments about saying this is the same and this is the same. Im not saying this approach solves that problembut im saying it gives us an opportunity to have a slightly clearer and more sensible argument about it. So the next thing i want to talk about is how things become can be seen as being interconnected my favorite diagram of interconnectedness. And it is an abstraction of the London Underground system we are not many details about where things are and in fact is not geographically accurate at all but its very useful for seeing how stations are connected by which lines but because its not geographically accurate you can end up slightly hapless tourists trying to take the train from say less garden even though their two minutes walk away because you cant tell from this picture so here is the geographically accurate picture of the London Underground which is a different abstraction and its not better or worse, its probably less useful if youre trying to train somewhere is quite interesting being where everything is so the point is that these are two different abstractions that eliminate different aspects of the situation and this is what math does read an abstract from the situation to see what we can learn so heres an abstraction that i find interesting to do with relationship breakdown so this is what often happens when relationships break down is that one person, ill call them alex feels disrespected and when alex feels disrespected alex is unable to show love and his partner stan on love as a result of which is unable to show respect alex feels disrespected and we have a vicious circle thatcan escalate. I can further abstracts and label these arrows as action arrows and these arrows as feelings. And this doesnt solve the problem but it makes the start because we can think about how we can break at least one of these arrows because you only have to break one to break the circle you can say is easier to t break an action arrow or a feelings arrow area maybe we can control our feelings but maybe we can decide to act on them. Even when alex feels disrespected they can s concentrate on showing love regardless of that and then then the situation will spiral out of control so we revisit to the two action arrows and we can argue about who should take responsibility for breaking the arrow and one possible theory is that whoever is more mature should do that. So we have this vicious circle. And this vicious circle as at an abstract level is very similar to even more tragic things. For example the situation of Police Violence which one could try and say happens like this but police feel threatened by black people so they defend themselves against black people which makes black people feel threatened by the police eyso they defend themselves against the police so the police feel threatened and i would like to point out im not saying this is what happens if this overview of what happens but it has been shown even when black people dont do anything to defend themselves and everything are psupposed to do there is violence against them so we can again say that we break the action arrows or the ceiling arrows and we might argue that maybe the police, why do they feel threatened . There the police, excavated trade , they feel less threatened by people and black people so maybe we can train them but we can also train them to take action differently the escalating rather than immediately escalating things and we can say take responsibility, some people yell and say thats the law. I would argue that its really the police who have the power in the situation so i think they should be the ones taking responsibility for changing it and if they dont that doesnt help the situationbut maybe we can find some more clarity about what is going on and this is something i think abstraction can help us with. Another way i use interconnectedness to help me is when there are very many factors prosecuting the same thing in an interconnected way so there will be a gracious incidence when they need someone off the flight because it was overbooked and asked someone to leave and he didnt want to leave so they called security and dragging out and he got injured and there were wonderful arguments on the internet going if you do what youre told and you wont get injured area it really is that simple and what it whenever somebody on the internet says its that simple it really isnt that simple like if someone says fact it usually means they justdont have an argument. And i read an editorial saying you know whose fault this is weston mark its your fault. All of you because you sometimes miss flights and thats why they are overbooked so its your fault and i thought lets think about this. The end result was that. Njury was caused injury was caused because the guy refused to leave and security used force. And also because the airline called security. Why did he refuse to leave . He was a doctor. One might say thats a reasonable reason for getting to work and theres also why the airline chose that person. Questions remain about racial profiling but why did the airline utdecide to kick people off . Because nobody volunteer and why did nobody volunteer . The airline didnt offer enough money and people wanted to get where they were going. And why do they even need to remove people . Because the flight was too full and they needed to get some crews somewhere and why did was that . Why was the flight to fall . 2 things again, the flight was overbooked and not enough people failed to show up so here finally the fact that people ffoffer a flight so this interconnected system is what happens. Its not the fall of any one of these things. I understand the world as a public place and we need to simplify it but keep forgetting most of the information or ignoring it is not a good way of simplifying. Better ways to become more intelligent because then the world becomes simpler relative toyour brain. And the way i think that abstract math can help us is because it gives us ways to understand interconnected systems on a single unit so that if we can understand this as a single unit, and we dont have to be afraid of it. Its still a very complicated but if we can understand the whole thing as a unit then math gives us a way to move things around in our brain have been packaged up in this way. I like to think likethose backing cleaner bags where you suck the air out and it makes it easier tomove around things under the bed. Heres another one that i grew. I use to be larger and i didnt want to be larger and so people would say itsnot Rocket Science, you just have to eat less. The thing is even Rocket Science is just applied math. Gaining weight, why do i gain weight . Cause i take in more energy that i burn which is because i too much and exercise little buddies also because of my metabolism and my bometabolism it might be too little and exercise too much so already its because i exercise too much and the two little. Also my metabolism is ic controlled by my genetics and also sleep and i eat too much cause i like food and also because i emotionally each and both of those are caused on my genetics and my upbringing and theres also shows social pressure too much and the social norms was social pressure and time pressure causes me to get emotional stress sleep last, life happens to and theres the entire Food Industry that ending tons of money trying to get us to more and the diet industry doesnt want any of us to succeed because how would they make money, plus when i do gain weight i start eating too little and exercising too much and getting stressed so its this. Simple, its not that simple. Its this simple but understanding this helps me see where the vicious cycles are and helps me understand which links i can try to break so i can put the data where iwant to be. So i did draw the diagram for the election. Here is. I got tired of people saying its just the fault of the people who voted third party. Its just the fall of the burning or bus people. Its just hillarys fault for running in the first place and i think it was all of these things including for example the voting system. The thirdparty voting thing wouldnt have been a day if thirdparty votes counted for anything. Theres other stuff maybe in this has come to light since then only down move quickly on. And talk about how abstraction can help us understand relationships between things so heres something that is more obviously a piece of mathematics that might seem a bit irrelevant. Maybe we can remember whatthe facts of 34. The factsof going into 30 are one , two , three, five , six, 10, 15 , 30. Very good. Its not that interesting. Its a bunch of numbers in a Straight Line and i always say we live in a threedimensional world so we write on twodimensional pieces of paper and onedimensional Straight Lines. Maybe they have natural geometry and iron notion and i also like to say this is why i do not the papers on my desk because they have an actual geometry so we can find some of the natural geometry of this situation by looking at which number are also facets of each other and drawing a family tree of those relationships. Those at the top of the greatgrandparents and if any of you came to hear me talk i showed this and ill take it further. Six, 1015 go into 30, 5015 and i dont need arrow from 35 because like a family tree for grandparents relationships as we continue stem from two levels of children. So 2006 and 10, 3006 and 50 one goes into two, three and five now we see its really cube area which is a little more interesting bunch of numbersin a Straight Line. And if we like a mathematician we go wide . What other numbers make you, does every number make a cube . But there are various ways you can take this but maybe you can see that its because these three numbers are prime numbers. Those are the ones that dont thave any other factors except one of themselves that gives us three dimensions of you so this level we have numbers that are products of two times factors and then 30 which is a product of 33 if i drive like this get the actual prime factors at each level there at the bottom, thats an empty cell where there are no prime factors then we can see maybe it didnt matter that this was to three and five. It could have been any other numbers like you say it could have been from a, bmc read are the numbers the letter. The point is now we can immediately try to switch Something Else out. 2c7 is 42. Here are all the factors of 42 and now i hope they are not from the bottom and i have to, three and seven at the bottom and there the product a few things the eproduct of three things at the top. The middle diagram is t analogous to the previous one but where every five has been replaced by seven and when we abgo up to the level of abstraction at 80 mc is not the same diagram so abstraction shows us something that is the same about different situations deep at their roots and im going to show you how that is powerful. First i want to stress something about this diagram which is six is less than seven. That might not sound very ht profound six is less than seven and six is higher than seven. Six is higher than seven in this hierarchy. And whenever you have to different hierarchies disagree on the same thing, that can be a source of antagonism. For example if somebody is older at work, more junior than someone else, that can be a cause of antagonism so i want to show what the point is going to this level of abstraction because 80 mc and now the connecting. They dont even have to the numbers read they could for example the three types of privileged is rich, white and male and so then what we have is here for people with those types of privileged that this level the people with one type of privilege that the bottom the people with none of those acts of privilege and as i fell back in the missing words which h, white, not an end. Nonwhite men nonrich man. And then fees and that the bottom of people with none of thosetypes of privilege, the nonrich, nonwhite nonmen. So the first thing i want to stress is whenever i talk about this everyone has a tendency toidentify icthemselves as not rich. And while this is true that there are many People Better than all of us, lets remember there are also many people far less rich than all of us depends how we want to see ourselves. So this diagram is a diagram showing direct losses of one type of privilege along those arrows and i think this is important to remember because sometimes people get upset about the theory of privilege and they say look super rich black sports star, hes richer than me so it shows that privilege doesnt exist and not what White Privilege needs. Everything about you stays the same but you move along with the arrows five apparently not a white anymore, then we would expect you to be worse off in ousociety. It doesnt mean all white people are better off than all those people in society. Theres Something Else i can learn from this because just like in the previous thing for six was lessons that we can compare the people this level. Are no arrows at this level because there is no direct loss of one type of privilege but we can consider how well we think those people are doing in terms of absolute privilege and i think that the rich white nonmen including rich white women are probably doing better than the rest nonwhite men who are in turn probably doing better than say or white men nonrich white men because money is money and the same along this level even further than, if we compare between the levels i think rich mom like nonmen are probably doing better and nonrich white men example, rich people like they Oprah Winfrey for Michelle Obama are definitely doing better than poor white men who are maybe unemployed or homeless were really struggling and so itsactually like this. Its a keyboard of privilege, not a cube. W and this has helped me to understand why some particularly white men are so angry about the theory of privilege because they are cold they have to types of privilege but they dont actually feel that manifestations of privilege they see people who have considered to have less privilege doing better than that in society and i think its much more productive to understand this actual force of their anger rather than simply get angry with them in return and its surprising that some abstractions dont understand. I would like to talk about how can use this type of abstract thinking to help us understand situations because in these situations 3042 and rich white men were analogous to read also apply the analogous position in those diagrams and we can look at a more analogous situation a power mail people have over analogous to the structural power that white people which is analogous to the structural power that people have and im not saying all mail people have power allfemale people. The structures of society are skewed in direction whereas if we look at mail people relative to email people, this is not analogous to female people over mail people. But theres also since there which it is different and once we acknowledge that instead of shouting about whether its at the same or not we can look at why were disagree at what the manifestations of that difference are andar whether its more useful to think about them as the same or different. This is another thing, math isnt right and wrong. Its about the sense in which something is right. In the s sense in which somethig else might be right in another. When were having arguments they can be productive to think about the sense that which they have a point even if we disagree. Something might be not at the top in one context but in the top, at the top end of the context. In this diagram the rich white men are at the top but if i focused my attention on this portion of the diagram now the rich white nonmen are at the top. We could restrict our whole context say to just thinking about women as then we could have a an analogous diagram will rotate through other types t of privilege among women such as rich white and cisgender. We have an entirely analogous to you involving the losses of those privilege with poorr nonwhite trans women at the bottom. This has helped me to understand why there so much anger at the moment especially towards rich white women in some part of the feminist movement. If they are prone to considering themselves underprivileged relative to men, especially what will happen if the spend most of the time surrounded by white people, then they will not understand how privileged they are relative to allel the other people and i heard some murmurings about this and i would remind you cisgender meet your identity matches the ones you were assigned to by doctors at birth. This helped me understand that anger rather than getting angry in return. We can all perform pivots in this way because we are all more privileged than somebody and less privileged than somebody else. We can understand what its like to be in different parts of this diagram and that can help us understand other peoples experiences or in different parts ofts the diagram relativeo us. I think as an asian person i have some lack of purpose compared to white people but it also acknowledge asian people are probably among the most privileged of nonwhite people. I can pivot between the situations one where i am lower debt and one where im higher up so i can understand the experiences of different people and think about how i like to be treated when im feeling lower down so i can then try and treat people well in situations when im higher up. Another one is about riches. Im not so rich i never need to work again. Not that i would ever be because i work because want to make the world a better place i am doing fine. Im working out and doing fine. Some people are struggling. They may be working hard and still unable to make ends meet. Maybe theyve many jobs that dont pay them enough or Health Problems or homeless. We are all rich than someone and more rich than some else so we can perform the pivot. Heres the one about white women wear white women are less privilege relative to white men but more privileged relative to normal white women. Everyone can do this pivots. I use these pivots to help me empathize with other people which brings me to the surprising conclusion that abstract mathematics helps me with empathy. It might not be something you put in the same sentence with empathy, at least not in a positive way. I think this is an important part of mathematical thinking. I would like to conclude a toggle what i think intelligence is and how this can help us be intelligent. Another diagram of interconnectedness, so i think intelligence involves being reasonable, being logical but also being helpful. Reasonable means you were able to be reasoned with. There are some people who hold views where no evidence of logic reason, nothing that i would ever get them to change their mind. That is unreasonable. I think reasonable means you have framework for deciding what you believe the things that you believe and especially a framework for deciding when its time to stop believing them so you change your mind. The reason part of it involves using logic. Being powerfully logical means you dont just use logic but you use logic with some kind of technique to build your logic up. If you say that some people say i dont believe in samesex marriage because marriage should be between a men and woman. That is not a logical. Its just you havent got any where. You said the same thing twice basically. Thats not illogical but you havent used in the steps of logic to develop your argument and that is what this is about. Finally being helpful is important because i dont think theres any point in sitting around using your brain a lot if it will not help anybody. This is my opinion but being helpful involves not just using techniques that engaging emotions and understand the emotions of others because if we keep telling the logic of people who are feeling emotions, then it wont help and we need to engage and empathize with people to understand why people disagree with us and to access some form of discussions that involve making human connections. Connections. We know this when were teaching mathematics that if we dont understand why a student takes away something, if they dont feel emotions everything will wash over and it will move on and never want to do it again. I think i believe in the theory of stupidity which says this, its a twodimensional three. Its a crap like this and this asked how much you benefit yourself and this asks how much benefit of the people. There are various different quadrants here and so if you are at the top left, you hurt yourself. Lets see, im not sure which one ive done first. Maybe its the bottom right. If you hurt other people while benefiting yourself, then he says you are a bandit. As in the top left your benefiting of the people while hurting yourself. He calls that unfortunate. We might think of it as being a martyr, and i used to believe that was a good thing to be and i think many women have been taught by society that we should sacrifice ourselves for the good of the people and thats one of the reasons i kept working in a job i do was make me miserable because i thought i would think for society. The bottom lefthand corner stats were you hurt other people and you hurt yourself at the same time. That is stupid. [laughing] the theory goes on to say, he reckons theres an equal number of, the same proportion of stupid people any group of people whether it is professors, students, children, convicted criminals, politics maybe theres more politicians. [laughing] angie says its always more people than youre expecting even when you take that into account. This is what he says is stupid, people who hurt themselves and others at the same time. This top righthand quadrant is were you benefit yourself and benefit of the people at the same time. He says this is intelligence. I agree i think thats what intelligences. I dont think it has entered into with the great you get a number of degree to have or how much money you earn or how many houses you own or how many people you have power over in your company. Its about how and to what extent you are able to benefit others and yourself at the same time. I think abstract mathematics can help us and we can create a virtuous circle where logic can help us by feelings, can help us understand the feelings of other people by doing this pivots at that empathy can also help us understand other peoples logic because because we need empathize with them know to understand the thought processes. Processes. I conclude that abstract mathematics can i think help us create this virtuous circle and help us go out into the world and be intelligent. And i hope that we will all want to do that. Thank you very much. [applause] [inaudible conversations] stick around to listen to her second speak. That was really fantastic, really hyped up for math right now. Im going to go up and get julie backed back from zeno who will introduce a near alexander. Thank you. [applause] that was amazing. I really enjoyed that conversation, or the talk. Just a quick announcement. If you want to have a more Intelligent Society and think i could happen to early math for kids, we would love to have you at the luncheon on october 23. October 23. If you want more information come to our table. Yes, awesome. Next up, Amir Alexander is a historian, author and academic who studies interconnections between mathematics and cultural and historical settings. His first book, geometrical landscapes, the voyages of discovery describes relationships between the 17th century english expiration of the americas and the Early Exploration by english mathematicians of infant decimals. His other books include dual at dawn, heroes, martyrs and the rise of modern mathematics, and infant decimals, how a dangerous mathematical theory shaped the modern world. Hes also computed pieces to the New York Times, science book review section, the Los Angeles Times ed, and Scientific American, and hes been interviewed on npr all Things Considered and interfaith voices. He currently resides in los angeles where he teaches history at ucla. Please join me in welcoming Amir Alexander. [applause] thank you, and thank you also, thank you eugenia, for a fascinating presentation. What are the advantages, you work out all the technical bugs now, so im told this works now. There it is. Beautiful. Also, i was and as eugenia told you, argued a think and is entirely convinced, mathematics and mathematical thinking really is, really does come is very useful and very helpful in our world, even in our chaotic world. So i will start with a person who completely disagreed with eugenia, was this man here. Hes a very, hes a mathematician, a very prominent mathematician in the 19th century, and in 1842, he was invited to speak at the British Society for the advanced science that was meeting in the city and daschle said of manchester. As he probably wrote his brother after, when he came back, he stood there before all those british, all those british men of science and he told them, it is the glory of science to be of no use. And in particular, mathematics. Mathematics, he said, mathematics he declared that it is only, the only purpose of mathematics is the honor of the human spirit. That it really has nothing actually useful in it. Andy said that is a great thing. Now, completely useless. The fact is that he did not make a lot of the people he was talked to were people who were making money from all those new technological and scientific innovations that they thought were all based and understood were all based on math, here comes this german with this funny accent to tell them that mathematics is completely useless. He did not make many converts among his audience. However, the view that mathematics is, in fact, useless and that as the Great British mathematician said, if it has to be justified as art, as beautiful art, that is to be justified at all, it is actually of view that was quite prevalent among mathematicians at that time and, in fact, ever since. Hardy, for example, thought that mathematics, yes, he thought of course mathematics can be used for various things like to describe, for scientific, to describe the loss of motion, mc squared, to make airplanes fly, cell phones work and all those build skyscrapers and send rover to mars. Theres also, teaches us how to think properly and think correctly and think in productive ways. But all of that, hardy said, was, that was not interesting. Thats not real math. Real math is really pointless and theres some truth. You can at least see what somebody like hardy means. After all, whoever actually used archimedes methods for calculating the area of a parabola . How useful is that . How useful really are the theory that you can count the different infinite, have different values and that we can rank them . Beautiful, amazing theory, but how useful really is it . What used did anybody ever make from it or recently the language program. I will say one day it may be useful. They be, maybe not. In the case of archimedes weve been waiting 2000 2000 years. Still waiting. Its also clear the pratt mathematical thinking has its value and teaches us to think correctly but its far from clear that actual mathematics is, in fact, useful in itself. What i would like to offer here is a different kind of perspective here that mathematics is fundamentally mathematics is fundamentally this. Mathematics is the science of, if theres something that is 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 and necessarily true, then that is, if we can prove that, and that is what mathematics is. That has enormous implications because that means that what we say about mathematics, but we say that mathematics, the kind of order that mathematics is, that our world is different depending on what kind of mathematics we ascribe to. Depending on what we think proper and true mathematics is. Natural world was different but also the human world is different. If we think mathematics is one way or another way in our home world, whether natural but also social, political, religious, philosophical, everything changes if we think that the deepest order of things, the one that includes everything that goes down to the very roots of creation is different, and that is mathematics. So today i would like to talk about the kind of mathematics that has a thickly long and illustrious history, and it is that really, that shaped, that because it told us about a particular kind of order in the world, it shaped not just our understanding of the Natural World, which it certainly did, but also changed our understanding of our relationship to each other, our institutions, our Political Institutions and our social institutions relationships. And that is the great and ancient science of geometry. So geometry i say matters. It matters a great deal. To show how it matters but me tell you a little story about some some famous personages from the past. Perhaps some of you have watched the Netflix Series on verse i. No . Maybe . Okay. I just want to say a nice series but anyway, sorry . [inaudible] it has louis xiv. Let me tell you if you ever do watch the show, that the with the 14th was nothing like this louis xiv. No relationship, no connection. That louis xiv was a very modern and democratic i. This guy was not at all. Figure was 1661, and louis xiv was picking already for 18 years and 23. He was baking since he was five years old but only a few months he was a real king because up until. He was under the tutelage of the region. Louis declared he would rule by himself. He will not have a minister anymore, chief minister. He will rule personally, he will rule by himself and usher in the great and glorious age for france. On august 17, 1661, louis came to visit the estate of his own superintendent of finances. He had just finished building a beautiful, beautiful estate in france with beautiful gardens, and the king dissented. The king came towards evening, he descended at the entrance to the chateau over here, and he was led by his host through the rooms of the chateau, decorated by the famous people, by the greatest artists of the day. And after that they proceeded down to the gardens. He walked down. This is the scene from the chateau. They walked down the central alley past those beautiful, symmetrical, geometrical to the circular pond here and then down past those pools of triton to the mirror pond here and then to the grotto here, where there presented with a new comedy. After that a grant entertainment. After that all of them were served with a lavish dinner including the 5000 soldiers of the royal house who accompanied the king. Just when night fell and the thought everything was over, then they had fireworks shoot up from the chateau, from the roof of the chateau and then defend on the garden, like midnight sun. So it was a grand entertainment, and the host was glorying in this moment of royal approval. However, the next day he saw the king away. The king was going back to his chateau nearby. He turns to his mother, and he tells her once their host, shouldnt we disgorge these people of all of that . Thats too much, basically. Sure enough he was a of his word. A few months later he summoned the man to the audience any of the room he asked the captain of the musketeers, and a sign from the king he sprung up, grabbed his former friend, putting under arrest and he spent the rest of his life in prison in the alps, and never saw his beautiful estate again. Died in 1680. A forgotten man. So the the question is, why did the king react so strongly . What raised the wrath of king louis xiv, a man who would been loyal throughout his life comes to buy him in uprisings, stood by him during troubles, never expressed anything but love and admiration and loyalty to the king. Why was it, what was it about, what was it that raised the kings wrath . A clue is what happened to this beautiful okay. It was nice while it lasted. Here we go. Okay. So the king, he goes, he says okay, now you cut them out of the way. He summons the gardener and he tells them, what you did there, now you do for me. Now you do for me but you do 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 that garden that he saw. I suspect since, not exactly a pleasure, its huge but it is certainly something that will make anyone forget them completely put together any competitor in the shadow. He pulled out the trees, he took the binders to the stature and brought them to the side and put them to work and tell them you do not know because in the end, it wasnt really his wealth, heres a very wealthy man. It wasnt that, it wasnt his patronage, the doomed, it was ultimately the geometrical garden. Thats what it was. The greatest and most beautiful geometric garden in france and that was the thing, that louis would not tolerate. That will be the one that will forever erase that memory. Why is it geometry, why is it geometrical garden box why is it so why was i so outrageous to the king conference . Your to go backwards quite a bit. 2000 years. Understand right geometry was so important and why geometry was so dangerous. At the time of louis the 14th. We dont know, its been created geometrical proof. We know he was greek, he lived in one of the greek cities. It was probably something simp simple, winds seemed very trivial to that but pretty soon others torrington and started producing proof by the year 400, quite sophisticated. The only mathematical tradition, amazing mathematical tradition. India and china, remarkable athletic tradition, not one of them thought of convincing proof because proof is not about measurement. Its not about finding proof, they are not about doing astronomical measurements are land measurements our accounting house, its not about that because the truth is about finding troops. Once youve proven something, and that something is proven, it is absolutely irrevocably true. Not because god said so or anything, but reason tells you it is absolutely irrevocably true. Thats the end of the argument. It is proven. It is absolutely true. That is a stunning thing. That is something very radical about that. At the discovery that you can actually prove something. I was a discovery made only once in human history. And never again. The first troops were in fact, the first troops were the person who united them and turn them was alexandria, we dont know exactly when he lived around failure 300. Thats what he probably didnt look like but thats his picture there. [laughter] pointed they do . Euclid, he starts out by definitions in common notion. Very simple and selfevident things, the whole is greater than its part. Something is equal to another thing and two things are equal to each other. So things that are nobody can deny. There obviously self evidently true. Thats where he starts. From there, he starts creating troops. Based on those proofs, he creates more proof and so on. Every proof is connected. Its not just that its true in itself, it is interconnected to all those other proofs. Line, trying the circles and so on. Its a whole world of those geometrical problems. Its a Perfect World because not only is everything true, everything there is true. Everything there is always true. It is all interconnected. Very specific strict fixed relationships to each other and a particular hierarchy to each other. There simply is at the top and then everything and theres one layer of proof and then based on another front and another one. They are all interconnected in one fixed eternal changing metric. A whole world of mathematic truth. That is the accomplished, thats what his world is like. A world of truth and rigor and an unchangeable he truth. That is quite an accomplishment. There are other competitors i guess, michael for example. But it has a claim. Thats not bad. Euclid is not known for any particular innovation. Hes known for putting it together in creating a world. The problem was, this is a beautiful world but theres that world is amazing but its not our world. Thats the Perfect World, our world is of shadows and imperfections. Aristotle taught mathematics cant really prescribed or describe our world. Later on when the Christian Church agreed, geometry was very nice but our world is a fallen and corrupt world. Certainly not something that can be described by geometry. Geometry gets all the praise. It pleased god to bestow our mankind but its also irrelevant because our world is Something Like that. That lasts for about 1700 years. By euclid until simple mathematic truth but until 1400, until pretty much the year 1400 and 13. Not a famous year for most people but its a year in which a man by the name of felipe conducting experiments on perspective. When youre perspective and then he has an artist inflator on, they developed and established a theory of linear perspective. Initially it is a theory of how to draw things, how to paint three dimensions on a flat surface. Basically theres a vanishing. You can draw a vanish anyway, theres a system that is on the horizon, this is a perspective exercise because you can see yeah, its doing what he wants. Like to get back to this. Oh. Anyway. Forwards. Okay, so this is basically its basically an exercise in perspective in which we see a parallel line on the bottom, they all point to a single position. It is much more, its not just a trick of painting because the implication is the space itself is geometrically structured. Those lines of perspective that go to the horizon, they are real. They are in fact, they embody, they are in fact the structure space itself so you see the difference for example in the ark between this is a perspective by the satchel in which he just does a few things. He touches to create parallel lines that gives depth to the picture. You have this other image, it doesnt have internal space. It has all the images and its a powerful image in itself. It simply does not have that interspace. This is a realistic picture in the fact very close to how we experience our life surrounded by a lot of people. You dont think of it as a geometrical space if yet, this one already has this geometrical space built in. In 1352, this one from 1480s they both depict the same thing in the city, it has not changed much except for the great dome of the cathedral which is also famous for. The world itself had changed. This city is very much how you experience a city surrounded by buildings behind every corner. Perhaps even more than this. It has become a geometrical principal. Every point is determined, predetermined by geometrical principles. That is how you can tell this was a turning. This was when geometry came down from the sky in a little city of 30,000 people in with just the few people we can name, they made the connection inside the world itself can be structured by geometrical principles. The world is structured by geometrical principal but the Natural World in perspective, the world was written and language of mathematics and its always looking for mathematical principles in the world. What about the human world . What does it mean to say our world is mathematical, mathematically structured . Its not long before they realized this was the significance of this idea that the world is geometrical because if they present themselves or if they believe themselves to be not just i am king of france because i will put you in jail if you think otherwise or i will cut off your head because being friends means that you are an expression of the deepest in the universe. The hierarchy of your kingdom is not just because you have military force but because you are an extension of a deep order in the world that has enormous power and implication. So the king of france adopted, the first to adopt, not the last of the first. Adopted this idea that power, geometry is power. Geometry is power, legitimacy on a scale and with implications far beyond anything i was offered previously. They did so in many ways presenting themselves of the geometrical order. Just to mention for example, they did so in their courts. The whole order of the court, its not just the old medieval jumble keeping people from buying order, there was order now. Strict hierarchy order in which everyone has their place from top to bottom, picking at the bottom. Everybody has their place. Everybody constantly negotiated their place very precisely. I was the essence of life imports. Finding your way in predetermined order geometrically. That was in fact invented precisely as a negotiation. Etiquette that determines whos at the top, was on the bottom, who sits, who stands, how you would greet and so on. It was all based on geometrical adjuster in geometrical movements. There were philosophy and it was treated but nothing equals the importance of geometrical guarding. They were the advent of french royalty. They started very simply with the couple gardeners and they produced very simple garden and over the next two centuries, this barn between the kings of france and geometry simply increased intergroup. This is on a larger scale, you see this geometrical order presenting a perfectly ordered geometrical land under the gaze of the palace at the top. So there are others, it became the emblem of royalty, french royalty of geography and nothing more than this geometrical garden. It was the emblem of their sovereignty, author right in of their life. Why . Because that Perfect World by came from euclid, that perfect ideal world that is orderly and hierarchy, that is what they were determined to create. Thats how they presented themselves. So when the we came over to visit his minister of finance, he saw this. This is geometrical garden in all its respect. You see this perfect symmetry, the geometrical pattern, the squares but even more so in this ways traditional. It is in fact a perspective painting. Hes marked by a statue of hercules. Its not just the geometry of pattern that holds it together, its the geometry of the world. It structures everything in perspective painting and holds it all together. Makes it one unified interdependent unit. It was the best geometrical garden thats ever been both artificial and natural. You can see the similarities here in the structure as a perspective goal garden. This was a royal garden in all respect because it was a geometrical garden and the greatest garden there ever was except one thing. It belonged to the king. A commoner whose presenting himself as the top of this necessary immovable hierarchy. This was not just on impact, not just somebody a little ambitio ambitious, this was an attack on the foundation. This was a geometrical attack on the foundations of the regime as he saw it. So he moved on to determined not just to crush it but to create something that would be his own. To create his own geometry felt present proper order of the world which is what he did precisely. A carton in the style except about 100 times longterm. Areas surrounding. His immediate area here is in the tradition and the kind of geometrical patterns you were familiar from the presenting and orderly hierarchy world. From there, again you have this mean axis leading to the horiz horizon, creating it as a skeptical painting. Its not just the deep parts here, this was an older garden that preexisting, the real magic is what happens here. This is the grand park over here in which he has the grand canal and surroundings because what you see there, if you look from a palace, it is simply open for us, you dont see any elaborately carved beautiful parts you see here but because it is this perspective goal painting, going after the horizon, even these open words are structured together through the deep order of the world. So underneath it all, this look like from a palace. Under it all, there are these geometrical paths. All of these straight arrows intersecting and all of them together appointing an arrow. Its aimed directly at the palace, the center of the palace and the palace is the kings. At the center is the kings bedroom. What you see and what this tells you is that beneath all these different from all the chaos we see in the world, all this mystery we see, there is a fixed underlying geometrical order. You dont see it when you look at it from afar but its structured everything. This geometrical order is not random, its hierarchy because it meets a layer upon layer, the kings palace in which it supports the kings palace is the natural necessary place of all. We go there and see this is very lovely but at the time, for somebody watching those paths, a natural geometrical order of the world, it was not just an abstract way. It was all around you. The entire world around you, this deep geometrical order of the world, everything had its place in the grand order and who presides over it, of course, became himself the king himself and his palace. I would like to end with another contemporary gesture here because i hope this was interesting but thats for you to judge. It was a long time ago. Died in 1715, is greatgreatgrandson, louis the 16th who was beheaded in 1793, this eternal geometrical order, we say thats how things work. The geometry and power of geometry was our outlook today. My answer is yes, just one example here. I think people are familiar with this appeal. Capitol hill and thursday pennsylvania avenue. Washington d. C. Is not that feel. Its not a museum of ancient monarch. His capital of the greatest republic in the world. It is the greatest, the most spectacular geometrical city. The story is the garden and cities. No city matches the grandeur of washington d. C. Somebody who grew up in the court of louis the 15th and 16th and resigned very intimately and thats why he used when he designed washington. Thank you look at this picture and say okay, extending the malls, you look at capitol hill, all the arrows in streets lead to the capitol hill. Here we have this obvious hierarchy with congress. The u. S. Is not a monarchy and what youre trying to do was present and use the language to present a language. You have this garden here. You also have that right angle to the wall, you have the president s palace, he is disappointed by the scale of the white house but i was supposed to be the other note of government. So there are already two at the right angle. Each one with their own mouth leading up to them and they are connected by pennsylvania and this is capitol hill, what we know as the mall. This is the president s house, the white house over here. They intersected right angle, by pennsylvania avenue. Each one of them a great number of lines, already you have to lines. You have not one center, you have two centers. Two Great Centers that are themselves competing with each other. Also in this careful balance. You have capitol hill and the white house, not by accident but design because they designed it that way. Thats not the end of it. On top of that, also created all these 15 squares. At the time, there were 15 states to the union. They called each one of those by the name of the different state but each one of these, dominates its immediate area. All connected by this network, a rigid network that is unchangeable, it overlays those two, the entire city and balances the two centers of power. What we get here, 1791, two years after ratification and when they use the language of geometry to create a capital that is designed to be our constitution. Presenting the constitution not as just a compromise that would reach but as a necessary inevitable deepest order based on the deepest order of geometry. Unshakable, eternal, stable because it cannot be changed and cannot be moved into thats how it was done. We talk about a political situation today, and whatever will presume about your political stats, i think most of us will agree its a time many of our assumptions are challenged, many institutions we thought are being challenged. He had expected the institution federal, white house and all seems in crisis and challenge. I have to say, this is just my opinion. I go to washington d. C. And you watch those geometrical streets into go through the mall and look at the houses of congress, you look at the white house, grand blvd. , that order was the geometrical order that they with there. I kind of think the message is still there. Its not that message but the living message. Theres more there. This deep this deep order will survive. If theres something more here in the particular politics at a particular time ors the particular resident, president of the white house. The message of geometry is still alive. Thank you very much. [applause] fifteen minutes of questions now. We have about 15 minutes for questions. Please try and keep your questions brief and in the form of a question. Will get through as many as we can. You can pick up copies of both books at the book table over here. Th thank you both. Wonderful asthmatic presentation. The question iue have, one of te things. [inaudible question] he shows up and he decides, i interpret as so furious that looks like the finance minister or whatever it was, could not have a better garden. That didnt sound particularly logical in one sense but as he kept going, maybe you have different views about that what you do with the kind of work coming out of it saying logic and reason and sometimes nice, but they are really not that important and driving people by creating emotions of fear and hate are much more effective than reason in terms of gaining power, control and so forth . I agree and i think one of the things i cite my book is that if we keep with emotion and logic together, emotions will keep winning. I think thats the situation we are seeing across the world. I dont think they are mutually exclusive and i think if one side keeps tellingop others ther emotional and not logical, the other thing about the site as well and we wont get anywhere. I think we can use logic to understand emotions because i think emotions do have reason inside them, its just that we have to understand them from the view of that persons emotion, not from our own logical system. One of the ways in which mathematics construct is it always starts with accident, we dont try to prove in the system and rebuild from those, using logic. If you start, you will get different conclusions. Its that they might have different starting points i can use obstructions to understand peoples emotion because for example, there are things i do that seem to be irrational. For example, i used to be afraid of flying even though statistically, its much safer, i was still completely afraid of flying. Instead of saint its just emotional, i thought about what was my fears based on being reminded of death. At the thing im afraid of. The fact that it was with basso using a process where you unpack some of these process and find what those are, i basically always find that i can see some logic in emotions so they are not separate we can actually use those at the samean time. I very much agree with that. I think you cannot really dissociate emotions into logic and reason and giving some of the o examples that i talked abt today, and building, is an ideologist, but also a great psychologist because when people go there and experience that grantor and absently necessary order, people react accordingly. People wont necessarily enjoy it, the garden in 1688 to 6085, they did not enjoy it because the french took the city but he got the message. Thats the very clear emotional psychological message. You go there, you understand and upset how you upset mostly with the proper order is. I dont think, theyre very much working together and i think the same in washington d. C. Like i said, when i go there, see what their reaction is but the reaction isn also 3d, its emotional. It was planned that way and geometry is what creates. One step further, its difficult to understand someone elses emotions using emotions unless they are actually the same emotions as yours. We get so caught up in our own emotional reaction, there are people quite discrete with. If i let the emotional response takeover, its difficult to see whats going on. Use that mathematical thinking logical step. I can separate out my own emotional disagreement with them and understand their view and understanding someone is i think the starting. For unifying and blessed divisive world. I really enjoyed your application of logic to social issues and if we were going to adopt that framework, how would you see that happening in the real world . Lets say framework on social media or newspapers, without mean no Opinion Pieces anymore . To be scientific papers for the framework x how would that work . Thats an interesting definition. Thank you. I think opinions, not all opinions are equally valid and that something the world seems to lose sight of of it. All opinions should be backed up by something. Its not about right and wrong but its about the extent to which a backup has been provided. There are many different ways im not trying to claim mathematical logic is the only good way to back things up. The scientific process is different from logical process. The scientific process is based on evidence and the ability and more statistics. Then there are other disciplin disciplines, a way that pieces access access in history. All of these disciplines provide a framework for assessing how valid we should consider a truth to be. I think if you just state an opinion with no backup, and way thats what an opinion piece is. That contains no framework. I dont see a place for that in my ideal world but if we can understand where the opinion is coming from and provide some sort of justification for it, but i think its interesting so in order for people to understand that logical framework or scientific framework, of course we have to improve the education around think things and we have to change the entire Education System and in order to do that, we get into other issues, we cant change the Education System so we changed the government but we cant change the government until we change the educational system so then what do we do . Thats why i write the book to bypass that. I would like to change the entire world but in the meantime, ill write books and try to understand outside of that system. Two questions. If youve got a classroom of reluctant geometry students, which one of your s books would you start them with . The second question, when the women demand bread, and the women in france demand bread, do the gardens change their tune at all . Is it Something Else . Ill start with that. Something interesting happens to the gardens in the later decad decades, even before the french revolution. This notion, this idea of this perfect geometrical world is being challenged particularly. The queen would adopt that philosophy and start creating enclaves within the garden that are not at all what he had in mind, not all about the primacy of the king but little enclave of supposedly nature, sheehan her court can play those and get away from that rigid geometrical order so consciously geometrical anti geometrical reaction. You see it on the ground, thats whats amazing what geometry, you see on the ground in the design of city gardens, its imprinted, that order is imprinted on the ground and shapes our environment in a matter of seeing it. What happens ultimately, the revolution, after the revoluti revolution, they are made into museums. They are preserved, as are most of the old geometrical gardens but they are preserved as museums. Their powers. Tail, there no longer the way the world is, its something we visit and say thats how things used to be so their power is neutralized. But not in washington. And unser to the other question, it sounds like i would recommend this book and the first one, which is about what math is for and the way in which it can be, for everybody and it can be fun and is all around us and is related and a something u can do for c yourself, even if t hasnt seems like you can do it for yourself. Thank you. Have a question for doctor alexander, whether you can tell me the alignment in relationship to the garden and whether theres an east and west alignment, whether it suggests the traditions that the east west alignment depicts, which in turn again is a symbol for the medieval world, the overall framework and tradition that again suggests we are looking not into something new, something that generated thorough tradition and time but something that is, a development of medieval thought. Thats fascinating because yes, first of all, yes. The gardens push west so like a cathedral, which is very interesting because your presentation and he had the stature of the end and initially he had the growth near the palace and supposedly apollo would transfers the sky except that he was doing backward which was always a bit of a quandary instead of moving westward, was moving east rather than west. So the pagan, theres definitely a pagan there in the presentation. Ive never heard the idea of the cathedral. Thats very interesting. The fact that it did preserve the cathedral, thats interesting. Thank you for that. Tragically increasing number of members in our society that have begun to reject the premise science or math orse logic whatsoever, people who deny evidence and say the globe is warming, the claimant is flat, weve never been to the moon and things like this, what do you say to those people who project that promised to begin with . How do you think our society can move forward that . Thank you. Wa easy to get depressed about that kind of situation and what i remind myself is that we cannot reach everyone at once and thats okay. Theres a whole range of people and maybe those are the most faraway people from where i am. There are people who are far away, people who really do want to believe those things who dont really know how or who dont do it right as well as they want to so they are trying to be logical but they make mistakes. People are trying to believe in science but they dont quite fact checked and immediately repulsed. We can try and reach those people first and if you immediately try to reach the people were the most difficult, then guess, you are doomed to get depressed and feel like everything is hopeless. If we decidele everything is hopeless, then it will be hopeless. I try to ascertain whether any chance i m can make any progres, i try to understand where they are coming from rather than trying to change their mind but also, its important to preserve your own Mental Health and if youre really going to get depressed and be attacked by people, i think its okay to decide youre not going to engage with that right now and try and improve everyone else because i dont think, now i dont actually have this but i dont think the majority of people who think the earth is flat so i think its all right, i think are more people can reach and if we can just shift the center of gravity of scientific thinking, logical and scientific thinking, i think that makes a huge difference. We know how to change everyone at once, we just have to shoot things a bit. Maybe if we shift where we can, then we can make progress and change things up. Es when you look at things like the golden triangle, two dimensional, when you look at the vanishing points, the simulation of three dimensions but its really twodimensional, when we look at things that are actually three dimensional, when you talk about geometry, look at them as somewhat chaotic. Do you see any evidence that we are moving toward whats actually encompassing the three dimensional mess of symmetry . More order in the things we creating chaos . Art or architecture . Thats an interesting question because of course youre right, when you use this when youre perspective, its not just a plain description of the world, its not just describing the world, its telling this is the real world, its geometrical in that sense. Of course has been developments in geometry that have moved away from that single necessary fixed order and geometry and the implication that there can be not just one necessary truth and one troop points of view but theres an infinity of possible geometries rather than single troop which is very challenging and disturbing. I think in some ways, you can say we are in it in a euclidean world, a postdoc living in a world in which we are all living in our own bubble, we have different assumptions. Art did try to deal with that, im not expert but clearly early 20th century art like cubism, doesnt effort to portray things from distant angles and different sides at the same ti time, clearly also response to move away from this single unifying euclidean view. Thats all i can say. Thank you so much. [applause] thank you all so much for being here. This was really fun. One more question, i think their product our stuff away but if you have questions about them, books are for sale over here in our guests will be signing in a moment. Thank you for coming. [applause] tonight on the communicators, mark randolph, cofounder of netflix and author of the book, that will never work, shares his experiences starting the online streaming service. April 14, 1998, we were live. It didnt take long and i got that first thing and we cheered and open bottles of champagne and two or three minutes later, ding, 40 more orders, we were so excited and we got two more orders and all the excitement, we lost track of some things until we notice it had been a while since the bells rung. Is there a problem . It turned out the first 15 minutes of being online, we crashed all of our service. Tonight 8 00 p. M. Eastern on the communicators on cspan2. Watching a special edition of book to be not airing during the week while members of congress are in their districts due to the coronavirus pandemic. Tonight, global history first, Brown Universitys peter talks about the relationship between six strokes. Alcohol, tobacco, amphetamines, cocaine and more. Harvard University History professor, Vincent Brown chronicles the 18 centuries that took place in jamaica known as techies revolt. Later, marie provides history of latin america at the wisconsin folk festival in madison. Introit book tv now and over the weekend on cspan2. The president , from public affairs, available now in paperback and ebook. Resented by biographies of the president , organized by their ranking, by nordic historians. From best to worst and features perspectives into the lives of our patients chief executive and leadership. Vi