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

Echo i am so excited to welcome you to this doubleheader with teethree and Amir Alexander this is part of the homecoming festival i hope many of you could be m returning to the building for the first time after a couple of years we remodeled the space maybe this is your First Time Ever this is exactly the type of thing we exist to do i am so pleased to present these two fantastic authors. All the lecture programs in political talk without a mathematical approach to look at the world so having a chance to interview Amir Alexander and teethree as a doubleheader is a great opportunity for this homecoming festival. So pleased to see everyone here tonight and our partners. We will open with a solo presentation from eugenia then take a short break while we switch over to Amir Alexander after which we will have joint in mindeep questions and talking about dynamics and then we take a broader historical view of the development around that thinking with Amir Alexander both will be happy to answer questions and after all of that pick up a book at the table with a book signing afterwards and the bar and cafe will be d open if you want to stick around to play games. We are a member supported organization thank you to the members in the room so now to introduce the first of our two speakers julie thank you so muc much. I am the executive director of this seattle nonprofit Everybody Knows they can do mat math. We achieve this through programming for families of color ages three through five and lowincome communities we are about making math fun and playful because theres no such thing as a life lived without math and a Strong Foundation is key to opportunity of success. We are so excited to be a communityow partner tonight. Doctor chang in residence at the school of the Art Institute in chicago in pure mathematics is tenured and now honoring fellow at the university of london. Previously taught university of cambridge, chicago with a phd in pure mathematics from the university of cambridge perk alongside her researching category theory and undergraduate teaching she wants to get rid of math phobia her math book how to bake pie was praised by the New York Times National Geographic and Scientific American and interviewed around the world including bbc and pr and the late show with stephen colbert. Her book beyond infinity with the Investment Society and an early pioneer of math on youtube and her videos have been viewed over 15 million times she is also a math columnist for the wall street journal a concert pianist. Please join me to welcome doctor chang. [applause] thank you very much for inviting me back here to speak on my next book was always very affirming to being invited back somewhere this is the first time i was invited here so thats triplefi its wonderful to be here in the sun does shine every time i speak at the townhall. [laughter] thank you where i will talk about my latest book the art oflo logic is that it can sometimes feel like we are drowning where the world is awash with divisiveness and conflict and fake news and victimhood f and bigotry and shouting and minuscule attempts and it can seem that we will never agree with each other ever e again and we are doomed to be stuck in the echo chambers is all hope lost. And so my teaching and that fall semester and the morningrn after the election and went to press i cried and i drink and i thought what can i do that is productive because i truly believe in doing something and i also believe in looking at your own combination of abilities to use them in the best way that you can. And in this political situation. And in those arguments. And i fell i could share that more broadly with that clarity some people of course are not but i believe there are those who want to understand what is going on. Im not saying it will solvell all the problems but we dont understand it we cant build the problem and thats why i wrote the book it grew out of discussions with my art students where i teach not remedial mathematics using mathematics as a way of thinking. [laughter] where is the computer . Should this work . [laughter] it is on. Thank you maybe the volume could be turned down . So i will keep going until we can find my next sli. So the students are very interesting they are not mathematicians at all because i really want to share how i feel about mathematics with all m people there are so many myths about math its more than just equations some people are math people and some people are not. If you cant do your times tables and you cannot be a mathematician. Thats math i try to dispel so i teach an art student so to find out more about what people love math and what can put them back on math and i reallyi believe if there are those that are educated in the room that you would agree t its important to tap into what motivates your students in order to motivate them rather than impose your motivation so it motivates my students is political justice somehow that motivated them with food so thats how i motivate them. Should i get closer . Should i go stand over there . I could give the rest of my talk without my slides but i love my slides. Thats complicated because i have a lot of transition so we will try it. Is not just aboutus solving problems so every academic discipline accounts for good information and thats what we need from education it is no longer add premium and that is based on logic. [laughter] so i believe there is an oldfashioned view of what mathematics is and that is useful for science which is useful for engineering and medicine i used to believe that was the extent of how my research would be used but to enable people to declare to say i will not go into those fields whereas i believe. Tmathematics is about how to think so therefore it is about the entire human world the part that thinks. [laughter] so it seems like the human world doesnt think very much. So first of all i will talk about analogies and the roles and mathematics then i talk about for those relationships we did not see before we can use those with different situations to understand more than we previously did and finally with what i believe is intelligence so another thing that we say is with analogies what i mean suppose we have two apples and bananas we can say there is nothing they have in common but if we forget the details then we say they are hith two things this is fundamentally how we come up with numbers in the first place they are abstractions from what we have in common if you h teach children then you just wait until they make that abstraction leap you cannot do it for them they just have to see whats going on every time we make another abstraction some people dont quiteca make it so one is it could seem pointless if not well motivated then you have to wait until you can do it and nobody can do it for you. So there are different ways to do it is not a completely Automatic Process this is very exciting. [laughter] so instead of saying what we had in common with two groups that would also be true but in that case we would not be able to include in that situation thats not an example so in that case we have to go up in which case we can encompass those i examples. One of the things i will argue to take us further away from real life that enables us to bring in far more examples than before so heres an example where if we look at one plus one and two plus three people say i was fine with math before. [laughter] i will show you the point of numbers but we can also say one times two and two times three. But now a b and a times be. [applause] thank you very much. So they are both examples so that is a further level of abstraction this is what you might do with Elementary School and what happens when you meet algebra. And then to be a math major thats not the point some people say its about right or wrong. But what light you are shedding on the situation so the aim is a defined that situation but a good level of abstraction. So to talk about things that arely analogous but not what makes them analogous so to leave those in the possibility of disagreement that we are not making clear. To be very explicit what we are using to remove that ambiguity. So here is how it comes in. Talk about samesex marriage. What is really going on . Are they using Different Levels of abstraction if you think marriage is about the unrelated men and women then samesex is not part of the picture. If its really about two unrelated adults then samesex marriage is a part ofg that. Now are not being first about which level if they disagree that they hallucinate get upset out to go further than weny have so thats whats going on so then we could go further we could say to humans or to living creatures or two creatures. [laughter] the point is just because we decided we want to go here we dont have to shoot all the way up to top but talk about the level of abstraction of what you think you could say this is not the same im not im saying there is the opportunity to go about it. So to talk about how things are interconnecteder this is my favorite diagram of interconnectedness with that telegram system we have forgotten many details of where things are is not geographically accurate at all but its very useful to see how things areng s connected but it is not geographically accurate you could try to take the train because you cant tell from this picture so here is an accurate picture with the different abstraction is not better or worse its less useful if you want to take theve train somewhere so these are two different abstractions to be temporarily abstract to see what we can learn so what i find quite interesting is relationship breakdown so one person to feel disrespected he cannot show love if he feels unloved he cannot show respect and now we have a vicious circle. I could further abstract enable these actions doesnt solve the problem that makes us think about how to break these arrows so you could say if you have to break that then maybe we cannot control that we just feel them so perhaps even when alex feels disrespected they canll concentrate on what they can control so with these action arrows and argue one possible theory to be mature so we have a vicious circle at the abstract level which is very similar for more tragic things like Police Violence one could say happens like this but the police feel threatened by black people so they defend themselves so black people are threatened against the police. Now i would like to point out im not saying this is what happened but even when by people dont do anything to defend themselves there still Police Violence against them so do we break the action or the feelings arrows so why do they feel threatened and they are the police they had been trained to kill they are less threatened by white people that maybe we could train them to take action rather than immediately escalate and say that we should s take responsibility i would argue the police have the power in p this situation some of course if they dont that doesnt help the situation that maybe we could find some clarity about what is going on. This is what abstraction can help with. Another way is if there are factors contributing to the same thing so egregious united incident they asked someone to leave he didnt want to leave so they Call Security on the way out. There were wonderful arguments on the internet just do what you are told and you are d not injured it really is that simple somebody said it usually is that simple than it usually is not. [laughter] normally that means they dont have ann argument. [laughter] i actually read an editorial that said its your fault because sometimes you miss the flight thats why they overbook and i said lets think about this the end result is that injury was caused because he refused to leave and security use force and also the airlinescu called osecurity now why quex he had ato get to work one may say thats a reasonable reason but also why the airline chose that person for racial profiling but also why did they decide to kick off because nobody volunteered because they didnt offer enough money and they needed to get where they were going. Why do they need to remove people because the fight was full and they need to get the crew somewhere so two things again and it was overbooked so this is the why people often miss flights so this disconnected system is what happens its not the fault of anyone. Understand the world is a complicated place but forgetting most of the information and ignoring it better way to simplify the world is intelligence because the world becomes simpler relative to your brain. [laughter] in one way it can help us it helps to understand those interconnected systems if its a single unit that we dont have to be afraid of it. Is still complicated but if we can understand as a unit and a way to move things around in our brain like to think when you put air in the bag and suck the air out but here is another so people say its not Rocket Science that even Rocket Science is just applied math. [laughter] so why do i gain weight yes because i take more energy than i burn but my metabolism slows down so already i eat too much and too little also it is controlled by my genetics and ate too much because i like food and ih emotionally eat and there are social pressures to be this much and that time pressure causes me to eat more than the entire Food Industry spending tons of money to get me to eat more because then how will whey make money . So i gain weight and then i get stressed so this is simple. Its not that simple but understand to see where those vicious cycles are so i did draw a diagram for the election. I got tired of people saying it is just the fault of the people. Was just the fault for running in the first place. I think it is all of these things including the Voting System the thirdparty Voting System is an issue. There may be other stuff in the gap over here so then we move quickly on so to talk about how abstraction can start the relationship so obviously this may seem irrelevant maybe we can remember the facts one, two, three, five, six, ten its not that interesting. Maybe we live in a threedimensional world. So maybe if they have natural geometry. [laughter] so it is that situation those are factors of each other with the family tree of those relationships. And i dont need to draw like in a family tree because we can deduce them. But in now to a little more interesting that there are various ways. So there are two prime factors so then i get the actual prime factor on each level and then we can see maybe it could be any other number it could be a or b or c. Then the products of two things. So the previous is analogous and when we go with that fellow of abstraction is not actually the same diagram. This is about different situations and to show you how that isha possible. That is pos. That might not sound very profound but six is less than. None. I would like to stress whenever i talk about them everyone has s a tendency to identify them as not rich. While its true there are many people richer than all of us o lets remember it is showing direct losses of one type of privilege along those arrows ano its important to remember because sometimes people get upset and say things like he is much richer than me and that shows it doesnt exist and that isnt what White Privilege means. If everything about you stays the same but just by this we would expect you to be so that doesnt mean all white people are better off than allll in society. If we could consider how well we think they are doing in termshif privilege. But they are probably doing better than the rich nonwhite men and the poor because money. The same along this level bridge people would say they are definitely doing better than poor white men who are maybe unemployed or homeless. This has helped me to understand why particularly some white men are so angry because they are told they have two types of privilege the manifestations of thel privilege and they see people who are considered to have less privileged thing better in society and i think it is morits more productive to understand this i would like to talk about how we can use this kind of abstract thinking to pivot and help us understand t the. Th they are analogous and we can look at it another more analogous situation for example it is analogous to the structural power white people have over what people which is analogous to the powerk people have and again the structure of the societ society argues in tht direction whereas if we look at real people billeted to female people which is not analogous because the power structure goes the other way up into this gives us a sense in which for example. We can say both cases are people being horrible to other people bubut there is also the sense in which ito is different and once we acknowledge that its more useful to think about them as the same or different in that this isth another thing they taught me. Its even if we disagree with it. Now something might be bought at the top in one context but in the top. The rich white men are at the top but if i spoke on this portion of the diagram now the rich nonwhite men are there to restrict or whole context just thinking about women and then we could have an analogous diagram if you take other types such as rich white men genders than we have an entirely analogous q. Analogous to those privileges with women at the bottom here and this has helped me to understand why theres so much anger at the moment especially towards rich white women because if they are prone to consider themselves as underprivileged relative to men especially if they spend most of their time surrounded by white people then they would understand how privileged they are relative to all the other people and i heard some murmurings about this and i would remind you that it means your gender identity matches the one that youny are assigned by e doctor after birth. This has helped me understand that rather than simply getting angry and return. We can all perform in this way because we are old more privileged than somebody and less privileged than somebody also be understand what its like to be in different parts of the diagram and that helps us understand what the peoples ots experiences are relative to us so here are some tidbits i do myself. I think that as an asian person i have privilege but i also acknowledge that i think asian people are probably among the mostng privileged and so i can pivot between these situations and understand the experiences and also think about how i like to be treated when im feeling blue or down so i can try to treat people well in situationsa when im higher up. Another one is about riches. Im notot so rich i never need o work again, not that i would ever be. But im working hard at doing science and some are struggling they may be working hard and still unable. Maybe they have jobs that dont pay enough. We are all less rich than someone at more than someone else salso be formed out of it. Heres the one about white t won wear white women are privileged than white men but more privileged billeted to white womenen. I use these to empathize with toer people which brings me the conclusion that helps me with empathy. It might not be something you put in the same sentence with empathy at least not in a positive way. But i think this is an important partner of mathematical thinking actually come and i would like to conclude why talking about what i think intelligence is and how i think this could help us be intelligent, so i thought about this and i thought another diagram is interconnected, so i think that intelligence involves being reasonable, powerfully logical proposal being helpful so what does reasonable means of access means that you are able to be reasoned with. Some people go to the view where no evidence of logic or reasoning, nothing at all whatever gets them to change their mind and that is in fact unreasonable, and so i think that reasonable means you have a framework for deciding why you believe the things you believe, and especially a frameworks to decide when its time to stop believing thebelieving them so l change your mind. And that i think the reasoning part of it involves using logic. Being halfway logical means you dont just use logic but yo youd use logic with some kind of technique to build your logic up because if you say for example that some people say i dont believe in samesex marriage because it should be between a man and a woman, that isnt illogical its just you havent actually gone anywhere you said the same thing twice basically, so that is not illogical to you havent used any steps of logic y develop your argument and i think that is what its about. And finally, i think that being helpful is really important. Sitting around using your brain a lot of this and goin is goingp anybody coming into this is a opinion, but ibo think that eatg hopeful involves not just using techniques but also actually engaging in emotions and understanding the emotions of other people, because if we keep selling logic at people t who ae feeling emotions, then it wont help them if we need to engage and empathize with people to understand why people disagree with us and to access some form of discussion that involves making human connections. We know this even when we are teaching mathematics that if we dont understand why a student thinks what they think that we will never persuade them with anything and if they dont feel the emotion while they are learning than they will push thd buffon and it never want to do it again. So, i think that i believe in the theory of stupidity which is aor two dimensional theory and its how much you benefit yourself and this axis is how much you benefit other people, so theres different quadrants here. If you are at the top left, you hurt yourself. Yourself. What co not quite sure which one of them first. Maybe the bottom right. If youve hurt other people while benefiting yourself and he says youre a bandit. Whereas on the top with one, your, youare benefiting other e while hurting yourself. And c he calls that unfortunate. [laughter] we might think of as being a martyr. I used to think w that was a god thing to be and many have been taught in society we should sacrifice ourselves for the good of other people and that is one of the reasons i kept working in a job that i was making me miserable because i thought i uls doing something good for society but the news he wouldvt about the bottom lefthand corner. That is where you hurt other people and your self at the same time. And that is stupid. [laughter] then he goes on to say hee reckons that there is an equal number of the same portion of stupid people in any group of people, whether it is professors, students, children, convicted criminals, politics, maybe theres more politics. [laughter] and he says theres always known more people than you are expecting to come even when you take that into account. And this is a piece is as stupid, people do for themselves and others at the same time. The top right hand is where you benefit yourself and other people at the same time. And i agree. I think that is what intelligence is. It doesnt have anything to do with the great phuket or the number of degrees you have or how much money youve earned or how many houses you own or how many people you have power over company. I think it is about how youre able to benefiyou wereable to bd yourself at the same time. And i think that abstract mathematics can help us with this and we can create a virtuous circle where logic can help us by feeling and help us understand the feelings of other people by doing those pivots and that it can also help us understand other peoples logic because we need to empathized to understand. I conclude abstract mathematics can i think help us create this 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. Costco the second speaker thank you all so much. That was really fantastic. Really hyped up. Im going to welcome julie back to the stage will introduce lamar alexander. Thank you. That was amazing. I really enjoyed the conversation. There was a talk by doctor. This is a quick announcement. If you want to have a more Intelligent Society and think that that can happen through early math for kids, we would love to have you at the luncheon october 23. If you want more information. Next up, mayor alexander is a historian, author and Academic Studies connections between mathematics and cultural and historical settings. His first book geometrical landscapes the voices of discovery and transformation of mathematical practice discusses the relationship between the 17th century english exploration of the americas and Early Exploration by englishs mathematicians of. His othernf books include deal t dawn heroes, martyrs and rise of auburn mathematics and infinitesimal how a dangerous mathematical theory shaped the modern world. Hes also contributed pieces to the New York Times, science and book review sections, the Los Angeles Times oped and scientific America Interview on npr all things considered. He currently resides in los angeles where he teaches history at ucla. Please join me u in welcoming a mere alexander Amir Alexander. [applause] thank you. For a fascinating presentation and one of the advantages he worked out all the technical bugs now so im told this works now. Okay, beautiful. Also, i argued i think i was entirely convinced mathematics and mathematical thinking really is and does and is useful and is helpful in our world even in our chaotic world and so i will start with a person who completely disagreed with virginia and was this man here. He is a mathematician who i wasa great prominent mathematician in the 19th century. Ceand in 1842 he was invited to speak atin the British Society r the advanced science and reading in the city of manchester and proudly wrote his brother after he came back eas he stood there before 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. He said mathematics declared that it is the only purpose of mathematics is the honor of the human spirit and that it really has nothing actually useful in it and he says so that is a great thing. Now, in fact completely, completely useless. Now, the fact is that he didnt make a lot and this is a city like manchester looked like in 1842 and the people that he was talking to people that were were making money from all of those technological and scientific innovations that they thought were all based on math and here comes this german with a funny accent saying mathematics is completely useless. He didnt make any converts among his audience. However, the view of mathematics is in fact useless and not as the Great British mathematician said that if it has to be justified as beautiful art is to justify it it is actually a view that was quite prevalent among the mathematicians at that time and in fact ever since. For example, he thought that mathematics gues yes he thoughtf course mathematics can be used for various things like to describe the wallsbe of emotion and to make airplanes fly, cell phones work into skyscrapers and send roversrs to mars. That is all well and good and also teaches us how to think properly and think critically and think in productive ways, but all of that, he says was not interesting. If it isnt real math. Real math is really useless. It is pointless if there is some truth. You can at least see what somebody like harvey means. After all, who actually used the methods for calculating the area, how useful is that and how useful really are the findings come afinite,this. You can count the different infinite values. The beautiful, amazing theory like how useful is it really, what is useful that anybody ever make if i of it or the language program. I will say one day maybe it will bee useful, maybe not. In the case of the committees 2,000 years still waiting. So, it isnt so clear that perhaps mathematical thinking has its value and teaches things correctly but its far from clear that actual mathematics is in fact useful in itself. What i would like to offere here is a different kind of perspective. Mathematics is fundamentally this. Its the science of order. That is if there there is somen 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 you can prove that is what mathematics is coming and that has enormous implications, because that means that what we say aboutt mathematics, but they sawhat wesay about mathematics e ekind of order mathematics is depends on what kind of mathematics we ascribe to, depending on what they think it is a Natural World is different also the human world is different. If we think that mathematics one way or another way the whole world with their natural but also social, political, religious, philosophical, everything changes but the deepest orde order of things, be that includes everything that goes to the very loops of creation is different and that is mathematics so today i would like to talk about the kind of mathematics that has particularly long and illustrious history of that really what shaped because it told us about the particular kind of order in the world. It shaped not just our understanding of the Natural World, but which it circulated but it also changed our understanding of the relationships with each other, our institutions, our Political Institutions and or social relationships and that is the great and ancient science of geometry. So, geometry i think matters and that is a great deal and to show how attackers, let me tell you a little story about a person from thehe past. Some of you have watched the Netflix Series on verse i. No, maybe. [laughter] its a nice series, but anyway, it out oenough of the week 14. Its nothing like this one. Theres no relationship, no connection. Its a very modern kind of democratic kind of guy. This one was not at all. 1661 and will be 14 was the king already for 18 years, 23yearsold, decaying since he was 5yearsold. Only a few months he was a real pain because upl until that point, he was under the tutelage of the region. Immediately he declared he would roll by himself. He will not have a minister anymore. Hean wont rule personally by himself and usher in the great and glorious of france. By 1861, he came to visit the estate of his own superintendent of finance is. That is this gentleman over he here. They just finished building a beautiful estate. In france you see it here at the beautiful chateau and beautiful gardens and the king descended and came to the evening and seno send it as 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 and aftr that proceeded down to the gardens that he walked down seeing from the chateau walked down theal alley and passed the beautiful symmetrical geometrically shaped to the circular pond here and defend down past the pool of the tried and to the pond here and went where they were presented with a new comedy. After that, there was a grand entertainment and after that all of them were served with a lavish dinner including those of the royal house to accompany the king and just when night fell and they thought that everything would go over and then the fireworks shoot out from the chateau from the work that caruso of the chateau to ascend on the garden like midnight sun. So, it was a grand entertainment, and a in this moment of royal approval, however the next day he thought he saw the king away. He was going back to his chateau nearby. He turns to his mother of austria and tells her shouldnt we discourage these people along these people, thats too much basically. He was a man of his word and basically in the other room he asked the captain of a man by the name assigned from the king he grabbed his former friend, put him under arrest and she spent the rest of his life in a prison cell in the else and never saw his beautiful estate again. A forgotten man. So the question is why did he react so strongly, what raged the wrath of king louis the 14th and a man that had been loyal throughout his life in the uprisings to never express anything but love and admiration and loyalty to the king. King. What was it about a hi thing tht heraised his glass. The clue is what happened to this. Now he got out of the way and he summons the gardener and tells him what you did there know you do for me but on a scale ten times or more greater than anything you saw the. You will create a garden like that that will make everyone forget the debt burden that he saw. He had been to the gardens of versailles and certainly a scale of that place is far above and beyond any garden that had ever been before. And told them do that now. It wasnt really if he pays well he was a wealthy man he had freedoms on his own and it wasntt his patronage but that a geometrical garden. That is what it was. Because it filled the mostea geometrical garden that he would build the own geometrical garden and that would fit the standard of forever so why is geometry the guarded why was that so outrageous to the king of franc france . So to understand that we have to go backwards quite a bit 2000 years to understand why geometry was so dangerous at the time of louis the 14. To create the first geometrical proof we know he was greek to live on the shores of the mediterranean and was probably something ysimple but soon others joined in that we know by by 400 bc so why did the greeks have geometrical proof they are not the only one that has tradition babylonians egyptians mayans their remarkable mathematical traditions but not one of them thought of proof. Thats not about measuring or doing astronomical measurements or land or accounting house its not about that proof is about finding a proof once you prove something it is proven it is a revocably true not because god said so or because of tradition but it is absolutely empirical and basically no one can argue thats the end of thee argument it is absolutely and necessarily true so there is something quite radical about that and that is a discovery that you could prove something and to prove it and then never again in the first proof was fact those were haphazard for who united them and to system it on systematize them and of course alexandria we know very little about it from the year 300 this is probably what they didnt look like. [laughter] what would he do . He starts out with the said postulates in Common Notions that though whole is greater than its part. Something is equal to another then they are equal to each other so nobody can deny selfevident true that is where he starts and from there he starts creating proofs that creates more proof and so on and every proof is connected its not that it is just true in itself that the interconnection so it is about liens and triangles and circles and angles so all of those geometrical objects in the Perfect World like no other not only is it true it i always eternally true but its all interconnected very specific relationships to each other in a particular hierarchy the simplest at the top then there is one layer of proofs based on another then another then they are all interconnected whole world of mathematical truth that is the accomplishment that is what the world is truth and rigor and eternally unchanging true that is quite an accomplishment in itself in fact is probably the most influential book ever written perhaps there are other competitors for example like my book so its not known for any particular innovation. The problem was its a beautiful eternal world the world is amazing but its not our world so that lead to the more Perfect World that it is a shadow world of imperfections and aristotle also thought you cant only describe our world but the christian world agreed very nice but it is fallen and corrupt certainly not can be described by geometry. It gets a lot of praise it is amazing, truth it pleases god but its also irrelevant because our world is nothing like that. So that lasted 1700 years from this breakthrough until here is a simple mathematical proof but until 1400 and pretty much the year 1413. As it happens y the year a man in florence conducting experiments on linear perspective and then he and his friends they established and popularized a theory of linear perspective it is a theory of how you draw things and paint three dimensions on a flat surface basically there is a vanishing point. So anyway there is a vanishing point that is on the horizon. Essentially its a perspective exercise because you can see that its doing what it wants. [laughter] would like to get back but anyway. Maybe the battery is weak go forward . Thank you. So this whole image is an exercise of perspective what you see they all point to a single position but it is much more. Is not just a trick of painting but space itself is a geometrical structure that go to the horizon they are real and embody to structure space itself see you can see perspective painting just a few touches not like the first one but two create those parallel lines that give depth to the picture just a few years earlier you have this other image to have internal space with all of the images its powerful in itself but it simply does not have that interspace is not that one is more realistic than the other but its very close to how we experience our life surrounded by people we dont think of it as a geometrical space. But yet this already has this geometrical space built in. These are two maps of florence. And they both depict the same city it has not changed much except the great dome of the cathedral that the world itself has changed in fact it is how you experience to be surrounded by buildings and churches and towers even more than this but the difference is using the space itself to that geometric principle every point is determined by geometric principles and that is how you can tell this was a turningtr point coming down from the sky 30000 people that we can actually name to made the connection the world itself can be structured by geometrical principles. Its one thing to say it is structured by the natural perspective or galileo has written the language of mathematics and the science itself always looks for the deep mathematical principles in the world. What about the human world to say it is mathematically structured . It wasnt long before some princes and you have realized the significance of this idea because if they believe themselves not just to be i am king of france i will cut off your head but that means you are an expression of the deepest order the hierarchy of your kingdom h not just because you have force but you are an extension of a deep order in the world that has enormous power and implication. So the king of france was the first to adopt the idea that geometry is power and legitimacy on a scale far beyond anything that was offered previously. So to present themselves of that geometric order now to just to mention a few things they did so in the courts the whole structure and the order of the court was not just the medieval people vying for powerr now there was order strict hierarchical order that everyone has their place from top to bottom to the king at the top to the dukes and accounts everybody has their place and constantly negotiated their place precisely that was the essence of life to find your way predetermined geometrically the french court invented the geometrical dance that we know as ballet but it was a stylization of those negotiations of Court Etiquette who determined who was on top or bottom. It was all based on geometrical movements. Philosophy to justify that treatise but not then equal the importance of the geometrical gardens were the emblem of french royalty. It started very simply a couple of gardeners from the failed campaign in italy to produce a simple guarded in his favorite chateau and over the next two centuries this bond between the kings of france simply increased and grew. So on a larger scale you can see this geometrical order perfectly ordered her geometrical land under the gaze of the palace at the top. There were others. It was the emblem of french royalty was geometry and nothing more so than the geometrical guarded why . That which came from euclid that is what they were determined to create and then came over to venice one visit the minister of finance he saw this geometrical garden is ines all respects you see the perfect symmetry and a geometrical pattern the Straight Lines and the squares. Even more so it is completely new because in fact it is structured as a painting. Leading up to the point marked by the statue of hercules. Not just geometry for the pattern to hold it together but the geometry of the world that structures everything and holds it all together to make it one unified interdependent unit the garden that was ever artificial and natural. You can see the similarities in the structure this was a royal garden in all respects because it was geometrical except for one thing it belonged to a commoner who presented himself at the top of this necessary hierarchy. This just wasnt somebody who was little ambitious but an attack on the foundation a geometrical attack of the regime as he sought. So at first i verse i said to create something he would create his own geometry that would have a path of order for him in the world which is what he did precisely. Very much a garden in the style about 100 times larger if you take all the areas surrounding the immediate area is in the tradition of the geometrical patterns you are familiar with of the hierarchical world. And from there you have this main access leading as a perspective painting but the real power of her sigh is not just a different palaces which is older which preexisted from leo the 14th but its what happens here. To have the grand canal because what you see theyre looking at the palace is open forest, open woods you do not see the elaborately carved beautiful that you see here. Because it is this painting to go after the horizon even in the open woods they are structured together through the deep geometrical order of the world this looks like open woods from the palace but underneath it all there are geometrical paths all the Straight Arrow intersecting and all of them together form an arrow at the center of the palace and that is the keys bedroom. What that tells you all the chaos that we see in the world all the mystery there is the underlying geometrical order. It structures everything the deepis geometrical order of the world its not random but hierarchical because it is layer upon layer all the way up as a natural necessary place. So if you think of your self with the museum that we go there but at the time for somebody to watch that path in versailles that natural geometrical order of the world it is a selfevident truth the entire world around you proclaims everybody has its place in the grand order but who else but the king himself and his palace. So i would like to end with a little more contemporary gesture perhaps i hope this was interesting. But this was a is a long time ago that we the 14 died his great great grandson louis 16 was beheaded so this supposedly eternal geometrical order shows up our geometry to shape that outlook of today so my answer is yes. I will just give one example. People are familiar with capitol hill and the mall and pennsylvania avenue washington dc is not a museum of a dead ancient monarchy it is from the greatest republic of the world and the most spectacular geometrical city in the world because they innovated with then gardens but to match the grandeur of washington dc but the design who is not only a french man but somebody who grew up in the we the 15 and 16 and knew him intimately and thats how he designed washington dc but if you look at this picture you say there is versailles. Capitol hill like the palace on the hill all three lead to capitol hill so now we have this obvious hierarchy with the houses of congress at the top but of Course Congress is not a monarchy they just to use that to present a republic so you have this versailles garden her here. And next at right angle to the mall so that was the intercepted angle and then they are connected. So this is capitol hill and on the south lawn and the garden each one in itself so already you have two lines not only the center at versailles but to a Great Centers that are competing but also a dynamic balance of capitol hill because they designed it that way. So you have those two great federal powers. It. Thats not the end of because on top of that there are 15 squares. Why 15 that was 15 states of the union each is the name of a different state that this is the immediate area. And they are all connected by this network that is unchangeable network to balance the two centers of power so two years after the ratification of the constitution to use the language of geometry and versailles to create a capital designed to be the constitution it was thought of as a compromise with that necessary and inevitable deepest order of geometry and unshakable. And it cannot be moved and thats how it was designed to. So talk about that situation today but most of us will agree those assumptions are challenged and then to be much more vulnerable than we expected from federal or state or congress and challenged but i have to say just my opinion when i go to washington dc , you walk those geometrical streets and you go to the mall and look at the houses of congress and up at the white house with the grand boulevard. And i think the message is still there. But there is more there that this order will survive. There is something more here than the particular resident of the white house the message of geometry is still alive. Thank you very much. [applause] we have 15 minutes for questions. Please make your questions brief and in the form of a question. That is a wonderful mathematic presentation one of the things the psychologist and sociologist tell us that it really doesnt drive us. But also the fact that we interpret as is so furious the finance minister could not have a better garden that did not sound logical to me in one sense but as you kept going maybe her different views about that. So what do youwh do with that were coming out of psychology to say its nice but theyre not important quirks and so by creating emotions of fear and hate are much more effective than reason in terms of gaining power and control. I agree in one of the things i say inhi my book if we keep putting logic and emotions in a battle that emotions will keep winning thats it were seeing across the world. But one doesnt exclude it people telling people they are emotional and not logical so then we wont get anywhere. We can use logic to understand emotions we just have to understand from the point of view not the logical system and one ofl the ways mathematics is constructed it is the axiom of those basic assumptions and we dont use that with logic you start with a different fundamental belief so its not that some people are not being logical that they may have that stopping point so i find those abstractions are emotions i have done it myself for example used to be extremely afraid of flying although statistically its safer than driving the saddest thing thats irrational i looked at what was going on. My fear isnt based on statistics but being reminded of death. So using an actual process to find out to see some logic in emotions and they are not separate and we can use them at the same time. I agree with that. You cannot associate emotions with logic and reason to give the reasons that i talk about today. But also a great psychologist because when the people go there to experience that grandeur and the necessary order that people react accordingly. They visited the gardens in 1688 they did not enjoy that because the french fleet just pulverized their city but he got the message that you go there then you understand and you accept emotionally what the proper order is. So they are very much working together and just like in washington dc the reaction is veryry deep. It is emotional it was planned that way. D in fact its difficult to understand somebody elses emotions unless they are the same as yours. We can get caught in our own iotional reaction. What i disagree with vehemently by let them take over than is very difficult to see whats going on but if i use that mathematical thinking to separate that emotional disagreement that i can understand someone elses point of view is a starting point. I really enjoy aid your application. If you are going to adopt that framework if we decided to use that framework on social media does that mean there are no Opinion Pieces were the framework collects how does that work quick. Thats interesting. Thank you. Not all opinions are equally valid. All opinions should be backed up with something. There are many different ways. Thats a way to back things up. It is based on evidence and more statistics. And the way it is assessed in history and with the right framework to how valid we should consider that truth to be if you have no backup whatsoever my opinion is this and it contains no framework in my ideal world if we can understand with that opinion comes from to give some justification then it is very interesting. In order for people to understand the logicalal framework we have to improve the education and change the entire Education System and then began to another vicious cycle inevitably change the government. So thats why i have been writing a book to bypass that because i would like to change the entire world in the meantime ill write a book to help them outside of that system. To questions. If you have a classroom of reluctant geometry students which of the books when you start them on quicks and the second question is when the women march on versailles did the gardens change at all quicks so i will start with that. Something interesting happens at the garden of versailles in a later decade even before the french revolution the notion of the perfect geometrical world of philosophy and Marie Antoinette to adopt that philosophy to create enclaves within the garden that are not at all that was in mind or the supremacy of the king but of suppose in nature that they could get away from that geometrical order it was anti geometrical reaction and you see it on the ground and in the design of cities and gardens that order is imprinted to shape our environment. After the revolution then versailles palace and garden are made into museums as are most of the old royal geometrical garden no longer the way the world is thats how things used to be and how the power is neutralized but in washington. It is neutralized. After my book my first one which is about what math is for and it is all around us and something you can do for yourself. Thank you i have a question for doctor alexander if you are in relationship to the garden and if so with that tradition if that eastwest alignment with the cathedral which in turn is a symbol for the medieval world and with that framework and tradition that we are looking not into something new but what is a tradition of time or that development. That is fascinating. First of all yes. So like a cathedral which is very interesting because that presentation was the son king he had the statue of apollo and that was near the palace except he was doing it backwards then was moving westward. So the pagan elements are definitely there i never heard the idea of the cathedral that is very interesting. But the fact that it did preserve the lining is interesting. Thank you for that. Increasing members have begun to reject the premise that science or math or logic that people can deny evidence the planet is flat weve never been to the moon so what do you say to those people that reject that to begin with and how do we move forward with that quick. Its very easy to get depressed about that k o situat. I remind myself we cannot reach everyone at once and thats okay and maybe there are the most faraway people from where i am but there are those who really do want to believe those things but dont know how to deal with it. So they try to be logical but they make mistakes but they dont quite fact check so we can try to reach those people first if you reach those who are the most difficult then you will get depressed but if we decide everything is hopeless then it will be for sure so i try to ascertain any chancen that i can understand where they are coming from rather than change their mind but also look at Mental Health if you will really get depressed and be attacked then its okay if youre not engaging with them right now now i dont have the statistics to back this up but the majority the people dont think the earth is flat so there are more people we can reach so we can just shift that thinking i think that could make a huge difference you dont have to convince everyone that maybe if we just try to shiftft where we can then we can make progress. So when things are twodimensional of vanishing points its really two dimensional look at those that are factual and talk about geometry it is chaotic do you see any evidence of symmetry with art orr architecture of course you are right when you use that linear perspective is not just describing the world but it is telling it is geometrical. And with that development in geometry moving away from that seeing goal fixed order and the implication that there isnt just one necessary single b truth but and infinity that is possible rather than a single truth which is very challenging and disturbing living in her own bubbles with different perspectives to hold different assumptions so we did try to deal with that. Im no expert that but the effort to portray things with that single view thats all i can say. The folks are still here if you have questions about them and books are for sale. On our. My husband was on the trip in chicago from work and went out to a bar owned by queer people of color so a middleage white man came in and sat down and struck up a conversation basically said that looks like so much fun on the dance floor i wish i was dancing my husband said go dance he said i am not allowed to dance. I came here last week and i was dancing with a woman and she said i dont want to dance with you and her friends got weird about it so i guess im not allowed to dance. Which is just such an agonizingly contortion of reality. To go into a space that is specifically not for you and then to violate peoples boundaries and then be victimized by their response its not that hes not allowed to dance but not whenever he wants to make himself the center of the moment. Will have a good time dont touch anyone but thats not what he wanted. He wanted interaction he wanted to do whatever he wanted and being told he was not allowed to which i think is very telling. And it gets to the broader overarching themes and one is that challenge of critique of those in power is a witchhunt that you return to that metaphor very often so those powerful people who have been critiqued for Sexual Harassment that in fact the language they use about themselves victimization that they have been killed their careers ended and by the way that actual victims have denied the use of. How much do we hear when do we hear about all the women quit because they were harassed at work. Whether they had careers or working in the environment where harassment and discrimination no bed he talks about their career. It is a National Emergency we figure out to get everything back that they wanted. What frustrates me is can we forgive or permit people to revolve . For those who abuse their power. It is framed as our collective ability for redemption or understanding the evolution if possible. I have been thinking about this a lot. So thinking why it is the path to redemption . I have been trying to come up with an answer because people keep asking me. I dont know. Figure it out. You workshop you troubleshoot. Keep trying until people forgive you. I dont know. You figure it out. O eleanor randolph, her new biography of Michael Bloomberg the many lives of Michael Bloomberg. Today was kind of a big day. Did it take you by surprise . Not very much, he said he wasnt going to run and i thought he wasnt running and that is the end of my book, he doest