Service, and brought to you today by your television provider. [background sounds]. Host good evening everyone and we are ready to get started and thank you all for being here here. On behalf of townhall, and technical books, set up in cafe over here in a special guest tonight, i hope everyone in the room will get a chance to visit. And so excited to welcome you tonight are very special doubleheader giving you with you gina chang. And Amir Alexander. I am hoping many of you may be returning to our building the first time after a a few years. We have been remodeling the space and for many more of you, maybe this is the First Time Ever to townhall. Welcome, this is exactly the type of thing that we want to do. Im so pleased that we have these two fantastic authors to present to you tonight. We love all of our lecture programs. All of the political talks, arts programming that we do here. But i am especially happy about this mathematical approach to thinking about the world. Im a reformed college math student and so having a chance to present these authors to you on a doubleheader, is a great opportunity for the special homecoming festival. Im so pleased to see everyone here tonight and thanks especially to our partners. So the format is a little bit unusual. It is a doubleheader. Were going to open with a solo presentation and we will take a very short break the loop switch the presentation over to Amir Alexander give his talk after which we will have a joint q a to keep the questions in my from botox. There actually m is this really beautiful residents tonight with a talk talks about mathematical thinking and is arches a presence political dynamic and we sort of take a broader historical view of the Historical Development of mathematical thinking. So hopefully that will be some residences but both of them will be happy to answer questions questions. You can pick up a copy of either book at the table and we will have a book signing afterwards in a bar and cafe will be open afterwards. The very last thing that i will say about townhall is that we tie a member supported organization. Thank you so much to the members of the room. Now to introduce you. Say a couple more words, julie. [applause]. Stu mckay and thank you. Im the executive director of zeno. Is a seattle based nonprofit. Julie ourr vision is that everyone can do math. We achieve this through programming trip families ages three five with a focus on families of color. And in local and income communities. For all about making math fun and playful. We know, that there is no such thing as life lived without math. Emily been a strong Math Foundation is key to life of opportunities and success. We are so excited to be a community partner. Doctor eugenia chang, school of arts of institute in chicago. Pure mathematics at that uk. It is now honorary visiting fellow at the city of university of london. He has previously taught at cambridge, chicago, and also phd in mathematics from the university of cambridge. Alongside her researchbr and category, and her undergraduate teaching, or a mystery the world of math phobia. Her first popular math book, how to make pie this praise with New York Times national geographic, and scientific americans. And she was interviewed around the world including in dc, npr and late show with stephen colbert. Her book beyond infinity Royal Society and site Investment Science book price of 2017. It was early pioneer on math on youtube. Videos have been viewed over 15 million times. Shes also a math columnist for the wall street journal. A concert pianist and founder of the leaders group. Please join me in welcoming her. [applause]. Dr. Eugenia cheng thank you so much to the panel for inviting me back here to speak on my latest book. It is always very informing to be invited back somewhere again. This is the third time i have been invited here so that is strictly affirming. And it is wonderful to be in saddle. Thank you, for joining ng this evening where and math evening where im going to talk about my next book, the art of logic in an illogical world. And the point about that illogical world is this prettys. Can sometimes seem like were edrowning in the current world and where the worlds of wash with divisiveness and conflict and think news and victims with exploit tatians privilege and bigotry. Shouting, meniscal attention spans. And it can seem that we will never a great ever again. And weth are doomed to be stuckn chambers. All hope lost. That is the question. I say no, all hope is lost. It can seem like that sometimes. This book arose when i was teaching our students. In a fall semester of 2016, somethings happened. On both sides of the atlantic. In the morning after, after the election, i did what many people dead. I got depressed, i cried. I drink. And i thought, but what can i do that is productive. I truly believe in doing something rather than sitting around and complaining. I also believe in looking at your own combination of abilities and trying to use them in the best way that you have to do something to help the world in a way that you see fit. What can i do is a pure mathematician. Was i using a principal of mathematical thinking to find things in his divisive arguments pretty my fellow ligature that, for broadly with everyone who wants to find that clergy, some people of course part of the interesting in finding clergy and those arguments but i believe there are people who do want to understand what is going on. If an understand what is going on in both sides of the arrow is the first step. It will solve world problems, rather that we dont understand it, then we cannot solve the problems. That is why wrote the book in a group out of the discussion i had with my art students predict i saw abstract mathematical. Is more the things that they learned in high school. How to use mathematics as a way of thinking. [laughter]. Silent. Wheres the computers. It is on. Doesnt work. Thank you. [background sounds]. Perhaps can you turn the volume down because this is how loud i speak. When im not interested, i speak very low. Thank you. I will just keep going i suppose. They are students of the school, are very interesting students. Theyre not mathematicians at all. My dream job is i really want to share what i feel aboutor mathematics to more people. In are so many myths about math that just about numbers any questions. That some people are meant people and some people are not math people. And that if you get new timetables, you cant be a madman tatian. Those are some teaching art students, its really wonderful place to find out about how people can put them back on math. And i really believe, i think the educators will all agree that its really important i think to tap into what motivates your students in order to motivate 20 or teaching. And rather to impose your motivations on top of them. Questions of social and political justice motivate my students. My students, somehow arm most motivated. And my first book was about math and food. Should i get closer to it. [background sounds]. Should i go and stand over there. I can give the rest of the type without my slides but i like my slides. [background sounds]. Okay thatth will be very complicated because i have aau t of transitions. But i guess we will try it. Pure mathematics is just not about numbers and equations and getting the right answer or solving problems i believe is a framework. Every academic, i think thats what we really need from education. At information is everywhere. So actually what is more important is a way of what counts as good. Pure mathematics is one particular framework based on logic. [laughter]. I believe theres been an oldfashioned view of what mathematics is. But its applied to appointment medics. The appointment medics is useful for science and bit sizes been useful useful for engineering and medicine. Numerical quantitative problems of the world. And that is true. I used to believe that was the extent of how my research would ever be used. It is very abstract. This t narrow view enables peope to declare that there is math. People can be glad that it exists and they can say, i dont need to do it myself because im a good at math. Whereas i believe that pureo mathematics is about how we think. And that therefore, it is about the entire human world. At least the parts of the human world think. Sometimes these days,. [laughter]. D seems like some of the human world does not think very much. So anyway, i am going to talk about analogies and what role they play in mathematics. The interconnectedness of things, and will talk about how abstract mathematics can see relationships that we did not see before. And that we can use those abstract situations. And finally, was like about how to fit with what i believe is intelligence. So first of all, analogies. Another thing that we can say is that so much of mathematics is analogies. And ill tell you what, i mean, by that. We have two apples, for example we can say oh well, there is something they have in common. We forget, the details about them being apples. Although both two things. This is fundamentally how we come up with the idea of numbers in the first place. On abstractions, they have something in common. If you teach children how to count, and if you try to teach them how to kill, you wait until the makeup abstractions leap. And you cant do it for them. They just have to sort of seat what is going on. And generally make another abstract leap in the process of math education, some people dont quite make it. There are various reasons for ndthat i think what is it seems pointless if its not well motivated and then the reason is they just have tol wait until yu can do it. Nobody can do it for you. So the other thing is there very different way to do it. Its not a completely automatic project. So if for example, we wanted to, a look at this very exciting. [laughter]. [laughter]. If instead we say two things, what we say what we have in a common with these two groups. This also true however in the case, we would not be able to include for example, two chairs in that situation. That is not an example of two groups. So in thatt case we have to go p one level further to do things. And we can c encompass those examples. One of the things i will argue is it seemed to take up further away from real life. It actually enables us to bring in more examples than we could before. So heres a more mathematical example. If we say will get one plus two and table three, those are examples of a b. People often say to me, i was fine with math until the numbers became letters. Ill show you the point. We could say one times two and two times three and theyre both examples of a and b but no. A b, and a times me. Oh, thank you so much. [applause]. Thank you. Theyre both examples of something. And yet that is a further level. The kind of the bottom line of what you might be doing an elementary school. And it when you might start to meet algebra and at this level, you might be a math major and a university intake abstract algebra. And none of these levels is right and wrong. Sometimes people think math is all about right and wrong. Its about what light yous are shedding on particular situation. And what my phd advisors taught me was that they missed out to find the most abstract situation, the aim is to find a good level of abstraction for what you are tryingg to do at this moment. I would have been a is that we talk about things being analysis to each other but we dont focus on what exactly is making them an analogy. And that argument leaves us in a discretdiscriminate. Based on Different Levels of abstraction that were not making clear. So we moved that particular and acuity. Heres an example. We talk about street marriage and samesex marriage. Some people say theres no difference in other people think is terrible. What is really going on, either using Different Levels of abstraction. So if you think that marriagee s about an unrelated man and woman and indeed, same marriage is not possible however so mostly vincent actually only about two unrelated adult and then they are the same. And then people disagree because of using Different Levels of abstraction. People disagree, about the upper level, can say that we have gone further than we have in the upset and say, well the next thing you know will be allowing and a few holdouts even if the art unrelated to date. Just in case there were children in theer audience, i was careful here. And then we could perhaps eight to living creatures always say, to creatures. [laughter]. The point is just because some of us want to go to here does not automatically mean that we have shot all of the way up to the top. Sort out being surprised about the little obstruction that we are using, it can open up those arguments about things. But im not saying that this approach solves that problem but i am saying it gives us an yopportunity to have a more sensible and more clear arguments about it. So the next thing i want to talk about is how things become or be seen as interconnected. Here is my favorite slide. This is an abstraction of the undergrounden system. We forgotten details about where things are. It is very useful to see how testations are connected to each other for which lines pretty but its not geographically accurate you could end up with tourists try to take the train from site, from the garden even though there only two minutes away. So here is the geographically accurate picture of the london underground. It is a differentnt abstraction. As a better or worse, is probably less useful to actually try tos take the train summer bt it is quite interesting seeing where everything is. So the point is that these are two different obstructions that illuminate different aspects of the situation. This is what math does. Temporarily abstract things and to see what we can learn from it. Heres an abstraction that i find quite interesting. It deals with relationship breakdown. I think also when relationships nbreak down, 1 percent, call him alex, is affected and alex is unable to show love. And his partner sam feels love as a result of it and unable to show respect. And we have a vicious circle that x collates. I can further out abstract, and these are feelings. And it does not solve the problem but it makes you stop and think about how we could break these released one of these arrows. You only have direct one break one to write the circle played and you can say, maybe we feel the feelings but maybe we can decide not to act on them. So perhaps even when alex feels disrespected, they can concentrate on showing love tregardless of that and then the situation doesnt get out of control. Then we reduce it to these two action errors we argue about who would take responsibility for breaking the arrow and one i possible theory is that whoever is more mature should be or do that. [laughter]. So we have this vicious circle. And at ten abstract level is very similar to even more tragic things for example, the situation with police. One could try and say, but they feel threatened by black people so they defend themselves against my people which make black people feel threatened about by the police. And its a vicious circle. Now i would like to point out that im not saying that this is what happened, but even when black people do what theyre supposed to do. Theres still Police Violence thagainst them. We might argue that the police or the police. They been trained to feel less threatened. Maybe we can train them but we can also maybe train them to take action differently and deescalate things and immediately escalate. And we could say who should take responsibility. Some people yell and say blah blah. But i would art argued that the police have the power the situation and so i think that they should be the ones. If they dont, that doesnt help n. The situation. Another way i use interconnectedness to help me, we can do things in a interconnected way. Could be a gracious way, when they need to kick someone, and they wanted to leave and they didnt leave so they called security. There are wonderful arguments on the internet. Love you just wouldve done what you are told, you would not get injured. It really is that simple. What if somebody in the internet said it really is that simple. Really is not. If someone say facts, usually dont really have an argument. [laughter]. Actually read an editorial saying, you know. This is, is your fault. All of you because you sometime miss flights and thats why they over booked the flights. So lets think about this,ut in result, injury. Also security used force. Well, and also because the airlines called security. Why did he or she refused to leave pretty was a doctor and needed to get to work. Somebody might say is reasonable. This also why the airlines chose that person, and it was about racial profiling. And nobody volunteers really. The airline didnt offer enough money and also somehow people really wanted to get where they were going. T why did they even need to remove people pretty well because the flight was too full and also they needed to get some people summer and why was it because they have an issue with the cruise scheduling. Two things again, the fight was over booked. And also not enough people failed to show up so here finally, is the fact why people often miss flights. So this interconnected system is really what happened. Is that the fault any one of these things. I understand the world is a complicated place in an order to understand that you need to slow the hyatt but we are forgetting most of the information. Ignoring it is not a very good way of supplying it. I think a better way is to become more intelligent. Because then the world becomeou simpler because in relative to your brain. [laughter]. And one way that i think that can help us is because it gives us ways to understand interconnected systems of a single unit. So that we can understand this is a single unit than we dont have to be afraid of it. Still very complicated. If we look at it as a whole, then math gives us a way to move things around in your brain in a different way. You can put things in a bag and suck all of the air out of it and it makes easier to move it around. This is another thing about why i gain weight. Ice to be larger. And i dont want to be larger. And people often say, its not rocket science, you just have to eat less and exercise more. Another thing says, even rocket Scientists Use applied math. [laughter]. Getting white. Why do i gain weight. It is because it taken more energy than they burn. Yes its also because of my metabolism. In a slow start, so already we have to eat too little and also exercise too much. Also, my metabolism is controlled by by genetic and i ate too much because i like food. And also because i emotionally eat and both of those of course obama genetic in my upbringing. In the social pressures to eat too much. And you put this altogether, life happens. And then there is the entire food industry. And they try to get thi they tro get us to eat more. Plus what i did gain weight, then he starts eating too little and exercising too much and getting stressed. It is the simple. It is not that simple. It is the simple. But understand, it helps me to see which link i can try to break. So that i can say the way i want to be. 50 pounds lighter. So i f did draw a diagram for te election. I got tired of people saying is just the fault of the people. I think it was all of these things including the voting system. Third party votes. Other stuff maybe in over here that has come to light as well. So maybe i will move swiftly on. [laughter]. Talk about how abstraction can understand the relations between things. Heres another piece of mathematics the may seem heirrelevant. One, two, three, five, six, ten, 15, 30. Very good. Its about numbers a Straight Line. We step our thoughts in a onedimensional Straight Line. I also like to say this is why i do not have so many things on my desk. So we can find some of these things in the situation by looking at which numbers are also related together going kind of a family tree. If any of you came to hear me talk about the family. Five goes into 15. I dont need to draw an arrow directly from 30 25 because like inn a family tree, we dont draw grandparents relationships. Becausee we can put those together with two levels of children. Now we see, this really a cube. Its a little bit more interesting than a bunch of numbers in a Straight Line predict anything like a mathematician, why did that happen. What are the numbers make use. There are various ways we can do this. But maybe, you can see that its because the three numbers are prime numbers. They dont have anyar other factors except one in themselves. Its the three dimensions to the cube. So this level, we have numbers, to prime factors. If i thought like this, if the actual prime issue level, and of empty set where there are no prime factors and c then we can see maybe, that ittt doesnt matter that this was to three and five. He couldve been any of the numbers be like we can say, it couldve been from a, b, and steve. Turn the numbers into letters. [laughter]. Say we use numbers to three and seven. And here are all the factors of 42. I have 23 and seven in the products of two things and in the products of three things as well. In the middle diagram is close to the previous one where everything has been changed fro five. It is not actually the samews diagram. So it shows us something that wasnt same about the situation. Im going to show you how that tis possible but first i want to stress something about this diagram. Six is lessut than seven. Tthat might not sound very soud but six is less than seven. And yes, six is higher than seven. It is higher than seven in his hierarchy. Whatever you have two different hierarchies, the display in the same thing, its going to be at the source of antagonism. For example of somebody is older at work, but more genius than someone else, that could happen. So now i want to show with the point is to go into this level of abstraction because a, b, steve, can be anything. They dont even have to be numbers. They could be three types of privilege. So then, what we have is that people with two of those privileges and then at this level, this people have one set itof privileges. And at the bottom none. And i have bridge white men. And non rich white men. And these at the bottom, our people work none of those work white or non, mormon. And so the final thing i would like to talk about, everybody tends to identify themselves as not to rich. Lets remember there are people who are much less rich than all of us. Sick direct losses of one type of privilege. I think this is important to remember because sometimes people get very upset about privilege. And they say things like look at that super rich guy. That shows that White Privilege does not exist. Thats not what it means. If everything about two, just like hypothetically not being quite anymore, then we would expect you would be better off than most people in society. Something else i would like you to learn from this. Six was less than seven, we can compare the people that are at seven. There are no arrows at this level. But weorec could consider how wl we think those people are doing in terms of privilege. I think the rich, white, non men are probably doing better who in terms are doing better than say, poor white men. Because money is money. But even further than that, compare between the levels, but i think rich, non white, non men, are probably doing better. Rich people like say, michelle obama, are definitely doing better than poor white men who were maybe homeless are really struggling. So actually, it goes back to the cuba skewed by the absolute level of privilege. This is something to understand why particularly some white men are so angry about their privilege is because they are told that they have two types of privilege but they dont actually feel the manifestations of that privilege. They see people are considered to have less, doing better than them in society. I think much more productive to understand the Structural Force when they are rather than to get angry with them in return. Almost where the mathematical abstraction helps me think. So i would like to talk about how we can use this kind of abstract sinking. To help us understand the situation because in the situation, rich white men, an allergist. We can look at another more an allergist situation. The power that mel people have over the female people, and its a narrative structural power. And again, im not saying that all male people have power over all female people. Whereas, if you look at mail people relative to female people, is not an allergist. Because the power structure goes the other way up. And for example, if men are sexist towards women it doesnt really work the other way. Then you have to look at the definition of sexism. Both cases are people being portable to other people. But theres also a sense in which they are different. Once he take notice of that, we can look at why we are disagreeing with the manifestations of that are. Whether it is more useful to think about the differences. In another thing that my phd supervisor told me us that is not about something is right or wrong but its the sense that something might be right or wrong. And when were having arguments with people, its a sense in which they have a point even if we disagree with it. And something might not be a thought in one context. The maybe in another class context. But in this diagram, and i focused myself on this the diagram, now the rich white non men are at the top. So we could change this to just thinking about women and then have another diagram or we take a privilege among women such as rich and white and another entirely in douglas q. With poor non whites. And this is help me to understand why there is so much anger the moment especially towards rich white women. Because if they are prone to considering themselves underprivileged relative to men, lyespecially, if they spend most of their time surrounded by white people. Then they will not understand how privileged they are relative to all of the other people. I will remind you, your gender identityty matches the ones that you were assigned at birth. So this is unde helped me underd to understand the angle other than to get angry in return. We are all more privileged and somebody and less privileged than somebody else principally understand what is like to be in different parts of this diagram. They can help us understand other people who are in different parts of the diagram relative to us. So this is what i do myself. I think it is an asian person, i have some lack of privilege compared to appeal but it also acknowledges asian people are probably among the most privileged among the nonwhite people. So i can pivot between these two situations. One where im higher up and one where im lower down pretty so i can understand the experiences of different people understand how it how i feel when im lower down in. I can treat people well when i am higher up. It enriches, i am not so rich that i never need to work again. Not that i would ever be. Ive worked because i want to make the world a better place. I am doing fine print some mpeople are really struggling. They may be working heart and still unable to make ends meet. And also the things, health problems, homelessness. So i am more rich than someone and i am less rich than someone. And here is one about to white women. When they are less privileged comparison to white men. But more privileged than that non white women. It how to use these pivots to help me empathize with other people which brings me to perhaps the surprising conclusion that after the mathematics has helped me with empathy, and that they might not be something that you put in the same sentence. At least not in a positive way. [laughter]. But i think this is an important part of mathematical thinking actually. I would like to conclude by thinking about what i think intelligence is and how i think it can help us be intelligent. I thought about this and the defendant about another diagram of interconnection. It seemed reasonable. Also being helpful. So what is reasonable mean. That you are able to be reasoned with. Some people hold views where nothing, no evidence or logic or nothing at all whatever get them to change their mind. That is in fact unreasonable. I think it reasonable means even if a framework for you believe the things that you believe and especially from mark deciding when it is time to stop believing them so that you will change your c mind. I think the reason part of this involves logic. Now getting theological means that you dont just use logic to use it with some kind of technique to build your logic up. Because if you say for example, the some people say that i dont believe in samesex marriage because i think it should be between a man and the woman. It is not illogical, it is that you havent actually gotten anywhere. And you said the same thing twice basically. So thats not illogical that you have not use any steps of logic to develop your argument. And i think thats what that is about. And finally, i think that being helpful is really important. I dont think theres any point in using your brain a lot if its not going to help anybody. This is my opinion but i think in couple involves not just using technique but also actually engaging in motions. In understanding the emotions of other people. Because of point keep yelling logic at people, sort of feeling emotions, and i want help. We need to engage in empathize with people to understand why people disagree with us. And to access some form of discussion that involves making human connection. We know this even when we are speaking mathematics. The understand whyrs a students takes away the think fred finley will never persuade them. And they dont feel the emotions while they are learning, they will just kind of wash over and never want to do it again. So i think, i believe in stupidity. It says this, two dimensionalhi theory. And this actually is, to benefit yourself. And other people. There are various different quadrants here. So if if you are the top left, you purchase of. Lets see, im not sure which one i done first. So if you hurt other people while benefiting yourself, that means that you are a babbitt. Whereas in the top left one, you benefiting the people while hurting yourself, any calls that unfortunate. [laughter]. We might think of it as being a martyr. I used to believe that was a good thing to be. I think many women have been taught by society that we should sacrifice ourselves for the good of other people. Thats one of the reasons that i kept working where i was making miserable money because i thought of something. But then what about the bottom lefthand corner. Thats where you hurt other people and you hurtst yourself t the same time. And that is stupid. [laughter]. Then he goes on to say it a reckons that the same proportion of stupid people in any group of people whether it is professor, student, children, convicted criminals, politics, maybe theres more there. [laughter]. And he says that theres a lot more people even that you are expecting. This is what he says is stupid. People who hurt themselves and other people at the same time. So this part you benefit people and you benefit of the people of the same time. And that is what intelligence is. It doesnt have anything to do with the number of grade you get for how much money you earn or how many people you have power over. I think it is how and what extent you are able to benefit others and yourself at the same time. And i think that mathematics can help us do this. I think that we can create where logic can help classify feelings. Hope is understand the feelings of other people by doing those pivots. And it empathy can also help us understand the peoples logic because we need to empathize with them. In order to understand the thought processes. I conclude that abstract mathematics candidate, help us create this vicious circle and help us go out into the world and be intelligent. I hope that we will all want to do that. Thank you very much. [applause] [background sounds]. That was really fantastic. It really hyped up. I welcome julie back onto the stage and she will introduce Amir Alexander thank you. Julie [applause]. Was amazing. I really enjoyed that conversation in the talk. Just asif a quick announcement,f you want, if you want to have a more Intelligence Society and that can happen through early math kids. We would love to have you on october 23rd. She will more information go to our table. So yeah. Awesome. Next up. A mere alexander, historian, academic, mathematics and cultural historical study connections. His first book geometrical landscape. In the transformation of mathematical practice is the relationship between history, english exploration of the americas in the early expiration might english mathematicians. His of thens books include dualt dawn, heroes martyrs and modern, mathematics. How a dangerous mathematical theory shakes the modern world. Alexander also contributed to the New York Times in science and look reviews section, los angeles times, and scientific american. Hes been interviewed on npr, all things considered. He currently resides in los angeles where he teaches easter history at ucla. Please join me in welcoming Amir Alexander. [applause]. Amir alexander thank you and thank you so much for coming. Thank you for a fascinating presentation and one of the advantages, if you work out all of the technical bugs now. So i know this is working now. Thats what im told. Beautiful. Also, i argue that i was entirely convinced a mathematic, mathematical thinking really is or does or is very useful and helpful in our world even in our chaotic world. So i will start with the person who completely disagrees with eugene. Eugenia. This man here. His mathematician. Very prominent mathematician in the 19th century. In 1942, a person was invited to speak at the british, Industrial City of manchester. As he probably wrote his brother after he or when he came back, he stood before all of this british math science and he told them, it is the glorious science to be of no use. And in particular mathematics. His in mathematics, he declared that is only the purpose of mathematics is the owner of the human spirit. There really is nothing actually useful. And he said that is a great thing. Its the fact, is completely useless. The fact is, then he did not make it lot of commerce. The people he were talking to were people who are making money from all of those new technological and scientific tinovations that they thought work of based on math. And here comes this german with his funny accents tell them that dthematics is completely useless. He did not make many converts among his audience. However, the view mathematics is in fact useless, and that as the Great British mathematician hrv said had to be justified as beautiful are, it is actually a view that was quite prevalent among mathematicians. At that time. And in fact, ever since. He thought that mathematics, yes of course mathematics can be used for various things like he described scientific laws of motion of course. And to make airplanes fly in cell phones work and all of those, build sky scape scrapers, that is allro well and good into this we can also add teaches us how to think properly. In a productive way. But all of that, hardin said, that was not interesting. Is not real math. Real math is really useless. Really pointless. Theres some truth pretty you currently see what somebody like he means. After all, whoever actually use his methods for calculating the area of say, how useful really are trance finite spring this. That you can have different incidents, they have different values and that you can rank them. Its an amazing theory. By how useful really isll it. What use to anybody would they ever made of it for the language programs. I will say that one day maybe it will be useful. Maybe but maybe not. So it is also clear that perhaps mathematical thinking has its value in teaches us incorrectly, but as far as clear actual mathematics is in fact useful himself. What i would likeat to offer hee is a different kind of perspective here. Mathematics is fundamentally, a science of order. As if there is something of the deepest order in the universe something that deep down is absolutely true, cannot be wrong, something that is unshakable and somehow somehow true necessarily true and that is if you can from that that is but mathematic is pretty but it has enormous applications cabecause that means what we say about mathematics, the kind of order that mathematics is, that her world is distant depending on what kind ofbe mathematics we ascribe to. What we think proper and true mathematics is rated the Natural World would be different and also the human world would be different. We think thate mathematics is in it another way, that the whole world, natural also social, religious, philosophical, everything changes if we think that the deepest order of things, the one that supersedes everything, goes down to the very roots of creation, is different. And that is mathematics. So to them, i would like to talk about the kind of mathematics that is particularly long and has a history. That it is, that really that shapes and because it told us about the particular kind of order in the world that shapes, not just our understanding of the natural work but also change our understanding of our relationships with each other, our institutions and our political institutions. And also our social relationships. That, is the great things in science of geometry. So geometry, i would say matters. It matters a great deal under show how it matters, let me tell you a little story about some famous person from the past. Perhaps some of you have watched the Netflix Series no, baby, okay. It is nice series. Its called bursitis, what is a culprit for site. Let me tell you, purity watch the show, is Something Like this louis the 14th. Theres no relationship credit no connection. Movie is a very kind of modern kind of democratic kind of guy. In the sky was another goal. 1661. Louis the 14th, he was a king already for 18 years. He was 23 years old. Five years old. But only a few months, he was a rookie because up until that point, he was under the tutelage of the region, must run. And then missouri and died and then louis declared he would rule for himself. No more minister anymore. He will rule personally. And then he will usher in the great and glorious state. On august 17th, 1961, louis came to visit the estate of his own superintendent of finances. He was this gentleman over here. And he had just finished building a beautiful estate. In france, he appeared in full. Any of beautiful gardens and the king descended. It any descended at the entrance to thee chateau over here. I was led by his host through the rooms of the chateau that was created by the famous people and by the greatest artists of the day. And after that, he proceeded down to the gardens. He plopped down into the chateau. Then this central alley past this beautiful jim, terkel circular pond here. And then down towards and pass those tritons to the spawn here. And then to the squanto here. Then they were presented with a comedy by a famous person. After that, there was a grand entertainment after that. All of them are served with a lavish dinner. Including the 5000 soldiers of the royal household. And just when night fell, they thought that everything was over, then they had fireworks shoot up from the chateau on the roof of the chateau and then descend on the garden light and like the midnight sun. So state grand entertainment. Os. Of his mother and austria, and sent madame, shouldnt t we disgorge these people of all of that . Thats too much. Basically, it was a man of his word and a few months later he summons to an audience and in the other a room he asked the captain of the musketeers and it was a the king he sprung up, grabbed this man, put him under arrest, and he spent the rest of his life in a prison cell. That was in the alps and he neverte says beautiful estate again, died in 16800 forgotten. The question is why did the king react so strongly, why raise the wrath of king louis the 14th from a man who has been loyal through all of his life. There was never anything but love and admiration and loyalty, and loyalty to the king. Why was it . What was it that raised the kings wrath . My clue is what happens to this beautiful, okay, well it was nice while it lasted. [laughter] here we go said the king okay hes out of the way he summons his gardener and he tells him 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, a garden like that that will make everyone forget that garden that he saw. Sure enough, if you have been to the gardens of her side, youll admit certainly the scale of that place, above and beyond any garden that had ever been before. And i suspect a sense produce not really called its a huge guarded not pleasurable. Its certainly something that will make anyone forget and will completely put any competitor in the shadow. He pulled out the trees, he took the fountains, he took the statues, brought the mall and broughtm the people put them to work and said you do that now for me. Because in the end it wasnt really his wealth. He is a very wealthy man. He had a fleet of ships, it wasnt that. It wasnt his patronage of the arts that doomed him it was ultimately this geometrical garden. Thats what it was. Because he invoked of the greatest and most amazing geometrical garden in france and that was something louis would not tolerate. He would build his own geometrical garden that would be the one to set the standard forever and erase the memory of the upstart king. So why is that geometrical . Why geometry why this w geometrical garden that doomed him why is that so outrageous to the king of france . To understand that, you actually have to go to a long time you have to go backwards 2000 years time to understand why geometry was so important why geometry was even so dangerous at the time of louis the 14th. We dont know who created the first geometrical proof, there some unknown jesus genius. Was he or they lived on the shores of the mediterranean the greek cities of the mediterranean, and is probably something simple about lines and angles, something that scenes very trivial, very soon others joined in and started producing proof that we know work quite sophisticated by 400 bc were quite t sophisticated. And theyre interesting why do the greeks invent geometrical proof not because they had the only mathematical tradition we know they are amazing traditions we know from babylonians, injections, mina engine mayans, remarkable mathematical traditions not one of them thought of inventing proofs. Because its not about measurement, its not about finding doing astronomical measurements or land measurements or accounting house, its not about that because proof is about finding truth. Once you have proven something, that something gets proven it is absolutely your revocable he a true. Not because god said so or tradition rethink that simply reason tells you it is absolutely your revocable he true and no one can argue that is the end of the argument. It is proven. It is absolutely a necessarily true. Thats kind of a funnyny thing, that is something very radical about that. That was a discovery you can actually prove something it was a discovery you made only once in human history. And never again. The first proofs were f in fact haphazard about Different Things the person that united them systematize them you could violate alexandria we know very well about them alexandria that would probably didnt look like but thats his picture there. What did he do . He starts out by different definitions and set of postulates and Common Notions that a very simple and selfevident greater than its part something thats equal to another thing another things equal than the two things are equal to each other. So no one can deny their obviously and selfevidently true, thats where he starts. From there, he starts building and creating proofs. Starts building proofs based on those proofs he creates a more proofs. And so on. Every proof is connected its not just its true in itself, its also interconnected to all of those other roofs about lawns and triangles and circles and angles and so on. The whole world of those geometrical objects it is a Perfect World, a Perfect World like no other because not only is everything true, everything there is true everything is always true eternally true, is all interconnected very specific fixed relationships to each other they are all in a particular hierarchy to each other. The postulates are the simplest than everything and theres one layer of proofs based on another one and another one and another one. They are all interconnected in one asked each journal and changing network. Whole world of mathematical truth thats the accomplishment creating a world, the problem is its a beautiful world and eternal world, but the little flaw is that world is amazing, but its not our world, right . Plato thought its the way to lead to the Perfect World our world is a shadow world the world of shadows and imperfection. Aristotle also thought mathematics cant really describe your cant really describe our world and not only that, later on when the Christian Church also agreed geometry is all well and good our world is a fallen world is a corrupt world, certainly not something that can be described by geometry. Its a lot of praise its amazing its truth some say its the only sign that pleased god to bestow on mankind. Also kind of irrelevant because our world is nothing in fact like that. And that lasts for about 1700 years. 1700 years from this breakthrough by. [inaudible] until the guy heres a simple mathematical proof. Until, until, until 1400 and until pretty much the year 1413. Not a famous year for most people that happens to be the year in which a man in florence conducted experiments on perspective. On linear perspective. Then he and his friend and artist they developed, established and popular lowrise the theory of linear perspective. Initially its a theory of how to draw things, how do paint three dimensions on a flat surface. So basically theres a vanishing point you can draw a vanish anyway, anyway theres a system of vanishing point off parallel line point to one particular point that is on the horizon. This is essentially like a perspective exercise. You can see, i guess, its doing what it wants. [laughter] i would like to get back, oh, alright, okay, anyway. Maybe the batteries week i dont know forward okay thanks okay this whole image basically exercise in perspective in which you see all those lines the bottom they all point to a single position. And as much or more. Its not just a trick of painting because the implication is the space itself is in fact you metrically structured. Those lines of perspective those lines ofhe perspective the go to the horizon they are in fact real. They embody, they are in fact the structured space itself. You see the difference example of the r at the respectable painting where he just does a few touches not like the first one a few touches to create those parallel lines that are to give depth to the picture just a few years earlier you have this other image which doesnt have that. Doesnt have internal space it has all of the images, its very powerful image in itself. The monaco picture. It simply does not have that inner space. Its not that one is more realistic than the other, this is a realistic picture in fact its very close to how we experience our life surrounded by a lot of people, we dont think about as a geometrical space. And yet, this one already has a geometrical space built in. Next slide please . This one, here, yes, yes. This is the difference heres two maps of florence one is in 1552 and this one is from the 1480s. They both depict the same city. The city is not changed much except for the great dome of the cathedral which he is also famous for for building the city the world itself has changed. The city is in fact a Medieval City heights how you experience Medieval City surrounded by buildings, towers, churches, behind every corner perhaps even more than this but the difference here is using perspective as a space itself has become infused with a geometrical principal every point in the second image is predetermined by geometric principles. That is how you can tell this was a turning point this was a time when geometry came down from the sky and in a little city of 30,000 people just a few people we actually can name, they made the connection and said no, the world itself can be structured by geometrical by geometrical principles. Its one thing to say the world is structured by geometrical principles Natural World or in perspective are galileo said the world is written in the language of mathematics. In a science itself is always looking for the deep mathematical principle in the world. But what about the human world . What does it mean to sayay our world is mathematically structured . Its not long before some princes in europe realized the significance of this idea the world of geometrical. Because if they present themselves or if they believeve themselves to be not just i am king of france because it will put you in jail if you say otherwise or i will cut offe your head, but because being king of france means that you are an expression of the deepest order of the universe. The hierarchy of the 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, enormous, and normas, enormous powers. And normas implication. So it was indeed the king of france that adopted, not the last, the first to adopt this idea the power, the geometry of power. Geometry is power is legitimacy on the scale and with implications far beyond anything that was offered to did so many ways present themselves avid apex of an sheol order. Next . , previous employees . For example, and, they did in their courts the whole structure its not just a jumble of different people vying for power, there was order there is strict hierarchy order where everyone had their place from top to bottom from the king at the top to the prince of the blood to the mere dukes to the accounts, everybody had their place. Everybody constantly negotiated their place very precisely. That was the essence of life in courts, finding your way in a predetermined Orderly Society that was ordered geometrical. The arts, the french courts as a geometrical dance. We know it as ballet but it was invented precisely as the spiral is asian of course etiquette that determine who is in the top, whos on the bottom, who sits, his stance, how they greet and so on. It was all it was all based on geometrical movements. There were philosophyy justifying the royal that was structured but nothing, nothing equaled the importance of geometrical gardens. Geometrical gardens were the emblem of french royalty. Next slide please . It started very simply, King Charlotte the eighth of brought gardeners from italy with the failed campaign they produce a very simple garden in his favorite chateau and over the next two centuries this bond between the kings of france and geometry simply increased. And grew. Next employees . This is on a larger scale geometrical land under the gaze of the palace, of the palace at the top. Next one. It became the emblem of royalty, french royalty was geometry and nothing more so than geometrical gardens. See emblem of sovereignty ofnt their right, why . That Perfect World that came from euclid, the perfect ideal world there was orderly in hierarchic coal, thats what they were determined to create. That is how they presented themselves, thats how they highly saw themselves. With louis came over to talk about his minister of finance, he saw this. This is a geometrical garden in all respects because you see there is a perfect, perfect symmetry geometrical patterns, the circles, the Straight Lines, the squares, but even more s so, some ways its completely new because it is in fact structured as a perspective dick painting. Leading up to point mark of the statue of hercules. Not just the geometry of patterns is a geometry of the world. At the deep geometry that structures everything. He puts everything in a. Spectacle painting unified interdependent units. It was best geometrical garden thats artificial and natural. Next employees. I can see the similarities here and the structure as a. Spectacle garden. It was a royal garden all respects because it was a geometrical gardens and the brightest geometrical garden driver was except for one thing. If tampa did not belong to the king it belonged to a commoner who is presenting him self as the apex, the top, the move verbal hierarchy this was not just un tactful. Not someone ambitious this was an attack on the foundation is a geometrical attack of the regime. And so he moved on to so louis determined not to just crush, but to create something that would be a zone to create his own geometry that would present the proper order of the world and him at the apex. Which is what he did. Which is what he did precisely. Besides very much a garden and the style except about 100 times larger if you take all of the areas surrounding. Its immediate area here pretty much in the tradition, the kind of geometrical, geometrical patterns you are familiar from their presenting and orderly fix hierarchy tickle world. From there, again you have this main axis leading too the horizon creating it as a. Spectacle painting. The palaces here this is the part that wasnt older garden that preexisted came from the age of louis the 14th. The real magic is what happens here. This is the grand part over here we have the grand canal and the surrounding. What you seee there, is the what you see there, if you look in the palace, what you see there is simply open crce, open wood, you did not see any of those you do not see any of those elaborately carved that you see here. But because, because it is once again can i have the next slide please . This perspective did painting, going out to the horizon all of this, even these open woods are structured together the deep geometrical order of the world so underneath it all, beneath this it looks like open woods from the palace. But underneath it all, there are these geometrical paths, all of these straight arrows intersecting at right angles and all of them together forming an arrow. An arrow here, and arrow here, and arrow here, her the palace also made the center is the kings. The centers the kings bedroom. What you see what this tells you, what this tells you is beneath all of this variety all of the chaos we see in the world, all the mystery we see in the world theres a sixth underline coordinator. It goes here when you look at it from afar but underneath it all that structures everything. The deep geometrical order of the world. This deep geometrical order is not random its hierarchy. It has layer upon layer of fun layer leads all loops the kings palace which supports the kings palace as the natural necessary place of all, of all authority. If you think of yourself as someone, today theres a museum we go there we say oh this is all very lovely. But at the time, for someone walking those paths, royal supremacy is that natural geometrical order of the world was not just an abstract place. It was selfevident truth. It was all around you, the entire world around you proclaimed this deep geometrical order of the world. Everything had its place, everything had the place in the grand order and who presides over, course, the king himself. The king himself and his palace rs in his palace. Ed likes and with another more contemporary more contemporary gesture here. This is perhaps, i hope it was interesting, thats for you to judge. Time ago. Ong louis the 14th died in 1715. You know, his great, great grandson louis the 16th was beheaded in 1793 you know, this order has eternal, eternal geometrical order. We go to it and say thats how things was, the power of geometry still shapes our outlook, our outlook today. My answer is, yes. I will give just one example here. I think people are familiar with this view of capitol hill andd the mall. Theres pennsylvania avenue washington d. C. , d washington d. C. El is not a museum, it is not a museum of a dead ancient monarchy. Its the capital of the greatest republic, of the greatest republic in the world. It is, the greatest say think in the most spectacular geometrical city in the world. The story is, the story is news impersonating gardens in cities but no city matches the grandeur of washington d. C. Washington d. C. Was designed by who is himself not a frenchman but someone who grew up in the court of louis the 15h and louis the 16th. He knew it all very intimately. Thats what he used when he designed washington. And then you look at this picture there is the mall you look up a capitol hill like the palace on the hill, all of the area unchecked arrows all streets lead to lead to the capital here. Still we have, here we have the obvious hierarchy with congress, houses of congress at the top. Of course the u. S. Is not it is not a monarchy. When he was trying to do was to presented as a used language for this garden here, next please. You also have at right angle, to the mall but he called the president s palace he was very disappointed by the scale of the white house which he called a pathetic country house. That was supposed to be the other node, the other node of government. There are alwayst entering already to and theyre intersected right angles each moment their own mall leading up to them. Then they are connected by pennsylvania, next slide please. Then they are connected as is capitol hill, we know this is the mall, this is the president s house, the white house over here. In the south lawn and the gardens are there. They intersect at right angles are connected by pennsylvania avenue over there, each one of them great known lines diversion on it. So you already have two lots not one center, you have two centers, two Great Centers that are too Great Centers that are themselves competing with each other. They also in this careful dynamic balance. Yep capitol hill in the white house, not by accident but by design because it was designed that way. You have those two great federal powers. Thats not the end of it. On top off it, also created 15 squares. Why 15 . Because of the time their 15 state to the union. He calls each one of them by the name of a different state. Each one of these dominates its immediate area. So its power. They are all connected by this network. A rigid network that is unchangeable network that overlays, those two, that overlays the entire city and balances those two sensors of power. What we get your comment 17912 years after ratification of constitution and he uses the language of geometry to create a capital that is in fact the constitution in stone. So presenting the constitution not just a compromise that was reached, but as a necessary, inevitable, deepest order of space deep on the deepest order of geometry, unshakable, it cannot be changed and it cannot be moved. That is how it was designed. I dont their ego what what i talked quite a bit about that. We talk about the political situations today. Whatever, i will not presume about your political stances but i think most of us agree at the time when many of our assumptions are challenged in many of our institutions were secure they are being challenged. Much more vulnerable than we had expected any of those institutions, federal, state, congress, white house all seemed in crisis and challenge. I have to say, this is just my opinion, when i go to washington d. C. You walk this geometrical streets, go to the mall, look to the houses of congress, you look up at the white house, the grand boulevard, that order that geometrical order that was put there, and i kind of think that message is there. The living message not the dead message. There is more there this order, the deep order were a child will survive. The something more here than the particular politics in particular time or the particular resident of the white house. The message of geometry is still, still live. So thank you very much. [applause] host thank you for being here today but i 15 minutes of questions. There is a microphone on either side of the stage if you have a question encourage you to use please try to keep your questions brief, respectful in the form of ale question paid willti get through as many as we can. Thank you both. Wonderful mathematicwo presentation. The question i have it both of these coming together. One of the things is the psychologist, sociologist and so forth tell us that human beings are rational really not driven as much as the other seems to respond to the culture when louis the 14th shows up and decides, i interpreted as so furious that the person whose finance minister or whatever it was, could not have a better garden. That didnt sound particularly logical to me in one sense. But as you keptca going, maybe you would have different views about that. What do you do with the kind of work thats coming out of ecology saying logicic and reason are really sometimes nice. But they are not really that important. Driving people by creating emotions of fear and hate are much more effective than reason intrinsic power control and so forth. I agree one of the things i said my book is if we keep pitching logic and emotions against each other that emotions will keep a winning parity think its a situation we are seeing across the world. I dont think the two are mutually exclusive. I think if once i keep selling other people there being emotional not logical the other side saying about the site as well as we wont get anywhere. I think we can use logic to understand emotions pretty think because emotions do have reasons inside them. Its just we have to understand them from the point of view of that persons emotions, not from our own logical system. One of the ways in which mathematic constructs logical system is always starts with the axioms which are the basic assumptions we dont try to prove in the system and that we built off from those axioms using logic. If you start with different fundamental beliefs you will get to different conclusions even though youre still using logic. Its not that some people arent being logical and some are, its that there might be different starting points. So i find, i used abstractions understand emotions because ive done this for myself there are things i do that seem to be irrational for example i used to be extremely afraidd of flying even the statistically its must safer than driving. Whatever. A still completely afraid of flying and sentencing okay thats us emotionally thought about what was going on. My fears not based on statistic my theories based on being reminded of death. Thats the thing im afraidd of. The fact it was linking with that and so using an actual process where you unpack someones process and find but there axioms are, i basically always find that i can see some logic and emotions. And so they are not separate and we can actually use both at the same time. What you think . I very much agree with that. Theres logic and reason, its valuable to give some of the examples that i talk about today. But louis the 14th in building this garden, he was an ideologist and he was also a great psychologist because when people go there and experience that grandeur and that absolute necessary order he is king, people react accordingly. People wont necessarily enjoy it, theres gardens in 1688 in 1685 he did not enjoy it because of the french had pulverized the city. But he got the message. That is very clear emotional, psychological message. You go there, you understand and you accept emotionally bothon logically and emotionally what the proper order is. I dont think they are very much working the very much working together and i think the same as in washington d. C. When i go there, the reaction is grand city but the reaction is also very deep. It is emotional, it was planned that way and geometry is what creates it. I think to take it one step further think its difficult to understand summons emotions using emotions unless they are actually the same emotions as yours. We can get so caught up in our own emotional reaction, there are people who i disagree with vina messily, and if i let those emotional response take over, thats very difficult this is going on. But if i abstract cement and use abstract and ethical thinking logical steps instead i can separate out my own emotional disagree with from them and understand from their point of view and understanding someone elses point of view is really the starting point to a more unifying and less divisive world for us. Iv i really enjoyed your application of logic to social issues. If we were going to adopt that framework, how would you imagine that happening in the world world . Lets say would use that framework on social media or in our newspapers, with that mean theres no Opinion Pieces anymore . With the articles have to be like scientific papers . What would the framework be kind of a lighthearted question how would that work . Thats an interesting definition of lighthearted. Thank you. I think opinions, not all opinions are equally valid and that something the world seems be losing sight of a little bit. All opinion should really 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 to back things up and im not trying to claim mathematical logic is the only good way to back things up because scientific protests are slightly different from the logical process the scientific process is banked on science, and more statistics. Then there other disciplines these Different Things. The way they assess in history way itsent than the a assessed and archaeology. All of these disciplines provide framework for assessing how valid we should consider a truth to be. If you state in a penny without no backup whatsoever, thats is my opinion is this that contains no framework. I dont see a place for that in my ideal world. But if we can understand where that opinion is coming from, and provide some sort of justification for it, then i think its very interesting. In order for people to understand that logical frameworks or scientific frameworks, of course we have to improve education around these things we have to change the entire Education System in order to that weakened other vicious cycle will recant changed Education System until we change the government we cant change the government to change education. Then later to . Thats what ive been writing books to try to bypass all of thatye part i would like to change the entire world but in the meantime ill write it few books and try to help people under think understand things outside of the system. Two questions. If youve got a classroom of reluctant geometry students, which one of your books would you start them with . And the second question is when the women marched demanding more from bread, do the gardens change their tune it all . Was it somethingng else . Okay i will start with that. Something very interesting happens to the gardens in the last later decades of the old regime. Even before the french revolution. This notion, this idea of the garden being a perfect perfect geometrical world is being challenged and is being challenged particularly with marie antoinette, the clean would adopt the philosophy and starts creating enclaves withinn the garden that are not at all what he had in mind, not at all about the supremacy of the king. But little enclave of supposedly which she and her where they can play and get away from that rigid geometric order. So its consciously anti geometrical reaction. And you see it on thed grounds. Thats what i mean with geometry you can see it on the ground in the design of cities and gardens. Its imprinted in that order is imprinted on the ground andpr shapes our environment. Its a matter of seeing it. What happens ultimately is the revolution. After the revolution then the allison gardens are made into museums. So they are preserved, as are most of the old royal geometrical gardens in vienna and st. Petersburg. They are preserved in a museum their power is curtailed there no longer the way the world is. It something we visit and quaintly say thats how things used to be. Their power is neutralized. But not in washington because washington is a lie. In answer to the other part of the question for reluctant geometry class i would recommend this book after my book i think my first one would have to be about what math is for. In the way in which it can be for everybody it can be fun andd is all around us and related. It something you could do for yourself even if it hasnt seemed like you could do it for yourself. Thank you have a question whether you can tell me the alignment, the chateau in relationship to the garden and whether there is an eastwest alignment and whether this suggests eastwest alignment depicts the cathedral which in turn again is a symbol for the medieval world. So it is overall framework. In the tradition again suggests we are looking not and do something new, one that was tradition in the time it is a further development of medieval thought. Thats fascinating. Yes, first of all yes. The gardens are pointing west board so is like a cathedral which is very interesting. Its very interesting because louisa presentation was as the sun king. He had the statue of apollo at the end and initially had the home near the palace. Supposedly apollo, the sun king would transfer to the sky aycept he was doing it backwards at which was always a little bit of a quandary with the sun moving westward. It was moving eastward rather than westward. So theres definitely the pagan elements are definitely there in the presentation as the sun king. Ive never heard rd the idea of the cathedral. That is enormously, very interesting. The fact that it does in fact preserve the old alignment of the cathedral. That is very interesting, thank you for that. Tragically increasing number of members in our societyun have begun to reject the premise of science or math or logic whatsoever people who deny evidence in sate the globe isnt warming. The planet is flat, we have never been to the moon, things like this. What you say to those people who reject that premise to begin with . How did he think our forward from that . Thank you its very easy to get very depressed about that kind of situation. What i remind myself is we cannot reach everyone at once and thats okay. As a whole range of people that maybe those are the most faraway people from where i am. Whereas American People who are less faraway, there are people who really do want to believe those things but dont really know how to deal with ry or dont do quite as well as they want to pray theyre trying to be logical but they make mistakes. The kinds of people are trying to believe but dont quite check and immediately repost. Think we can try to reach those people first. If you immediately try to reach the people who are the most difficult, then yes, you are doomed to get depressed and feeling everything is hopeless. The thing is if we decide everything is hopeless, then it will be hopeless, thats definitely for sure. I tried to ascertain whether this any chance i can make any progress. I try to understand where theyre coming from rather than try to change their mind. Its also important to preserve your own mentalinm health. [laughter] if youre really going to get depressed and be attacked by people that i think its okay to decide youre not going to engage with that right now and try and improve everyone else. For example i dont think, i dont actually have the stats to back this up. I dont think its a majority of people who think the earth is flat. [laughter] i think its alright think there are more people who we can reach in if we just shift the kind of center of gravity of logical and scientific thinking further back towards the logical and scientific thinking that could make a huge difference between him have to change everyone at once we just need to shift things. Things only shifted a bit thats what i suspected maybe we should just try to shift where we can, then in fact we can make progress and maybe change things a bit. Stuart one last question. When you look at things like the Golden Triangle the very twodimensional we look a lot of art the simulation of three dimensions but its really two dimensional bird from a look at are actually threedimensional your tagamets spherical geometry for and since we look at them somewhat is chaotic. You see any evidence or moving towards art that actually encompasses the three dimensional of symmetry and more order in these things we create is chaos whether stalking about art or o architecture . Guest thats an interesting question. Of course you are right, when you use this linear perspective its not just a plain description of the world, its not just the world geometrical, it is telling this is the way the real world is its geometrical in that sense. There has been developments in geometry that have moved away from that single necessary single necessary fixed order. The implication theres not just one necessary single truth and one true point of view. In fact there is an infinity of possible geometries rather than a a single. Its very, very challenging in fact disturbing. I think in some ways you can say were not moving in that world were living in a postworld war i or all living on her own bubbles, our own different perspective theyre all equally true because we hold such different assumptions. Arjun fact, modern art certainly did try and do with that. I am no expert of that clearly early 20th century art. The effort to portray things from different angles and different sides at the same time. Thats also clearly a response to the move away from the single unified view. Thats what i can say. Host thank you soth much. [applause] thank you all so much for being here. [applause] this is really fun. I think theyre putting their stuff away but the folks are still here give question about them books are for sale over here and our guests will be citing a just a moment. Thanks much for coming. [applause] you are watching a special edition of book tv now airing during the week while members of congress are in their district due to the coronavirus pandemic. Tonight global history first, Brown University peter andres talks about the relationship between drugs, alcohol tobacco opium amphetamines, cocaine, and war. And then Harvard University history professor Vincent Brown chronicles the 18th century slave revolt that took place in jamaica, known as techies revolt. And lady maria from latin america at the wisconsin book festival in madison. During book tv now and during the weekend on cspan2. Sunday night and q a the videogame developer is bringing peace and conflict revolution to a wider audience. Because. [inaudible] these are all young people in the war so the mindset in the refugee come out of war. When i was playing i was like how about these young people Start Playing this videogame. [inaudible] in the videogame its the same thing happening in my country. Thats how things are done. Theres peace and conflict. [inaudible] watch sunday night at 8 00 p. M. Eastern on cspans q a.
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