tv Eugenia Cheng The Art of Logic in an Illogical World and Amir... CSPAN October 6, 2019 7:00am-9:01am EDT
hall seattle and we are set up in the cafc right over here and our special guest tonight is you know howard, they've been set up in the library showing off really cool mask games and i'm so excited to welcome you to tonight's very special math theme doubleheader with eugenia cheng and amir alexander. this event is presented by townhall as sort of our big homecoming festival. i'm hoping many of you might be returning for the first time after a couple of years while we've been remodeling the space and for a lot of you this might be your first time at town hall.this is the type of things we exist to do. i'm excitedto present these fantastic authors tonight. we love all our lecture programs, all the political costs, all of the art programming that we do but i
am especially fascinated by mass, mathematical approaches to thinking . i'm a reformed college math student so having a chance to present eugenia cheng who we posted and a couple of times and amir alexander as a doubleheader was a great opportunity for this special homecoming festival so i'm pleased to see everything here tonight. the format is a little unusual. you've been to other townhall talks because it's a doubleheader. were going to open with a solo presentation from eugenia cheng and take a short break while we switch the presentations over and amir alexander will give his talk after which we will have a joint un day. keep questions in mind from both talks. there is this thematic residence where eugenia cheng talks about mathematical thinking in its dynamic and we take this broader historical view of these sort of historical developments of mathematical thinking with amir alexander's talk so hopefully there will be residences but both of them will be happy to answer questions and after all that you can pick up a copy of either book at the book table and we will have book
signings afterwards and our bar and cafc will be open afterwards if you'd like to break play some of those great xeno games. we are a member supported organization, membership is a great show of support and all the programs we do but now to introduce eugenia and after a few wordsabout xeno, i'd like to welcome julie newmar to the microphone . [applause]
>> i am the executivedirector of zeno and zeno is a seattle-based nonprofit. our vision is a word world where everyone knows they can do math. we achieve this through programming for families ages 3 to 5 with a focus on families of color and low income communities. our work is all about making math fun and playful because we know that there is no such thing as life lived without math and believe that a strong math foundation is key to a life of opportunity and success . we're excited to be a community partner townhall for tonight's lecture. doctor eugenia cheng is a scientist in residence at the school of the art institute of chicago.she one tenure in pure mathematics at the university of sheffield uk and is honorary visiting fellow at the university of london. she has previously taught at universities of cambridge, chicago and nice and holds a phd in pure mathematics from the university of cambridge. alongside her research and category theory and undergraduate teaching are goal is to rid the world of math phobia. her first popular book how to bake pie was praised by the new york times national geographic and scientific american and she was interviewed around the world including on the bbc, npr and
the late show with stephen colbert. her book beyond infinity was shortlisted for the royal society inside investment society book prize . eugenia was an early pioneer of math on youtube and her videos have been viewed over 15 million times to date . she is now columnist for the wall street journal, concert pianist and founder of the leaders. join me in welcoming doctor eugenia cheng. [applause] >> thank you very much. thank you to the townhall for inviting me back here to speak on my next book. it's always very affirming to be invited back somewhere again and this is the first time i've been invited here so that tripoli affirming and it's wonderful to be in seattle . the sun is outside every time
i speak of the townhall so thank you for joining us for a mass evening where i'm going to talk about my next book "the art of logic in an illogical world". and the point about that illogical world is that it can sometimes seem like we're drowning in the world. the world is awash with devices miss and conflict and the fake news,victimhood, expectation, privilege, blame, bigotry and minuscule attention spans . and it can seem that we will never agree with each other ever again and we're doomed to be stuck in echo chambers and just yelling backwards and forwards into nowhere and is all hope lost is the question? i say no, all hope is not lost. it can seem like that sometimes and this book arose from my teaching art students and in that fall semester of 2016 somethings happened. various things on both sides
of the atlantic and the morningafter the election i did what many people did . i cried, i drank and i thought what can i do that's productive because i truly believe in doing something rather than sitting around complaining and i also believe in looking at your own combination of abilities and trying to use them in the best way you can to do something to help the world in a way that you see fit and i thought what can i do as a pure mathematician in this situation and i realized what i'd been doing with my students all semester was using the principles of mathematical thinking to find greater clarity in those divisive problems and i felt i could share that more broadly with everyone who wants to find that clarity. some people of course are interested in finding clarity but i believe there are people who do want to understand what's going on and understanding what's going on on all sides of the
argument is the first step. i'm not saying it will solve all the problems but if we don't understand it we can't talk about it and that's why i wrote the book and it grew out of discussions i had had with my art students where i teach abstract mathematics. it'snot remedial mathematics, it's not the things they've from forgotten from high school. it's how to use mathematics as a way of thinking . and -- [laughter] there's somebody here with a question, where's the computer? does this work? it's on. thank you. perhaps, could the volume be
turneddown? you see how loud i speak . at least when i'minterested . when i'm not interested i don't speak very loud. well, i'll just keep going i suppose until we can findwhat my next slide is . i teach art students and art students are very interesting students. they are not mathematicians at all and it's my dream job because i really want to share what i feel about mathematics with more people and there are so many myths about math that it's just about numbers and equations, that it's not for everybody, that some people are math people and other math people and i said if you don't do your tables you can be a mathematician, things like that are myths i'm trying to dispel so teaching art students is a wonderful place for me to find out more about what people put off math and what can as it were put them back on math and i really
believe and i'm sure if there are any educated in the room you'll all agree that it's really important to tell into what most motivates your students in order to motivate them and what you're teaching rather than trying to impose your motivation on them and what motivates my students is social and political justice and that's why this book came out. my students in sheffield and what most motivates them is food and that's why my first book was about math and food . it still doesn't -- should i get close to it? should i go and stand over there? could give the rest of the talk without my slides but i like my slides.
okay, that's going to be very complicated because i have a lot of transitions but i guess we'll try it. mathematics is not just i think about numbers and equations and not about getting the right answer and it's not just about solving problems even. i believe it's a framework for agreeing on things and what counts is good information and in the current world i think that's what we need and there's tons of information everywhere, information is no longer at a premium so what's more important is a way to decide what counts as good information and pure mathematics as one framework based on logic . so i believe there have been an old-fashioned traditional view of what pure mathematics is but pure mathematics applied to applied mathematics and applied mathematics is useful for
science but science isn't useful for engineering and medicine which is useful for cutting numerical quantitative parts of the human world and that is true and i used to believe that was the extent of how my research would be useful because my research is so abstract but this narrow view enables people to declare that people can be glad that this exists but they can say i'm not ever going to go into that field so i don't need to do it myself whereas i believe pure mathematics is about how to think and that therefore it is about the entire human world. at least the parts of the human world that think and sometimes these days it seems like him of the human world doesn't think very much. anyway, i am going to talk about first of all analogies and what role they play in mathematics and the interconnectedness of things. then i'll talk about how
abstract math allows us to feel relationships we didn't see before and that we can use those abstract relationships to pivot in different situations so we can understand more things than we previously did and finally i will talk about how to get them with what i believe is intelligence. first of all, analogies. another thing we can say is that pure mathematics is a theory of analogies and here's what i mean by that. supposing we have two apples and two bananas, then we can say there's something they have in common and if we forget the details about them being apples and bananas we go they are both two things and this is fundamentally how we come up with the idea of numbers in the first place. numbers are an abstraction from sets of objects that have something in common and if you teach children how to count, you just have to wait until they make that abstraction leap and you
can't do it for them, they just have to see what's going on and every time we make another abstraction leap in the process of math education some people don't quite make it and there are various students with that and one of those is it can seem pointless if it's not well motivated and another is you have to wait until you do it, nobodycan do it for you . theother thing is there are different ways to do it . this is not a completely automatic process so if for example we wanted to -- oh. this is very exciting. but if instead of saying two things we said what this had in common was two fruits that would also be true and that's also an abstraction but in that case we would not be able to include for example two chairs in that situation. that is not an example of two fruits so in that example we have to go up one level further to two things in
which case we can encompass those examples and one going to argue is that although abstraction teams to take us further away from real life it actually enables us to bring in far more examples than we could before so here's a more mathematical example where if we say, if we look at one +2 and 2+ three, they are both examples of a+ b people often say i was fine with math until the numbers becameletters . i'm going to show you what the point is of numbers becoming letters so we can look at one times to 2c and they're both examples of a times be but now, this is supposed to work. a+ b and eight times be, thank you very much. [applause] thank you. so a+ b, a times b are all examples of a dumping be and
that is a further level of abstraction and these levels are bottom levels of what you might do in elementary school and this level is what happens when you start to meet algebra and this level is what happens if you go to be a math major in university and you take abstract algebra, maybe group theory and none of these levels is rightor wrong, that's not the point . people think math is all about right and wrong and it's not, it's about what light your shedding on any particular situation and one of the things my phd advisor taught me was the aim is to find the most abstract approach, the aim is to find a good level of abstraction for what you're trying to do and what happens in normal life typically is we talk about things being analogous to each other that we don't focus on what is making them analogous and that ambiguity that we leave leaves open the possibility of disagreement based on using different levels of abstraction so that we're not making clear whereas in math where very specific about which level were using so that we remove
that particular ambiguity so here's an example of how that ambiguity comesin . it's down. if we talk about straight marriage and same-sex marriage, some people say oh no, it's terrible and what's really going on is this, people are using different levels of abstraction. if you think marriage is about an unrelated man and woman, same-sex marriage is not part of that picture some of us believe it's actually really about two unrelated adults in which case sex marriage is part of that and people disagree because they're using different levels of abstraction and the next thing that happens because were not being precise about which level were using, the people that disagree about upper-level can hallucinate that we've gone farther than we have and they get upset and they say next and we know will be allowing any two adults even if they aren't unrelated .
i've redacted in case there were children in the audience because then we could go up further and just have say three humans or we could say to living creatures or we could say to creatures. and the point is that just because some of us have decided we want to go to here does not automatically mean we have shot all the way up to the top but when we're not being precise about what level of abstraction were using it can open art of those arguments about saying this is the same and this isn't the same so i'm not saying this approach off that problem but it gives us an opportunity to have a slightly clearer and more sensible argumentabout it . the next thing i wanted to talk about is how things can be seen as being interconnected. here's my favorite diagram of interconnectedness and itis an abstraction of the london underground system . we forgotten many details
about where things are and it's not geographically accurate but it's useful for seeing how stations are connected by which lines but because it's not geographically accurate you can end up with slightly hapless tourists trying to take the train from leicester square to common garden only even though there two minutes walk away. here is the geographically accurate picture was which is a different abstraction and it's not better or worse, it's probably less useful if you're trying to take the train somewhere but it's interesting seeing where everything is so the point is these are two different abstractions that eliminate aspects of thesituation . this is what math does, it abstracts to see what we can learn from it. here's an abstraction that i find quite interesting. i think this is what often happens when relationships break down that maybe one person, i'll call them alex, eels disrespected and when alex disrespected alex is unable to show love and sam
eels unloved as a result of which sam is unable to show respect so alex feels disrespected and we have a vicious circle that can escalate. i can further abstract these are the kind of action arrows and these arrows are feelings and this doesn't solve the problem but it makes a start because we can think about how we could break these, at least one of these arrows because you only have to break one to break the circle and you can say is it easier to break an action arrow or a feelings arrow, maybe we can control our feelings but maybe we could decide not to act on them so perhaps even when alex feels disrespected they could concentrate on still showing love regardless of that and then the situation won't spiral out of control so we reduce it to these two action arrows and we could argue about who should take responsibility for breaking the arrows and one possible theory is whoever is more mature should be the arrow so we have this
vicious circle and this vicious circle at an abstract level is very similar to even more tragic things. for example the situation of police violence which one could try to say happens like this but police threatened by black people so they defend themselves against black people which makes black people threatened by the police and so the police feel threatened by them. i'm not saying this is what happens, it's an overview of what happens but it's been shown even when black people don't do anything to defend themselves and do everything they are supposed to do, there's still violence against them. we can say should we break the actionarrows or the feelings arrows and we might argue maybe the police, why do they feel threatened ? they're the police and they're trained to feel less threatened. it's been shown they feel less threatened by white people and black people but we can teach them to take
action differently ratherthan escalating things and we could say who should take responsibility ? people yell and say black people should just obey the law. but i would argue that it's really the police who have the power in this situation though i think they should be the ones taking responsibility for changing it and if they don't it doesn't help the situation but maybe we can find more clarity about what is going on and this is something i thinkabstraction and help us with . another way i use interconnectedness is when there are many factors contradictory to the same thing. there will be a grievous united incident when they needed to kick something off of a flight because it was overbooked and he didn't want to leave so they called security and dragged him off and he injured on the way out and there were arguments on the internet saying youshould just do what you told and you won't get injured . it really is that simple and never someone on the internet says it really is that simple usually isn't that simple. it's like if someone says fact, it usually means they
don'thave an argument to back themselves up . i read an editorial saying you know was focuses? it's your fault. all of you, because you sometimes miss flights and that's why they overbooked flights so it's your fault and i thought let's think about this. the end result was injury was caused. injury was caused because the guy refused to leave and security used force and that's the wrong button. and also because the airline called security . why did he refuse to leave but he needed to get work, one might say that's a reasonable reason to want to get to work. there's also why the airline chose that person . questions remain about racial profiling butwhy did the airline decide to kick people off in the first place ? because nobodyvolunteered . two things, the airline didn't offer enough money and people wanted to getwhere they were going . why do they even need to
remove people? because the flight was too full and they needed to get some crews somewhere and why was that mark today have an issue with their crew scheduling ? why was the flight soulful? because it was overbooked and not enough people failed to show up and here is the reason people miss flights . this interconnected system is what happened. it's not the fault of any one of these things. i understand the world is a complicated place and to understand that we need to simplify it but ignoring it is not a good way of simplifying. i think a better way to simplify the world is to become more intelligent because then the world because simpler relative to yourbrain . one way i think that abstract math can help us is because it gives us ways to understand interconnected systems of a single unit so that if we can understand this is a single unit then we
don't have to be afraid of it. it's still very complicated but if we can all understand the whole thing as a unit, math gives us a way to move things around in our brain that have been packaged up in this way.i like to think it's likethose vacuum cleaner bags and you suck the air out and it makes it easier to move around or put under the bed so here's another one that i drew . i used to be larger and i don't want to be larger again, i lost 50 pounds and i'd love to leave it that way and some people say it's not rocket science, you have to eat less and exercise more. the thing is even rocket science is just applied math. gaining weight, why do i gain weight? it's because i take in more energy than i burn and i eat too much and that exercise too little but it's also because of my metabolism and my metabolism slows down if i eat too little and exercise
too much. also i exercise too much and i exercise too little. also my metabolism is controlled by my genetics and also sleep and i eat too much because i like food and also because i emotionally eat and both of those of course are caused by my genetics and my upbringing and there's also social pressure to eat too much and social norms cause social pressure and time pressure causes me to get emotional dress and sleep less, then there's the entire food industry that's spending tons of money trying to get us to eat more and a diet industry that doesn't want any of us to succeed because of how they make money and when i do gain weight i starting eating too little and getting stressed . so it's this simple, it's not that simple. it's this simple, but understanding this helps me see where the vicious cycles are and helps me understand which links i can try to break so that i stayed away i want to be which doesn't mean everyone should try to do that but that's what i wantto do i did draw a diagram for
the election . here it is. i got tired of people saying it's just the fault of, it's just the fault of thepeople who voted third party . it's just the fault of the bernie or bust people. it's just his fault for running in the first place so i think it was all of these things including for example the voting system. a third party voting thing wouldn't have been an issue if third-party votes counted for anything. there's stuff in this gap over here that has come to life since then so maybe i'll move quickly on . and talk about how abstraction can help us understand relationships between things.here is something that is more obviously a piece of mathematics that might seem relevant. maybe we can remember what the facts ofthe 30 are, the numbers that go into 30 are one , two, three, five , six, 10, 15, 30, very good .
it's not that interesting. it's a bunch of numbers in a straight line and i always say we live in a three-dimensional world so we write on two dimensions two-dimensional pieces of paper in straight lines so we stuff our thoughts into straight lines when maybe they have a geometry and a higher dimension and this is why i try not to do papers on my desk because they have geometry in higher dimensions so national geometry is the situation by looking at which numbers are factors of each other and drawing a family tree of those relationships so as is at the top like a great-grandparents and if any of you came to hear me talk about how to make hi i will take itfurther. six, 10 and 15 going to 30, five those into 10 and 15 and i don't need to draw an arrow from 35 because like in a family tree we don't draw
grandparent relationships because we candeduce them from two levels of children . greed goes into six and 15 and one goes into two, three and five so now we see that it's really a cube . but a little bit more interesting than a bunch of numbers in a straight lineand everything like a mathematician we say why that happened ? does every number make a cube? but there are various ways we can take it but maybe you can see that it's because the three numbers are prime numbers, those are the ones that don't have any other factors except one and themselves and that gives us three dimensions to the cube so at this level we have numbers that are products of two prime factors and 30 which is a product of 33 if i drive like this i get the prime subjects the level and at the bottom there's a set where there are no point factors and we can see that didn't matter thatthis was 2, 3 and five. we can say it could have been a bnc . turn the numbers into letters. the point is we can try to do something else, say, two,
three and seven. here all the factors are 42 and now i have two, three and seven at the bottom and then the product is two things and then the product is readings at thetop . the middle diagram is analogous to the previous one but where every five hasn't been replaced by a seven and when we go up to the level of abstraction, it's not actually the same diagram so abstraction shows us the thing that is the same about this situation because they are roots and i'm going to show you how that is powerful but first i want to stress something about this diagram which is six is less than seven. that might not signed very profound but six is less than seven and yet six is higher than seven. six is higher than seven in this hierarchy and whenever you have two different hierarchies that disagree on the same thing, that can be a source of antagonism. if somebody is older at work but more junior than someone else that can be a cause of antagonism .
now i want to show what the point is of going to this level of abstraction because a, b and c and now we anything . they don't even have to be numbers. they could for example be three types of privilege such as rich, white and male so now what we have is here that people with two of those privileged and then at this level the people with one type ofprivilege and at the bottom the people with none of those types of privilege and if i fill back in the missing words i've got rich, white, non-men , rich white nonwhite men and non-rich white men and these and at the bottom the people with none of those provisions. non-rich, nonwhite, non-men so the first thing i'd like to address is whenever i talk about this everyone in the room has to have and identify , seems to identify themselves is not rich and while this is true there are many people richer than all of us there are also people much less rich than all of
us. this diagram is a diagram showing direct letters of one type of privilege and i think this is important to remember that sometimes people get upset about the beer he of privilege and a savings look at that super rich black sports car, that shows white privilege doesn't exist and that's not what white privilege means. white privilege means everything about you stays along but you moved around one of the arrows by hypothetically not being white anymore, we would expect you to be worse off. it doesn't mean all white people are better off than all black people in society and there's something else i'd like you to learn because i can the previous thing where sex is less than seven we can compare the people at this level. there are no arrows at this level because there is no direct loss of one type of privilege but we can consider how well we think those people are doing in terms of absolute privilege and i think the rich white non-men
including rich white women are probablydoing better than the rich white nonwhite men who in turn are doing better than for white men and non-rich white men because money is money. and the same along this level even further , if we compare between the levels i think that rich nonwhite non-men are probably doing better than non-rich white men. for example rich people like say oprah winfrey or michelle obama are doing better than poor white men who are maybe unemployed orhomeless or struggling and so it's actually like this, it's a cuboid of privilege, not a cube . and this is how we need to understand why particularly some white men are so angry about the theory of privilege because they are told they have to two types of privilege but they don't actually feel the manifestations of that privilege and they see people who are considered to have
less privilege doing better than them in society is much more productive to understand this source of their anger rather than get angry with them in return and it's almost is a surprise that mathematical thinking of me understand. i would like to talk about how we can use this abstract thinking to pick to help us understand different situations because in these situations rich white men were analogous, they occupied a analogous position in those diagrams and we can look at a more analogous inflation, the power that mail people have over the female people is analogous to the structural power that white people have over black people which is analogous to the structural power rich people have over poor people and i'm not saying all mail people have power over all female evil, but structures of society are skewed in that direction whereas if we look at mail people eligible to female people this is not analogous to female people over mail people because the power structure goes the other way
out and this gives us a sense in which for example if men are sexist towards women that is different from women being sexist towards men and we think that counts as sexism which depends on your definition of sexism but is the same because both cases are people being horrible to other people but there's also a sense in which it is different and once we acknowledge that instead of just shouting about whether it's the same or not we can look at why we're disagreeing and what the manifestations of that are and whether this is more useful to think about them at the same or different and it is another thing that my teacher taught me that math isn't about right and wrong, it's about the sense in which something is right in this situation andthe sense in which : help me might be right and another and it can be productive to think about the sense in which they have a point even if we disagree . something might be not at the top in one context but in the top or at the top in another context.
in this diagram the rich my white men are at the top but if i focus my attention on this portion of thediagram , now the rich white non-men are at the top there though we could restrict our whole context to say just thinking about women and then we could have an analogous diagram where we take three other types of privilege among women such as rich white and since gendered and we have an entirely analogous to involving those types of privilege with poor white non-trans women at the bottom and this is helped me understand why there's much anger at the moment especially towards rich white women in some parts of the feminist movement because they are prone to considering themselves as underprivileged relative to men especially and that's what happened if they spend most of the time surrounded by white people , then they will not understand how privileged they are relative to all the other people and i heard some murmurings and i'd remind you
cis gendered means your gender matches the one you were assigned at birth. this has helped me understand that anger rather than getting angry in return and we can all perform edits in this way because we are all more privileged than somebody and less privileged than somebody else so we can understand what it's like to be in different parts of this diagram and that can help us understand other people's experiences in different parts of thediagram relative to us so here's pivots that i do myself . i think that as an asian person i have some lack of privilege compared with white people but i acknowledge i think that asian people are probably among the most privilege of nonwhite people so i can fit between these two situations. one where i'd lower down and one where i'm higher up so i can understand the experiences of different people and think about how i like to be treated when i'm feeling lower down so that i can try and treat people well in situations when i'm higher upand another one is about riches .
i'm not so rich that i never need to work again, not that i would ever be because i worked because i want to make the world a better placebut i'm doing fine. some people are struggling . they may be working hard and stillunable to make ends meet . maybe they have jobs that don't pay them enough or all sorts of things. so i am both, we are all rent less rich than someone and more rich than someone else so we can perform that it and here's the one about white women wear white women are less privileged relativeto white men but more privileged relative to normal white women . everyone can do those tickets and i use these benefits help me empathize with other people which brings me to perhaps the surprising conclusion that abstract mathematics helps me with empathy and abstract mathematics might not be something you put in the same
instance with empathy, maybe not in a positive way but i think this is an important part of mathematical thinking and i like to conclude by talking about what i think intelligence is and how this can help us be intelligent . i thought another diagram of interconnectedness. i think intelligence involves being reasonable, being a logical and also being helpful so what does reasonable mean? reasonable means you're able to be reasoned with. there are people who hold views where no evidence of logic would ever get them to change their minds and that is unreasonable so i think reasonable means you have a framework or deciding why you believe the things you believe and especially a framework for deciding when it's time to stop believing them so you will change your mind and that i think, the reason part of it involves using logic. being powerfully logical means you don't just use logic but you use logic with some kind of technique to build your logic up as if you say for example that some
people say i don't believe in them sex marriage because i think there should be between a man and a woman, that is not illogical, it's just you haven't got anywhere. you said the same thing twice basically. that's not illogical but you haven't used any steps of logic to develop your arguments andthat's what i think being powerfully logical is about .being hopeful is important because i don't think there's any point in sitting around using a blank brain a lot not going to help anybody. being helpful involves not just using techniques but engaging emotions and understanding the emotions of other people because if we keep yelling logic at people who are feeling emotions, it won't help and that we need to engage and empathize with people, to understand why people disagree and to access formal discussions that involve making human connections and we know this even when we're teaching mathematics if we don't
understand why a student takes this way will never persuade them of anything and if they don't feel emotions while their learning everything will wash over and they'll move on and never want to do it again . i think that i believe in the period of stupidity which says it's a two-dimensional theory, it's a graph like this and this is how much you benefit yourself and this is how much you benefit other people. there are various different quadrants here and so if you are at the top left, you got yourself. i'm not surewhich one i done first . if you hurt other people whilebenefiting yourself , then he says you are a bandit. whereas in the top left one you are benefitingother people while hurting yourself and he calls that's unfortunate . we might think of it as being a martyr . and i used the believe that was a good thing to be and i think many women have been taught by society we should
sacrifice ourselves or the good of other people and that's one of the reasons i kept working in a job that was making me miserable because i thought i was doing something good for society but then what about the bottom left-hand corner -mark that's where you hurtother people and you hurt yourself at the same time . that is stupid. and the fear he goes on to say he reckons that there is an equal number, the same proportion of stupid people in any group of people whether it isprofessor, student, open ,convicted criminal , maybe there's more politicians. he says it's probably more people than you're expecting even when you take that into account and this is what he says is stupid. april hurt themselves and other people at the same time . this quadrants is where you benefit yourself and benefit other people at the same time and he says this is intelligence.
i think that's what intelligence is, it doesn't have anything to do with the grades you get or the degrees you have or how much money earned or how many houses you own or how many people you have power over in your company area and i think it's about how and to what extent you are able to benefit others and your self at the same time and i think abstract mathematics can help us with this and we can create a circle where logic can help us my feelings to understand the feelings of other people by doing those benefits and that empathy can also help us understand other people's logic because we need to empathize with them in order to understand their thoughtprocesses . so i conclude that 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. you very much.
[applause] >> got around to listen to our second speaker. that wasfantastic . really hyped up for math right now. i'm going to welcome julie back onto the stage from zeno who will introduce amir alexander . [applause] >> that was amazing, ienjoyed that conversation . there's a talk by doctor chang. as a quick announcement if you want to have a more intelligent society and think that could happen through early math for kids, we'd love to have you at zeno's
luncheon on october 23 so if you want moreinformation come to our table . awesome. next up, amir alexander is a historian, author and academic who studies interconnection between appomattox as cultural and historical settings. his first book, the voices of discovery in the transformation of mathematical process discusses relationships between the17th century english exploration of the americas and early exploration by mathematicians of infinitesimal . his otherbooks include dual don : heroes, martyrs and the rise of modern mathematics and in similar testable, how a mathematical theory sheet the entire world. alexander has contributed pieces to the new york times i and and book review section, los angeles times op-ed and scientific american and he's been interviewed on
npr's all things considered and interfaith voices. he currently resides in los angeles where he teaches history at ucla. please join me in welcoming amir alexander. [applause] >> thank you and thank you eugenia for a fascinating presentation and one of the advantages, you worked out all the technical bugs now so i'm told this works now. beautiful. also, i was and as eugenia argued and i was entirely convinced, mathematics and mathematical thinking really does, is very useful and very helpful in our world, even in
our chaotic world so i will start with a person who completely disagree with eugenia, was this man here . he is a mathematician called gustav young kobe, he was a prominent mathematician inthe 19th century and in 1842 , gustav kobe was invited to speak at the british society for the advancement of science in the industrial city of manchester and as he proudly wrote his brother when he came back, he stood there before all those british men of science and he told them, it is the goal of
science to be of nouse and in particular mathematics . mathematics hesaid , he declared that it is only, the only purpose of mathematics is the honor of the human spirit. that really has nothing actually useful in it and he said that is a great thing. that it is in fact completely useless . now the fact is that jacoby did not make a lot of congress in manchester and this is what manchester look like in 1842 and the people he talked to were people making money from all those new technological and scientific innovations that they thought were all based and they understood were all based on math andhere comes this german with this funny accent who tells them mathematics is completely useless . he did not make many converts among his audience. however, the view that
mathematics is in fact useless and that as the great british mathematician dh party said, if it has tobe justified as art , as beautiful art to be justified at all, it is actually a view that was quite prevalent among mathematicians. at that time. and in fact ever since. party for example, he thought that mathematics that yes, he thought of course mathematics can be used for various things like to describe for scientific, to describe the laws of motion and square of course, to make airplanes fly, cell phones work and all
those, build skyscrapers and rovers to mars, that is all well and good and to this we can add what eugenia said also. it teaches us how to think properly and think correctly and think in productive ways but all of that party said was, that was not interesting . that's not real math. real math is really useless. it's reallypointless and there is some truth . you can see what somebody like party means. after all, whoever actually used archimedes methods for calculating the area of a parabola. how useful is that? how useful really are cancers transpire nights, this eerie
that you can count the difference in minutes have different values and we can rank them but beautiful, amazing theory but how useful really is it? what use to anybody could anybody make of it or more recently the language program and i'll say one day maybe it will be useful, ab, maybe not . in the case of archimedes we've been waiting 2000 years so it's not clear that perhaps mathematical thinking as its value and teaches us to think correctly but it's far from clear that actual mathematics is in fact useful , useful in itself. what i like to offer here is a different kind of perspective. that mathematics, that mathematics is fundamentally,
that mathematics is fundamentally this. mathematics is the science of worthiness. if there is something of the deepest order in theuniverse , something that the down, is absolutely true, cannot be wrong and orders everything in the universe. the thing that is unshakable and somehow true and necessarily true, that is if we can prove that, that is what mathematics is and that has enormous implications because that means that what we say about mathematics, what we say about mathematics and the kind of order that mathematics is, that our world is different depending what kind of mathematics we ascribe to. depending on what we think proper and true mathematics is. natural world is different but also the human world is different so we think mathematics is one way or
another way in our whole world whether natural but also social, political, religious, philosophical. everything changes if we think the deepest order of things, the one that includes everything, that goes down to the roots of creation is different and that is mathematics so today i'd like to talk about the kind of mathematics that has a particularly long and illustrious history. and it is that really that shaped that because it told us about a particular kind of order inthe world , it shaped not just our understanding of the natural world which it certainly did but also change our understanding of our relationships to each other, our institutions, our political institutions and our social relationships. and that is the great and ancient science of geometry.
so geometry i say matters and that is, it matters a great deal and to show you how it matters let me tell you a story about some famous personages from the past. perhaps some of you watched the netflix series on verse i . no? maybe. okay, i just want to say it's a nice series anyway, sorry ? [inaudible] it's called verse i. we've had louis xiv. if you ever do watch the show, that's louis xiv was nothing like this louis xiv. there's no connection.
that louis xiv in the show was amodern democratic kind of guy, this guy was not all . here was 1661 and louis xiv was, he was king already for 18 years at 23 years old. he was a king since he was a child but only a few months he was a real king because up until that point it was under the tutelage of the region cardinal maserin. he declared he would not have to have a chief minister anymore, he will rule personally, he will rule by himself and usher in the great and glorious age for france and on august 17, 1661, louis came to visit his estate of his own, superintendent of finance who is this gentleman overhere . and he had just finished
building a beautiful estate. called ludovico in france with beautiful gardens and the king descended, the king came towards evening, he descended at the entrance to the chcteau over here and he was led by his host through the rooms of the chcteau, by the greatest artists of the day and after that he proceeded down to the gardens. he walked down from the chcteau. they walked down this central era alley past those beautiful geometric geometrical partitions to the circular pond here and down
past those pools of triton to the mirror pond and then to disgruntled here where they were presented with a new comedy by moliere. all of them were served a lavish dinner with the 5000 soldiers of the royal household who accompanied the king and just when night fell and they thought everything was over they had fireworks shoot up from the chcteau, from the roof of the chcteau and descend upon the garden like midnight sun so it was a grand entertainment and the host was glorying in this moment of royal approval. however, the next day he saw the king away. the king was going back to his chcteau nearby and she
turns to his mother and austria and once their host, he says madame, shouldn't we disgorge these people? that's too much, basically. sure enough he was a man of his word and a few months later he someone's the minister of finance to an audience and asks the captain , and at a sign from the king dark onion sprung up, grabbed his former friend, put him under arrest and foucet spent the rest of his life in a prison in the alps and never saw his beautiful state again .
died in 1680. the question is why did the king react so strongly? what rows the wrath of king louis xiv that a man who had been loyal through his life, stood by him and uprisings and during the troubles, never express anything but love and admiration and loyalty to the king, why was it, what was it that raised the king wrath? and my clue is what happened to this beautiful bouquet. it was nice while it lasted. there we go. here we go. all right. so the king, he goes, he says okay, now you've got foucet
out of the way and he summons foucet's gardener. 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 10 times or more greater than anything foucet saw, anything you ever saw in ludovico. you will create a garden like that that will make everyone forget that garden that he saw at ludovico and sure enough, anybody who's been to the gardens of versailles will admit the scale of that place, the scale of that place is far above and beyond any gardenthat has ever been before . and i suspect since. it's not exactly a pleasure garden. it's not pleasurable, if you'd but it is certainly something that will make anyone forget that anyone
could completely put any other competitor in any competitor in theshadow . she pulled out the trees, she took the fountains. he took the statues, brought them off to versailles, put them to work and told them you do that now for me to cousin the end, it wasn't really foucet's wealth. he was awealthy man . he had a suite of ships on his own area and it was sad, it wasn't his patronage, patronage of the arts. it was ultimately his geometrical garden. >> that's what it was. because foucet invoked the
most beautiful garden in france and that was something that louis did not tolerate area he would build his own geometrical garden and that would be, that would be the one. and forever erased the memory of the upstart. or the upstart king. so why is that geometrical, why isgeometry , why is it that geometrical garden that doomed foucet, why is that so , why was that so outrageous to the king of france? and to understand that, you actually have to go a long time. you have to go backwards like a bit of time. 2000 years of time to understand why young tree was so important and why geometry was even sodangerous . at the time of louis xiv. we don't know who created the first geometrical proof.
there's some unknown genius and we know he was greek. we know the presumably he or they live on the shores of the mediterranean, one of the great cities that got the shores of the mediterranean. and it was probably nothing simple about lines and angles, something that was very trivial to that but there is others joined in and started producing proofs that were we know quite sufficient, my dear 400 bc were quite sophisticated. and proofs are interesting. why did the greeks invent geometrical groups -mark not because the greeks had the only mathematical tradition, we know they're amazing mathematical traditions from the babylonians, the egyptians in india and china. remarkable mathematical traditions. not one of them thought of inventing proof. because proof is not about
measurement. it's not about finding approve or not, they're not about doing astronomical measurements or land measurements or accounting house. it's not about that because proof is about finding truth. once you prove, once you've proven something, that something is proven. it is absolutely revocable he threw. not because god said so or traditionally, anything like that but simply reason tells you that it is absolutely and your appropriately true and no no one can argue. at the end of the argument. it is proven. it is absolutely and necessarily true and that's kind of a funny thing. that's a very, you know, that is something very radical about that. that was a discovery that you could actually provesomething
. that was a discovery was made only once in human history. and all of it, never again. the birth proof were in fact, the firstfruits were in fact haphazard about everything. a person who then united them and turn them into systematized them was euclid. euclid of alexandria. we know very little about him. we only went around the year 300 and alexandria. this is okay. that's what euclid probably didn't look like. but that's his picture there. and how did he do what he did? what do you? he starts out by sort of definitions and a set of postulates and common notions
that are very simple and self-evident, things the whole is greater then its parts. something is equal. if something is equal to another thing, that is equal toanother thing , then two things are equal to another. things that are, nobody can deny. they are obviously, obviously self-evidently true. that's where he starts. and from there, he starts building, start creating basically proofs. start building groups and based on those proofs he creates more proofs and so on. and every proof is connected. it's not just that it is true in itself, it's also interconnected to all those other groups. groups about lines and triangles and circles and angles area is a whole world of those kind of geometrical objects and it is a perfect world area it is a perfect worldlike no other because not only is everything true .
everything there is true, everything there is always true, eternally true but itis all interconnected . they are all very specific fixed relationships to each other and their all in a particular hierarchy to each other. the postulates are the simplest at the top and then everything and then there's one layer of proofs and then based on them another one and another one read and they're all interconnected in one fixed eternal unchanging network. a whole world of mathematical truth. that is the accomplishments of euclid. that is what the world is like. a perfect world of truth and rigor and that is eternally unchanging way true. so that is quite an accomplishment. that is quite an
accomplishment in itself. in fact, it's probably most influential book was ever written perhaps. there are other competitors i guess . michael, for example but it has a claim, let's put it that way and that's not bad . euclid is not known for any particular innovation area is known for putting itall together and creating a world . and the problem was, this is a beautiful world, and eternal world but the only, there's the little fly is that world is amazing but it's not our world. plato thought that it's the way to lead to the perfect world ofthe form, our world is a shadow world, the world of shadows and imperfections . aristotle also thought that mathematics can't really describe or can't really describe our world and not only that later on when the christian church also agreed
our world is, geometry is well and good, very nice but our world is a fallen world, it's a corruptworld . certainly not something can be described by geometry so imagery is a lot of praise. it's amazing, it is true. some say it's the only science that it's gone to dispel on mankind it's also kind of irrelevant cause our world is nothing in fact like that. and that lasts for about 1700 years. 1700 years on this breakthrough of, by euclid until -- here's a simple mathematical proof . until 1400 and until pretty much theyear 1413 .
not a famous year for most people, but it is as happens the year in which a man in florence by the name of burlesque he conducted experiments on perspective, on linear perspective and then he and his friends and artist and later on his friend alberti popularized the theory of linear perspective. it is the theory of how to draw things, how to paint three dimensions on a flat surface. so basically there is a vanishing point, here. this is from alberti's book. you can draw a vanished --
anyway. anyway, there's a system. there's a vanishing point, all parallel lines point to one particular pointthat is on the horizon . this is masaki and this is a perspective exercise because you can see i guess -- it's doing what it wants. anyway. i'd like to get back to mosacchio. anyway. maybe the battery is weak. forwards. thank you, it's probably
forward. basically this whole image, it's basically an exercise in perspective in which you see all these parallel lines from the bottom area they all point to a single position. but it is much more. it's not just a trick painting because the implication is the space itself, that space itself is in fact geometrically structured. those lines, that those lines of perspective, those lines of perspective that go to the horizon, they are in fact real. they are in fact, they embody. they are in fact, their structure space itself. so you see the difference for example in the arts. between this is a perspective of painting by most audio in which he just doesn't a few
touches, not like the first one. a few touches to create those parallel lines that already get debt in the picture versus just a few years earlier, you have this other image. which doesn't have that. it doesn't have internal, it has all the images andit's a very powerful image in itself . the monaco picture, but it simply does not have that, it simply does not have that interspace. it is not that one is more realistic than the other. this is a realistic picture. it is in fact very close to how we experience our life surrounded by a lot of people. we don't think of it. you don't think of it as a geometrical space . and yet, this one already has this geometrical space built in. this one? yes.
and so this is different. you see two maps of florence, one from 1352. this one from the 1480 three you can't see, i guess from the 1480. and they both dominated the same city and the city has not changed much except for the great dome, the great dome of the cathedral which brunelleschi is also famous for , the city does not face much the world itself has changed. this city is in fact very much the medieval city is in fact very much you experience a medieval city rounded by buildings and towers and churches, behind every corridor. perhaps even more than this, perhaps even more than this one. using perspective as a space itself has become imbued with geometrical principle. every point in this second
image is predeterminedby geometrical principles . that is how you can tell this was a turning point area this was a time when geometry came down from the sky and by in a little city of 30,000, 30,000 people in just a few people that we can name, they made the connection and said the world itself can be structured by my geometrical principles. one thing to say that the world is structured by geometrical principles . the natural world whether in perspective or as galileo said, the world is written, the language of mathematics. and in the science itself, it's always looking for the mathematical principles in the world, but what about the human world.
what does it mean to say that our world is mathematically structured. and it was not long before some princes in europe realize that this was, the significance of this idea that the world is geometrical because if they present themselves or if they believe themselves to be not just i am king of france because i'll put you in jail if you say otherwise or i will cut off your head but because being king of france means that you or the king , that you are an expression of the deepest order in the universe , the hierarchy of your kingdom and not just because you have military force but because you are an extension of the order of 80 order in the world that has an enormous, enormous power and enormous implications. so it was indeed the king of france that adopted, that were the first to adopt,
first, not the last but first you about this idea that power geometry is power. geometry is power, its legitimacy on a scale and with implications. far beyond anything that was offered previously. and they did so in many ways. presenting themselves as the apex of a geometricalorder . next. just to mention and we go to someplace, just to mention they did forexample , they did so in their reports. >> the whole structure, the whole order of the court. not just the old medieval jumble of different people
buying for power. there was order now. there was hierarchical order in which everyone had their place from the top to bottom, from the king at the top to the princes of the one the mere dupes to the counts so that everybody had their place and 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 geometrically. and the arts, the french courts invented the geometrical path read the geometrical dance that we know as ballet but was in fact invented precisely as a silent of various kinds of negotiations of course advocate that determines was on top, who was on bottom, who said, who stands, how do you greet and so on and it was all based on geometrical gestures geometrical
movements. there were philosophies, philosophy justifying the royal was structured as philosophical treatises but nothing equals the importance of geometrical gardens. geometrical gardens were the emblem of french royalty. could i have the next please? it started very simply. making sure they brought a couple of gardeners from his campaign. from his failed campaign in italy and they produce a very simple garden in his favorite shadow of memoirs and over the next two centuries, this bond between the kings of france and geometry simply increase and increase and grew.
can i have the next one? this is for example in the 1470s on a larger scale. you see this geometrical order resenting a perfectly ordered geometrical land under the gaze of the palace at the top. next slide. and so, there were others. there was luxembourg. and so on. it became the emblem, the emblem of royalty, of french royalty was geometry and nothing more so than the geometrical garden. it was the emblem of their sovereignty, of their right and of their rights. why? because at first this came from euclid, that perfect ideal world that is orderly and hierarchical. that is what you were determined to create.
that is how they presented themselves, that all they saw themselves so when lily came over to visit his master, his minister of finance he saw this area and he saw this. this is the geometrical garden. visit geometrical garden in all respects because you see there is these great perfect symmetries. the geometrical patterns but the circles, the straight line. the square. but even more so, it is in some way completely new because it is in fact a structure as a respectable painting. leading up to a point on the horizon marked by the statue of hercules so it's not just the geometries of the patterns,is the geometry of the world . it is that the geometry that structures everything in a perspective painting and hold it all together.
makes it one unified interdependent unit. it was the best geometrical garden that has ever been both artificial and natural. next one, please. you can see the similarities here in the structure as a perspective garden. this was a royal garden. this was a royal garden in all respects because it was a geometrical garden and the greatest geometrical garden that ever was exceptfor one thing . except that it didn't belong to the king. accept it belonged to a commoner who was presenting himself as the apex, at the top of this necessary immovable hierarchy of this was not just an tactful, not just somebody a little bit ambitious and overly grand. this was an attack on the
foundation. this was a geometrical attack on the foundations of the regime as he saw it. and so at versailles, louis endeavored not just to crush them but to create his own geometry that would present the properorder of the world and him and it's apex. which is what he did, and the next . which is what he did precisely at versailles. versailles is a part and in the style of ludovico hundred times larger. it's immediate area is in the
tradition of the kind of geometrical patterns you were familiar with from there presenting an orderly , fixed , hierarchical world. and from there, again you have this main access leading to the horizon creating it as a perspective painting but the real power of versailles, this is calledthe petite part . it was an older garden that creates, that came from the age of louis xiv. the magic of versailles is what happens here. this is the grand park over here in which you have the grand canal and the surrounding because what you see their is the, what you see there if you look from
the palace, what you see there is simply open for us, open woods. you do not see any of those very elaborately carved beautiful part is that you see here. because it is once again, can i have the next please?this perspective painting, you see going out to the horizon and all of this, even these open woods, even these open woods are structured together through the deep geometrical order of the world. can i have the next please? so underneath it all, beneath these woods, this looks like open woods fromthe palace . but underneath it all, there are these geometrical paths. all of these. straight, arrow, intersecting
. intersecting at right angle and all of them together forming an arrow. an arrow here. an arrow there that is aimed directly at the palace, at the center of the palace and in the palace ultimately at the center is the king and the king's bedroom and what you see and what just tells me and what this tells me is any all this variety, all these different, all the chaos that we see in the world, all this mystery that we see in the world there is a fixed underlying geometrical order.there is. you don't see it when you look at it from afar but underneath it all it structures everything.the deep geometrical order of the world and this deep geometrical order is not random. it's hierarchical because it leads layer upon layer, it leads all the way up to the
king's palace and which supports the king palace as a natural necessary place of all authority. so if you think of yourself as someone, today versailles is a museum. we go there and saythis is all very lovely but at the time , for somebody walking those paths in versailles, this claims royal supremacy at the natural geometrical order of the world was not just an abstract place. it was self-evident truth. it was all around you. entire world around you proclaim this the geometrical order of the world and everything had its place. everything had its placein the grand order and who presides over it ? of course, the king himself . the king himself in his palace. now, i'd like to end just a
little with a more contemporary gesture here because this is perhaps i hope it was interesting. at four you to judge. but it was a long time ago louis xiv died in 1750. his great-grandson louis xvi was beheaded in 1793. so this order, this supposedly eternal geometrical order, we go to it and say that's how things work. because geometry and the power of geometry does it still shake our outlook today? and my answer is yes. but i'll give just one example here.
right. i think people are familiar with this view. capitol hill and the mall. there's pennsylvania avenue. washington dc, washington dc is not a museum. it's not a museum of a dead ancient monarchy. if the capital of the greatest republic, of the greatest republic in the world area is the greatest i think in the most spectacular geometrical city. in the world because the store is bursae was an imitated first in gardens and also in city but no city matches the grandeur of washington dc. washington dc was designed by a man called pr l'enfant
wasn't himself not only a frenchman but somebody who grew up in the court of louis xv and louis xvi and viewed versailles intimately and that's what you use when he designed washington. that's what he designed washington dc area you look at this picture and you say there's versailles, you stand in the mall, you look at capitol hill like the palace on the hill. all of the arrows, all streets lead to the capital here. here we have this rate obvious hierarchy with congress. houses of congress at the top but of course the us is not a monarchy. and what levon was trying to do was present it as use the language to present a republic so you have this versailles, this garden here. next please. you also have right angle, to the mall, you have this of
course what he called the president's palace . >> .. >> .. >> by pennsylvania. next, please. and then they're connected. so you have, this is capitol here, what we know as the mall. this is the president's house, the white house over here, and the south lawn and the garden. they're connected by pennsylvania avenue over there. each one of them is, in itself, a great node of all lines converging on it. so already you have two lines, you have not one center as you had at versailles. you had two great centers that are themselves competing with each other, but also in this
careful dynamic balance. you have capitol hill and you have the white house. not by accident, but by design. they designed it that way. so you have those two great federal powers. but that's not the end of it, because on top of it also all these 15 squares. why 15? because at the time there were 15 states to the union. and he calls each one of those by the name of a different, of a different -- each one of these dominates its immediate area. it's a local power. and they're all connected by this network, a rigid network that is unchangeable network that overlays those two, that overlays the entire city and balances those to two centers of power. so what we get here, this is 1791, two years after the ratification of the constitution
and uses the language of versailles, the language of geometry to create a capitol that is, in fact, designed to be the constitution extolled. presenting the constitution not as just a compromise that was reached and so on, but as a necessary, inevitable deepest order of, based on the deepest order of geometry. unshakable, eternal, stable because with it cannot be changed, and it cannot be moved, and that's how it was designed. now, i know we go and virginia talked quite a bit about our political situation today. which is, and whatever -- i won't presume about your political stances, but i think most of us will agree that it's a time when many of our assumptions are challenged and many of our institutions that we
thought were secure are being challenged and, in fact, seems much more vulnerable than we had expected whether any of those institution -- federal, state, congress, white house -- are all seemed in crisis and challenge. but i have to say, this is just my opinion, you know, when i go to washington, d.c., you know, and you walk those geometrical streets and you see that, you go to the mall and you look up at the houses of congress, you go look up at the white house, the grand boulevard, the grand
>> what about ways in which mathematics constructs, it always starts with the axioms which are the basic assumptions that we try to prove in the system. you will get the different conclusions even though you're still using logic. they might have different starting points. and so i find that i can using using -- use abstraction to understand people's emotions. there are things that i do that seem to be irrational. for example, i used to be extremely afraid of flying even though it's statistically much safer than driving. and instead of saying, well, that's just emotional, i thought about what's going on. my fear isn't based on
statistics, my fear is based on being reminded of death, and that's the thing that i'm afraid of. and it was linking with that. using an actual process where you unpack somebody's process and find what their axioms are, i basically always find that i can see some logic in emotions and so that they're not separate and that we can actually use both at the same time. >> i very much agree with that, and i think, yeah, i think that you cannot really dissociate emotions and logic and reason just, you know, to give some of the examples that i talked about today. what louis xiv in building this garden, he was a ideologies, but he was also a great psychologist because when people go there and experience that grandeur, grandeur of the king and that
absolute necessary order, people react accordingly. people won't necessarily enjoy it. general what, for example, visited the garden in 1688, 16853. he did not enjoy it because the french had just pulverized his city, but he got the message, and that is a very clear emotional, psychological message. you go there, you understand, you accept how, you accept emotionally, both logically and emotionally what the proper order is. so i don't think -- i think they are very much working together, and the same, i think, at washington d.c. i have to say, like i say, when i go there, the reaction is, well, grand city. but the reaction is also very deep. it's emotional. it is a, it was planned that way, and geometry creates it. >> and, in fact, take it one
step further, i think it's very difficult to understand someone else's emotions using emotion unless they're actually the same emotions as yours because we can get so caught up in our emotional reactionings. there are people who i disagree with vehemently, and if i let the emotional response take over, then it's very difficult to see what's going op. but if i abstract from it and use mathematical thinking, logical steps instead, then i can separate out my own emotional disagreement with them and understand it from their point of view. and understanding someone else's point of of view is, i think, really the starting point to a more unifying and less dicive world for us -- divisive world for us. >> so great. eugenia, i have a question for you. i really enjoyed your application of logic to sexual issues, and if we were going to adopt that framework, how would you envisage the happening in the real world? let's say we decided to use the
framework on social media or in our newspapers, would that mean there's no opinion pieces anymore? would our articles have to be like scientific papers? if just any, more of a light hearted question. how does that work? >> interesting definition of lighthearted. thank you. i mean, i think that opinion, not all opinions are equally valid, and that's something that the world seems to be losing sight of a little bit. and all opinions should really be backed up by something. it's not about right and wrong, but it's about the extent to which a backup has been provided. and there are many different ways to back things up, and i'm not trying to claim that math mathematical logic is the only way to back thicks up. -- things up. the scientific process is based on evidence and rep lick about. and there are other disciplines
that use different things. 9 the way it's assessed in history is slightly different, and all of these disciplines provide frameworks for assessing how valid we should consider a truth to be. and i think that if you just state an opinion with ono backup whatsoever d with no backup whatsoever, in a way that contains no framework. i don't see a place for that in my ideal, 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 it's very interesting. so in order for people to understand that logical frameworks, all scientific frameworks, of course we have to improve of the education around these things. and then we have to change the entire session system. we can't change the entire education system until we change the government. we can't change the government until we change the education
system. so then what do we to? that's why i have been try writing books. in the mean time, i'll try and help people understand things outside of that system. >> okay. two questions. >> [inaudible] >> if you've got a classroom of reluctant geometry students, which one of your books would you start them with? and then the second question is when the women march on versailles demanding bread -- >> [inaudible] >> when the women in france march on versailles demanding bread, do the gardens change their tune at all, or is it something else? >> shall i try to start? okay, i'll start with that. something very interesting happens to the gardens of versailles in the last, in the later decades of the old regime, even before the french
revolution. this notion, this idea of the gardens as this perfect gee i don't mean metrical world is being challenged, particularly marie antoinette who adopt that philosophy of russo and starts creating end clays within the gardennen that were not at all about the supremacy of the king, but little enclave of supposed nature with she and her, when he and her -- [inaudible] can play and get away from that rigid geometrical order. consciously anti-geometrical reaction. and you see it on the ground. that's sort of amazing with geometry, you can see it on the ground in the design of cities and gardens. it is imprinted, that order is
imprinted on the ground and shapes our environment and, you know, kind of seeing it. after, what happens ultimately the revolution, yeah, after the revolution then versailles, the allison gardens are made into museums. so they are preserved, as are most of the old royal geometrical gardens in st. petersburg, but their power is curtailed. they are just something that we visit and quaintly say that's how things used to be. so their sort of, their power is neutralized. but not in washington because washington is alive. >> in answer to the other part of the question, for reluctant geometry class, it sounds like i would recommend a new book. [laughter] out of my books i think my first one, which is about what math is
for and the way in which it can be for everybody and that it itn be fun and is all around us and is related, and it's something that you can do for yourself even if it hasn't seemed like you can do it yourself. so i think that one. >> thank you. i have a question for dr. alexander, and my question is whether you can tell me the alignment of versailles, the chateau in relationship to the garden, and whether there's an east-west alignment. and if so, whether this suggests medieval traditions in that the to east-west alignment is symbol or depicting the medieval cathedral which in turn, again, is the symbol for the medieval world with. so a very medieval overall framework and a tradition that, yeah, again suggests that we are looking not into something new, something that was general rated
in the baroque tradition and time, but something that, yeah, is a further development of medieval thought. >> that's fascinating because, yes. first of all, yes, the gardens are pointing westward. so like a cathedral, which is very interesting, which is very interesting because the presentation was as the sun king, and he had the statue of apollo at the end of the park. and initially he had the -- [inaudible] near the palace. and supposedly a apollo, this is the sun king, would transverse the sky, especially that he was doing it backwards which was always sort of a little bit of a quandary, you know? the sun was moving westward -- was moving eastwards rather than, rather than westwards. so the pagan -- yeah.
so there's definitely the pagan elements are definitely there in the presentation as the sun king. i've never heard the idea of the cathedral. that's, yeah, that's honestly very interesting. the fact that it, in fact, did preserve the old a alinement of the cathedral, that's very interesting. thank you. thank you for. that -- thank you for that. >> tragically increasing number of members in our society that have begun to reject the premise of science or math or logic whatsoever, people who deny evidence and say the globe isn't warming, that the planet is flat, that we have never been to the moon, things like this. what are you saying to those people who reject that premise to begin with, and how do you think our society can move forward from that? >> thank you. it's very easy to get very depressed about that kind of situation, and what i remind myself is that we cannot reach
everyone at once, and that's okay. and that there's a whole range of people and that maybe those are the most faraway people from where i am. whereas there are some people who are less far away, there are people who really do want to believe those things but don't really know how to deal with it or who don't do it quite as well as they want to. so they're trying to be logical, but they make mistakes. the kinds of people who are trying to believe, but they don't fact check all the articles that they just immediately repost. so i think that we can try and reach those people first. and if you immediately try to reach the people who are the most difficult, then yes, you're doomed to get depressed and feel like everything is hopeless. and the thing is that if we decide everything is hopeless, then it will be hopeless are. that's definitely for sure. so i try to ascertain whether there's any chance that i can make any progress. and i try to understand where they're coming from rather than try and change their mind. but then also it's important to
preserve your own melter -- [laughter] -- mental health if you're really going to get depressed and attacked, then i think it's okay to decide you're not going to engage with that right now and try to improve everyone else. now, i don't think -- i don't actually have the stats to back this up -- but i don't think it's a majority of people who think the earth is flat. so i think it's all right. i think there are more people who we can reach and that if we can just shift the kind of center of gravity of logical and scientific thinking a bit further back towards the logical and scientific thinking, i feel that can make a huge difference. we don't have to change everyone at once. we just have to shift things because i think things have only shifted a bit, that's what i suspect, and maybe if we can shift where we can then, in fact, we can make progress and maybe change things a bit. >> [inaudible] so when you look at things like
the golden triangle, they're very two-dimensional. a lot of art, the vanishing point, the simulation of three dimensions but it's really two-dimensional a. when we look at things that are actually three-dimensional when you're talking about spiritual geometry, we look at them as somewhat chaotic. do you see any evidence that we're moving towards art that actually encompasses the three-dimensionalness of symmetry and sees more order in these things that we create as chaos whether it's talking about art or architecture? thank you. >> yeah, that's an interesting question because, of course, you're right when you use this linear perspective. it's not just a plain description of the world, certain view of the world. it's not just describing the world as geometrical, it's just telling this is what the real world is, it's geometrical in its, in that sense.
and, of course, there have been developments in geometry that have moved away from, away from that single, necessary fixed order. non-euclidian geometry and the fact that there is not just one single necessary truth and one true point of view but, in fact, there is an infinity of possible , possible geometries rather than a different, rather than a single, rather than a single truth which is very challenging and, in fact, disturbing. yeah, i mean, i think in some ways you can say we're not living in a euclidian world, we're living in a post-euclidis ian world. we're all living in our own bubbles with our own
perspective, and they're all equally true because we hold such different assumptions. and art, in fact, modern art certainly did try and deal with, deal with that. i'm no expert of that, but clearly early 20th century art, there's this effort to portray things from different angles and different sides at the same time. clearly, also a response to this move away from this single, unified euclidian view, so that's all i can say. >> all right. thank you so much. [laughter] thank you all so much for being here. [applause] this was really fun. one of our -- i think they're putting their stuff away, but the folks are still here if you have questions about a them. books are for sale over here, and our guests will be signing in just a moment. thanks again for coming.
[applause] >> every yearbook tv covers book fairs and festivals around the country, and here's a look at some of the events on the calendar. on october 10th-12th, it's the fall for the book festival at george mason university in fairfax, virginia. that same weekend tune in for our live coverage for the southern fest sal of books in -- festival of books in nashville. on october 19th and 20th, the boston book festival will welcome over 300 speakers, and we'll be live from the wisconsin book festival inned madison. and later in the month look for us in austin during our live coverage of the texas book festival. for more information about upcoming book fairs and festivals and to watch our previous festival coverage, click the book fairs tab at our web site, booktv.org. >> on our monthly author call-in program, "in depth," journalist and historian evan thomas
discussed his biography of richard nixon. >> i think it's the 13th nixon biography. there are a lot, so what was i going to say that was new. i was, this is going to sound kind of conceited, but it's -- i represent the east coast, you know, establishment press, you know? i'm not d my own politics are actually moderate. i'm not sure i have any politics, but i'm a type. i went to harvard, you know? i'm a type. and the type that nixon hated. nixon hated people like me. not personally, but he hated people like me. [laughter] and i thought it'd be interesting to try to reverse engineer this. in a sympathetic way, how did he see me, how did he see the establishment, "the washington post" company for which i worked, how did that world look for him. that's why the book is called requesting nixon -- being nixon.
instead of me looking at him, in a way it's him looking at me. it's much more than that, but that was the impetus of the book. and the best parts of the book really are sympathetic about these moments he had with the east coast establishment where they treated him terribly, and you begin to understand why he was resentful. he let the stuff get out of control, he really did, and he ended up getting brought down by "the washington post." ironically or maybe suitably, i'm not sure what the right word is. i am sympathetic about that because he was treated badly by my kind, he really was. why? stupidity, snobbery. i mean, there's a scene in the '60 election, and they're all at some garden party in georgetown and it's arkansas sure
shlaesenier -- arthur schlessinger, and there's a smugness and a primness and a kind of aren't we better with, aren't we better looking, aren't we better dressed, aren't we just better than nixon. and, of course, nixon would know about all that and feel put down, and, you know, there was an arrogance to it that nixon was right to be aggrieved. but also cleverly played off of some of our politics today is a descendant of richard nixon figuring out, hey, you can get votes by running against these people, this establishment, the mainstream -- they didn't have that word then, but this can work for you. populism, not all the way out there. and he discovered it, and whittier collins -- i'm just going to tell you one story about this because it's so revealing to me. nixon's not very popular. he's not that like bl. he's not an ooh easy guy.
but at whittier college the issue was dancing. it was a quaker school, conservative, no dancing. nixon runs on the pro-dancing ticket. nixon himself couldn't dance at all. runs on it because he realizes that the rich kids can go dancing. they can go to clubs in l.a. and country clubs. it's the poor kids who can't. there are a lot more poor kids than rich kids at whittier college in 1932. nixon wins in a land slide. it's a rich against poor thing the, but it's being sensitive to the needs of the needier kids against -- and running against the rich kids. there was a snooty fraternity, and nixon was very -- an opposing fraternity, kind of the little man's party. it was, you know, there were more than halfbacks, you know?
smart politics, the silent -- richard nixon coined the word, not a speech writer, richard nixon coined the word the silent majority, and he happened to win. the next election he ran, he won with more votes and a greater percentage of votes than anybody but, i think lbj in '64 was a hair better, so it worked. >> the watch the full interview, visit our web site, booktv.org, and click on the in depth tap tab. ..