What Happens When Maths Goes Wrong? - with Matt ParkerMay 31, 2021
oh calm down thank you all so much for coming to an exciting math night my name is
parkeri used to be a math teacher thats why i know that person is on the phone as i speak honestly once a teacher always a teacher so can you all hear me properly loud amplified through the mic great people the top we're all happy wonderful right so the plan for tonight as our peter said very kindly in his intro and then he went home that's a big vote trusted in tonight's hook, as you very kindly said, I do a wide range of things that involve promoting math or just generally trying to get more people more excited about math and I do things like YouTube videos, which is where I suspect the vast majority of young people know me and I do BBC Radio 4 which is the rest of you so loud I cover the whole spectrum so just I recently wrote a book Humble Pie and had previously written a book called things to make him do in the fourth dimension which as mentioned in the intro is currently the second most viewed video on the RI channel even though it's all math abstract and I figure tonight with some applied math I'm taking number one so I wrote the first book and Penguin the publishers were would you like to write a second book and the problem with the things you are forced to do in the fourth dimension is that even though I was incredibly proud of it and even though it sold very well for a massive book, it sold average for a correct book, which is great, correct average is I'm over 50% of books.
I'm very happy with that, okay, but penguins don't care
what's in the book, do they? They could post it. Do you know another celebrity cookbook or anything? so I had to convince them that it was a good decision to publish a book on mathematics and I suggested that I could write a book on my favorite math mistakes, which is where a comedy of math errors came from. and they liked that because people like disaster stories they like stories of things gone
wrongthey enjoy laughing at other people I've made a career out of being on the receiving end of it and that's it yeah write that book that's a great people who are specifically math nerds which is your polite way of describing my correct target demographic people still enjoy reading these stories and my ulterior motive was to show examples of where the math fails in everything from financial engineering you know, statistical medicine,
whatever, I can show. it's an excuse to talk about the mathematics that is required for these areas of our modern society, right?
Obviously, math works pretty well most of the time, so much so that most people have no idea how reliant we are on math and people often don't. i value math for that reason so i thought this is a great excuse to talk about all the places math is used but by using things going
wrongas my way in and actually because i, because I used to be a math teacher, actually, can you cheer for the math teachers hiding at the top? Doesn't sound exciting, it's the end of half term, right? Okay so I used to be a math teacher like the good people huddled at the top of the room and then I quit teaching but I still remember how many young people because
whenyou're in school they force you to do math well
whenthey force you to do it a Many people perceive mathematics as a subject in which you have to do well.
Getting the correct answer is everything as the ultimate goal of mathematics and as a teacher you know that is not always strictly true. Proper math is about trying something and getting it wrong and then trying again and hopefully getting it less wrong and then more wrong and hopefully converging on as few bugs as possible, but it's a long slow process of not getting it and not getting it right, and it's always very disappointing. when students or even people you know, standard humans are afraid to try some math because they think if they don't get the answer right they haven't done it correctly and that's not true. and you're trying good math is all about learning and teaching your brain to think so I thought how can I bring that approach to what is otherwise just a random collection of massive errors that have no real meaning ? and you know i started with an inspirational poster i had when i was a teacher and inspirational posters are the staple of the world of teaching it's what you decorate your classroom with and this was one of my absolute favorites it's education works best when everything the parts are working now let me break it down so you have gears that represent students, teachers and parents and the problem is when that big gear on the right that represents students if it spins it says clockwise because using it meshes with the masters the masters have to rotate counterclockwise that's great but i'm not going anywhere either because the parents are bogging down the whole system obviously people just haven't thought about the geometry From this situation, if you have sprockets, they have to go clockwise counterclockwise counterclockwise rived clockwise, so in Manchester we're introducing their new approach to public transport that used the classic three cogwheels. make the city work together or people pointed it out and proceeded to 3d render that's just this point of view possibly from the sides okay it's like well played well played before you see it's like that you don't look so steep that's it They were thinking they were several steps ahead until I saw an article where President Trump in the United States was negotiating the North American free trade deal and when that was put in the papers to show how all active parties in North America North should be moving in unison, the newspapers use this illustration, wait, you already used your third dimension, right?
They won't get that back so I paid money. i paid a lot of money to license that image to put it in my book just so i could use the caption making the gears cool again so it paid off and finally two pound coins when the two pound coin came out to celebrate the Millennium so there was a competition to design this was the winning entry and it has different concentric circles I guess parts where it shows different stages of UK history and the one in the middle is some kind of mechanical age here is a series of gears and because if a gear
goesclockwise the one next to us to go counterclockwise and then counterclockwise you have to have an even number of teeth as that you advance the two pound coin has an odd number of teeth would not work people on the internet were unimpressed and smug i In equal measure the Royal Mint issued a statement ation that said it doesn't
It's just what you're saying, it's just meant to represent that age and I was kind of curious, I wonder why there's a 50/50. I don't know what a great example would be to simulate a 50/50 chance. Imagine flipping something right. It could come out either way if you randomly get an order and an even number of gears so I looked up the person who designed this type of coin is called Bruce Russian. He is an art teacher in Norfolk and on his website he has his original design that would have worked. It is an even number of teeth.
The actual coin that was made. It didn't work I said wow you wish you would get it right and Royal Mint broke it but it was deliberate so I emailed you. I think I'm very sorry. I'm sure people have pointed this out. I'm just curious because I realized that you did well was that you deliberately thought about but it was a concern, but what happened. I'm writing a book on math errors. I'm curious what your thought process was and he replied that he didn't think as an artist it should be correct. the thought is representative of a bunch of gears it doesn't make a difference to the artistic value of the design and to be honest I somewhat agree with him then he said he decided to make it work anyway because otherwise it would be very annoying. emails from her I don't know why that part was involved there you say so and so yeah he just thought people would complain and go on and on about it and now this is the unfortunate edge because when I was writing a book like mistakes .
I didn't want it to be just final theoretical math problems where there are things that people thought proved something and didn't and that's interesting for a small demographic that includes this guy, but then there's also the kind of pedantic you're wrong i'm right right which is the opposite of it's okay to make mistakes which is one of the things i want to get across and a lot of mistakes don't really matter so i found a copy of this book. I remembered it from years and years and years ago I forgot it well I didn't have it when I was a kid I must have seen some I mean a lot of my friends procreate and I saw this book somewhere this is a Barrio book Sesame, this is Ernie expressing his disgust at the prospect of being forced to live on the moon, which feels like a niche concern, but there you go and I can't get my hands on a copy of this book.
I found it on the internet and there's one thing about it that really bothers me. It's not important. It's not important. problem, apart from the boy who had a very strong epiphany, he likes to say what is wrong with him, these stars, where the moon should be, he is one hundred percent right, what are they? There isn't a hole in the moon as far as I can tell I am aware that in the extended universe of Sesame Street there are not the Muppet bases that we can see twinkling in the moon to the right, so you often see a crescent moon and then you see stars shining through it and no, the moon is fine from our point of view, a disk to the right and it's always there, it blocks it out. the stars we just see different bits depending on how it's lit and that's an artist's version of that I'm weirdly ok with that but I think they shouldn't show stars through the crescent moon come on a bit of astronomy everyone and then I've been looking at other examples and actually Sesame should have done this more than once and I was looking at separate license plates in the state of so this is a Texas license plate and as you can see it's celebrating the fact that the the shuttle was involved in texas and there's the shuttle which is not a bad angle actually for takeoff of the shuttle which surprisingly doesn't have any of its thrusters or anything anymore so maybe that's what it landed on I don't know .
I was distracted by or See here that star that star is dangerously close to that but the only way I could be sure would be to somehow buy some Texas license plates so I did and they came in the mail there we are this It's really I scanned it. to be able to get a high resolution version because everyone online was too low resolution and if you zoom in and fill in the rest of the lone star ripped Texas moon then people have pointed out that maybe it's marking with the first Apollo landing site was and is very close, I could give you that to be completely honest, but I think these issues make it not okay if we're just talking, are there practical implications for the issues in this case?
If you don't get me wrong I'm a big fan of mob being right and good mob and mob PR being important but because in practice they are important and unfortunately in those cases they're not really important but sometimes Sometimes mass can be so important. You may have noticed I'm dancing around a very large Jenga tower and thought I'd have this set up during my show to artificially increase the amount of suspense for storytelling purposes, nope so this is for show a fantastic effect on resonance so this is a building and we'll show you in a second how a building hopefully resonates to destruction.
We'll see how lucky or unlucky we are depending on what you're trying to do at the time. You'll usually hear about resinous when it comes to bridges and so there are small bridges that have had resonance problems dating back to I think what I came across was in the 1800's near Manchester where there is now sulphate there was a bridge and there were some troops marching on the bridge because they were all on the pass and they hit a resonance frequency of the bridge and the bridge started to move which apparently they thought was kind of funny so they started singing a tune to match the bouncing bridge they really got involved and i collapsed and no one died no one died it's ok it's hard to write cause you're doing your covermedical and engineering errors when i was putting the book together like i didn't like every second story they all die i can't have a comedy book about math and every second crowbar every couple of pages and then they all died well so i think in all the examples I'm going to give you no one died I think and all the aviation stories in the book no one died don't get me wrong folks They die in aviation problems but not the ones I put in the book so that was a problem with the bridge in Manchester in London.
You still have this here. This is the Albert Bridge. All troops must break step when marching over this bridge. that sign is still there troops need to break step interestingly though not to break very different dance rules and when i mentioned many of you are now thinking of one of the two famous bridges Tacoma Narrows Bridge this was a t-bridge The US Decco bridge absolutely phenomenal amazing amount of twist now that's not your standard resonance of Just people marching or even gusts of wind as you'll occasionally read online this is resonating but this is flutter this is aerodynamic flutter from wind going up down the valley where you were and the flapping basically caused this runaway feedback loop as the drawbridge went up more wind pushed you higher when you finally bounced back and down more wind pushed you down and you got this feedback which took you to go further and further someone finally decided maybe his car should go, he also has the Millennium Bridge in Lon drs it opened in 2000 and some of them were around a couple of days before they closed it look at the pictures now if they all walk randomly it should be fine because no they are not all going to coincide with a particular frequency but looked at the pictures, about 20% of the pedestrians in the middle of Lee is quite crowded, but 20% of them were marching in sync.
The bridge is moving about three inches to the right, which is about three inches too far, so they had to shut it down and do all kinds of crazy things to get it wet because what was happening was the bridge was moving a little bit. and people were moving with it and then they were walking at the same time as the bridge, so the movement of the bridge was causing the pedestrians to sync up and the timing of the pedestrians was causing the bridge to move and you get this feedback with the official wording if it was synchronous lateral excitation just if there was a feedback energy coming in and it coincided with a resonant frequency which of course is totally terrifying.
I'm more like I'm obsessed with bridges, they're a thing, they're easy to move and we're kinder. we partly now understand that this is why the millennium bridge was so amazing for the most part now the bridges work well the buildings not so much so there was a building in south korea in 2011 that is eerily recent anything nifty in a decade seems scary to me it was a 39 story building and one day in 2011 the people on the 38th floor evacuated because they thought there was an earthquake or something that was shaking like crazy they left the building no one else knew what they were going to about the building was okay now what they did some research and recreated this so this is actually true it turns out that on the 12th floor there was an exercise class and about 20 people decided to exercise to a different song that day they exercised two snapshots I have the power if you're not familiar with snapshots i have the power it would be better if it's dramatic if you're not familiar with snapshots i have the power and that's all i can play without the bad situation receiving a copyright strike on their channel they dance to that song the song coincided with the resonant frequency of the building and the 38th floor moved ten times more than normal absolutely incredible so in building design of people have to try and keep this in mind and it's a big deal which is actually kind of a teaching aid for learning about building residents and I've borrowed it from a friend of mine who is an engineer and they've actually I come. to help me because I'm not qualified to run this and see what it can show us about the residents so please welcome to the stage from Bath University Paul Shepherd welcome I haven't seen you since we put this back up . together it's ok it's been minutes so don't pick it up yeah i get nervous ok first of all what are you doing at bath university?
We are going to teach math to civil engineers. I research how we can use computers to design better buildings and I also have a role at our institution, the Institute for Mathematical Innovation, helping companies with their math problems. Fantastic. No, he started and finished math to keep me happy. kinda f kit literally it's a washing machine motor but let's not go there this is a box there's some magic in the box it makes the base move back and forth yeah it vibrates and here i got a button that's not rated to push that's the one and a dial to make it go faster or slower we can be there like a slope for sure we can catch it if it's going really slow yeah you know it's unbelievably slow if someone starts watching the video Right now it's like it's playing at the wrong speed.
I'm still awake, that's right, and on top of this, we built a Jenga tower, yes, and what we wanted to show with this is that if you hit the resonance frequency of the Jenga tower, it's going to fall over, but to make it a challenge first we'll start with a frequency it won't fall off so we think we've found one we're not convinced we put it back together and now it's subtly different and we will have a slightly different resonant frequency let's give it give it so she we crash straight to the right to the right in case we get unlucky ok look at him he would happily live in that building so we have him moving quite often he's shaking never get me wrong he's shaking him all over the place but it's not falling off what we're going to do now is keep the amplitude the same because we can't adjust it and we're going to lower the frequency so we shake it less so you want to lower the freq uence the frequency down now can pull back now less tremors so yeah well I feel safe now less tremors and in theory even though we are tremors less if we hit a resonant frequency it will drop I think we're close of one 30 barrow's asthma is shivering lower we're putting less energy into it we were just putting energy at just the right time to build and accumulate in the system instead of canceling and yeah what then?
So you showed this to which civil engineering students yes I mean we don't want t What would happen to the buildings and there are a certain number of things that we can change in the building to make sure that the frequency at which it would be different than the frequencies you would see in your daily life ok so you can tune in it's far from the building and it doesn't test us by putting models on this no it runs like simulations or something we do math on the obviously correct answer and there are buildings like can you give us examples of buildings or are you like me? i'm under a lot of confidentiality agreements not anymore well i was working on a bridge i won't say which one at the same time the wobbly bridge across the thames was having problems so we were working i was working for come on let's say a different company and of course we saw that and thought it would be better to make trouble sure you liked what happened to them first so I mean it took the engineering world a little bit by surprise that it had happened so seriously so yeah , you know we can't w under the element of person we need math but we didn't quite understand how people timed their are unpredictable and now in the two decades since people design bridges do you or any building guess you have to do it ? now take human movement into account too, yeah after that happened a lot of people did a lot of experiments and research to find out how it
happensand quantify it and now that kind of new research is taken into account when we design bridges today. a big river break for the poor herdsmen ok i think he's literally there now ok but his mic's gone off ok so i think this is great because engineering is we're often building things beyond our current full correct mathematical understanding we use math to build things that don't make intuitive sense anymore because if you look at something like the Millennium Bridge you can't just go it will wobble or not or indeed most of it of performance.
Perfectly stable buildings before we had computers and advanced math, we built them out of huge chunks of rock where you can look at them and say, yeah, that's not going anywhere, whereas now we need computers and math to check and occasionally check the things go wrong, we'll forget about it. about a factor or a new math behavior will emerge and then the Indian engineering industry learns to improve and math develops and we continue to build more and more ridiculous stuff ok so I'll leave this here and keep dancing carefully. turn them around which I thought I would do because I have one more guest at the end who brought something else to show you but from time to time I had so many stories because this one like I had hundreds and hundreds of stories of which a couple hundred made it to the book and I couldn't decide which ones I was going to show you here today so I thought I'd pick them randomly so here I have a spinning wheel and so what we can do is if we turn the wheel to the right it will decide on one of the colors , it doesn't, we'll do it again in a second to get a color and up here I have a breakdown of what the colors mean so we'd do a programming story write the programming story I have a programming straw in the laptop what we do we have a lot of fun we do this several times then we bring in the final guest very simple so i'm going to get some volunteers to come and know they haven't heard all the rules.
I'm going to think I'm going to do this three times, I guess three times, so my plan is if we have three different volunteers, we'll do it. Start with a very young volunteer, then we'll have more of a high school teen volunteer and then we'll have an adult volunteer, so if people look at this quickly or just or the editor there, it's going to look like the rapidly aging volunteer throughout of the talk. ok yeah is there somewhere mmm where i am for him in prayer any young volunteers i would like to come down and be first there ok the back give me a wave you get a round of applause come downstairs wrestle nice to meet you whats your name mario nice to meet you come on here mario so you can look i got my twist here why don't you?
It's grabbing one of these and just giving it a real spin and we'll see which of the colors it ends up in, go well, spin whatever color it is. listen category nice and strong oh it's just green what's green thank you very much give it a round of applause give me a second to find my probability slides there we go ok so let's start with a story about probability and how humans are bad at odds and this is one of my favorite examples where we can try to scam someone right? We can try to trick someone into thinking it's fair game when it really isn't.
For this, I need a volunteer. one of someone at the top there is someone because you don't have to go down for this you stay fully instituted let's go with the person over there leaning on the railing in the back yes rat me out what's your name very strong yes we love you good so what we're going to do well we'll do it toss a coin down here it's going to be heads or tails and you're going to try to predict if it's heads or tails if someone down here has a coin any of the adults have a coin they're willing to flip for Me too Are you happy?
Are you happy to be our coin flipper? Ok, you can stay there. Tails, you feel like this is going to be a two-sided coin. I feel like we're having more of a conversation than I expected. Let's take a look at it, you, me, the coin. a human the one next to you choose a human who is closer to me than you ok i have a solution d Don't worry someone would like it no ok ok ok can you take a look? Is it a head on both sides? here you are now you are trustworthy just saying the word heads for the word tails or what do you think will be tails ok everyone in their own mind decides what they think will be heads or tails anyway ok come on turn around and then call it nice and nice we can all hear it okay flip solid flip whats tails whos right hands up if you right its worth half your hands up if youre wrong ok yeah its worth a little bit more cause you know adorable boy okay ok what what is that fair?
And by the wayIt's not a trick coin, there's nothing fancy about it, it's not because there's more metal on one side than the other, assuming it's a perfectly fair coin, everyone should be happy, it was a perfectly fair challenge. in fact if we were to bet money you young you shouldn't do it right but if you would do something like that you would have a 50-50 chance of winning versus losing and if you played it over and over again you would win as often as you lose you play with the same person as you. you would end up paying the money back almost randomly no one has an advantage in that game we could make the game a little more exciting by having more than one release so if instead of asking you what would be a release I could say we are going to flip it over, it will do two somersaults so you can choose heads heads or heads tails or tails heads or tails what would you like actually what do you like says says okay and everyone here could think of whatever they want we have and if we flip it over everyone has a one in four chance of hitting or if we're playing two of us if we don't get it right away we could keep flipping it until one of us has our run raise first still a fair coin must still be fair what if we hit three so done, everyone? my in their own minds they decide what three cartwheels in a row heads tails head tails tails right what's in their own minds they decide what they think it's going to be? tell the cell heads that indeed here they are all, there are all the options, so you may have chosen one of those and they are all equally likely.
Now I'm going to bet all of you simultaneously that mine will show up before yours, so I want you. to take a look at this and I want you to pick which one is yours make sure you pick which one is yours and then I'll add my predictions next to yours so if you predicted heads heads tails I predict tails heads heads because I I am playing them all individually if they choose tails tails heads I have chosen heads tails tails I have different predictions I mean some of them are the same I mix up the predictions based on what you said so everyone makes sure you are happy what which one is yours in my nexor prediction you all got it right so what we are going to do now is start flipping the coin until you win or I win and we will continue until each game is over so first flip the coin whatever have you had heads second oh third tails so many people now are happy they just won if you said heads heads tails you just beat me I said tails heads heads it hasn't come out but some people yours hasn't here yet ía, can you turn it over again?
Okay I love it you're getting more enthusiastic every time tails so now his last three are now heads tails tails so if you had heads tails tails now you've won if I had heads tails tails. Now I won or if I had heads, heads, tails against yours. Now I won, you have to keep track of who wins first, you or me, so if I beat you heads, heads, tails or I beat you heads, tails, or tails. Just keep that in mind, okay, give us another head to head, so next up is tails, tails, head, tails, tails, heads, tails, tails, head, tails, tails, head tail cross tail head tail tail ok head tail tail tail head tail tail tail is anyone still in the game what are you thinking whats yours head head head head and what did i predict against that tail head head it doesnt come out oh my god ok let's get on well next time going to win heads tails head tails tails head tails they are still in the competition someone else will do the one it will come out right yes head tails head it's the start of your run here we go but you're about to win Oh is anybody still in the game?
What were you doing? Hey tails heads I predicted heads heads tails which one came first so okay don't worry we'll edit this out of the video real quick before it
happens. it was heads or tails about half the audience understood correctly raise your hand if I won the game against you that's the vast majority of you and hands up if some people won okay? What did the people who elected me want? you're going for heads tails that came straight out of the game, so one in eight of you will win outright if you play this game over and over again and the person you're playing against picks at random.
I'll win 74% of the time about three-quarters of the time, the one I put in white will beat the one in orange next to it and the reason this works there is it's not fair because we don't flip the coin three times and then we start over if we did it three times start over three times start over would be perfectly fair because they overlap they are no longer independent probabilities they are now dependent probabilities and if you look at mine all of mine will be mine or end where your prediction begins i am trying to make mine happen right before yours that's why I got yours because I knew if you got heads heads heads unless the first three flips are heads heads heads I'm going to win because tails heads , face will always come first, so let's say. we've been tossing the coin for a long time and something I took out all the tails the opposite of you and someone chose I chose heads tails tails if the coins have been flip flip flip flip and you're right ah here we go finally it's going to be tails tails so soon as you get the first two the race i already won unless the first three tosses are tails tails or heads heads you can't win so there's a one in eight chance you'll win and there's a seven to eight chance you'll win and the others are different variations on that theme with different probabilities and if you average them all you get the 74 percent figure and then people don't really think straight when you get these unusual odds combining them.
I actually carry around with me a set of dice that I thought would be salt if we get chance on the spinning wheel these are called grinding dice and they have unusual numbers on them and I appreciate that you can't really see them so I have a shot on the screen here so you can see the other look it's got ok it's got an 8 it's got some three's the green has a 0 what's going on there they've got crazy numbers it's not one two six and the game you play is choose a die, so you choose a color, I choose a different color. roll them together the highest number wins very easily except they don't all have the same chance of winning because they have different numbers but it's very hard to tell at a glance which is the best dice now i can reveal to you that if you roll the red against blue red will win more often than blue not all the time but more often is over 50% blue wins more often than green green wins more often than the other yellow wins more often than magenta until you get this fantastic order from best ice which is red to worst die which is magenta you would also think if you play magenta against red magenta wins more often than red if you remember no there is better dice this loop and the person you're playing picks first you can always pick a die that has a higher chance of winning than them, just like penny-ante craps right you've always wanted the person to pick first you can always pick one that's better which feels weird but it's the same as rock paper scissors it's like playing rock paper scissors but you go first then i'll choose there's no better option but each one is better than another in each loses to another. higher scale if you play this, though it gets a little scary because if people realize you're beating them they'll make you tell them the secret and then you say I'll get you, I'll teach you the secret and now let's go. they will play two dice together why not what they don't realize is if you play two dice simultaneously the order is reversed so now you will pick first and then they will deliberately pick the loser because you have to. that's the single dice game that's the double dice game if you're wondering what the hell is going on here?
I have a quick equation, there you go, it also has more than one loop because there's another inner loop, all five in a different order and if you double the dice, the inner loop doesn't reverse everything. what it does is the top one evens out so there's a double die there's the single die and the outside ones are flipped but the inside one isn't if you're wondering what's going on there there's the new equation there's good and I love them if you want some details, they are the colors. I am half of the colors. one letter as you go through the outer loop so it's magenta not purple purple as in enough letters and then James said if I do this olive green instead of green the inner loop is now in alphabetical order sorry , so now you can remember both cycles by looking at a t the colors if you want all the stats here are their advantages for any pairing given the inner cycle actually draws a little harder the other one here are all their numbers each one is above the 50% other than we couldn't get this one to fifty it's just below because unfortunately there's nothing magical about these dice, there's no amazing mass property, it's just that when you put numbers on some dice it's very hard to tell if they form a non-transitive trans loop or a transitive and non-transitive loop just means that the numbers are transitive because if three, let's say seven is greater than three and three is greater than one, then if te is greater than one is a transitive property that is passed down the chain just because you know that red beats blue and blue beats green.
It doesn't mean that red wins fast, true, it's not a property that is passed down the chain and it's things like this that baffle humans when we think we understand probability, but then it's a bit off. so I think we have time for another quick spin of the wheel. I need a teenager this time. Anyone who's prepared to come down and give me a hand. get the applause once you get to the hallway now it doesn't get awkward it gets awkward i was we were applauding other people moving clumsily no good what's your name Sasha nice to meet you Sasha so you saw how this is going grab it you take it for a spin, whatever color it ends up on say out loud what was right go away let's talk about probability deal great ok hold on Sasha how what are the chances So probability I think I have a second probability thing here give me a second oh yeah not right this is kind of funny this is an old classic so long ago in the distant past 2010 I saw a story in a newspaper about someone who had looked at the locations of the ancient monolithic sites in the UK and they realize that for patterns put together specifically if you took the top 1,500 ancient monolithic sites these are prehistoric sites and you look at their positions they formed much more triangles than that, so they form very precise triangles isosceles sigh hint but isosceles triangles where two sides are exactly the same length and were within a half percent of incredible precision and the person who found this put out a press release saying that in all The newspapers claimed that it was some kind of ancient satellite navigator and that they used these geometric arrangements of monolithic sites. icos to navigate across the UK and the researchers said the results were so precise that they could not have happened by accident; in fact they couldn't rule out extraterrestrial help so I thought I'd check so I went and also got some ancient sites and started plotting them on a map of the UK the first three I found around Birmingham made a triangle perfect equilateral within the required half percent and then I forgot to add more triangles you also have to sauce these triangles on either side both within the half percent another couple of us missed these triangles within the half percent required, the base and perpendicular bisector traverses four new locations the location at Connor Ways within twelve meters of this line then travels one hundred and seventy miles across the UK just through the base of the triangle reaches Luton where it is nine meters from that spot incredibly accurate patterns I was like wow this is this can't have happened by accident except I wasn't analyzing sit Ancient monolithic ios.
I looked up the old Woolworths stores that had gone bankrupt a little bit earlier and we had already forgotten how 2000 people lived, I mean how they bought plastic items and clothes on discount, we just don't know, and for the young people who aren't familiar with Woolworths, they had a business model where they said just get all the candy and put it in open bins, let people help themselves and assume nothing will go wrong with that business model, so they closed. I found all 800 Woolworths locations across the UK and analyzed them and found the same patterns with the same level of accuracy as the other person I had found claiming ancient wisdom or aliens or all of these things right so I posted my findings as a press release on how we might learnabout the old Woolworths.
The Guardian civilization went with aliens and found the Woolworths civilization, which was kind of funny. Turns out there are a lot of stores to choose from so specifically here are the ones I had with their zip codes, they are all legit stores you can check. this, but here are all the stores, if you have. I checked the numbers. If you have 800 Woolworths stores. There are 85 million possible triangles. If you have 85 million triangles, no. It would be more surprising if none of them were isosceles. There are so many options. If you search hard enough, you'll definitely find this pattern or any pattern from your mathematically weakened state.
You can find any pattern you want with any level of precision you want. you're prepared to ignore enough data the 1500 stores the other person had used gave them 561 million triangles of course in 561 million triangles there will be some that will line up we're just ignoring a bunch of data and picking out the little bits that they confirm whatever our bias is and from time to time this person would post more findings and I would post other ridiculous press releases including a programmer friend of mine Geico Tom Scott programmed the websites based on the worst of the wool. except he used monolithic sites and postcodes so he found that for every postcode in the UK there are three ley lines running through it joining other monolithic sites and one of t hem will be Stonehenge every postcode I can ensuring that you can now tell everyone that your home your postcode is definitely in the center of three ley lines one of which
goesthrough Stonehenge because it's true everywhere in the UK there's just a lot of old stuff out there true and I I'm afraid I get really upset and people say this data confirms whatever my theory is and they don't ask how much data didn't confirm it you always want to know if you're doing good correct science how much you're ignorant of what your method was, how can you falsify what you believe and then verify it honestly and rigorously and then have other people verify it properly, don't let people like me make fun of you in the newspaper, this is Well, I think we have time for one.
Let's do one last quick spin of the wheel and then I'll bring our last guest. For this one, I need an adult who is prepared to go down. Has anyone fixed it? I mean you're practically here. ya give 'em a round of applause and that was your name Matthew that's easy to remember okay so Matthew we're going to spin the wheel on whatever lands we're going to talk about it and voila oh probably yeah around the balls on you now. who pays their attention to colors oh well ok i'm going to quickly talk about wow three i never did a third chance oh i don't have one here lemme get it i'll show you my old time stick with me. all my favorite photo of all time this is my absolute favorite photo and it was taken in 1980 that is donna she was on vacation she is american going to one of the disney world or lands and when she was there she got this photo taken with us my lady .
Smith, sure, and the probability that what's amazing about this isn't that someone actually wanted a picture with Smith, but what was going on in the background because many years later she met her fiancé Alex, sure, they obviously got engaged and one day she was showing the photographs to Alex. from his childhood she showed him this photograph and he said oh how strange that he looks like my dad wait that's me he was accidentally photographed with the person he would later marry decades before they actually met and that's unbelievable like the media lost their mind like imagine imagine being in a photo as a kid and someone just pushes your future spouse into the background is unbelievable but i was like no it's not fate it's not romance, are statistics because the likelihood of this being okay is unlikely to happen to any given person. human because in the course of your life, particularly now, there are cameras absolutely everywhere with which you will be photographed, I don't know, a thousand or so. random people in the backgrounds of the photos who knows well, say about a thousand and it's reasonably unlikely that you'll have a meaningful relationship with any of those random people, there are possibly billions of people you could have relationships with right and So a thousand out of billions, I mean obviously it depends on how big you know, how much mixing and the populations you're in are the factors, but it's very unlikely, except it can happen to a lot of people. for you, it could happen to everyone, it could happen to those billions of people, I would say population size cancels out, there should be thousands of photographs like this, right?
This is not surprising and we expect it to happen, we just don't expect it. if it happened to someone specific we wouldn't know who donner and alex are they're just random you know americans you have no idea it's just because the photograph happened it's a bit like winning the lottery right it's awesome if you win the lottery that's amazing it's not surprising if someone wins the lottery don't you watch the paper oh my god someone won the lottery again it keeps happening yes millions of people play the lottery well people forget how many chances these things have and i'm gone tour a couple of years ago and there are quite a few ninjas and we approached her.
I showed him this photograph and talked about how likely I thought it was and sure enough, at a show someone came up to me and said oh this happened to some friends of mine, a friend of mine Kate met someone called Chris in Sheffield in 1993 and they got engaged and they went on a world tour to celebrate their engagement and as they traveled the planet they went to visit some distant relatives of Kate in the outback of Western Australia which really is in the middle of nowhere right. I was there and they were visiting a particular family on a particular farm. and the wife and that family said oh it's great you're here my husband and I went to the UK once years ago we took a bunch of photos and we have one photo one specific photo we don't know where we take it every Else we have written the location on the back this one we have no idea and they say ok let's take a look so they went in got the picture they took it out. and Chris looked at him and said oh it looks like it oh that's Trafalgar Square right you're feeding the pigeons in Trafalgar Square wait a minute that's me imagine traveling to the other side of the world to remember the amount of denim What did you wear when you were a kid?
I mean it's Wow and it was like the only time his family went to London when he was a kid and it was photographed by a distant relative of the person he was going to marry and then it was the only photograph they wanted to show you when you stop by to visit on this It's just crazy, right? And again they showed th is at their wedding about how amazing it was that they had this photo and that's true it's amazing to them it's just not amazing to happen I always use I have to remember how many chances things have to happen actually , you can mine that I have this is an old school pound coin, the old circulars before they got rid of them.
I'm going to flip it so it lands on the right edge, so flip it over to the edge of the coin ban land, wouldn't it be here? let's go set set that's dangerously close oh we've been amazing I mean I thought it would stay here doing the same thing over and over again but no no actually that was the pound coin I think it would most likely land on its edge and you just know that doesn't always happen by the way, there isn't an advantage. It happens that I am lucky on the first launch. It really happens.
I could, in fact, I could sit here because, oh, that was close. thousands of times it would eventually land on its edge. What I know because I did it, was me flipping a coin until it landed on its edge. I wanted to see how many chants I could get and some of them I wasn't sure if they should count or not so I want your input. on this one ok here we go this is me flipping a coin so it lands on its edge place the coin look at that wait wait idk no no oh that counts vote vote if you think that that counts, but if you believe. you're not right i didn't continue i flipped this specific coin ten thousand times so i haven't put the video out yet so people who see this spoiler won't tell anyone else that their video will be out soon. flipped it coded as fun videos like here's a coin toss for it to land on a stage boom thanks there's a video and kept going 1414 edges out of 10,000 tosses I think the old circular pound coin has the best odds of dropping his edge of all coins that's my theory and it seems very likely i couldn't believe i almost have an edge only platform ok so if you ever want to spend my experience three days of your life get involved ok ok so I think we've done enough ridiculous probability parts, we'll be back on the show as originally planned I want to be honest.
I'm very happy because it's a great example of probability. If you do something often enough, strange things will happen. I like the fact that we have three probabilities in a row. I think it's actually quite good. A pretty good message, albeit a strange one. The thing is this is the first time I've ever done this talk right and it happens right away and for those of you watching the video it's because we just sat here and kept spinning until we got the capacity every time this is the most patient audience that i have had for some time and this is a lesson in not believing the stuff you see on the internet such good morals man the second one took forever ok ok thats not the action world the story is ok i'm going to bring my final guest and show you a thinner g and then a summary and as mentioned at the beginning there are books available on the way out.
I'm also doing a show at the Edinburgh Fringe soon and then I'm doing a book tour which is completely different from this so if you watch this or see it online I'll be doing shows after it's a humble cake but I deliberately made This a special show just for the wrong institution, because I won't do that again, so if you see me on tour. it's going to be a totally different show and it would be cool to see some of the shows right so the last thing i show is a problem that again with engineering we did structural engineering as a civil that now we're going to look at. well in engineering that shot down a rocket there was a rock on the Ariane 5 rocket that was being launched by ISA and 40 seconds after it took off it exploded luckily it had no staff there were no humans on board it was just the payload of another spacecraft but of course someone had built those spaceships and they were obviously very attached to them and a simple math error caused the rocket to explode and the spaceship to rain down on the swamp below and I'll explain what the massive error was in a second but the pieces of the spacecraft to which they were then sent back by the people who had made them and were waiting to send them into space and show us the shattered fragments of the spacecraft from the Mullard Space Science Laboratory at UCL, please welcome Lucy Greene. go away again and then come back so i asked Lucy very nicely if she could go and get the pieces of paper you were very careful ok we're front lit here so these are so what what a spaceship was this so these are fragments of instruments that we flew in the cluster spacecraft so there are four of them four of them on the same rocket all on the same rocket and they sent them back to the lab yeah so when the rocket officer went down like you said not long after launch and fell into the French Guiana swamp so the European Space Agency had people who could go out and salvage the rocket and get the parts back so they sent us our instruments and apparently I wasn't there at the time but the story goes we got the box and they opened it up and there were still bits of swamp and pieces of our instrument so this is one of the brains of one of e the instruments in the group so he built the instrument that measures what we can talk about what the mission did but he was sent to study the environments around the earth, the earth's magnetic field and the particle environment and this it's the brain of the instrument that measured the electrons in the environments around the earth and what research do you do so my research is really related.
I study the Sun and I'm interested in how the sun's activity impacts the Earth's magnetic field creating something called space weather and this cluster. The mission was designed to study space weather, so one of the things it did was look at the physical processes behind aurora generation. The northern lights and aurora are generated by solar activity. That sounds useful. I don't know, I'm actually married to Lucy, only yesbecause otherwise I thought it was pretty convincing if your parents are watching they're like he never asked we've got meteor rings look at us nerds you're doing well with those fights I guess you.
You wear it well, so by the way, read the clothing because why do you have to wear gloves to handle this well? We think it's probably still covered in rocket fuel, so that's not good for you. I don't want to get on. hands and I eat my dinner later but I want to say it's great to see these parts that are completely trashed and normally our instruments don't come back so these parts were built in our labs and we have them back I think I'm one of them there was a little label that said UCL Mullard Space Science Laboratory someone is like you you know if they find him please send him home they thought it would take you millions of years and it would be a far away civilization but it wasn't and so when you got there you started working there after this happened right after this happened so when we launch the spaceship of course we want to have a big party where one gets together to celebrate and they bought champagne to drink after the launch and I got about two years later and that the champagne was still there sadly under UNK yeah but I mean we could talk about the success story because we continue s rebuilding these instruments so they were launched again launched again yes so the European Space Agency gave us the money to rebuild the instruments and it took a lot less time so in four years they were rebuilt and relaunched and they are still running and they're still running so we launched in 2000 and what are we now 2019 who ar The ones in space now are still running successfully because it blew up in '96 so they really turned around pretty quick yeah yeah , so we were actually talking to a friend of yours and not really last night, we were talking to a friend. and she was like oh she was watching the live stream because my PhD was going to be on Cluster and she was a first year grad student watching the live stream and we were like what happened and she was like the room was silent and then they all left wow he's like a very different phd i guess so where do these live now?
So these live in my apartments and we have some on display because like I said we built four instruments and we have a lot of this mangled hardware and we, yeah, we keep them outside. We talked to people about the mission talks about what we would do what you know what we did successfully to launch again and I think it just serves as a reminder that it doesn't always work well so we'll get them out before I touch them, so a big round i already have a teacher lucy greene people spend as much time working on a spaceship as miche decades to make it work and they have some of them in the lab coffee room just like in the display case like so What a reminder to the next generation of space scientists.
It's possible that your decades of work could be gone in a split second and land in a swamp and what happened with that was there was a sensor in the navigation part of the Ariane 5 rocket that, Well, this part of the rocket received information from various sensors, took the raw data coming from those sensors, turned it into meaningful navigation information, and then sent it to the main processor. the one that was propelling the rocket, so to speak, and when the numbers came in, they had to figure out how big they were. they were going to be because you have to allocate a certain amount of memory and they tended to allocate only 16 bits, 16 ones and zeros for an incoming value, but some of them could be bigger, they could be up to 64 and so what they did because there could be written something in the program that was for each input that comes in to check how big it is before trying to send it to memory, but that's pretty processor intensive and they had some pretty hard limitations on you k now how much power they got allowed to use and instead of checking each sensor they looked for all the sensors that could give a number greater than 16 binary digits and would check them to avoid problems and the ones that could never be that big they didn't bother to check correctly and were able to save some of processing and everything worked very very well on Ariane 4 then they copied it to Ariane 5 without double checking and because of a different take off trajectory and because of the way it l The sensors worked one of the sensors that was previously not being checked well it still wasn't checked but now it should have been checked and it didn't actually have to be on they just left it on after launch it was a pre launch sensor because if there was it was ever a launch and then they aborted before takeoff and then restarted it took forever to restart so they didn't turn them off right away let them run and then turn them off once they were safe.
It was definitely safe, however, it continued to run as it took off, got a value that was too large, didn't fit in memory, put it in, went into memory next door and everything crashed so what. would you know by itself? It wouldn't have been the worst because it could have been a reboot or something except it was designed to give a crash report so you know like the stereotype of someone like oh you know tell my spouse I love him good but this it's like telling my debugger the following failure context information correctly and then it sent the debug message over the same link to the main processor i didn't know what could happen it thought it was nav data thought the rocket had taken off suddenly one side tried After correcting it, it hadn't deflected to the side and the correction threw it to the side, ripped it open, the self-destruct sequence started and because an attempt was made to put a 64 digit number in a 16 digit space to the right all this rocket blew up a d possibly because the spaceship was uninsured which is amazing how every third decided to refund it right so a massive little mistake can have involves phenomenal performances and that's all from me.
I guess in conclusion I started with the theory of major errors. and in some cases, yes, we have to make the dough correctly. I mean, occasionally we'll get it wrong, but we have to get it right in a lot of these critical situations and that means we need people who are good at mass and repair to put in the effort because with math we can do more than our brains were built for. originally to do well we can go beyond our intuition which I think is amazing but ironically to get mathematicians and people who are prepared to put in hard work and more The most important thing is to create systems that accept that humans they will make mistakes and we can use our same mathematical logic to have strong systems where mistakes don't turn into disasters.
To have all that, we need people who are not afraid. making mistakes to learn math correctly, so I guess the other goal of my book is also to show people all the amazing critical math that underpins our society. enjoy math and not the people who find it easy, it's the people who enjoy how hard it is, it's hard work, you're wrong, but gradually it would teach your brain to think and gradually you'll get better at math, so i will be here physically signing books if you want to get one later this video will end up on the internet if you're watching it on the internet you can order it from that it's not a bug in the url it only works if you put the dot in the wrong place because i think i'm hilarious , actually penguin will like it, but it doesn't work if you put it as a humble: PI communication doesn't work, I don't like it, yes, people have to earn the book like us.
I don't think you understand marketing. t, so I'll also be signing books and calculators right now, I'm done though, thank you very much for your patience, thank you very much for making it work.
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