What Happens When Maths Goes Wrong? - with Matt Parker

Oh calm down thank you all very much for coming along for an exciting evening of mathematics my name is Matt Parker I used to be a math teacher which is why I know that person is on their phone while I'm talking honestly once a teacher always a teacher so can you all hear me adequately loud amplified through the microphone excellent people the top we're all happy marvelous right so the plan for tonight as our Peter very kindly said in his introduction and then went home that's big vote of confidence in tonight's hook as he very

kindly said I do a wide range of things involving promoting mathematics 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 from and I do BBC Radio 4 which is the rest of you so high I cover the whole spectrum and so I recently wrote a book humble pie and I'd written one book previously called things to make him do in the fourth dimension which as was mentioned in the introduction is currently the second

most viewed video on the RI channel despite the fact that it's all abstract mathematics and I figure tonight with some applied mathematics I'm taking number one so I wrote the first book and Penguin the publishers were like would you like to write a second book and the problem with things to make him do in the fourth dimension is even though I was incredibly proud of it and even though it sold very well for a mass book it sold average for a book right which is great right average is I'm above 50% of books I'm very

happy with that all right but penguin don't care what's in the book right they could publish you know another celebrity cookbook or anything I mean that's the one option actually and so I had to convince them was a good decision to publish a book about mathematics and so I suggested to them I could write a book all about my favorite mathematics mistakes which is where humble pie a comedy of maths errors came about and they liked that because people like tales of disaster they like stories of things going wrong they enjoy laughing at other people

I've made a career of being on the receiving end of that and so I that's it yes write that book that's great people who are specifically math nerds which is their polite way of describing my target demographic right people were still enjoy reading these stories and my ulterior motive was by showing examples of where maths goes wrong in everything from finance engineering you know statistics medicine you name it I can show it's an excuse to talk about the maths that's required for these areas of our modern society right and so obviously math works pretty flawlessly

most of the time so much so that most people have no idea how dependent we are on mathematics and people often don't value maths for that reason so I thought this is a great excuse to just talk about all the places maths is used but by using things going wrong as as my way in and actually because I because I used to be a maths teacher actually can you cheer any maths teachers in hiding at the top not sounding exciting that's it's the end of half term isn't it right okay they were so I used

to be a math teacher just like the fine people cowering at the top of the room and I then I left teaching but I still remembered how a lot of young people because when you're at school you're forced to do maths right when you're forced to do it a lot of people perceive mathematics as a subject where you have to get it right getting the right answer is everything as the be-all end-all of mathematics and as a teacher you know that that's not always strictly true right maths is about trying something and getting it wrong

and then trying it again and hopefully getting it less wrong and then more wrong and hopefully it converges in on the minimal amount of wrong possible but it's a long slow process of not understanding it and not doing it well and it's always very disappointing when students or even people in you know standard-issue humans are afraid to try some maths because they think if they don't get the right answer they haven't done it correctly and that's not true if you get the wrong answer you may still be me correct and you're trying it right mathematics

is about learning and teaching your brain how to think and so I thought how can I kind of bring that approach to what will otherwise just be a random collection of mass mistakes they haven't got any real meaning and you know I started with an inspirational poster that I had when I was a teacher and the inspirational posters are the staple of the teaching world is what you decorate your classroom with and this was one of my absolute favorites they are education works best when all the parts are working now let me just break this

down for you so you've got cogs representing students teachers and parents and the trouble is when that big cog on the right which represents students if that rotates that say clockwise because it meshes with teachers teachers have to rotate anti-clockwise that's all very nice but neither am i going anywhere because parents are jamming up the whole system if surprisingly more applaud with the teachers and the parents surprisingly accurate poster in my humble experience alright and then obviously people just haven't thought through the geometry of this situation right if you have cogs they have to go

clockwise anti-clockwise clockwise anti-clockwise so in Manchester we're unveiling their new approach to public transport they went with the classic three cog making the city work together or the people did point out and proceeded to render in 3d there that's just this one point of view possibly from the sides it's fine it's like well played well played before you see is this right you don't look that steep that's they they were thinking they were several steps ahead until I saw an article where President Trump in the United States was negotiating the North America free trade agreement

and when that was put in the newspapers to show how all the working parts of North America should be moving in unison papers use this illustration wait you've already used your third dimension right you're not getting that back so I paid money I paid good money to license that image to put it in my book just so I could use the caption making cogs great again so totally worth it and finally two pound coins when the two pound coin came out to celebrate the Millennium so there was a competition to design that this was the

winning entry and it's got different concentric I guess circles bits where it shows different stages of UK history and the middle one you're kind of mechanical age here is a series of cogs and because if a cog goes clockwise the one next to us to go anti-clockwise then clockwise anti-clockwise you have to have an even number of cogs as you go around the two pound coin has an odd number of cogs it would not work people on the Internet were unimpressed and smug in equal measure and the Royal Mint put out a statement saying that

it doesn't matter right it's just what are you going on about it's just meant to represent that age and I was like that's curious I wonder because there's a 50/50 I don't know what would be a great example to simulate a 50/50 chance imagine flipping something right it could it could go either way if you if you do it at random you get an order and even number of cogs and so I looked up the person who designed this coin guy called Bruce Russian he's a art teacher in Norfolk and on his website he's got

his original design which would have worked it's an even number of cogs the actual coin that was made these three cogs were removed which meant that it wouldn't work I said wow he like he had it right and the Royal Mint broke it but was that deliberate so I sent him an email I think hey I'm really sorry I'm sure people have pointed this out I'm just curious cuz I noticed you got it right was that deliberate did you think about it was it a concern but what happened I'm writing a book about math mistakes

I'm curious to know what was your thought process and he replied to say that he didn't think as an artist it should have to be correct he thought is representative a bunch of cogs it doesn't make a difference to the artistic worth of the design and to be honest I kind of agree with him he then said that he decided to make it work anyway because otherwise he would get loads of annoying emails from her I don't know why that bit was involved over there you go so-and-so yes he just thought people are gonna complain

they're gonna go on and on about it and now this this is the unfortunate edge because when I was writing a book as mistakes I didn't want it to be all about nish theoretical maths problems of which there are things people thought they proved something and they hadn't and that's interesting to 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 fine to make mistakes which is one of the things I want to get across and a lot of mistakes

don't really matter so this I hunted down a copy of this book I remembered this from years and years and years ago I forget well I didn't have it as a child I must have seen some I mean a lot of my friends procreate and I saw somewhere this book this is a Sesame Street book this is Ernie expressing his dislike of the possibility of being forced to live on the moon which feels like a niche concern but there you go and I I can't down a copy of this book I found it on the

internet and there's one thing about this which really bothers me it's not important it's not a major issue does anyone apart from the child who had a very loud epiphany over there like to tell what's wrong with it this stars where the moon should be you are a hundred percent correct what are these there's not a hole in the moon as far as I'm aware in the extended Sesame Street universe there are not Muppet bases that we can see twinkling on the moon right and so you often see a crescent moon and then you see

stars shining through it and no the moon is well from our point of view a disc right and it's always there it blocks out the stars we just see different bits depending on how it's lit and that's an artistic version of that bizarrely I'm fine with that alright but I'm like they they shouldn't show stars through the crescent moon right come on bit of astronomy everybody and then I was looking around for other examples and actually Sesame should have done this more than once and I was looking at separately the license plates from the state

of so this is a plate from Texas and as you can see it's celebrating the fact that the shuttle was involved in Texas and there's the shuttle that's not a bad angle actually for the shuttle taking off that surprisingly it's already it hasn't got any of its boosters or anything so I maybe that's it landing I don't know I was distracted by over here that star that star is dangerously close to that but the only way I could know for sure would be to somehow buy some license plates from Texas so I did that and

they arrived in the post there we are these this is actually genuinely I scanned it so I could get a high-resolution version because all the ones online were too low res and if you zoom right in and you fill in the rest of the moon Texas undone by a Lone Star so people have since pointed out that maybe it's marking with the first Apollo landing site was and it's very close I might give them that to be entirely honest but believe these problems these to it that they're not okay if we're just talking about are

there practical implications for the problems in this case if we don't get me wrong I'm a big fan of getting mass correct and good mass PR and mass being important but because practically there are they important and and sadly in those cases not really not really important but sometimes the mass can be important so you may have noticed I am dancing around a very large Jenga tower and I thought I'd have this set up during my show to artificially increase the amount of suspense for narrative purposes no so so this is to show a fantastic

effect about resonance so this is a building and we're going to show you in a second how a building resonates hopefully to destruction we will see how lucky we get or unlucky depending on what I'm trying to do at the time normally you'll hear resinous discussed when it comes to bridges and so there are little bridges which have had resonance problems dating back into I think the guess what I've come across was in the 1800's up near Manchester where sulphate is now there was a bridge and there were some troops marching over the bridge because

they were all in step they hit a resonance frequency of the bridge and the bridge start to move which apparently they thought was kind of fun so they started singing a tune to match the bouncing bridge really got involved and it collapsed and no one died no one died it's okay it's difficult writing because you're doing your cover engineering and medical mistakes when I was putting the book together like I don't like every second story everybody dies I can't have a comedy book about maths and every second lever every couple pages and then everybody died

right so I think in all the engineering examples I'm gonna give you nobody died I think and all the aviation stories in the book nobody died don't get me wrong people do die in aviation problems just not the ones I put in the book so that was a problem with the bridge up in Manchester in London you've still got this one here this is the albert bridge all troops must break step when marching over this bridge that sign is still there troops are they must break step interestingly though they must not break dance very different

rules and when I mentioned there's a lot of you are now thinking of one of two famous bridges Tacoma Narrows Bridge this was a bridge in the US Decco bridge absolutely phenomenal incredible amount of twists now that's not your standard resonance from Just's people marching on or even bursts of wind as you will occasionally read online this is resonating but this is flutter this is aerodynamic flutter from the wind coming up the valley where it was and the flutter basically caused this runaway feedback loop whereas the lift bridge came up more wind pushed it higher

up when it finally bounced back and down more wind pushed it down and you got this feedback which led it to go more and more someone finally decided maybe they should leave their car you also you've got the Millennium Bridge in London this was opened in the year 2000 and it was any of them for a couple days before there to close it they looked at the footage now if everyone's walking randomly it should be fine because no they're not all gonna match one particular frequency but they looked at the footage about 20% of the

pedestrians amid Lee is quite crowded but 20% of them were all marching in synch the bridge is moving about seven and a half centimeters either way right which is about seven and a half too many and so they had to close it and do all sorts of crazy things to damp it because what was happening was the bridge was moving a bit and people were moving with it and so they were then stepping in time with the bridge so the bridge moving was causing the pedestrians to synchronize and the pedestrians synchronizing was causing the bridge

to move and you get this feedback with the official wording was it was synchronous lateral excitation right if there was a feedback energy was going in and it was matching a resonant frequency which is of course totally terrifying I'm more as though I became obsessed with the bridges are one thing they're easy to move and we kind most part now we get which is why the Millennium Bridge was so amazing for the most part now bridges work fine buildings less so so there was a building in South Korea in 2011 which is disturbingly recent anything

within a decade I find terrifying it was a 39 storey building and one day in 2011 the people on the 38th floor evacuated because they thought there was an earthquake or something it was shaking like crazy they left the building no one else knew what they were going on about the building was fine now what they did an investigation and they recreated this so this is genuinely true it turns out on the 12th floor was an exercise class and about 20 people decided to exercise to a different song that day they exercised two snaps I've

got the power if you're unfamiliar with snaps I've got the power that would be better if it's a dramatic if you're unfamiliar with snaps I've got the power and that's as much as I can play without the wrong situation getting a copyright strike on their channel they dance to that song the song happened to match the resonant frequency of the building and the 38th floor moved ten times more than normal absolutely incredible so in people design buildings they have to try and factor this in and it is a big problem which is what this is

actually kind of a teaching aid for learning about residents in building and I've borrowed this off a friend of mine who is an engineer and they've actually come along to give me a hand because I am not qualified to run this and see what it can show us about residents so can you please welcome to the stage from the University of Bath Paul Shepherd well welcome I haven't seen you since we put this back together okay it's been minutes so don't pick that up yeah I get nervous okay so first first of all what do

you do at the University of Bath let's I teach mathematics to civil engineers I research how we can use computers to design better buildings and I've also got a role in our institution Institute of mathematical innovation helping companies with their maths problems fantastic no he started and ended with maths to keep me happy so you use this in your lectures I believe yeah and just talk us through what is this bit of 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 causes

the base to move back and forth yeah vibrate and I have here a button that you're not qualified to press that's the one and a dial to make it go faster or slower can we is there like a safe slope can we I'll catch it if it goes really slow yeah you know that is that is fantastically slow if anyone starts watching the video right now they're like it is playing at the wrong speed I'm still awake so that's it right and on top of this we built a Jenga tower yeah and what we wanted

to demonstrate with this is that if you hit the resonant frequency of the Jenga tower it will fall over but to make it a challenge first we're gonna start with a frequency where it won't fall over so we think we've found one we're unconvinced we put it back together and when now its subtly different and we'll have a slightly different resonant frequency let's give it let's give it so she would we slammed straight into the right into the right just in case we get unlucky it's fine look at it I would happily live in that

building so we've got it moving at quite a frequency it's shaking never get me wrong it's shaking it all over the place but it's not falling over what we're gonna do now is we're gonna keep the amplitude the same because we can't adjust it and we're going to reduce the frequency so we're shaking it less so you want to reduce the frequency the frequency down now you can stand back there's now less shaking so yeah well now I feel confident less shaking and in theory even though we're shaking at less if we hit a resonant

frequency it will fall over I think we're near one [Music] the 30 Barrow asthma shaking its lower we're putting less energy into it we were just putting the energy in at just the right time to build and accumulate in the system rather than canceling out and yeah so what so you showed this to what civil engineering students yes we I mean we don't want that to happen to buildings and there's a certain number of things we can change to the building to make sure that the frequency at which it would do that is different from

the frequencies that it would see in its daily life okay so you can kind of tune it the building away from and you don't test us by putting models on this no you run like simulations or something we do maths on obviously correct answer and are there any buildings like can you give us examples of buildings or you are you like I'm under a lot of non-disclosure agreements not anymore now well I was working on a bridge I won't say which one at the same time as the wobbly bridge across the Thames had problems really

so we were working I was working for let's say a different company and of course we watched that and thought we better make trouble he sure like what happened to them first so I mean it did take the world of engineering a little bit by surprise that it had happened so seriously so yeah we you know we we can now under the person element that we we need a maths but we didn't quite understand how people synchronized their they're unpredictable ones and now in the two decades since when people design bridges do you or any

any building I guess do you have to now factor in human movement as well yeah after that happened people a lot of people did a lot of experiments and research to work out how it happens and to quantify it and now that sort of new research is taken into account when we design bridges today a huge river pause for poor shepherds all right I think it's literally just set over there now okay so but his mic has been turned off okay right so so I think this is great because thing about engineering is we're often

building things beyond our current full mathematical understanding right we used math to build things which no longer make sense intuitively because if you look at something like the Millennium Bridge you can't just go that will wobble or that won't or indeed most of the perfectly stable buildings before we had computers and advanced maths we built them out of massive bits of rocks where you can look at it and go yep that's not going anywhere right whereas now we need computers and mathematics to check and occasionally things go wrong we will forget about a factor or

there's a new bit of mathematical behavior will emerge and then the Indian engineering industry learns improves and the maths is developed and we carry on building more and more ridiculous things okay so I'm gonna leave these here and continue to carefully dance round them what I thought I would do because I've got I've got one more guest at the end who's brought something else along to show you but between now and then I had so many stories because this like I just had hundreds and hundreds of stories of which a couple hundred made it into

the book and I couldn't decide which ones I was going to show you here today so I thought I would do is pick them at random so I have here a spinning wheel and so what we can do is if we spin the wheel right it'll settle on one of the colors this is not it we'll do it again in a second so we get a color and up here I've got a breakdown of what the colors mean so we would do a story about programming write the programming story I got a programming straw in

the laptop we do it we have a great time we do this a few times then we bring on the final guest very straightforward so I'm gonna get some volunteers to come down and know you haven't heard all the rules I I'm gonna think I'm gonna do this three times that's my guess three times and so my plan is if we have three different volunteers we will start with a very young volunteer we will then have more of a teenage high school volunteer and then we'll have an adult volunteer so if people watch this quickly

or they just or editor down there will look like the one volunteer aging rapidly throughout the talk okay so yeah are there any mmm where's for him in the sentence any young volunteers who'd like to come down and be first over there alright the back give me a wave you get a round of applause come on down fight very nice to meet you what's your name Mario nice to meet you let's come over here Mario so you can see I got my spinning here why don't you do is to grab one of these and just

give it a real spin and we'll see which of any of the colors it ends up on off you go good spin whatever color it is just hear the category nice and loud oh it's just in green what's green thank you very much give her a round of applause [Applause] give me a second to find my probability slides there we go okay so we're going to start with a tale about probability and how humans are bad at probability and this is one of my favorite examples where we can try to scam someone right we can

try and trick someone into thinking it's a fair game when actually it's not so for this I need a volunteer however I'm gonna take one from someone right up the top is there any one because you don't have to come down for this you you remain completely institute let's go with the person over there leaning on the rail at the back yep give me away exit what's your name very loud yeah we kind of you okay so so what we're gonna do right we're gonna flip a coin down here it's gonna be heads or tails

right and you're going to try and predict if it's heads or tails is anyone down here got a coin any of the adults got a coin they're prepared to flip for me so are you happy are you happy to be our coin flipper okay you can stay there you put the coin very straight forward okay right so what we're gonna do is we're gonna flip the coin you're gonna predict it would you like heads or tails you feel like this is going to be a double sided coin I I feel like we're having more of

a conversation than I expected let's have a look you me the coin oh my goodness okay ready can who would you like to verify the coin pick a human the one next to you pick a human who's closer to me than you it's okay I've got a solution don't worry would anyone like no okay okay hoo-hoo there there that one okay can you have a look at that is it is it a is it a head on both sides no is it tails on one side excellent Wow that was anticlimactic huh here you are you

are now deemed trustworthy by simply saying either the word heads for the word tails or what do you think it's gonna be tails okay everyone in your own minds decide what you think it's gonna be heads or tails me anyways okay flip it and then call it out nice and nice we can all hear it good flip solid flip what is it tails who's right hands up if you're right okay half of you hands up if you're wrong okay yeah okay slightly more because you know adorable kid okay so what's that fair though and by

the way it's not a trick coin there's nothing fancy going on it's not because there's more metal on one side than the other right assuming that is a perfectly fair coin everyone should be happy that was a perfectly fair challenge in fact if we were to bet money which young people you shouldn't right but will you to do such a thing 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 loser you play the same person you would end up

passing money back pretty much at random right no one has an advantage in that game we could make the game slightly more exciting by having more than one flip so if instead of asking you what one flip would be I could say we're going to flip it will do two flips so you can choose heads heads or heads tails or tails heads or tails tails what would you like actually what do you like tells tells right and everyone here could think of their own their own one that they want to have and if we we

flipped it you've all got a one in four chance of being right or if we're playing two of us if we don't get it straight away we could keep flipping it until one of us has our run come up first still a fair coin must be still fair what if we did three in fact everyone in your own minds decide what three flips in a row heads tails heads tails tails tails heads tails tails right what are you in your own minds decide what you think it's gonna be what did you what did you slide

up there tails tails you get one more hits tell cells heads right in fact here they all are there's all the options so you may have picked one of those and they're all equally likely I'm now gonna bet all of you simultaneously that mine will come up before yours so I want you to have a look at this and I want you to choose which one is yours make sure you choose where's yours and then I'm going to add my predictions next to yours so if you predicted heads heads tails I predict tails heads heads

because I'm playing you all individually if you pick tails tails heads I've picked heads tails tails I have different predictions I mean some of them are the same that I mix up the predictions based on what you said so everyone makes sure you're happy which one is yours in my prediction nexor you all got that okay so what we're gonna do now is we're gonna start flipping the coin until either you win or I win and we'll keep going until every single game is finished so first one up flip the coin what have you got

heads second one Oh third one tails so a lot of people are now happy they've just won if you said heads heads tails you have just beaten me I said tails heads heads which has not come up but some people yours isn't here yet so can you flip it again okay I love it you're being more enthusiastic each time tails so now can his last three are now heads tails tails so if you had heads tails tails you've now won if I had heads tails tails I've now won or if I had heads heads tails

against yours I've now won you need to keep track who wins first you or me so if either I beat you with heads heads tails or I've beaten you with heads tails tails just bear that in mind okay give us another flip heads so the next one up is tails tails heads tails tails heads up next tails heads tails tails heads tails tails his tails okay heads tails tails heads tails tails is anyone still in the game what are you thinking of which one's yours heads heads heads and what did I predict against that tails

heads heads doesn't come up oh my goodness okay let's keep going okay next one who's gonna win heads tails tails heads tails heads tails they're still both in the competition someone else do the one will gone out right yep heads tails heads it's the beginning of your run here we go but you're about to win Oh is anyone still in the game what were you on hey tails heads I predicted heads heads tails which was the first one out so it's fine don't worry we'll edit this out of the video so very quickly before when

it was heads or tails roughly half the audience roughly got it correct put your hand up if I won the game against you that's the vast majority of you and hands up if you won a few people okay what did you want the people who picked me what did you go for heads heads tails which was straight out of the game right so one in eight of you will win straight out of the gate if you play this game over and over and the person you're playing against picks randomly I will win 74% of the

time roughly three-quarters of a 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 is we don't flip the coin three times and then start again if we did it three times start again three times start again it would be perfectly fair because they're overlapping they're no longer independent probabilities they're now dependent probabilities and if you look at mine all of mine will mine or end in what your prediction starts with I'm trying to make mine happen right before yours

which is why I got yours because I knew if you've got heads heads heads unless the first three flips are heads heads heads I'm gonna win because tails heads heads will always come first so let's say we've been flipping the coin for ages and someone picked all tails the opposite of you and someone picked I picked heads tails tails if the coins been flip flip flip flip and you're right ah here we go at last it's gonna be tails tails tails as soon as you get the first two in the run I've already won unless

the first three flips are tails tails tails or heads heads heads you cannot win so there's a one in eight chance you will win and there's a seven and eight chance I will win and the other ones 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 through when you get these unusual probabilities combining I actually I carry with me a set of dice which I thought I'd get out if we have probability on the spinner wheel these are

called grind dice and they have unusual numbers on them and I appreciate you can't really see them so I've got a shot up on the screen here so the other one you can see there has got well it's got an 8 it's got some threes the Green has got a 0 what's going on there right they've got crazy numbers on them they're not one two six and the game you play is choose a dice so you pick one color I pick a different color we roll them together highest number wins very straightforward right except they're

not all equally likely to win because they've got different numbers but it's very hard to tell at a glance which is the best dice I can now reveal to you that if you roll the red one versus the blue one the red one will win more often than the blue not all the time but more often it's above 50% the blue one wins more often than the green the green wins more often than the other yellow wins more often than magenta until you get this fantastic ordering from the best ice which is the red down

to the worst dice which is the magenta also you would think if you play magenta versus red the magenta wins more often than the red one there's no best dice if you remember this cycle and the person you're playing picks first you can always pick a dice which has a higher probability of winning than they do same as the dice game penny-ante right you've long as it person picks 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 go you go first and then

I'll choose there's no best option but each one's better than another one in each one loses to another one same deal on it on a higher scale if you do play this though it gets a bit terrifying because if people realize you're beating them they will make you tell them the secret and then you say I'll catch you I'll teach you the secret and now we'll play two dice together why not what they don't realize is if you play two dice simultaneously it reverses the order so they will now you'll pick first and they will

then deliberately pick the one that loses because you've got to so that's the single dice game that's the double dice game if you're wondering what on earth is going on here I've got a quick equation there you go it's also got more than one cycle because there's another internal cycle the five in a different order and if you double the dice the internal cycle doesn't reverse all it does is the top one becomes even right so there's a double dice there's the single dice and so the outside ones flipping but the inside one isn't if

you're wondering what's going on there there's the new equation all right and I absolutely love them if you want some details they the colors I'm half of the colors friend of mine Gaikwad James grime did the numbers I did the colors I'm helping because I said if they're these colors then the length of the color goes up by one letter as you go around the outside cycle which is why that's magenta not purple purple as in sufficient letters and then James was like well if I make this one olive instead of green the inner cycle

is now alphabetical order sorry so you can now remember both cycles by looking at the colors if you want all the stats here are your advantages for any given pairing the inner cycle is actually extract slightly stronger the other one here's all your numbers every single one is above 50% apart from we couldn't quite get this one up to fifty it's just below because sadly there's nothing magical about these dice there's no incredible mass property it's just that when you put numbers on some dice you it's very hard to tell if they form a trans

non-transitive cycle or a transitive cycle and non-transitive just means like numbers are transitive because if three let's say seven is bigger than three and three is bigger than one then seven is bigger than one it's a transitive property that passes down the chain just because you know red beats blue and blue beats Green doesn't mean red beats quick right it's not a property that gets passed down the chain and it's things like this which throw humans when we think we understand probability but then it's just a little bit off so I think we've got time

for another quick spin of the wheel I need a teenager this time anyone prepared to come down and give me a hand you look very keen right in the center would you like to come down and spin the wheel you get the applause once you get to the aisle not now it gets awkward gets awkward I was we were just applauding other people awkwardly moving it's not good what was your name Sasha very nice to meet you Sasha so you saw how this goes you grab it you give it a spin whatever color it ends

up on you say very loudly what it was okay off you go okay we're gonna be talking about okay probability excellent right a pause for Sasha how what are the chances so probability I think I've got a second probability thing here give me a second oh yeah no okay this is kind of fun this this is an old classic so way back in the distant past 2010 I saw a newspaper story about someone who had analyzed the locations of the ancient monolithic sites in the UK and they realize that they formed patterns specifically if you

took the 1,500 main monolithic ancient sites these are prehistoric sites and you analyze their positions they formed triangles much more than thats therefore they form very precise triangles isosceles sighing track but isosceles triangles where two sides are exactly the same length and they were within like half a percent incredible precision and the person who found this put out a press release it was in all the papers they claimed it was some kind of ancient sat-nav and that they used these geometric arrangements of monolithic sites to navigate across the United Kingdom and the researchers said that

the results were so precise they could not have happened by accident in fact they couldn't rule out extraterrestrial help so I thought I would check so I went and also got some ancient sites and started plotting them on a map of the United Kingdom in the first three I came across around Birmingham formed a perfect equilateral triangle within the required half-a-percent and then I forgot added in more triangles you've also got to uh sauce these triangles neither side both within the half-a-percent another pair of us lost these triangles both within the required half a percent

the base and the perpendicular bisector go through four new locations the location in Connor ways within twelve meters of this line it then goes over a hundred and seventy miles across the United Kingdom right through the base of the triangle hits Luton where it's within nine metres of that spot incredibly precise patterns I was like wow this is this can't have happened by accident except I wasn't analyzing ancient monolithic sites I've looked up the ancient Woolworths stores who had gone bankrupt slightly before and we had already forgotten how the people of 2000 they lived I

mean how did they buy discount plastic goods and clothing we just don't know and for the young people who aren't familiar with Woolworths they had a business model where they were like let's just get all the confectionery and put it in open containers let people help themselves and assume nothing will go wrong with that business model there all right so they went out of business I found the 800 Woolworths locations around the UK and I analyzed them and I found the same patterns to the same level of precision as the other person who had found

who was claiming either ancient wisdom or you know aliens or all these things right so I put out my findings as a press release about how we could learn about the ancient Woolworths civilization The Guardian went with aliens found Woolworths civilization which it was pretty funny it turns out they're just lots and lots of stores to choose from so specifically here are the ones I had with their postcodes they're all legitimate stores you can fact check this but here are all the stores right if you've got I checked the numbers if you have 800 Woolworths

stores there are 85 million possible triangles if you have 85 million triangles it would be more amazing if none of them were isosceles right there are so many options if you look hard enough you will definitely find this pattern or any pattern of your mathematically weakened state you can find any pattern want to any level of precision you want if you're prepared to ignore enough data the 1,500 stores the other person had used gave them 561 million triangles of course in 561 million triangles there are going to be a few that line up right we're

just ignoring loads of data and cherry-picking the little bits which confirm whatever our bias may be and every so often this person would put out more findings and I would put out other ridiculous press releases up to and including a programmer friend of mine Geico Tom Scott programmed the websites based on the wool worst thing except he used monolithic sites and post codes so he found for every single post code in the United Kingdom there are three ley lines that go through it by joining up other monolithic sites and one of them will be Stonehenge

every single postcode I can guarantee you can now tell everyone your house your postcode is definitely at the center of three ley lines one of which goes through Stonehenge because it's true of everywhere on the United Kingdom just a lot of old things are lying around right and I fear I get so annoyed and people go this data confirms whatever my theory is and they're not asking how much data didn't confirm it you always want to know if you're doing good proper science how much you're ignoring what your method was how you can falsify what

you believe and then honestly and rigorously checking that and then getting other people to check it right don't leave it to people like me to make fun of you in the newspaper okay I think we've got time for one let's do one quick last spin of the wheel and then I'll bring on our final guest so for this one I need an adult who's prepared to come down is there anyone who's repaired - I mean you're practically here already give them a round of applause and that's was your name Matthew that's easy to remember okay

so Matthew we're gonna spin the wheel whatever it lands on we're going to talk about it off you go oh is that just in probability yes around the balls about you now who does lend their on the colors oh well okay so I'm very quickly gonna talk about Wow three I did never third probability oh I haven't got one here let me get that I'm gonna show you my old time stay with me everyone my all-time favorite photo this is my absolute favorite photo and this was taken in 1980 that is Donna she was on

a holiday or vacation she's North American going to one of the Disney World or lands and when she was there she got this photo taken with us me mrs. Smith right and the probability the amazing thing about this it's not that someone actually wanted a photograph with Smith but what was happening in the background because many years later she met her fiance Alex right they obviously got engaged and one day she was showing Alex the photographs from her childhood showed him this photograph and he went oh that's odd that looks like my dad wait that's

me he was accidently photographed with the person she would later go on to marry decades before they actually met right and that's that's amazing like the media lost their minds like imagine imagine being in a photo as a kid and someone just wheels your future spouse into the background it's incredible but I was like no it's not fate it's not romance it's statistics because how likely is okay this is unlikely to happen to any one given human because over the course of your life particularly now there are cameras absolutely everywhere you'll be photographed with I

don't know a thousand or so random people in backgrounds of photos who knows right let's say about a thousand and it's reasonably unlikely that you will go on to have a significant relationship with any of those random people there's possibly billions of people that you could go on to have relationships with right and so a thousand out of billions I mean obviously it depends how bigger you know how much mixing and the populations you're in there are the factors but it's very unlikely except it can happen to a lot of people all right it couldn't

just happen to you it could happen to everyone it could happen to those billions of people I would argue the population size cancels out there should be thousands of photographs like this out there right this is not amazing and we expect it to happen we just don't expect it to happen to anyone's specific we wouldn't know who Donner and Alex are that they just random you know North Americans no idea right it's only because the photograph happened it's a bit like winning the lottery right it's amazing if you win the lottery that's incredible it's not

amazing if someone wins the lottery you don't see the newspaper oh my goodness someone won the lottery again just keeps happening yes millions of people play the lottery right people forget about how many opportunities these things have and I went on tour a couple years ago and there's a good number ninja and we rose on to her I showed this photograph and talked about how likely I thought it was and sure enough in one show someone come up to me and said oh this happened to some friends of mine a friend of mine Kate she

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 were travelling around the planet they went to visit some distant distant relatives of Kate's in outback Western Australia which really is the middle of nowhere right I've been there right and they were visiting one particular family on one particular farm and the wife and that family said oh it's so great you're here my husband and I we went to the UK once years ago once right we took a whole bunch

of photos and we've got one photo one specific photo that we don't know where we took it all the other ones we've written the location on the back this one we have no idea and they're like okay well let's let's have a look right and so they went in they got the photo they pulled it out and Chris looked at it and went oh that looks like oh that's Trafalgar Square right you're feeding the pigeons in Trafalgar Square wait a minute that's me imagine traveling halfway around the world to be reminded of how much denim

you wore as a kid I mean that's Wow and it was like the one time as a kid his family went down to London happened to be photographed by a distant relative of the person he would go on to marry and then it was the one photograph that they wanted to show you when you happen to visit in this it's just insane right and again they showed this at their wedding about how incredible it was that they had this photo and that's true it is incredible for them it's just not incredible that it happens I

always use gotta remember how many opportunities things have to happen in fact you can kind of exploit that so I've got a this is an old school one pound coin the old circular ones before they got rid of them I'm gonna flip it so it lands on its edge right so flip the coin ban land edge okay wouldn't this be here we go ready ready that's dangerously close oh we've been amazing I mean I thought he's gonna stand here doing the same thing over and over again but no no actually that was the pound coin

I think is the most likely thing to land on its edge and just you know that doesn't always happen by the way there's not an edge I happen to get lucky on the first flip right it genuinely does happen I could actually I could sit here for oh that was close I could sit here and flip it thousands of times eventually it would land on its edge which I know because I did so this was me flipping a coin until it lands on its edge I wanted to see how many edges I could get and

some of them I wasn't sure if they should count or not so I want your opinion on this one okay here we go this is me flipping a coin so it lands on its edge set the coin look at that wait wait I don't know no no no ah does that count vote vote if you think that counts but if you think it doesn't you're right it does not I kept going I flipped this specific coin ten thousand times so I haven't put the video out yet so people watching this spoiler don't tell anyone else

their video will be out soon I flipped it coded like funny videos like here's a flip a coin so it lands on a stage boom thanks right there's a video and I kept going going going 1414 edges out of 10,000 flips I believe the old circular pound coin is the most likely to land on its edge of all the coins that's my theory and it seems very likely I couldn't believe I almost got an edge just right right and so if you if you ever want to pass in my experience three days of your life

get involved okay so I think we've done enough ridiculous bits of probability we'll go back to the show as I originally planned I want to be honest I am I am quite glad like it's a great example of probability if you do something often enough weird things will happen I like the fact that we got three probabilities in a row I think it's actually quite good quite a good message although the bizarre thing is this is the first time I have ever done this talk right and it happens straightaway and for those of you watching

the video it's because we sat here and kept spinning it until we got from ability every single time this is the most patient audience I've had for some time and this is a lesson in not believing things you see on the internet so good moral man the second one took forever okay so okay that's not the action world the story okay I'm gonna bring on my final guest and show you one more thing and then a wrap-up and as was mentioned the beginning there are books available on the way out I'm also doing a show

at the Edinburgh Fringe coming up and I'm doing a book tour afterwards which is completely different to this so if you watch this or you watch this online I'm doing shows after it's about humble pie but I've deliberately made this a special show just for the wrong institution um because I'm not doing that again so if you see me on tour it'll be a totally different show and it'd be great to see some of the shows right so the very last thing I show is a problem that once again with engineering so we did structural

like civil engineering we're now gonna look at well in engineering that brought down a rocket there was a rock at the Ariane 5 rocket which was being launched by ISA and 40 seconds after it took off it exploded thankfully it was unstaffed right there were no humans on board it was just payload of other spacecraft but of course someone had built those spacecraft and they were obviously very attached to them and a simple mathematical error caused the rocket to explode and the spacecraft rained down on the swamp underneath and I will explain what the mass

mistake was in a second but the bits of spacecraft they then sent them back to the people who had made them and were waiting to send them into space and to show us the mangled bits of spacecraft from the Mullard Space Science Laboratory at UCL please welcome Lucy Greene it's gonna go get it again okay I say welcome she's gonna arrive in and go away again and then come back so I asked Lucy very kindly if she could go and find the bits of paper you were very careful well we're we lit out the front

here so these are so what what what spacecraft was this so these are bits of instruments that we flew on the cluster spacecraft so there's four of them actually so four of them all the same rocket all on the same rocket and they posted them back to the lab yes so when the rocket officer came down as you said not that long after launch and it fell into the swamp in French Guiana and so the European Space Agency he had people who could go out and rescue the rocket and get the pieces back so we

then got our instruments sent back and apparently I wasn't there at the time but the story goes that we got the box and they opened it up and there were still bits of swamp in it and bits of our instrument so this is one of the brains of one of the instruments on cluster so we built the instrument that measures what we can talk about what the mission did but it was sent up to study the environments around the earth so the magnetic field of the earth and the particle environment and this is the brains

of the instrument that measured the electrons in the environments around the earth and what research do you do you 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 mission was designed to study space weather so one of the things it did was look at the physical processes behind the generation of the Aurora the Northern Lights and the Aurora are generated by solar activity that sounds useful I mean I say what do you do like

I don't know I'm actually married to Lucy just yes because otherwise I thought was quite convincing if your parents are watching they're like he never asked we've got meteorite rings look at us nerds you go those fights fine I assume you're wearing it okay so you read the clothes by the way because why do you have to wear gloves handling this well because we think it's probably still covered in rocket fuel so and that's not good for you I don't want to get on my hands and eat my dinner later but I mean it's pretty

cool to see these bits that are completely mangled up and normally our instruments don't come back so these bits were built in our laboratories and we've got them back again I think I'm one of them there was a little tag that said UCL's Mullard Space Science Laboratory someone's like you know if found please send it home to us they figured that would take you know millions of years and be some distant civilization but no it was and so when you arrive you you started working there just after this had happened just after this has happened

so when we launched the spacecraft of course we want to have a big party of one gets together to celebrate and they'd bought champagne to drink after the launch and I arrived about two years later and that champagne was still there sadly under UNK yeah but I mean we could talk about the success story because we did go on to rebuild these instruments so they launched again they were launched again yes so the European Space Agency gave us the money to rebuild the instruments and it took much less time so within four years they had

been rebuilt and relaunched and they're still running and they're still running so we launched in 2000 and what are we now 2019 the ones are in space now are still operating successfully because it blew up in 96 so they really did turn around quite quick yeah yeah and so we actually we were chatting to a friend of yours and we didn't really last night we were chatting to a friend and she was like oh I was watching the livestream because my PhD was going to be on Cluster and so she was a first year PhD

student watching the livestream and we were like what happened and she was like the room was silent and then everybody left wow he's like well different PhD I guess so where do these live now so these live in my departments and we have some on display because as I said we built four instruments and we've got quite a lot of this mangled hardware and we we're yeah we keep them out we talk to people about the mission talk about what we would what you know what we did successfully to launch again and I think it

just serves as a reminder that it doesn't always okay so we will wheel these off before I actually touch them so a big round already have a professor Lucy Greene people spend so long working on a spacecraft like a miche's decades to get it to work and they have some of them out in the coffee room at the lab right just like in the glass case so a reminder for the next generation of space scientists that your decades of work may disappear in a fraction of a second and land in a swamp and what happened

with that was there was one sensor in the navigation part of the Ariane 5 rocket which well so this part of the rocket took input from several sensors it took the raw data coming in from those sensors converted it into meaningful navigation information and then sent that to the main processor that was kind of driving the rocket if you will and when the numbers were coming in they had to work out how big they were gonna be cuz you have to allocate a certain amount of memory and they tended to allocate just 16 bits 16

ones and zeros for a value coming in but some of them might be bigger they could be up to 64 and so what they did because they could have just written something in the program which was for every input that comes in check how big it is before you try and send it into the memory but that's quite processor intensive and they had quite you know strict limitations on you know how much power they were allowed to use and so instead of checking every single sensor they looked for all the sensors which could give a

number bigger than 16 binary digits and they would check those to avoid any problems and the ones that never could be that big they didn't bother checking right and they could save some processing and that all worked really really well on the Ariane 4 they then copied it into the Ariane 5 without double checking and because of a different takeoff trajectory and because of the way the sensors worked one of the sensors that previously wasn't being checked well continued to not be checked but now should have been checked and it actually didn't have to be

on they just left it on after launch it was a pre launch sensor because if there was ever a go to launch and then they aborted before takeoff and then they reset it took forever to reset so they didn't turn them off straight away they let them run while and then turn them off once they were sure it was definitely you know safe however it continued to run as it took off it got a value that was too big it didn't fit in the memory it put it in it rolled over to the memory next

to it and the whole thing crashed and what would you know of itself wouldn't have been the worst thing because it could have been a restarted or something except it was designed to give a crash report so you know like the stereotypical someone's like oh you know tell my spouse I love them right but this is like ah tell my debugger the following crash context information right and so it sent the debug message up the same link to the main processor which didn't know that could happen it thought it was navigation data thought the rocket

had suddenly got off to one side tried to correct it hadn't gone off to one side and the correction threw it off to one side it tore it apart the self-destruct sequence kicked in and because a 64 digit number was tried to put in a 16 digit space right this whole rocket exploded and possibly because the spacecraft weren't insured which is amazing how every third did decide to refund it right so one slight mass error can have phenomenal implications and that is pretty much it from me I guess in conclusion I started with the theory

of mistakes important and in some cases yes we have to get the mass right I mean we'll get it wrong occasionally but we have to get it right in a lot of these critical situations and that means we need people who were good at mass and repair to put the effort in because with maths we can do more than our brains were originally built to do right we can go beyond our intuition which i think is incredible but ironically to get mathematicians and people who are prepared to put the effort in a work hard and

more importantly come up with systems that accept that humans will make mistakes and we can use our same mathematical logic to have robust systems where mistakes don't become disasters to have all of that we need people who weren't afraid to make mistakes to learn mathematics right so I guess the other goal of my book as well they're showing people all the incredible critical mathematics that underpins our Society I also wanted to encourage people to haven't go maths is difficult but the people who enjoy maths and not the people who find it easy they're the people

who enjoy how difficult it is it's hard work you get it wrong but gradually it would teach your brain how to think and gradually you will get better and better at mathematics so I will be around physically here signing books if you want to get one afterwards this video will end up on the internet if you're watching it on the internet you can order it from that is not a mistake in the URL it only works if you put the dot in the wrong spot because I think I am hilarious actually penguin will like but

it doesn't work if you put like an humble - PI comm doesn't work I don't like yeah people have to earn the book like we don't think you've understood marketing that so I will also be around signing books and calculators at this point though I am done thank you so much for your patience thank you so much for making that work