LMS Popular Lecture Series 2010, Clutching at Random Straws, Matt Parker

all right thank you very much for a very kind introduction as you're aware the title of my talk is clutching at random straws most its information was just presented to you my name is Matt Parker as advertised I'm based at Queen Mary University of London in East London and this is my email address and I'll put this up again at the end if you've got any questions or overly elaborate heckles and the like you're welcome to email them to me I should point out though and this was mentioned before it came up in the phrase stand up maths there's only two rule promises that I'm committing to one I will be standing up done and that's which believe me is about to occur there is no guarantee of entertainment although just for you tonight I have written and will deliver a joke and I'm cut I thought it's quite the joke I'm looking forward to this and if you are on Twitter if you include the @ symbol that's me on Twitter although don't attempt to do that during the lecture or I will victimize anyone a who I spot using a phone or if any of them ring I'm totally qualified to confiscate an answer in that order any course I will any calls that come in because I actually I used to work up you guys had a little group discussion single boom there see I can detect people talking as like a teaching ninja by gesture wouldn't that be great a maths ninja instead of sure consult Rosa Joshi it gets better I used to work as a math teacher originally I went to the University of Western Australia and I started off studying of all things mechanical engineering before I realized the very real risk of me being employable at the end of it so I switched into physics and and then into maths and absolutely loved maths and that's when I thought what can I do for a living where I just get to talk about maths so became a maths teacher I moved to London after having taught in Australia for a bit I taught in London for a while and then I got into kind of support education so I work with universities and other organizations to do talks about maths and how much I enjoy maths and someone opened a can of drink we've been through this where I have what is it no it is not television I can see you did we're having a conversation it's a non-consensual conversation I'll give you that much but it's happening what are you enjoying Pepsi oh you can keep that right coke or better you'd be in trouble right now ah okay okay I'd be nice to you guys from now on that's what we're yeah pops from Pepsi boy it's on you and group theory lat both of you are what one false move from either of you for those of you watching the DVD it's a hilarious reference to the previous lecture anyway I've only got a finite amount of time for this as well anyway what I was apt to fire yeah so I worked with some universities for a while I started as the teachers here will appreciate I started to get a bit nostalgic for the classroom so just recently I went back to two terms I thought it's only going to be six months I can survive a lot so I went to a North London comprehensive school for two terms and that just that cleared that right up I'm good with teaching now so now I'm based at Queen Mary University I'm in the math department and because they ask very nicely a dabble in the physics department and it's my job to both work with the academics and the students and then post grads and whatnot to help them communicate their maths and what they do to other people and I go into schools and do to do talks like this and I have the joy of doing bit of media work and writing about maths and generally anything I can do to get more people more excited about maths and just to see where the audience is at I'm going to do a quick informal survey if you I'll state my definition first if you are a math teacher or a mathematician or an overly passionate math student are going to classify you as in the math friendly group or the mass friendly people give me a cheer now and one round of applause who is that well well there you go well thank you very much the trouble with applause as you will notice very much a group activity but it was a good start and everyone everyone who is in the compliment set the other people give me a cheer now at the back of course don't think I can't see you have established that I like to tie to check the people I'm talking to and if I'm not in a situation where I can do an informal survey I have a very simple litmus test if you will let me know how any given math talk is going to go and you guys have passed in flying colors because of this guy here serve the glasses and a very nice beer would you mind standing up for a second just yet I know a gig will go well if someone's made their shirt out of graph paper that is a good sign anyway my talk today I'll explain more about what I'll be talking about but I thought before I even do that you know you know it involves randomness and they're both clutching at things I thought I would just start by showing you what got me into this area to start with and it was on my way actually all done the tube on the way to Queen Mary one morning and I was flicking through the fine scientific journal known as the Daily Mail and I came kind of a punchline that's long there isn't and I came across this article here and this is the picture that went with the article there were words and it was a retired marketing executive who lives in Devon and what he had done has gone through and taken all the ancient prehistoric kind of monolithic sites in the UK put them on a map join them up with some lines and discovered that some of them wait for it form triangles I haven't not just any triangles there there was some equilateral triangles there were some isosceles triangles and they got very excited about these and he wrote to all sorts of various publications they talking about these triangles and his theory was that these triangles were so precise they must have been done on purpose he actually said you cannot do that by chance these triangles are so precise the isosceles triangles are so precise the elektra ones are so spot-on and his theory was that there was some form of ancient sat-nav or that there were a way of navigating so you would use these incredible triangles to navigate from one spot to the next and he figured that the ancients are living in the UK had positioned these sites partly for that purpose and he actually said I haven't put it up on the screen here he said he couldn't rule out extraterrestrial help so precise were these triangles now some of you are shaking your head in a skeptical fashion I thought well maybe he's onto something maybe I mean these are I don't get me wrong the triangles he found are incredibly precise and so I got to work went up to my office in the mass building and thought I if I could use this same technique and so I did here is a map of the UK centered around where we are right now in Birmingham and I looked up where a whole set of ancient sites were and I found three of them that go right around Birmingham and form an incredibly precise equilateral triangle within a percent accuracy and I thought well I've got to step this up a notch two isosceles and so I found two more sites on either side that give isosceles triangles within half a percent accuracy and indeed another two sites which can extend a bigger I saw so there are soft leads within half a percent of the two sides that should be the same length and then I took I extended the base of the equilateral triangle and I put the perpendicular bisector through it and formed this cross structure centered around four additional sites and just to show you how accurate this is that the base line goes right through the base of my working triangle up here is Conway down here is Luton this line is one hundred and seventy three point eight miles long it is within 40 feet of the Conway site it is within 30 feet of the Luton site these are mind-numbing ly precise geometric arrangements and I've just amazed how the unfortunate thing was I wasn't looking at prehistoric ancient sites the ancient sites I was looking at are the old Woolworths stores please they're there if you want a copy of these I will email them to you later these are where we'll wear stores used to be and they do form these incredibly precise triangles and so I mean but we don't know what they use them for I mean who knows how the ancient loom where civilization lived I mean how did they well how did they buy discount CDs and cheap kitchen Goods we just don't know we can investigate it that with this and at this point to be honest I can't rule out extraterrestrial help Chris how else could they offer the Lady Bird clothing range it's up low low prices anyway ah these are the real stores they are that accurate I wrote this up as a pseudo I haven't published this as a real paper any mathematicians who wish to lend some of their time to me I'm keen to do some more with this but I put out a press release which is a lovely thing to do and it was picked up by bits of media and I got media coverage of the ancient Woolworths civilization research that I was doing and a lot of our archaeological kind of magazines wrote to me and said look we really appreciate what you've done because now we know this kind of it bit of a crackpot ah be careful what I say here so we know that these triangles could have happened by accident because they have happened by accident with the Woolworths stores in fact if you look at all the Woolworths stores in the UK I had all of these to choose from it's it's not hard to find triangles when you've got that many sites I literally printed out the Google map of the UK with all the sites on it and got the ruler and just worked around until I found these and then put the locations into the computer and crunch the actual numbers for the alignments and how accurate it was and then put it out as just a case of I had enough data admittedly effectively random data I had enough of it that I could just flip through find the few sites that matched what I was after and ignored the rest of them and that is the whole point of the talk I want to do today is that if you've got enough data you can find patterns that no meaning to them they're only there because you've got enough data but if you're prepared to ignore most of your data you can pull one of these patterns out and prove pretty much anything you want um one of the best things about doing this I got an email from a math department which oh I shouldn't get this wrong I think I look Liverpool I think it was limp all-university someone sent me an e-mail is it in their group that I've now got a new expression for when people are selectively analyzing data it's called pick-and-mix data analysis that's brilliant uh but there's a whole area of maths it's called Ramsey theory if people want to look it up afterwards and the idea is if you get enough data you can find any pattern you want but more than that if you have a sufficient amount of random data you can find any pattern you want to any level of accuracy that you want you just need enough data to start with and I thought I'd illustrate this with a simplified version of Woolworths so imagine this rectangle which is ever so slightly off to the left is our entire world and we're looking for equilateral triangles when we get random points put on this surface so let's say we've got one point there no triangles yet we've got another point over here still no triangles now at this point the next spot we put in if it falls into either of these two zones we will have an equilateral triangle and the size of that disc is the level of accuracy I'm after if I wanted more accurate triangles I could have smaller disks if I thought I don't care so much we can have bigger disks as the next point comes along and let's say I miss those days up there now all these spots have opened up as potential equilateral triangles if the next dot doesn't fall in those these spots would now give me an equilateral triangle if I miss those now these spots open and after a while it becomes more likely that we will get an equilateral triangle than we want and with enough data it becomes inevitable we're given on your level of accuracy so I give the smaller I make these dots I just put more and more points in until it's impossible to not have an collateral triangle and it's bordering on something called the pigeonhole the personal concept will run with that where often you can tell that something has happened just because you've had enough data as such and a great example that is with the room here I checked and there were 350 tickets sent out for the talk tonight and with other people in the room and whatnot we're dangerously close to three hundred and sixty-five people in this room but if you imagine it if we all started outside the room and we started sending people in and we said we look we've got this great idea for seating we've marked all the seats with a day of the year find whichever seat has your birthday on it and sit there and we start sending people in sooner or later there will be a chance that someone's going to walk up and find someone else is already in their seat there's a chance that two people in here will have the same birthday and if we send in more and more people it greatly becomes more and more likely that's going to have happened and at what some point once you have sent in 365 people conceivably everyone is sitting in a different seat or if we include leap years if you send 366 people you'd know that there could could possibly one person could be in every single to be incredibly unlikely but it could happen the moment you send in the 360 seventh person they have to sit in a seat with someone else already there and if we then send another 365 people eventually would be guaranteed that three people in here would share a birthday so that becomes a point we have enough people in the room it's inevitable that there will be a birthday in common now that's in the extreme case now what's interesting and this is a slightly different concept and I will elaborate on this afterwards but it's curious to think how many people would it take where's that crossing point between where it's unlikely two people are sharing a birthday to where it's likely and a lot of people have heard this it's called the birthday problem and we're going to do it here today live in front of you but I want you to don't call anything up and just have a think how many people you think it would take in a room so just imagine you in a room with loads of other people for there to be a greater than 50% chance as a birthday command people have seen this before I'm also curious where the 70% line is so if you know how many people it takes 50% see if you can have a guess at 70% just to keep the game fresh now we can work this out we can do this with maths and the best way to do it is to imagine you've got a party so I've got a picture up here with my there's my room this is this is a party in progress this bear with me here and what I've done with my parties I've made everyone leave the party go outside queue up and I'm going to bring them back into the party one person at a time and I'm going to keep track of what the probability is that there's a birthday in common so the first guy comes back into the park and he's very happy to be back and at the moment he can't share a birthday with anyone and so now it's a hundred percent chance there are no birthdays in common we bring in the second guy who's even happier to be back now there's a chance their birthday is the same there's a chance their birthday is different because the maths is slightly easier I'm going to look at the probability their birthdays are different I'm going to ignore leap years for now because without leap years when the second guy comes in his birthday just has to be different to the first guy and there are 364 possible days at a 365 where his birthday is different so that's our probability that his birthday is different quite high we then bring in the next guy who promptly has a seizure a hump and there's now 363 days that his birthday could be so we need the first guys to be different to lose the second guys be different from the first guy and the third guy to be different from the second guy and the first guy so we multiply this by the 360 365 chance the third guy is different to the first two we bring in the next guy yeah I got nothing for that and we then multiply that are running toes would buy the 262 days his birthday and we can carry all the way down and so you gradually fill the room with people and you keep track of fractions now a few people very correctly and now thinking that this doesn't look much like a party I'd like to say if you're thinking that you're completely wrong this is one joke enjoy don't forget it forget it that was that was dramatically funnier on the inside of my head than there you will do this is a table right so over here we've got the number of people in the room we've got the point during their birthday is different and we can do this as our fractions which we had to start with we can then take those fractions convert them into set percentage and then to get the probability of one or more birthdays in common we detect the complementary probability and we can run that all the way down here and by five people it's only 2.7 percent not dramatically high and by the time you get down to ten people it's an eleven point seven percent now think of the number where you think the 50% line is if you come all the way down it's actually at twenty we're at forty percent there is that twenty-three people the moment you have 23 people in a room there's a better than 50% chance there's a birthday in common and for the people trying to guess seventy percent that's down here at thirty thirty people in a room seventy percent now we have a dramatic leap where we got a much bigger group in 30 so we can test this because the math does not agree with our intuition our intuition most people I ask what they think the probability is they guess between one and 200 on average but yet the actual number is 23 so we're going to check and we're going to do this quite systematically and what we're going to do is I'm going to use the front row to styling I'll start with you sir I'm going to come across the front row and we're going to weave our way back and the way this works is when I point at you I'll go first and show you when I point at you court your birthday not the year just the date so I don't think make sure you know your birthday it's it's really embarrassing if you do it'll arias for me embarrassing for you when I point at you shout it out so for example my birthday is a 22nd of December and so as I go around if you hear your birthday called out don't ruin the surprise if you hear it it's your job to remain completely calm wait until I get all the way along go give it away when I get to you that's your moment to explode what I want X you can you jump up this is compulsory jump up and shout my birthday is a 22nd of December or whatever my birthday isn't so birthday here same as that got and this is also compulsory and point out whoever it is whose birthday the sake I already okay here we go without talking okay here guy are you ready except 21st of a 21st of April 4th of Elka's 4th of August 7th you could you lie 17th of July 11th of December 1st of January 1st of January 17th of August 17th of August very confident good it seemed to shove your 13th of Feb 2 of August 12th of August 1st of April 1st of April 12th of May proper holiday way ok no matches yet ok 1 2 3 4 5 6 7 8 9 10 11 okay we've gone through 11 where's 11 hey wait sorry sorry ok 14.1% chance that will have worked so far a much greater chance at worth of works I'm not nervous just yet ok where are we up to mrs. 20 of lemberg 28 booth December December 14 of August 14th of August 7 September 7th of September 18th of June I think the June 10th of October 10th of October 20 said 23rd of March I can hold that 11 12 13 14 15 16 17 still not nervous 30% now just as a challenge for the microphone people next row back sir we go 27th of March 27th of March 15th of April 15th of April 19th of June 19th of June 3rd of April 3rd of April 30th of January 30th of January 22 2013 would you do a favor district feedback 23rd today hasn't changed yep you're trying to hack into my email aren't you and now do the same game with mother's maiden names no 5th of November what fifth of November November 25th of July holiday hold it there hold it there where were we up to 11 12 13 14 15 16 17 18 19 20 21 3 to 23 24 25 so at the moment 57% chance so now I start getting marbly nervous I won't get truly nervous until the end of the front row 22nd of January 22nd of January 17th of September 17th of September 1st through December 1st of December December 18th I take them I'll mess with the format hey 21st of June 21st of June so it's October 30th of October 19th of December 19th of December 17th of July which is the same as yours pause the cameras can we try to go do it again we'll go back one everyone Angie producer faces back on 90th December yes and you sir at 17th of July the segment yeah should be able to have a close anyway m39 1333 people okay and this is a quick test we only called up 33 people's birthdays if you'd heard your birthday put your hand up now whoo okay so a substantial number and that's just calling out these it goes up exponentially the further along we go I think this is phenomenal this is a great example of counterintuitive probability and I'm going to go through a series of things in this talk which are why we leap to the conclusion we reach our conclusions based on patterns and evidence which in fact are meaningless and the first way that we jump to meaningless conclusions is when we don't appreciate just how much data there was and we'll just selectively picked out the bits that match what we want the next thing I'm talking about is that we often did appreciate just how likely some things are if you meet someone with the same birthdays you you get amazed if you believed in fate related things you could attach all sorts of meaning to that and in fact meaning something with the same birthday as you is quite unlikely but you do meet hundreds of people and if you don't care who it is so we didn't get to something the same birthday as me we're just looking for any match and that gets incredibly likely very quickly and you can actually use this to win hypothetical money off your friends if you're so inclined because if you look at the graph and I do enjoy drawing graphs and on the x-axis you have the number of people in the room y-axis probability of there being a birthday in common the graph starts zero and flies up very sharply and then flattens out and our 30 people line is up there at about 70% probability by the time you get to 60 people that is over 99 percent and it will sit just below a hundred percent all the way along until you get 360 well 365 or six or so depending on how you're doing your calculation but once you get there it's almost it's mind-numbing Li likely for me though 70 percent is pretty good because 70 percent of time I do that I get it within the first 30 the other 30 percent I don't so what you can do right is the next time you're in a room with 30 people or more you just bet someone 10 quid there's a birthday in common and seven hypothetically and 70 percent of the time you will win baby sometime you will lose and today I would have lost I would have lost 10 pounds on this but that's the great thing about probability even though you don't know if you will win or lose you know what will happen in the long run and should you simulate your results and plot them on a graph and I do enjoy drawing graphs ah it will look a bit like this some of the times you will win and your takings will go up and sometimes you lose and they'll go down number of bets on the x-axis money on the Y and in fact I mean here there's a big losing streak a couple in a row there but you know if you win more often than you lose over time you have to go up its our casinos work that they hire mathematicians and experts to make sure every single game there's a slightly greater chance the casino will win then you will so even though some people win some people lose overtime the casino always wins more than it loses they can't help but make money in the long run so I hope you're not covering up your graph paper t-shirts with a is it a gray cardi that is acceptable carry on yeah um and I have the Pepsi going we're good cute cute and group 3 boy any comments yet nope Marvis just thought I'd check in with all the people who have met I think there will be more uh-huh yeah good just to keeping everything under wraps somebody troll good good good I rely on you to keep conscious anyway I'd like to show you another example based on a very similar concept I've got three packs of cards here and I'm going to give them to three volunteers one of which has to be you hey I can you take those and can you start shuffling them someone over here who looks oddly interested you and then someone they are some of the back cooking cooking catch you guys are way over optimistic ready ready go now if you've got a pack of cards can you start shuffling them so that you think they're in a random order and just there's a full deck they are they started in a random order I gave them a pre shuffle and this has actually been done as a magic trick a magician will get someone to shuffle cards you could hypothetically bet hypothetical money on the outcome and you will say I bet while you're shuffling these cars I can control them I can control specifically the king and the Queen I will make the King end up next to the Queen or most one card apart get them to shuffle for a while then get them to check if you got the cards can you flick through now see if there's a king next to a queen or at most one card apart so a king something else then the Queen can you ever flick through and you're just showing off now aren't you this now you decide to shine not when I needed you okay you can you have a flick through and see if my not one card at a time just you think I want to live my lesson laughs my window that's okay can you ever look through let me know if you found the next to each other next to up the back next to and then over here yeah I'm gonna go with yes you did you don't like a three next to each other give these guys a huge round if I said what are the chances if you shuffle a pack of cards that the King ends up next to the Queen you would think that would be quite an unlikely event but we just had to occur three times in a row and I have actually got enough quite are quite lucky actually next to each other comes out at about 48 percent probability and I'm being vague for a reason I'll explain in a moment and next to all one apart is more than sixty seven point two percent and I've heard arguments it's about 74 percent it's not as easy to work out as you would think if you're bored have a go it's a brilliant activity start with next two and you should get something about 48 percent if you try and work it out logically and then if you've got a handle on that have a go at next two or one apart I've seen I've seen people argue that it should be about 74 percent in theory and I've seen people simulate it and come out at about 67 percent but it both methods are trickier than mate than you expect so please do have a go not not now some people are know yes you with the pen I can see I was good and the show adding a note to the person next to you you wouldn't believe what he's asking us to do now is yaddam it maybe tonight tomorrow night you're busy tonight maybe tomorrow night invite some friends over right have a mass party yes you've had a mass party they're great aren't they and so you can all talk later you can you can you get on really well with group Theory guy all I'll introduce you guys afterwards seriously anyway um whether or not add a bath party you can try and work it out and it's harder than you think but it is without a doubt more likely than you expect it's yet another case where our expectations is for a much lower probability than actually happens again partly it's because you underestimate the number of opportunities it's had to happen there are a lot of pairings in a pack of cards and even though it is quite an unlikely event there's a lot of opportunities for it to happen same with the birthday thing there are a lot of pairings by the time we get to 30 people that even something quite unlikely becomes very likely my all-time favorite example of this is this photograph here this is a photograph taken in Disneyland and dick did you learn that are they annoy me for several mathematical reasons but one of them is is there a just assault on the notion of scale how can you have a giant version of a dwarf no one part of that makes sense in any way the point the point in case here is this this character here with her arrow not mine is indicating Donner this is a kid a photo from when she was a kid she's now growing up and she was sitting down with her fiance Alex and they were flicking through photos of her childhood because we all know that's an enthralling experience and and they were looking at the photos of her trip to Disneyland and Alex looked at I went wait a minute that guy in the background that looks like my dad and that is Alex they didn't meet until decades after this photo was taken but in their childhood they were accidently photographed together just because they happen to be at Disneyland on the same day and I think that is amazing this ranks as one of my all-time favorite photos this is I think this is absolutely phenomenal and for the people involved it's amazing for these guys I mean what a thing to have and they check they got photos from Alex's trip and compared and his dad was wearing exactly what he's wearing in the background of this photo an incredibly unlikely event but I would argue that despite being an amazing unlikely event it is still to be expected just due to the sheer number of photographs that we all appear in if you think how many times across the course of your life particularly now you've been photographed it with other random people in the background and you try and work out how many random people you've been photographed with it's it's not as alarmingly unlikely it's do my numbing Lee unlikely but not quite as mind-numbing Lee and then if you think that that applies to every single one of us there are so many opportunities for one of us to happen to been photographed with someone that we then met later on in life so it's a bit like winning the lottery in my mind it's amazing if it happens to you but it shouldn't be a surprise that it happens at all a very unlikely event will still occur if they have enough opportunities with enough opportunities that come inevitable and this is a kind of my my second and a half point there are things that we think are really unlikely in fact they're much more likely and a lot of the times we don't appreciate just how many opportunities something has had to happen I don't want to diminish amazing things when they happen these these freaky coincidences are amazing but we shouldn't be surprised when they happen we should be more freaked out if they never happened because then we know something strange is up but the fact they do occur periodically and if you never have anything freaky happen throughout your life you'd be unlucky if something amazing does happen then that that's kind of your allotment I guess you could say and enjoy it is phenomenal but it doesn't mean it's unexpected I think I've laid at that point sufficiently I'll labor it some more afterwards please come and see me if you require more laboring hi anyway I did actually write down important points I wanted to get through okay here we go this is kind of fun moving into my third point we want to see patterns as humans we thrive on patterns and I think that's great originally I mean I'm not very good with our biology and the like but you can see why evolving the ability to search out patterns and to be hyper sensitive to rounding up risk very good survival tactics and the notion of but we spot patterns we round up to the nearest pattern is what I'm trying to say here and that's a great thing to have and it's the reason we do Matt it's because we love spotting and working with patterns as why mathematics exists partly people can come and argue with me afterwards but I will label you and I think that is great but we forget just how tuned we are to wanting to see patterns where there may not be any and one of my all-time favorite examples of this is what's called backmasking which is where a band is recording an album and they're laying down the songs anything guys guys you know house taken is our unholy master we should record some messages about him backwards and hide them in the song and this was all the rage in the 70s and 80s and and people used to I'd either I don't want to I don't want to speculate who sits at home listening to album after album backwards in the hope they will find someone trying to brainwash the youth of work now yesterday but they're still going so here's an example this for those of you who are unfamiliar is a lady Gaga her husband Lord Gaga is not featured in this photo and you should all be ashamed for laughing at that I should make that very clear anyway she had a hit who has several hits and one of them was pepper Otzi and if you're unfamiliar with it it goes not unlike won't see it sue was dying blah blah blah so okay that's the song for words I'm now going to play part of it backwards see if you can spot what people think this says here we go any guesses they don't want to hazard a guess even a word they think might be in there Lucifer very good guess Beelzebub nice just you try and top top Trump his number of syllables I so you say maybe loose of Emilia's what no one heard evil save us the stars above above we model it on the arts of Lucifer - points - you thought you had exactly that word it might be best for you to leave by a different exit are you a teacher a little bit I dabble I'm not invite to the school but I go I'm liking you more and more anyway I'll play it again watch this and you will hear this word for work you look I'm convinced nothing you can't the second time through I'll bring it up again now people often aren't convinced just how important the suggestion is people think maybe you hear it a few times your start that you start to spot it or recording each time and I want to clear all those notions out I want to show you it is solely the fact that you have been like biased before you hear it and if you're biased you will spot the words if you're not you won't and to do that and you use a different song this is a freddie from queen who was gay who knew you should be more ashamed of that so getting the lady go anyway quite a nice song another one another one another one buster done if you when you go home you can download it having paid but legally on iTunes if you want print laugh at that this guy's here going I'm gonna do it illegally I'm gonna play it backwards if you think you hear what this is don't call it out just see if you can work it out I'm gonna learn the same bit over and over here we go right some people think they might have here's what we're going to do and then this relies on you playing along correctly I guess that the room in half so down here right down the middle there this whole half here I want you to when I say go not now you're going to close your eyes and this half I'm going to show you what he saying so this half will know this half will not I you guys are actually the lucky side to be more amazing for you okay ready if you're on this side close your eyes now everyone on this side don't call it out that that is what he's saying okay this side open your eyes again I'm going to play it again if you can hear this put your hand up I think that is absolutely amazing that it is if you had that suggestion you will hear that over and over again if you haven't been primed we want and this comes up time and time again if you're told there is a pattern you will spot it and now all this stuff starts to come together so if you get enough random data and first of all you're told there's going to be a pattern you'll be searching for it if you have enough data you will find it and if you're unaware of just how likely it becomes you will think it's amazing when in fact it's unavoidable and it means that we are constantly coming across people who will back up their argument with with patterns and with evidence that simply does not stand up but that's why we have science that's why we have maths it's so we can overcome our human intuition and actually get to the cause of the problem and actually see is this a significant finding or is it just random noise that is the beauty of maths maths exist separate to our brains maths doesn't care how our brains work it exists but we can use it and we can learn how to think in ways our brains normally wouldn't and we can use it to overcome this problem and so for example I just very quickly I've got a little bit of spare time there's a problem when you do surveys like food testing surveys that you don't know if the results you're getting a significant or not so if you wanted to decide between Kohler a and Cola be you so drinking Cola B and so you asked a bunch of people here drink Collard a drink call the Beatles which one you prefer if one of them does genuinely taste better or whatever you're trying to find out you should get more results that say Kol array of a Cola B or whatever your investigation is if however they are actually identical people are still going to pick one or the other so you ask one person call the raid call abhi they say caller a you go very nice you ask someone else caller a call the B they pick caller a you go well it must be caller a tastes better or so what's called the null hypothesis assuming that there is absolutely nothing to assume both the drinks are the same assume the medication doesn't work assume that there isn't another planet around that star whatever the zero case option is assume that and see how likely the outcome is now and if both caller identical you can say well if they're picking perfectly at random there's a 25% chance I would have got this result and now that's not it's a 25% chance that there is nothing to find it's saying if there is nothing to find this is a 25% chance you get these results it's subtle but that's the power of maps we can pin this right down and it's generally agreed if you get that probability down to under 5% you found something worthwhile bigger than 5% you need to put a bit more work or do more studies or maybe there is nothing and we can do these things properly if people just pluck out random locations in the UK and make triangles and pick the ones that fit and then and then publish it in the potentially not peer-reviewed Daily Mail then these things go straight into the public eye and this this is where I'm going to go into my call to arms phase which is why I asked for the close-up shot you notice also I asked very nicely if they could organise me to have a piano on stage which they did we should there was going to be my closing number but I don't think I'm going to have enough time to fit it in but they that was very good at them too and I said look don't just put it there make sure you put a crash barrier in in case the crowd rushes forwards Thank You University of Birmingham but I'm not going to be using it well are you called to arms I hope they're with me here um if mathematicians don't speak up if scientists don't speak up for what is good science and what is good maths then people will put out these crazy stories and it will look like it's good because they will have evidence they'll have data unless people come out and say well actually this is how science works this is how we do the maths you can find these patterns or it's more likely than you think or that's because you were looking for it then the pseudoscience stuff will continue and I'm adamant that we need more people mathematicians prepared to step out into the media domain and do this and so if I can get one passionate plea is if we don't people want to hear about scientific breakthrough they want to hear about good maths and if we don't fill that void crazy people will and so read to get there and do it if the crazy people speak up we should say something and and this is kind of I call it the specialism fallacy in in science where scientists are so used to having their specialism and they won't speak outside that which works wonders in science but if you're the person thinking am i quite qualified to speak about this it's not quite my area you're exactly the person just that thought process alone means that you have someone who should be out there speaking up for logic and I've got a whole rant about homeopathic remedies that I'm not going to do now but these things continue if people aren't prepared to say this is how we do science this is how we know what works that is a pattern that has no meaning behind it and I'm done for my rant that's it my my opinions on homeopathic remedies are a matter of public record I'm being careful I don't want this to all go off Simon Singh on me if you will uh-huh anyway I thought I would end with one of my all-time favorite examples of if you have enough data you can find whatever you want actually any guesses they don't want to hazard a guess what I haven't covered what was that what the Bible the Bible if you write enough books that your spot no he's right it's the Bible code I would like to end to talk briefly about the Bible code and the Bible code goes like this you get part of the Bible and you should do this in the original Hebrew or for ancient Greek New Testament Greek or whatever it was originally written in white today you take the spaces out and I'm going to do it for the purposes of this in English this is the NIV translation this is a first Kings chapter four verses 13 to 23 in case you're playing along at home and I'm not saying anything about the Bible as a religious text I'm just saying if you take any book and you take out the spaces you end up with a grid of words now the way the Bible code works is they look at all these letters and they ignore the original surface reading the original text and you try and find hidden words by starting with one letter skipping a set amount to another letter skipping a set amount to the next letter and you spell that hidden words so I thought I would check the Bible for any predictions about today because what people do is they go back and they say i if you jump every 17th letter this spells out one word and if it's been this way another word and it was a prediction of the assassination of someone or a particular tragedy or whatever and they can so all these words crossed and predicted this was going to happen so I checked this morning before I started if there's anything for today and some of you may have spotted the word 20 is here and that's just in the text as such the word 20 and that is allowed that's just a jump of one letter each time but it's not the 20th today it's the 29th and so the word 9 appears up there and jump I jump and jump 8 equal distance each time and because the way I've wrapped the text it means they line up because there I've got the same number of letters per line so the 29 of September area septa I got bored so 29 September all crossed in this part of the Bible in first Kings chapter 4 and so this must be the bit about today and what's happening today well I'm here giving a talk to you as was a Dorothea buck and so here is Matt em it's thirty letters M thirty letters a thirty letters T thirty letters the next team Matt bang on and some of you will have spotted down here buck there we go so Matt and buck will be giving a talk at all about what you would want to know so I had a closer look and Dorothy was talking about here at camp where where is the music I can spot it there is that K jump one n jump one OH jump one T talking about a knot there you go and I'm talking about odds here we are odds that legs I'm getting a bit creepy now the more the more OCD of you will have spotted and I'm not even going to point this out but at the top here where is it where is it ah there it is ah Matt look at that Matt but I'm not going to highlight that if it had been mathematics or maths or any other actual word I would have highlight not good enough and this is freaky but it's exactly the same thing I could find today's date with both of the speaker's names and both of the topics we're talking about because there's just so many letters to do you think of how many letters in the Bible and for each of those how many different jumps you can do from it that it just becomes inevitable I've been the talk a few times and I can always find a prediction for me during the talk every single time and it is just because the sheer amount of data so I want to end on on the the three ways that you end up thinking as part of a pan you've got enough data you can find anything you want we want to find these patterns and we don't appreciate just how likely some of them are and I thought just to show you just as a finishing point the predictive power of this because some save you are still looking for words I can tell and and I'll save some of you the pain to predict what's going to happen in the future because there's still some of today left who knows what could happen today we should check well the word drink appears there this is more aimed at the organizers and those of you above 18 but bear with me but drink what you're thinking of course al appears at the top there so I hope that's inevitable and I'm going to finish by taking that e taking that D in between it exactly is an N so we've got the word end there and it's there and it's there and there and there and there and one other that's all them there are actually ten of them where are we so I should bet that are there six there another four to find um if you get bored but I am going to end on that you guys have been fantastic thank you very much an evolutionary advantage being able to spot patterns but surely there's also an evolutionary advantage to being able to calculate risks accurately why are we so bad at it the question was I mentioned in Ocean Airy benefits of the spotting patterns but wouldn't there be an advantage to be able to calculate risks and I'm not an evolutionary biologist or behaviorist or or any house of thinkers would be but to my layer understanding of this you want to overestimate your risk because there's no harm in running away if there wasn't a danger but there's a big price to pay if you don't run away and there is danger and so we are hard-wired to overestimate the odds of something happening because a false positive is dramatically safer than getting eaten by a mammoth that sentence got less factually corrected that went on everyone fill in your own hilarious prehistoric animal it's only chance of you actually playing the piano no no not only is it small it's zero that's I was wondering whether you've heard of kind of a pattern that was spotted in like this text on contem computer call winnings we typed it you've heard of a a veneer but the font yes yeah technically typeface and seeing how we're all parents here right yeah and you typed in 911 and then the airplane number that crap okay this was if you get the wind windings font slash typeface ah and you bring it up and what Microsoft thought was it would be a good way to have lots it was like a precursor to clipart so it was a typeface that was just characters instead of letters it comes in as the second most annoying typeface ever slightly behind Comic Sans possibly the best title typeface ever and if you put in 911 it shows a plane flying into two rectangles some would say not in good taste but the problem with that is after 9/11 after a tragedy of that magnitude it's burnt into the public consciousness who were born since then are aware of it and all the visual aspects and and and the notion of it and every told them everything that goes with it and so if there's anything out there that accidentally looks like that or looks like a coincidence it will be found same thing happened when Michael Jackson died because people started filming everything around his house and sure enough a bit of footage showed up with the shadow that looks like the ghost of Michael Jackson it's because one thing that big happens people look everywhere for for a freaky part of it and I would be amazed if there's ever something of that scale and then you don't get something like that popping up the trouble is when you see that because it was an email forward a couple years back went around you see that and you're freaked out but you never see the thousands of people who who are at home that have gotten tired of listening to records backwards if they decide to search for other meaningless patterns and you don't see that you just see the amazing result a longer answer then was required but I enjoyed it there's that guy who looks a bit to learn it for my liking do you have anything to say about data mining and the supermarkets and your shopping do I have anything to say about data mining and the supermarket's and shopping and personally I might I don't I think life's too short for loyalty cards to be entirely honest I think it's a bit of a false economy anyway no it's not it's attacks on people like me who can't be bothered to carry one around but if you collect enough data and you process it well incredible things happen a lot of our modern medical breakthroughs because of our ability to collect lots of meaningful data and process it in a meaningful manner and get proper results out and supermarkets aren't stupid Amazon isn't stupid Google isn't stupid they have huge amounts of data and it's incredible things you can do with it really really freaky things so Amazon's book where it predicts a book you might like it gets scarily accurate and it's because they're using data correctly personally I I have some hypothetical liberties issues with quite how it's done but I like the concept and I think it's more benefit than harm to be entirely honest but that's yeah dardo mining is a good thing that can be used for evil much like the Internet I did a week people do need to leave for trains I've heard some of you have homes to go to we may have to wrap this up fairly quick just a very quick simple one then would you play a lottery ticket with one two three four five six on it ah will I play a lottery ticket with one two three four five six I do take the lottery because a nonzero probability rather small can still happen the winning lottery is still slightly more likely than me playing that piano the trouble with one two three four fighters is I forget how many people play I play that same number if you want to win the lottery and not share it with anyone else you want to pick numbers which are bigger than 31 because people like to pick birthdays and you want them to be randomly spread out and it's harder than you think to do that but if you do win then you've got less chance of sharing it with someone else so I would not play one or any other I often play prime numbers to be honest if you want to know my secret or primes one day I will loiter afterwards if people have overly personal maths questions or anything we didn't get to come and see me you

Channel: London Mathematical Society

Views: 187,466

Rating: 4.9522591 out of 5

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Id: sf5OrthVRPA

Length: 63min 7sec (3787 seconds)

Published: Thu Apr 24 2014

Reddit Comments

[u/Daemonax]

That submission title reminds me of a line from the film The Man Who Knew Infinity.

"We [mathematicians] are merely explorers of infinity."

In a sense mathematicians explore an infinite domain in search of patterns, being infinite it's easy to find a lot of tantalizing patterns which when subjected to the rigors of mathematics end up being flawed.

A similar thing happens in science, a theory seems to offer promising results. The difference between a scientist and a pseudoscientist is that when the theory breaks down, the scientist will abandon it, while the pseudoscientist will ignore contradictory evidence or more reasonable explanations.