Instant Genius - Matt Parker: What happens when maths goes horribly, horribly wrong?

Episode Date: March 13, 2019

Sums are hard, but imagine the consequences when getting the wrong answer leads to disaster. Comedian and maths whizz Matt Parker explains what happens when rounding errors and miscalculations get the better of our equations. Hosted on Acast. See acast.com/privacy for more information. Learn more about your ad choices. Visit podcastchoices.com/adchoices

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more. I love the story of the election in Germany where each party had to get more than 5% of the vote to get a seat in the parliament. And the Green Party thought they had their 5%. It was reported they got 5.0%. And I guess we get a seat. But it turns out it was rounded to, you know, one decimal place and they actually got 4.97%, which was not enough to get a seat. You're listening to the Science Focus podcast from the BBC Science Focus magazine team. with the UK's best-selling science and technology monthly, available in print and in several digital formats throughout the world. Find out more at sciencefocus.com or look out for us in your app store.

Hello and welcome to the Science Focus podcast. I'm Helen Glennie, editorial assistant at BBC Science Focus magazine. Throughout history, engineers have watched their bridges disappear into the waters below, all because of tiny changes in design, unexpectedly affecting their structural integrity. Elsewhere, generals have stood aghast as missile defences missed their target by a country mile thanks to rounding errors,

and bankers have seen their profits tumble as a result of spreadsheet quirks. Maths can get a bad rep, especially when even the slightest miscalculation can lead to catastrophe. In his new book, Humble Pie, a comedy of maths errors, stand-up comedian and General Maths was Matt Parker

digs out his calculator to work out why so many disasters can arise from simple mistakes, often with deadly consequences. In this week's Science Focus podcast, he speaks to online editor Alexander McNamara about some of history's most incredible maths mistakes and how they were made. He also explains the joy of calculators and how, despite many teachers' best efforts to crack a joke, maths can actually be funny. So you are both a stand-up, comedian and a mathematician.

Correct, correct. So I was under the impression, given the dabblings of maths I've had up until about university, is that maths has never been particularly funny. Is there something that I'm getting wrong about that? Yeah, no, it's a good point. So, I mean, maths teacher humour is kind of its own unique brand of comedy, and that's what most people come across when they're at school, mass teachers trying to be hilarious.

but I happily came at it from the direction where I was really doing stand-up, and then I was just like, hey, I wonder how much maths I can fit in this while still successfully entertaining an audience, otherwise I don't get paid, right? So I had to keep it entertaining, but it was my own mission to put some maths in there. And was that an easy fit? You know, it was easier than I expected, partly because, I mean, one of the golden rules of stand-up is talk about something that, you care about because, you know, it's one thing just to do, you know, standard jokes and don't

get wrong. There's some great, like, one-liner comedians out there. But a good way to connect with an audience is to be, you know, talking about something that you personally care about for me that was math. But I also realized that an audience will go a long time without noticing they're not laughing if they're still being entertained or engaged or they're still interested. And so obviously, you still go to talk jokes occasionally, but I've discussed. but I could go quite a while and they'd be interested in what I'm doing, even though it wasn't like traditional set-up punchline comedy. And then that's the inherent interest there is things about mathematics.

Yeah, so I would, I mean, I tested the water by, I started solving a Rubik's Cube on stage. And that, because they're like an easy, easy gateway because it was like, it was interesting, but it's also a performance. and so that's when I was kind of toying around with, can I do something that's not strictly jokes, but it's still entertaining and is a bit more mathy. And that gradually moved into doing more and more maths. I have to admit,

when I started doing actual, like, math content, that's when I was doing my own shows or doing specifically nerdy shows. So when I was booked as a nerdy comedian or like we do a thing called Festival of Spoken Nerd, and I've got a night in London, and caught an evening of a necessary detail. And these are like explicitly nerdy gigs.

Then you still got to, you know, make them entertaining. But you've got a lot, you know, more range to actually try and communicate some actual mass content that you don't get if you're just a comedian booked at a, you know, generic comedy club. And do you find that your audience is actually want to come for both comedy and to be, you know, learn some sums? Yeah, absolutely. I mean, they get upset if they don't, you don't get sufficient amounts of both. So if anything, I've made it harder. But, you know, there's a great community of, you know, comedians who love science and scientists who love comedy that, particularly when I'm organizing a variety night, there's loads of great people I can get involved. And for me, I would miss either half. So, so, you know, the comedy stuff, it tends to be, you know, more comedy, but with enough maths in there to. keep me entertained. And then also when I'm doing like a math talk, like if I'm, you know, going to a university somewhere to speak about maths or mass communication, then I put in enough comedy to keep me entertained. So, you know, the balance shifts depending on the audience, but there's always a bit of both. I guess one of the things that are that our listeners really

enjoy and readers of the magazine, they do like that sort of interesting science and technology and everything, but also they like to be entertained and engaged. Are there any sort of areas that you've noticed in the world that when you're sort of melding both the science and the comedy together that there's stuff that just isn't funny. That's, wow, yeah, that's a good point. So, I mean, actually, yeah, two things. Occasionally, and this is to be expected, something is just too either ethoteric or involved or detailed

to get across in a way that's funny, right? Because you can get enough momentum with funny to get you through a few details and things. But something like, there's a number called Graham's number, and it's famously like the biggest number that was ever constructively used in a math proof and it's just mind-bogglingly big and early on I was like you know what I'll do a hilarious routine about the biggest number ever used and I just never I could never crack it but then that's when things like writing articles or doing particularly books actually I always want to do

the Riemann hypothesis on stage but there's so like to do it in a meaningful fashion in a way that's different to what other people have done, which is more of like a highlights tour. I could never really think of a way to do it on stage. But then when I was writing a book a couple years ago, I was like, ah, perfect. This is the long form situation where I can do all the setup and the required background

in a way that's still entertaining, but in a book form, you know, people can put the book down and go away. It's a very different process. But the other problem I've had now, which I hadn't run into before, is so the book that's just come out, It's called Humble Pie, a comedy of math errors.

And there's the problem. It was a comedy of mass errors. And that's what my publisher signed off on. A funny story about, you know, funny book about mass goes wrong. Trouble is, a lot of maths is used in engineering and medicine and all these places. And when it goes wrong, a bunch of people die. And I couldn't have like every, like if I wasn't careful, every second story in the book would just be. And then everybody died.

And so I had to, I had to, you know, ration the stories wherever. Everyone dies. I deliberately only put in aviation stories where nobody dies, but there's still like an engineering story about a bridge collapse where people died. There's an evacuation of a theater several times, actually, where everyone dies because of the geometry of how the doors and the exits moved and were arranged. And then the medical stuff, you know, because of a programming error, someone died from an overdose on a radiation machine.

And occasionally I've tried to, because I think it's important, to bear in mind the severity of what happens when maths is being used in these life critical situations. I've tried to put them in a comedy talk about maths, but I've never found a way to successfully include a story where a bunch of people very sadly died because of an error, and it just changes the mood so much. I don't, I'm yet to crack how to do that successfully and appropriately because they're real people, right, in a show where people have,

you know, paid to be entertained. And it can be done because, I know, people talk about some very serious and important topics in comedy. That's one of the great things about stand-up. You know, you can do whatever you want as long as the audience enjoy it.

I'm yet to crack away for the audience to be able to appreciate it and then then return to enjoying the funnier stories. No, there's definitely one of the things. things about the book is that you know, I was always under the impression that when I was going, I was at the whole point of maths, is that ultimately you get to the right answer.

It's usually the equal sign is the giveaway there on that one. But in the book, obviously, there are these things where these tiny little things that we just miss out. For instance, the section about rounding errors, which has got quite a, quite something how we don't quite realize quite how significant an effect that can have. It's phenomenal. A slight, you know, a bit of rounding can do. So I love the story of the election in Germany, where each party had to get more than 5% of the vote to get a seat in the parliament. And the Green Party thought they had their 5%. I think this was about 1992. If people can look it up. And it was reported they got 5.0%. And I guess we get a seat. But it turned out it was rounded to, you know, one decimal place. And they actually got 4.4. 97%, which was not enough to get a seat. And so the result changed from them having a seat to not having a seat when people realized that what they were going on initially was a rounded figure,

and the more precise figure actually wasn't the other side of the threshold. And is that one of the reasons why we, you know, is that one of the reasons why we make so math's mistakes that are so, that happens so frequently? Or is there other other things about it that we just get wrong? It's a good point, because what a lot of people, had the impression that you've come away with, which is what you get from doing math at school, that it's all about getting the correct answer. And, you know, math is kind of

unique. I mean, some science is quite close to this, to be fair, where there's a definite right answer, like in maths. And people find it's funny when I'm doing my math degree. And when I finished an exam and my mates had met me afterwards, they were amazed that everyone comes out of the math exam. And they're discussing, oh, what was the answer to this one? Oh, you got that one right, I got that one wrong. And immediately, we would know if we were right or wrong, because it's right or it's wrong. Whereas they're like, you know, philosophy and English students who are like, I don't know, I wrote a bunch of words. Someone's now going to decide, you know, could have assigned a percentage to that. And that's very, very different. And so people kind of think math is all

about the right answer, which it is when you're doing tests. However, you know, actually doing math is about getting the wrong answer over and over again and trying to be a bit less wrong. And exploring and learning maths, it's just, you know, a long journey of getting it wrong. Because as you said, I mean, it's not just that, you know, things like rounding can trip us up. It's the fact that humans aren't very good at mathematics. Like just our brains, our brains are very good at learning maths, which make that very clear, but they're very bad at doing it just intuitively. We have to teach our brain.

We've got to train it to do the maths in the first place. And so we're kind of trying to do a subject with equipment that's not quite up to the task. But the benefit of that is, is that if we do learn the maths, it lets us go beyond our intuition. It's enabling the human brain to do working out and to come to conclusions that it wouldn't be able to do naturally. And is that why we had things like calculators and from everything from a calculator to an advanced computer to sort of get us that one step further? I mean, I'm very pro-calculator. I've gone, you know, as a matter of public record. I mean, I do calculator unboxing videos on YouTube, so I'm not really one to talk here.

I think any, I mean, three million views can't be wrong. Well, they can actually. So, you know, I'm all for as many aids as possible. So I love calculators. I love anything which can help with the maths, anything which takes away the more tedious bits, that once you've got them, it's just slowing you down from getting to the interesting bits of mathematics. But even bigger than that, I'm a big fan of, because assuming humans are always going to make these mistakes. And yes, we can help with calculators and these things.

But we can also have built into our various systems and organizations, ways to stop the inevitable math mistakes from becoming disasters. And there's this, you know, using maths to design logical systems to stop that from happening. So something like calculators, there have been people who have people who have, died because of a drug overdose because the people, like, so some drugs that are administered by an automatic pump, the people who are programming the pump, used a calculator or did some working out on a bit of paper and got it wrong and administered the wrong rate of a drug and there have been deaths as a result of this. And what's interesting is when you look at the investigations into it or you look at the people doing research to try and stop it, they refer

to the medical staff as using a general purpose calculator. And when I first saw that in one of these medical reports, because I read a lot of reports for this book, I'd never come across the phrase general purpose calculator. I was like, man, I know, you know, I consider myself, you know, an appreciator of calculators, but I'd never come across general purpose calculator. And then they made the point that if it was a, like, why not design a specialty calculator for hospitals where it knows some of the context of the calculation you're doing. So like I say, it might know what drug or what type of drug or all these different ways, which are easy to build into a calculator on a knife, you know, like some kind of, you know, a tablet or something. And then it wouldn't just blindly give you back whatever number happens to match the buttons that you mashed with your fingers. It would be able to intelligently say, no, this is right, this is wrong, you've done this wrong, you've done that wrong.

even things like different calculators respond differently depending on if you enter two decimal points in a number, which one, like one by axis, so one will be axon, one's on purpose, how it decides which one, if it even tells you, most calculators just go, oh well, must be the first one, and no error appears. So I think, yeah, we can definitely, you know, calculus are very useful, but we can do even better in some situations. So these are sort of contextual calculators in a way? Yeah, yeah, a contextual calculator that knows, why you're doing the calculation and has a vested interest in flagging up any possible problems instead of just, you know, happily going with the flow. It reminds me of one part in the book where you talk about how, say, for Excel, for instance, has got, you know, it's a great spreadsheet, does good calculations and stuff, but it makes errors in there that are built into it. I was just wondering if you'd be able to explain what the error is and why it's happening.

Yeah, so Excel, while wonderful, can do so many things wrong. And to be honest, we don't need any help getting spreadsheets wrong. There's an organization called the European spreadsheet risk interest group, who I love. I've never been to their conference, but I really want to go. And they do research into risks from spreadsheet use. And what they've done is they have sampled whenever there's a big, like, release of spreadsheets into the public. domain from within a company. So if there's like some kind of leak or often if there's court proceedings and they have to hand over all this stuff or for some reason it enters the public domain, they will then go through and analyze them all. And they have found that roughly 24% of all spreadsheets that contain some kind of formula or mathematical calculation contain a mathematical error, at least 24%. It's just terrifying. But on top of us using them badly, You're right. Excel has some problems built in. And actually, I had this problem.

Just yesterday, I had a spreadsheet open. I was looking at sales of books from, I have a website called Maskier. I'm not trying to plug this. It's genuinely, I started this story without realizing it's going to come across like a plug. We saw lots of books on Maskgea.com.org for all your mass needs. And so I was sorting through the sales of the books for the week. And Excel converted the ISBNs. the number for each book into an order of magnitude because they're so long.

So instead of getting the ISBM being like 9,37, whatever, it was like 9.3 times 10 to the 12. I'm like, that's not helping. And so it sees a number. It doesn't realize there's actually like a product serial code. It's not a genuine number. It does it to phone numbers all the time. Like a lot of phone numbers will be converted into scientific notation automatically and And if you're not careful you, you can lose some of that detail.

And, I mean, a phone number, I mean, it's not really a number, is it? Like, my rule of thumb is, if you ask someone for half of a number and they half it, like, divide it by two, it's a number. If they give you the first lot of digits, it's not a number. So I said, like, what's half your phone number? People would give you the first half of the digits. And okay, so actually, you never do maths with it. It's not a number. And Excel is just when people use it as a database.

It's not aware enough of the context, I guess. Yeah, and I've found that with phone numbers, the fact that all phone numbers tend to start with zero, which immediately gets deleted. Yep, that's gone. I had a credit card, which I don't have any more. I can talk about this. And the three digits on the back started with a zero,

and it lead zero. And so some websites, when it says enter in the three digits on the back, I'd enter them in. And if the website wasn't well coded or wasn't set up properly, it would then remove that zero and then complain it didn't match just drove me up the wall. I had to get a new card, which is insane.

I guess these are the small little like maths errors and things that we just don't really notice or people just don't really think about that then come into our real world, as it were, that just sort of niggle away at us in a way. Yeah, it's just a lot of it's kind of fun because there's things that you never really spot,

but then occasionally if it goes wrong, you can have big ramifications. So, I mean, you talk about a spreadsheet, abuse. Some people at, I think this is all public record, J.P. Morgan Chase, they had a series of spreadsheet problems within the last decade. And some of it was how they were using the spreadsheets and some was just actual calculation errors. And they were trying to calculate or at least keep track of their value at risk, which was for all the money they're investing, how much risk are they facing? Because while it's hard to predict profits, it's a lot easier to predict risk,

and so you can keep on that. And they ended up through a series of spreadsheet problems, including things like there was a calculation for value at risk where they were adding two cells instead of taking their average. Like, just stuff like that, we all do. And they lost $6 billion US dollars as a result of their miscalculate. It's just insane. And so these little mistakes that we all make all the time, occasionally in the wrong situation, they flare up and cause a major problem. Or six, you know,

six billion major problems. Six billion major problems. Yeah. It puts my math issues into perspective and that sort of thing. Yeah, and that's just it. We all make these mistakes. And I had to strike a careful balance in the book

between everyone's bad at maths. It's fine to make mistakes with sometimes we need to be, you know, we need to be aware that everyone's going to make mistakes and find ways to stop them before they become disasters. So I'm just moving on slightly. I just wanted to have a quick word with you because obviously this week is probably

Sounds ominous This week's quite a big week I imagine that mathematicians around the world This is kind of a big week Leading up to the Mathematicians Christmas This is it, the big pie day Very exciting, yeah What is pie day all about

As opposed to sounding delicious Oh my goodness And you know British Pie Week is around the same time as well And I think they've just kind of, they're trying to get in on the excitement. So, so probably the mathematical number, everyone's favorite 3.14, 159, etc., etc. Some countries in the world write their dates by the month and then the day within the month. So March 14 is written three, either slash or dot or something, one, four, and then the year.

Although if you follow the official one and you have year first, you then have month and day. So it works in different formats, and it's not quite as North American-centric as some people like to complain about, although for me, any excuse to celebrate a mathematical constant. And so on the 14th of March, because the date can look like 3.14, mathematicians celebrate Pi all around the world. It's a big day. I personally, my tradition is I try and calculate pi a ridiculous way. And every year I either do a long tedious calculation by hand or I do some kind of physical experiment where the result gives pie. So previously I've put like hundreds of pies in a giant circle and then counted how many pies are round and put pies across the diameter. I've done probability experiments where the answer is pie.

This year I had a balancing beam, like a six metre long beam. balanced right in the center. And then I suspended masses from different distances along the beam because I knew this series, if you add all the square fractions together, equals something based on pi. And so I had the series done by masses on one side, and then by working out how much mass at a unit distance on the other side

was required to balance it, I could then use that to get pi. And I got 3.12, which I was very proud of. For hanging things on a beam, 3.1.2 is pretty pleasing. But I'm always keen if people have different Pi-day traditions or suggestions, drop me a line. Is there something that, you know, a relatively simple way that I would be able to demonstrate Pi in my own real world with things I might find in my house or desk? That's a good question. Yes, there is. So, obviously, there's measuring a circle, right? The lazy way. So you could find a circle, measure a round.

around it, measure across it, divide the circumference by the diameter, you get pi, right? That's fine. Nice entry level. Next step up, you want to do something without circles. So, the period of a pendulum, the way you calculate that physics has a pi symbol in it, is 2 pi times a square root of the length of the string, or whatever your pendulum length is, divided by acceleration due to gravity. And this is great, no circles now. And I often flick through. I'm trying to find physics equations with a pie on them. So what this means is if you can

get a pie or any other object, but obviously you want to start with you know, I'm just assuming you're going to use a pie for this. Because why why go halfway? Plus you've got a meal at the end of it. Exactly. And then you can celebrate by eating it. Like all good bits of mass

working out. So like all good experiments, make sure you eat. Don't do that. Right. So if you look at the equation, for the period of a pendulum. And you set the length of your pendulum to be a quarter of the value of acceleration due to gravity,

so acceleration due to gravity is about 9.8, 1.81, depending on where you are. And a quarter of that is 2.45. So if you have 2.45 meters length pendulum, it will take pi seconds to swing backwards and forwards. And so what you can do is instead of swinging and time, it's period, and you'll calculate pi.

And so that's my favorite non-circle way to get pi. I just need to dangle something 2.45 meters from the ceiling. Yeah, I did it once with, we did the full 9.81 meters. Because then the period is 2 pi, and so just each pass, like from one side to the other is pie and then pie back for the full period. And so you need a lot more space for that, but you do, you get pie in fewer swings. I guess also that way you get rid of some of the rounding errors. when you're multiplying it.

Yes, yeah, yeah. It's a bit harder. What we found was when we did the 9.81, before we were ignoring the mass of the string and the rigging. We were just doing the mass of the pie in terms of working out with the center of masses to work out the effective length of the pendulum. But when we did the really long one,

the center of mass moved up quite a bit. It was no longer in the pie. And so that complicates thing. I'm just giving literal practical advice. I assume people are going to do this. At some point, you've got to remember the string and the rigging. The other thing you can do is if you've got very sensitive scales, you can weigh a square of cardboard and then cut out a circle and then weigh the circle,

and then you can use the two different masses to work out the ratio of the surface areas, and that will give you pie based on the area of a circle, which is quite a mess. Sounds like a simpler way of doing it. I might give that one to go and say. Most things are simpler than hanging a pie from 10 meters of string. Do you think there are any other mathematical constants worthy of their own special day? That's a good point. So I celebrated Thirds Day this year, which was on the 3rd of January, because, again, same with the date system in American style.

The 1 over 3, 1 forward slash 3 for 3rd of January, looks like a third. And it was a Thursday. So a Thursday. And so a mathematician in the US, like with James Prop, decided to declare that whenever the third of January is a Thursday, we'll call it Thursday. And so I celebrated by calculating a third. I mean, to be fair, on Pi Day, some schools have like a, how many digits a pie can you memorize competition? On Thursday, that's a lot less exciting. But easier, it's more inclusive.

everyone can get involved, I guess. So I think there needs to be more rational celebration of mathematical constant days. That was Matt Parker explaining some of maths biggest mishaps. His new book, Humble Pie, is available now, and you can find him on Twitter and YouTube at Stand Up Maths. So be sure to tweet him any math jokes, disastrous rounding errors, or novel uses you found for Pi.

We'd love to hear them too at Science Focus. In the latest issue of BBC Science Focus magazine, the first featuring our brand new design, we explore the hidden power of the brain. We also take a look at the oldest galaxies in the universe, explain why charismatic leaders can be successful despite a lack of competence, and we introduce a new section called Reality Check.

As always, there's much, much more inside. Thank you for listening to the Science Focus podcast from the BBC Science Focus magazine team. with the UK's best-selling science and technology monthly, available in print and in several digital formats throughout the world. Find out more at sciencefocus.com or look out for us in your app store. This podcast is sponsored by Name, Audio and Focal. The texture and emotional depth of music can be lost through digital sources or poor signal. Name audio believes you can have digital precision with analogue warmth.

Alongside French acoustic specialist focal, Name creates high-end audio systems combining innovation with craftsmanship so you can listen to music, just as the artist intended. Discover more at name audio.com. Ambition comes in all shapes and sizes. At First Citizens Bank, we roll with your goals because we're built for what you're building. Fit for your ambition for Citizens Bank.

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