Short Wave - Humble Pi: When Math Goes Awry

Episode Date: March 12, 2020

Pi Day (3/14) approaches. To help honor the coming holiday and the importance of math, stand-up mathematician Matt Parker unspools a common math mistake known as the off-by-one-error. His new book is called 'Humble Pi: When Math Goes Wrong In The Real World.'Email the show at [e-mail] pcm.adswizz.com for information about our collection and use of personal data for sponsorship and to manage your podcast sponsorship preferences.NPR Privacy Policy

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Maddie Safai here with a math problem. Don't be scared. Say you're trying to build a fence 50 feet long. and you need a post every 10 feet. How many posts do you need? Got your answer? Okay, just hold that in your head for a second while we introduce Matt Parker.

Oh, hey, can you hear me coming through? Yeah, Matt's kind of like... Can you hear me? Part comedian... Hey, Maddie, yes I can. Part math nerd. Matt, how should we describe what you do? That's a great question.

I go with... You sound like my accountant. I go with stand-up mathematician. So I'm probably a mathematician first and a comedian second. Matt's got a big YouTube channel. He's an author. He works with schools, all trying to blend math and comedy. Here is a timely example.

So I've done stuff like I've used a pendulum. In fact, I swung a baked pie from a piece of string. And the way you calculate how long something takes to swing backwards and forwards, that calculation has the mathematical number pie in it. Pi, of course, is the ratio of a circle's circumference to its diameter, which calculates to 3.14159-265358-9-7-9. We love it because it appears in unexpected places. You'd be doing some completely unrelated mathematics and suddenly pie's there.

And we celebrate Pi Day every year on March 14th. But the kind of pie we're focused on today is humble pie. the kind you eat when you make a mistake, which brings us back to that math problem, in a 50-foot fence, a post every 10 feet, how many posts? And people listening are now thinking, oh, okay, 50 feet, one every 10 foot, then there must be 5.

Because we can all divide 50 by 10. But actually, you need 6. Right. Because you need the first one. And so it's actually the number of stretches of fence plus 1. If you guessed 5, no shame. You made a classic math mistake called an off-fifference. by one error. It's one of a bunch of math mistakes that Matt unspools in a new book called

Humble Pie, When Math Goes Wrong in the Real World. I always enjoy a pie pun. So Humble Pie is kind of admitting that you've got things horribly wrong. And then bringing that approach to math and saying, look, sometimes we make mistakes and math is not all about always getting the right answer. It's about giving it a go. This episode, to honor Pie Day and the importance of giving it a go with math. Matt Parker helps us puzzle more off-by-one errors and what happens when math goes awry. So you said you wanted to write a book for anybody

who ever sat in a math class and asked when am I ever going to need this in real life? Yes, and I was that teacher. So I taught high school math for four years. I was in Australia for a while and then I taught in London over in the UK. And that question's like the staple of math teaching, right? Yes, and I want to give you an opportunity right now to defend every high school math future in the world.

Go ahead. Good. I mean, that's no pressure. Excellent. It's interesting because you can threaten students with all sorts of you're going to need to know this in the future because you're going to get a mortgage or a loan or you're going to have salary negotiations, all the reasons why you're going to need math in the future. But it's a little bit hypothetical and it's hard to get kids' attention. So I thought, you know what, things going wrong. People love things going wrong.

I thought I would focus on what happened when someone didn't remember their math. Right. And in it are all sorts of stories. When students say, why do I need to know about rounding, they can find a story. Ah, here's what happened when someone didn't get the rounding right. Right. It's kind of a fear-based approach. I appreciate it.

A little bit of that. No, I'm just kidding. I'm just teasing. Okay. So we're going to focus on the off-by-one error. So first, can you kind of define what that means before we jump into it? So, I mean, off-by-one error is, it comes kind of from. programming. Lots of things in counting can have you unexpectedly off by one. And often it comes down

to defining where you start and stop counting and using zero. So my favorite example is if you ask people what number they can count to on their fingers, the standard answer is 10. Right. So you count to 10. You've got 10 fingers. Well, actually, you can count to 11 because you've also got zero fingers. Right. So if you start from zero fingers and then one and then two all the way up to 10, there's actually 11 different numbers you can count on your fingers. And so often people forget about zero or these sorts of situations where it's very easy to be just off by one. Right. And you've said that that kind of, you know, counting from zero breaks that link between what you've counted to what the total is.

So even if you're counting 210, technically you're counting 11 distinct numbers when you're starting with zero. And that's why we don't use it in normal life. So the reason it comes up in programming so much is if you want to get everything out of your, computer code you've got to start from zero and if you're numbering things in a list in a computer you always start with the zeroth item yes so item number zero is the first item an item number one is the second item right and I found I as far as I could find this was the earliest mathematical mistake I could find documented was Vitruvius who the the Vitruvian man is named after so from way

back, classic, the the divinci, the guy that's standing with his arms up and his legs out. Okay, okay. That's the one. So he was writing about math and architecture way back in the day, and he pointed out that if you want to make a temple, which is twice as long as it is

wide, because apparently that's quite a nice ratio, you can't just double the number of columns on the front to get the number of columns on the side because you will have an off-by-one error. Gotcha. And if people know an earlier document warning against a classic math error.

I would love to hear it as far as I'm aware, that's the first. Well, if it's there, the internet will tell you, I'm sure. Oh, yeah. And so that's our classic off by one. Can you get the same thing with ages where you don't become an age until you're finished the year? Yeah, so that's another example of counting by zeros is, you know, in the U.S., at least, is birthdays, right? So when I turned 30, really, I was entering my 30. first year of life. Yeah, you're always older than your age, right, is my motto. And no, no, I don't live by that.

But when, so what I find out of thing is like, so when someone turns 39, that's their 40th birthday. Right. Because in theory, the day you're born is your first birthday. And it's kind of hard to argue, I would say, that the day of your birth is not a birthday. Yeah. You know, I'd like to, I'd like to think that's not controversial, but evidently, it is. And so, so that's your first. birthday and then a year later you turn one on what is now your second birthday and then later on on what is now your third birthday because you've just completed the second year of your life right and then you go all the way up but it turns that if you give people a card when they're turning 39 and it says happy 40th birthday right even though that's true and correct they don't seem to appreciate

it that's weird that hasn't worked out for you in the past I said no you can try anything you'll ice it into a cake they're still unimpressed I don't know okay so let me ask you a more general question then. So this book is full of math mistakes over time. What is your favorite? Oh, that's, oh, it's hard to choose a favorite. I know. It's a challenging question.

My current favorite at the moment, and I'm given you're a fan of the metric system. My favorite was a flight. This was a flight in Canada in 1983, and this is right when Canada was switching from imperial units to metric units. There, and

as Air Canada were adjusting, they were getting new aircraft into their fleet, some were using Imperial and some were using metric units. And for this specific flight, it was a Boeing 767, they calculated the amount of fuel they would need in kilograms, and then they fueled

the aircraft in pounds. Yeah, exactly. Because a pound, just under half a kilogram, and ultimately the plane ran out of fuel mid flight, and the pilot, before they became a commercial pilot, they were a glider pilot, they were able to land a Boeing 767 with no active controls.

When it unexpectedly ran out of fuel. And so there were these huge consequences, but yet nobody died. That's a good one. That's a good one to pick. There were so many stories like, because in engineering, aviation, medicine, you make a math mistake. People can die, right? But I promised my publishers a comedy book about math. And so I could only have so many stories at end and then everybody died.

Right. And so in this case, I could show how a simple unit conversion error had these huge, massive consequences, but thankfully, nobody died. That's a good one to pick. That's a strong choice, math. That's my current favorite. Yeah. Yeah. Okay. So in your book, you've talked a little bit about how humans don't seem to be good at learning from mistakes. Probably, I would say, a good overall generalization. But in the math world, what do you mean by that? And why is that so important? important. That's great. So there's two things going on here. On one hand, humans are not naturally good at mathematics, because everyone thinks if they're not naturally good at math, then it's not for them. But the crazy thing is, everyone finds math difficult, and the people who are into math are not the ones who just find it easy. They're the ones who enjoy the fact

it's difficult. The other half, though, is sharing when we make those mistakes. Engineering is the classic example of this. When we're pushing the limits of how big we can make a bridge, how tall we can build a building. We are trying to approximate reality using mathematics, and we've gotten very good at doing that, and we can build some incredible things. But every now and then, we discover a new thing about the math of the universe

and how reality behaves mathematically that we didn't know before. And it's a shame that a lot of the time, in things like engineering, because everyone's under, like, non-disclosure agreements or they don't want to show that they made a mistake, They are reluctant to share that. I think that's a real shame that we are not optimizing for learning from our math mistakes.

Matt Parker, his book is called Humble Pie, when Math Goes Wrong in the Real World. We here at Shortwave, hope you have a happy pie day. This episode was produced by Brett Bachman, edited by Viet Le, and fact-checked by Emily Vaughn. I'm Maddie Safaya. Thanks for listening to Shortwave from NPR. Thank you.