Note: Transcripts may contain errors. If you wish to re-use all, or part of, a transcript, please contact CBC for permission. Please check the corresponding audio before quoting in print. Copyright © CBC 2019

Episode 6: Which is cooler, zero or infinity?

TAI: I want you to try to imagine a box of nothing. You can't really right because a box would be containing something, but if it's containing something then it’s not containing nothing. Okay now try to imagine a box of infinity. Like everything. And you also can't really because it just kind of goes on and on and you can't contain it if it keeps going, right? What's up with that?

[THEME]

Hi there. I'm Tai and this is my podcast, Tai asks why. There are so very many great questions out there. You just want to get answers. Questions like, should you trust your gut? What happens after you die? Why do we dream? What is love? How are we going to fix climate change? And which one is cooler, zero or infinity?

TAI: Numbers have always meant a lot to me. My first language might have actually been math. When I was young and I still really didn't understand English that well, I knew how to talk, but I was still trying to grasp a hold of the many concepts of English, but math is just like, it was there. Although I could understand the math at a raw level, I couldn't really express it and apparently it always came out as jumbly and confusing and I don't really fully remember how I would express myself, but my dad does

MINH 1: Mom and I called it made up math because what you would do is you would quiz me or mom with a math question that you'd come up with, but since you didn't know add or multiply or divide that well yet, you would just make up words. You'd say something like, “Hey dad, what's 11 tiddly 59?” and I would have no idea because you were the only person who would know what the answer was. Do you remember that?

TAI: Yeah, I remember asking about some sort of like pancake.

MINH: Sure.

TAI: And you’re like Tai I have no idea how to do a pancake and then I had to like explain it to you.

MINH: Yeah I think you've been explaining math to me for a long time.

TAI: Since the simpler times of the pancake functions, I've spent a lot of time reading old secondhand textbooks from this old bookseller in our neighborhood and I would absorb more knowledge. I’d be like a sponge soaking up the math. There are numbers that can be put to fractions. Numbers that can't be put into fractions and just go on forever. You guys know the Fibonacci sequence right? One plus one would be two. Two plus three equals five. The length of your bellybutton to your feet to your head, the ratio of that equals the golden ratio and then there are just numbers that we just can't comprehend like 0 and infinity. They're both kind of just like the ultimate mind bogglers. What happens if I pit their coolness against each other? Which one’s more important? More expansive?

The mind blow up factor. The best in kind of only people that I would really talk to about it would be none other than mathematicians.

JAMES: Hi.

EUGENIA: Hi.

TAI: Do I have both of you?

EUGENIA:You have me.

JAMES:Hi.

TAI: OK. So on the phone right now I was able to call up James Grime and Eugenia Cheng. They are both super awesome math people who do a lot of thinking about the importance of these numbers.

JAMES: I give lots of talks around the world and people might see me on the Youtube channel called Numberphile.

TAI: Now Eugenia is the scientist in residence at the School of the Art Institute of Chicago, which is pretty cool.

EUGENIA: And I've written several books and the second one was called Beyond Infinity.

TAI: I have that book actually.

EUGENIA: Oh

TAI: Yeah.

EUGENIA: I'm so glad to hear

TAI: This is the crazy super debate about coolness of zero versus infinity. James, can you explain to me what zero even is as a mathematical concept?

JAMES: Okay so on one hand, zero is a number. It's like the other numbers, one, two, three, four, five up to nine. You know zero times one is zero. Zero times two is zero, but also that means that it can be cancelled out the zeros and you have one equals two. Well no we can't, so we do have to treat zeroes slightly differently from the other numbers. It's a number that represents nothing. Both of them are very abstract ideas in their own ways, but that's what math is about. Math is about going to the abstract to solve problems.

TAI: Because like even if we just have the drawing of the number one, that doesn't mean it's one. That's our interpretation and our symbol to represent the concept

JAMES: You could point out one sheep, one cow, one coin, but what do those things have in common is this idea of oneness that they have in common, which is not something you can point at, but is something that they all share.

EUGENIA: When you try and teach a small child how to count, you keep showing them objects and going one, two, three, one, two, three. But they have to make a leap inside their head from the objects in front of them to this concept of, as James says, oneness. And you can't do it for them. You can't point at it. You can't see it. You can't touch it. You can't feel it. You can't eat it and so you just have to do it in your head.

TAI: It's weird because it's there, but at the same time, it's not there.

EUGENIA: That's how I think of math. It's kind of it's definitely there in my head, but it's also not there because it's just in my head.

TAI: The same applies to zero. You can't really point at nothing.

JAMES: Zero is the harder idea. It’s harder than one, two, three.

EUGENIA: One sheep and one cow have something in common, but zero sheep and zero cows almost have more in common somehow. At least to me it's much easier to get zero sheep and zero cows. I've got them right in front of me now.

TAI: What about infinity? You can't go up to your kid and be like look this is one cow. This is no cows. This is everything. It’s infinite cows.

EUGENIA: Yeah, unfortunately we don't even have infinite cows on the entire planet. So we couldn't even try to assemble infinite cows and it's so it's really something that happens inside your brain. But something that you can show to any child and they've probably understood it themselves is that if you eat half of your chocolate cake, then you have half left. And then if you eat half of what's left then there's still some left and if you eat half of what's left there's still some left. If you keep eating half of your remaining chocolate cake, you can take an infinite number of bites of chocolate cake and there will still be some left.

TAI: I have the best producers in the world and they actually brought me a cake. Oh my God, this is just so awesome. I'm going to trying to cut it infinitely and see if it goes to zero. Okay, here we go. So I'm cutting the cake

VOICE 1: You think you could cut it infinite times still?

TAI: Yup.

VOICE 2: We’ll just keep eating whatever you gives us.

TAI: To half again. I’m going to make the third cut. Two eighths. Five Sixteenth. I could keep cutting it forever and ever and ever. Forever and ever and ever. Anyway back to the question at hand.

JAMES: Zero is a lot less flashier than infinity. It's something that you would use in everyday life. It actually came from merchants and traders and accountants, rather than these sort of intellectuals studying maths.

EUGENIA: But then again, infinity turns out to be practical as well and it also turns out to be everywhere through the field of calculus, which is a piece of mathematics that really governs everything that changes continuously and that means practically everything in the modern world, including things like well electricity and that's how infinity can be thought of as very practical, as well as having a mind bending and weird properties where you can play around and create strange beasts and strange universes in which peculiar and amazing things happen.

JAMES: Yeah infinity is the one that's the strangest. I mean the strange paradoxes that I can't understand.

TAI: One example of those paradoxes is that cake conundrum, which I explained in the cake break and another one is Hilbert’s hotel.

Eugenia: That was proposed by the mathematician Hilbert where he said let's imagine we have a hotel with an infinite number of rooms.

TAI: Now Hilbert’s hotel is confusing, but bear with me. Imagine you have a really big hotel. Now this hotel has infinite rooms and let's say that one man walks in one night and says, “hey, I want to book a room.” You know you can't just send him to the infinite floor that doesn't really seem fair. You know because he has to walk all that way. So you just send him to room one and send the person on room one to room two and then send the person on room two to room three and keep going. So instead of this one guy have to travel so incredibly infinitely far, everyone just travels one, which works out. Such a small number, but it eventually converges into infinity.

EUGENIA: And that's quite odd because in a normal finite hotel, if it's full, you can't just fit another guest in without asking them to share a room, which they probably won't want to do.

TAI: Yay my head hurts.

EUGENIA: Hooray. We're all getting cleverer.

TAI: Now James, what do you think of what Eugenia is saying and why do you think zero is cooler?

JAMES: Oh I think we're going to find that these two ideas are going to be very connected because they are related ideas: one being nothing and one being everything. But without zero, you wouldn't have any of modern mathematics today. The reason zero is so important is because without it, you wouldn't have a place value system. So in the old times when you wanted to count thirteen sheep or something like that, you would have to make a mark for each sheep. So you have to make thirteen marks so you can count them. What the Egyptians and the Babylonians did is they started using new rules to represent larger numbers. So now if you want to count thirteen, you can just use a one and a three. So now you need a zero in here because what is the difference between 32 and 302. Well you need that space in the middle. In the old times that would be actually a space. It was only later that zero was recognized as a number, but with place value system, you can now do the whole of mathematics we know today

TAI: Oh man, if it wasn't for the concept of the number of zero, we would still have to use the tally system. You know the one where it’s like one, two, three, four and then five is just this horizontal line. That would be pretty bad. It's like that boat will cost $13,000. One, two, three, four.

EUGENIA: I agree with James that zero is really important and possibly even more important than infinity because more maths depends on zero, really. But just because something's important, I personally don't necessarily think it's cool. There are plenty of things in life that are really important without being cool to me at all. Like for example, sleep, which I find pretty boring, but I recognize that it's very, very important.

TAI: Hey if you wanna learn more about the importance of sleep then check out my episode about dreams

EUGENIA: Not everybody has to understand it in order for it to do its thing in the world around us. If we didn't have access to an infinite number of numbers then we’d get into trouble because we'd have to stop somewhere and if you stop somewhere then everything would implode backwards.

TAI: Oh no.

JAMES: Zero, at its time was a weird idea, but turned it out to be the more practical. Our computers, the internet and with just using zeros and ones, you can send any number or any message around the world.

TAI: It still is a pretty weird idea.

EUGENIA: Things that seem weird at first get to seem less weird the more time you spend with them. I like things when they make my mind bend. If I feel like my brain is kind of exploding out of my skull then I feel like I'm making some progress. And that's why I really personally find infinity cool because they are mind bending things like that maybe one plus infinity is actually different from infinity plus one and maybe there are actually different sizes of infinity. So that there's the smallest infinity, but then there's a bigger infinity and then there's an even bigger infinity and you can keep going like that infinitely, so that there are infinitely many bigger and bigger infinities.

TAI: That was just the sound of my brain exploding.

EUGENIA: Those sorts of weird things are why I really love maths because it's a place where I can explore things that don't really happen in the real world. The real world is very important and it's where we live our lives, but I really like the world of ideas.

TAI: It doesn't matter which one’s cooler. They're both so interesting and so elaborate. They're different and they're beautiful. Math is messy, but yet in its messiness, there’s a beautiful elegance. Math really is able to take you away. That's what I love about it.

[TAI SINGS INFINITY SONG]

TAI: On a dark desert highway, box of nothing in my hand.

Up ahead in the distance, rising up from the sand.

Stretching above the clouds, it’s the Hilbert Hotel.

And on and on and on.

At the Hilbert Hotel.

And on and on and on.

Passing infinite buses, through the sliding glass door.

Get my infinite key card, it’s for the infinite floor.

I must be at the Hilbert’s hotel.

And on and on and on.

At the Hilbert Hotel.

And on and on and on.

At the Hilbert Hotel.

And on and on and on.

At the Hilbert Hotel.

And on and on and on.

TAI to KIEN: What's thirteen pancake five with the flip over of six?

KIEN: 84. Tai?

TAI: Yeah?

KIEN: Did I get the question right?

TAI: Sure.

KIEN: Yay.

TAI: Thank you so much for listening. I'm Tai Poole. This show was produced by Veronica Simmonds and Yasmine Mathurin. Our digital producer is Olivia Pasquarelli. Today my guests were Dr. James Grime and Dr. Eugenia Cheng. You guys are awesome. Thanks to Crystal Duhaime for the editorial assistance. The theme music is by the legendary Johnny Spence and also thanks to Johnny for helping me write and record the Infinity song.

KIEN: Next time on Tai asks why: climate change.

TAI: Do you ever lose hope?

CATHERINE: Yes.

TAI: Till next time. I’m Tai. Keep asking why.

TRANSCRIPT: Tai Asks Why - Season 1, EP 6

Social Sharing