Editor's Note: This transcript was automatically transcribed, so mistakes are inevitable. You can contribute by proofreading the transcript or highlighting the mistakes. Sign up to be amongst the first contributors.
I want you to try to imagine a box of nothing. You can't really write because a box would be containing something. What if it's containing something? There's not containing nothing? OK, 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? And why? Hi there, I'm tired, this is my podcast. Asks why there are so very many great questions out there to get answered questions like, Kitty, trust your gut.
What happens after you die? Why do we dream? Was luck, how are we going to fix climate change? And which one is cooler, zero or infinity numbers have always meant a lot to me, my first language might have actually just been math when I was young and I still really didn't understand English that well.
I knew how to talk, but I still trying to grasp a hold of the many concepts of English. But math is just like is there. Although I could understand the math at a raw level, I couldn't really express it. And apparently it always came out as jumbling and confusing.
And I don't really fully remember how I would express myself, but my dad does mom and I called it made up math, because what you would do is that 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, divide that well, yet you would just make up words. You'd say something like, hey, dad, what's 11 tidally? Fifty nine. And I would have no idea because you were the only person who would know what the answer was.
Do you remember that. Yeah, I remember asking about some sort of like pancake. Sure. And you're like I have no idea how do you do a pancake. And I like to explain it to you.
Yeah. I think you've been explaining math to me for a long time. 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 would absorb more knowledge, be like a sponge, soaking up the math.
There are numbers that can be put into fractions, numbers that can't be put into fractions and just go on forever. You guys know the Fibonacci sequence rate one plus one will be two. Two plus two equals five through 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 zero and infinity. They're both kind of just like the ultimate mind boggles.
What happens if I pit their coolness against each other, which is more important, more expensive, the mind blow up factor, the best and kind of only people that I would really talk to about it would be none other than mathematicians.
Hi. Do I have both of you? You have me high.
OK, so on the phone right now, I was able to call up James Grine and Eugenia Chan. They are both super awesome math people who do a lot of thinking about the importance of these numbers.
I give lots of talks around the world and people might see me on a YouTube channel called No File.
Now, Eugenia is the scientist in residence at the School of the Art Institute of Chicago, which is pretty cool.
And I've written several books. And the second one was called Beyond Infinity.
I have that book actually. Oh, I'm so glad to hear 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?
OK, so on one hand, zero is a number. It's like the other numbers, one, two, three, four, five, up to nine know zero times one is zero.
Zero times two is zero. But also that means that it can be cancel out the zeros and we have one equals two. Well, no, we can't. So we do have to treat zero slightly differently from the other numbers.
It's a number that represents nothing. Both of them are very abstract ideas in our own ways. But that's what matters about math. It's about going to the abstract to solve problems. Because like, even if we just have the drawing of the number one, that doesn't mean it's one that's our interpretation, our symbol to represent the concept.
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 it's something that they all share 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.
It's weird because it's it's there, but at the same time, it's not there.
That's how I think of maths. It's kind of it's definitely there in my head, but it's also not there because it's just in my head.
The same applies to zero. You can't really point at nothing.
Zero is the harder idea. It's harder than one, two, three, 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.
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 infinite. 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 over.
I have the best producers in the world and they actually brought me a cake. Oh, my God, this is so awesome. I'm to try to cut it infinitely and see if it goes to zero. OK, here we go. OK, right.
So I'm cutting the cake, huh.
I had it even at times done well.
Just keep eating whatever you have again. We make the third date. I have a sixteen working through it.
I could keep cutting it forever and ever and ever. Forever and ever and ever.
Anyway, back to the question at hand zero is a lot less flashier than infinity is something that you would use in everyday life. You actually came from merchants and traders and accountants rather than the sort of intellectuals studying maths.
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 mind bending and weird properties where you can play around and create strange beasts and strange universes in which peculiar and amazing things happen.
Yeah, infinity is the one that's the strangest. I mean, strange paradox is that I can't understand.
One example of those paradoxes is that cake conundrum, which I explained in the cake break.
And another one is Hilbert's hotel that was proposed by the mathematician Hilbert's, where he said, Let's imagine we have a hotel with an infinite number of rooms.
Now, Hubert's hotel is confusing, but bear with me macchi of a really big hotel. Now, this hotel is infinite rooms. And let's say that one man walks in one night and says, Hey, I want a book room. You know, you can't just send them to the infinite floor. That doesn't really seem there, you know, because you're starts to walk all that way. So you send him to room one and send the person on room one term to and then send the person en route to two and three and keep going.
So instead of this one guy, I have to travel so incredibly, infinitely far. Everyone just travels one, which works out such a small number, but it eventually converges into infinity. 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.
Yeah, my head hurts. Ray, we're all getting cleverer now.
James, what do you think of what Eugene is saying and why do you think Zero's cooler?
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 13 sheep or something like that, you would have to make a mark for each sheep. So you have to make 13 mark so you can count them. What the Egyptians and the Babylonians did is they started using numerals to represent larger numbers. So now if you want to count 13, 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.
Oh, man, if it wasn't for the concept of the number zero, we would still have to use the talents. You know, the one words like one, two, three, four and then five is just the horizontal line. That would be pretty bad. It's like that boat will cost thirteen thousand us one, two, three, four.
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.
Hey, if you wanna learn more about the importance of sleep to check out my upset about dreams.
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 backward. Oh, no. Zero at its time was a weird idea, but it turned out to be the more practical our computers, the Internet, and we're just using zeros and ones, you can send any number or any message around the world.
It still is a pretty weird idea. 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 there 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 for the center of my brain exploding.
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. 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 is a beautiful, elegant math really is able to take you away.
That's what I love about it. On a dark desert highway, boxer Nelson in my up ahead in distance.
It up from the sand stretching above the clouds. It's the. Passion in the finned buses. Through the sliding glass door. I get my infinity card. It's for the infinite floor. I must be at the. What's 13 pancake five with the flip over of six eighty four tie. Yeah, did I get the question right? Sure, yeah. Thank you so much for listening. I'm typing the show was produced by Veronica Schuman's and Yasmin Materne, our digital producer is Olivia Pasquarelli.
My guests were Dr. James Grime and Dr. Eugenie Chang. You guys are awesome. Thanks to Crystal. Do him for the editorial assistant. The theme music is by the legendary Johnny Bench and also, thanks to drive, helped me write a record, The Infinity Song.
Next, I want to ask why climate change?
Do you ever lose hope? Yes, till next time I'm Ty. Keep asking why. Support for tracks comes from the Corporation for Public Broadcasting, this is tracks from P, R, X.