Which is cooler, zero or infinity?
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. Okay now try to imagine a box of infinity like Everything. And you also can't. Really. Because just Kinda goes on and on and you can contain it if it keeps going. Right. What's up with that? Hi. There I'm. This is my podcast tasks asks why there are so many. Great questions. To get answers questions like. Do you trust your. What happens after you die? On we train. was. Long. How are we gonNA fix climate change. and which one is cooler. Zero. Or. Infinity. Numbers of always meant a lot to me. My first language might have actress been math. When I was young and I still really didn't understand English that well, I knew what a talk but it was still trying to grasp ahold of many concepts of English, but math is just like. Is there. Although I could understand the math at a role level, I couldn't really express it, and apparently it always came out as jumbling 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 would come up with but since he 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 eleven tiddly fifty nine and I would have no idea because you're the only person who would know what the answer was. You remember that yeah. I remember asking about some sort of like a pancake. Sure you like Thai I have no idea how to do a pancake night like explain it to you. Yeah. I, think even explaining math to me for a long time. Since the Simpler Times of the pancake functions I spent a lot of time reading old secondhand textbooks from this old bookseller in our neighborhood that would absorb more knowledge be like a sponge sir. there. Are numbers that can be put into fractions numbers that can't be put into fractions interest go on forever you know the Sequence right wobbles will be two to three goals five through the length of your belly button to your feet to your head. The ratio of that equals the Golden. Ratio. And then the numbers that we just can't comprehend like zero and infinity. They're both kind of just like the. Ultimate mind boggling what happens if I pit their cruel nece against each other, which was more important more expensive. The mind blow up factor best and kind of only people that I would really talk about it would be none other than mathematician. Hi Do I have both of you you have me. Hi. Okay so on the phone right now, I was able to call up James Grind and Eugenie Chin. There 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 Youtube Channel could number 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 cooled 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 explain to me what zero even is as a mathematical concept. Okay so on one hand zero is a number. As, like the other numbers one, two, three, four, five, two, nine. Zero Times one is zero. Zero. Times two is zero but also that means that it just come. You come sit out Zeros. I'm have one goes to 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 of an abstract ideas in ways, but that's what matters about. Mathis 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 are symbol to represent the concept you could point out one sheep, one, cow, one coin but one of 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 they all share? When you try and teach small child how to count You keep showing them objects in 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 one nurse. And you can't do it for them. You can't point that's it. You can't see 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 fair because it's just in my head the shame applies to zero you can't really point at. Zero is the harder idea. It's harder than one, two, three, one sheep and one cow have something in common but zero sheep 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 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 Hof left and then if you eat half of what's left, then still some left and if you eat half of what's left there, still some left. If you keep eating Hof of your remaining chocolate cake, you can take an infinite number of bites of chocolate cake and there will still be some left. I have the best producers in the world and they actually brought me a cake God this. Oh, awesome on the traffic cut infinitely and see if it goes to zero. Okay. Here we go. So I'm cutting the cake. Eaten at times? Dom. Yep. We'll just keep eating whenever you. Half again, make the third. Sky The sixteenth. Through I could keep calling it forever and ever and ever ever. Ever ever. Anyway. Back to the question at hand. Is a lot less flashier than infinity is something. That, you would use in everyday life actually came from merchants and traders and accountant rather then they sort of intellectuals studying Matt's 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 I'm 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 way you can play around and create strange pistes and strange universes in which peculiar and amazing things happen. Yeah. Infinity is the one that's the strangest I mean strange paradoxes the I can't understand. One. Example of those paradoxes that cake conundrum which 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 hotels confusing for bear with me. matchy of a really big hotel. Now, this hotel infinite roofs. and. Let's say that one man walks in one night and says, Hey, on the book room, you know you can't send him. To the infant floor that doesn't really seem fair. You know because you still have to walk all that way. So. You sent him to room one and send the person on route one term deal. Then send the person on route to to room three and keep going. So instead of this one guy after travel. So incredibly infinitely far everyone just travels wants. 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 in other guests dune without asking them to share room which they probably wouldn't want to do. Yes my head hurts. We're all getting clever. Now, James, what do you think of what you genius saying and why do you think Zeros Cooler Think, we're going to find that these two ideas are going to be very connected because they are related ideas. One being nothing won't being everything, but without zero, you wouldn't have any of modern mathematics today the reason zero. 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 make thirteen marks you can count them what the Egyptians and the Babylonians did is they started using news to represent lodging numbers. So now if you want to count thirteen, you can just use. A one and a three. So now you need zero in here because what is the difference between thirty two and three hundred to? Well, you need that space in the middle in the old times that would be actually a space. It was any later that zero recognized as a number. But with place value system, you can do the whole of mathematics today. Oh Man. If it wasn't for the concept of the numbers zero, we would still have to use the talents just be no the one where it's like one, two, three, four, and then five is the horizontal line. That won't be pretty bad. It's like that boat will cost thirteen, thousand dollars one, two, three, four, I agree with James 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 funeral learn more about the importance of sleep. To check. My upset. About. Dreams. Not. Everybody has to understand 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 get into trouble. Because we'd have to stop somewhere and if you stop somewhere then everything would implode backward. Oh No. At is kind was a weird idea, but it turned out to be the more practical. I'll computers the Internet with just using Zeros and ones you can send any number or any message around the world. It's still is a pretty weird idea. Things seem weird I get to seem less would 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're mind-bending things like that. Maybe one plus infinity is actually different from infinity plus one a maybe there actually different sizes of infinity so that there's the smallest infinity but then there's a big 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 infinity's Baugh does just. Exploding. Those sorts of weird things all why I really love maths because it's a place where I can explore things don't really happen in the real world. The real world is very important and it's where we live our lives I really like the world of ideas. It doesn't matter which ones cooler. They're both so interesting. So elaborate, they're different and they're beautiful math is messy but yet in its message is a beautiful elegance math. Really is able to take you away. That's what I love about it. Mawlid Dr Desert House. Walks. In my own. Head. From this earth. Stretching of. ood. Passing defended bosses. Through the sliding glass door. Get, my infinite key car. It's four. Finished floor. I'm must be. What's thirteen pancake five with the flip over of six, eighty four. Thai? Yeah. To the question. Sure. Thank you so much for listening. I'm type the show was produced by Veronica Simmons and Yasmin Return. Our digital producers Livia Pasquarelli. Guests were Dr James Grime and Dr Cina Chang. You guys are awesome. Thanks to crystal do him for the editorial assistance the theme music is by the legendary Johnny Spence an also thanks to drive me writer record the Infinity Song. Next time on tasks Y. climate chain. Do, you ever lose hope. Yes TILL NEXT AREN'T. KEEP BASKING WHY Support. For tracks from the corporation for public broadcasting. This is tracks from P. R.. X..