Which is cooler, zero or infinity?
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Now, try to magin a box of Infinity like everything. And you also can't really because it just kinda goes on and on and you can't contain it. If it keeps going, right? What's up with that? Hi there. I'm tired. This my podcast Tosks. Why there are so very many great questions short to get answers questions. Like could you trust your doctor for happened? If do you die when we dream was long harbour, we're gonna fix climate change, and which one is cooler zero or infinite. 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 while I knew what a talk but still try to grasp ahold of the many concepts of English but masses 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 his 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'd 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 pancake. Sure. And you like Thai have no idea. How to do a pancake in explain it to you? Yeah. I think even explaining math to me for a long time. Since the simpler times of the pancake functions. Spent a lot of time reading old second hand textbooks from this old bookseller in our neighborhood note absorb more knowledge be like a sponge sooking up the math. There are numbers that can be put into fractions numbers that can't be put into fractions. Just go on forever. You guys know finan trait wobbles won't be two to three five three two length of your belly button to your feet to your head the ratio of that equals, the golden ratio. And then they're just numbers that we just can't comprehend like zero and Infinity. They're both kinda just like the ultimate mind boggling what happens if I pit their coolness against each other, which was more important more expensive the mind blow up factor. Best in 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. Hi, okay. So. So on the phone right now, I was able to call up James grind and Jana chin. There are both super awesome math people who do a a lot of thinking about the importance of these numbers. I give lots of talks around the world. And people might see me on each channel. Could number file now Gina is the scientist in residence at the school of the Art Institute of Chicago, which is pretty cool. And I've written several books on the second one was cooled beyond Infinity. I have that book. Actually, oh, I'm glad to hear. This is the crazy super debate about coolness of zero versus affinity. James? Can you explain to me what zero even is as a mathematical concept? Okay. So on one hand zero is a number as like the numbers one two three four five two nine zero times. One is e zero times two is era. But also that means that to come come sit out zeros, I'm have to well now, 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, abstract ideas in any ways. But that's what matters about math is 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 at one sheep one cow one coin. But one of those things have in common is this idea of oneness. They have in common, which is not something you can point at. But is something they will share when you try and teach 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 the head from the objects in front of them to this concept of as James says one nece. And you can't do it full them. You can't point. That's 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 tier you can't really point. At nothing zero is the hawed idea is 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 INFINITI you can't go up to your kid? Will look this is one cow. This is no cows. This is everything. Infinite on. Fortunately, 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, if you eat off of your chocolate cake, then you have Hof left, and then if you eat Hof of what's lift, then there's still some left, and if you eat of what's left, the still left 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. Aveeno? I have the best producers in the world. And they actually brought me a cake. God, this is so awesome. On the try to cut it infinitely and see if it goes to zero. Okay, here we go. Proper. So I've cutting the kick. At times. Yup. We'll just keep eating whatever you give half. Again. We make the third eight nine sixteen working through good. Keep calling it forever and ever and ever forever. Never never. Anyway, back to the question. Zero is a lot less flashier than Infinity is something that you would use everyday life actually came from merchants and traders and accountant RAV then the 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. And that means practically everything in the modern world, including things like well eletricity, and that's how Infinity Camby photo of as very practical as well as having mind-bending and with 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. Paradoxes the icon understand one example of those paradoxes that cake conundrum, which I explained in the cake break and another one is Hilbert 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 who are toes confusing bear with me matchy of really big hotel. Now, this hotel, infinite roofs, and let's say that one man walks in one night and says, hey on group, you know, you can't just send them to the infinite floor that doesn't really seem fair. You does to walk all that way. So you sent him to room one and send the person on one term to send the person on two to three and keep going. So instead of this one guy to travel so incredibly infinitely far everyone just travels want which works out such as small number. 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 went want to do. Yeah. My head hurts. Where will get and clever now James, what do you think of what you genius saying? And what do you think zeros cooler? Oh, I think we're going to find that these two ideas, we're going to be very connected because they all related ideas, one being nothing won't being everything. But without you wouldn't have any of modern mathematics today. The reason zero potent is because without it, you have a place value system. So in the old times when you wanted to count the teen sheep or something like that you would have to make a Mark for each sheep. So you have to make thirteen Mark. So you can count them what the gyp shins, and the Babylonians did is they started using new moves to represent larger numbers. So now, if you wanna count thirteen you can just use a one and three so now you need zero in here because what is the difference between thirty two and three hundred. Into. Well, you need that space in the middle in the old times. That would be actually a space any 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 talent beetle. The one words like one two three four and then five is horizontal line. That would 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 cause 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 a tool like for example, sleep which I find pretty boring, but I recognize that it's very important. Hey, if you wanna learn more about the importance of sleep to check on my upset about dreams. Not everybody has to understand it in order 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 backwards. Oh, no. Oh, no. Dear. At his time was a weird idea, but it turned out to be the mall, practical, I'll computers the internet. I'm with just using zero-some. Once you can send any number any message around the world. It's still is a pretty weird idea things that seem with 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 they're actually different sizes of Infinity. So that there's the smallest indeffinitely, but then there's a big Infinity and then as an even bigger Infinity, and you can keep going infinitely. So that there are infinitely many bigger and bigger Infinity's bar. The my brench, boating. Those of weird things all why I really love maths because it's a place where I can explore things, but don't really happen in the real world. The real world is very important. And it's why 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 meshing is a beautiful elegance mass really is able to take you away. That's what I love about it. Dr Dez it. How way? Walks in. Head. From the Senate. Stretching of the class. Has finished bosses. Through the sliding gloves stove. Get my in finit key car. It's four. Flow. I'm must be. What's thirteen Penn? Kick five with the flip over of six eighty four Thai. Yeah. To take the question. My share. Sure. Thank you so much listening. I'm type the show was produced by Veronica Simmons, and has matern our digital producer is Livia Pasquarelli guests were Dr James grime, and Dr Cina Chang guys are also thanks to crystal Doohan for the editors the theme music is by the legendary Johnny spent and also thanks to dry throat me writer for the Finnity. So next time on tire Twi climate chain. Do you ever lose hope? Yes. Till next. I'm tie keep asking why? For more CBC podcasts. Goto CBC dot CA slash podcasts.