字幕列表 影片播放 列印英文字幕 - What am I ever gonna need this? I'm looking at your screenshot, and I think the answer is never, you are never gonna need this. I'm professor Moon Duchin, mathematician. Today, I'm here to answer any and all math questions on Twitter. This is "Math Support". [upbeat music] At RecordsFrisson says, "What is an algorithm? Keep hearing this word." Hmm. The way you spelled algorithm, like it has rhythm in it. I like it. I'm gonna keep it. A mathematician, what we mean by algorithm is just any clear set of rules, a procedure for doing something. The word comes from 9th century Baghdad where Al-Khwarizmi, his name became algorithm, but he also gave us the word that became algebra. He was just interested in building up the science of manipulating what we would think of as equations. Usually, when people say algorithm, they mean something more computery, right? So usually, when we have a computer program, we think of the underlying set of instructions as an algorithm, given some inputs it's gonna tell you kind of how to make a decision. If an algorithm is just like a precise procedure for doing something, then an example is a procedure that's so precise that a computer can do it. At llamalord1091 asks, "How the fuck did the Mayans develop the concept of zero?" Everybody's got a zero in the sense that everybody's got the concept of nothing. The math concept of zero is kind of the idea that nothing is a number. The heart of it is, how do different cultures incorporate zero as a number? I don't know much about the Mayan example, particularly, but you can see different cultures wrestling with. Is it a number? What makes it numbery? Math is decided kind of collectively. Is that, it is useful to think about it as a number because you can do arithmetic to it. So it deserves to be called a number. At jesspeacock says, "How can math be misused or abused?" 'Cause the reputation of math is just being like plain right or wrong and also being really hard, it gives mathematicians a certain kind of authority, and you can definitely see that being abused. And this is true more and more now that data science is kind of taking over the world. But the flip side of that, is that math is being used and used well. In about five years ago, I got obsessed with redistricting and gerrymandering and trying to think about how you could use math models to better and fairer redistricting. Ancient, ancient math was being used. If you just close your eyes and do random redistricting, you're not gonna get something that's very good for minorities. And now that's become much clearer because of these mathematical models. And when you know that, you can fix it. And I think that's an example of math being used to kind of move the needle in a direction that's pretty good. At ChrisExpTheNews. That is hard to say Analytic Valley Girl. "I honestly have no idea what math research looks like, and all I'm envisioning is a dude with a mid-Atlantic accent narrating over footage of guys in labcoats looking at shapes and like a number four on a whiteboard." There's this fatal error at the center of your account. The whiteboard, like no! Mathematicians are fairly united on this point of disdaining whiteboards together. So we really like these beautiful things called chalkboards. And we especially like this beautiful fetish object, Japanese chalk. And then when you write, it's really smooth. The things that are fun about this, the colors are really vivid and also it erases well, which matters. You just feel that much smarter when you're using good chalk. One thing I would say about math research that probably is a little known, is how collaborative it is. Typical math papers have multiple authors and we're just working together all the time. It's kinda fun to look back at the paper correspondence of mathematicians from a hundred years ago who are actually putting all this cool math into letters and sending them back and forth. We've done this really good job of packaging math to teach it, and so that it looks like it's all done and clean and neat, but math research is like messy and creative and original and new, and you're trying to figure out how things work and how to put them together in new ways. It looks nothing like the math in school, which is sort of a much polished up after the fact finished product version of something that's actually like out there and messy and weird. So dYLANjOHNkEMP says, "Serious question that sounds like it's not a serious question for mathematician, scientists, and engineers. Do people use imaginary numbers to build real things?" Yes, they do. You can't do much without them and particular you equation solving requires these things. They got called imaginary at some point because just people didn't know what to do with them. There were these concepts that you needed to be able to handle and manipulate, but people didn't know whether they count as numbers. No pun intended. Here's the usual number line that you're comfortable with, 0, 1, 2, and so on. Real numbers over here. And then, just give me this number up here and call it i. That gives me a building block to get anywhere. So now I come out here, this will be like 3+2i. So i is now the building block that can and get me anywhere in space. Yes, every bridge and every spaceship and all the rest, like you better hope someone could handle imaginary numbers well. At ltclavinny says, "#MovieErrorsThatBugMe The 7th equation down, on the 3rd chalkboard, in A Beautiful Mind, was erroneously shown with two extra variables and an incomplete constant." Boy, that requires some zooming. I will say though, for me and lots of mathematicians, watching the math in movies is a really great sport. So what's going on here is, I see a bunch of sums. I see some partial derivatives. There's a movie about John Nash who is actually famous for a bunch of things in math world. One of them is game theory ideas and economics. But I do not think that's what's on the board here, if I have to guess. I think what he is doing is earlier very important work of his, this is like Nash embedding theorems, I think. So this is like fancy geometry. You can't tell 'cause it looks like a bunch of sums and squiggles. You're missing the part of the board that defines the terms. [chuckles] So do I agree with J.K. Vinny that stuff is missing from the bottom row? I don't think that I do, sorry Vinny. [chuckles] At ADHSJagCklub asks, "Question... without using numbers, and without using a search engine, do you know how to explain what Pi is in words?" You sort of need pi or something like it to talk about any measurements of circles. Everything you wanna describe about rounds things you need pi to make it precise. Circumference, surface area, area, volume, anything that relates length to other measurements on circles needs pi. Here's a fun one. So what if you took 4 and you subtracted 4/3, and then you added back 4/5, and then you subtracted 4/7, and so on. So it turns out that if you kept going forever, this actually equals pi. I don't teach you this in school. So this is what's called the power series and it's pretty much like all the originators of calculus. We're kind of thinking this way, about these like infinite sums. So that's another way to think about pi if you like are allergic to circles. At cuzurtheonly1, "Bro, why did math people have to invent infinity?" 'Cause it is so convenient. It completes us. Could we do math without infinity? The fact that the numbers go on forever, 1, 2, 3, 4... It would be pretty hard to do math without the dot, dot, dots. In other words, without the idea of things that go on forever, we kinda need that. But we maybe didn't have to create like a symbol for it and create an arithmetic around it and create like a geometry for it, where there's like a point at infinity. That was optional, but it's pretty. At TheFillWelix, "What is the sexiest equation?" I'm gonna show you an identity or a theorem that I love. I just think is really pretty. And that I use a lot. So this is about surfaces and the geometry of surfaces. It looks like this. This is called Minsky's product regions theorem. So this is the, a kind of almost equality that we really like in my kind of math. The picture that goes along with this theorem looks something like this, you have a surface, you have some curves. This is called a genus 2 surface. It's like a double inner tube. It's sort of like two hollow donuts kind of surgered together in the middle. And so this is telling you what happens when you take some curves, like the ones that I've colored here and you squeeze them really thin. So it's the thin part for a set of curves. And it's telling you that... This looks just like what would happen if you like pinched them all the way off and cut open the surface there, you'd get something simpler and a leftover part that is well understood. At avsa says, "What if blockchain is just a plot by math majors to convince governments, VC funds and billionaires to give money to low level math research?" No. And here's how I know. We're really bad at telling the world what we're doing and incidentally getting money for it. Most people could tell you something about new physics ideas, new chemistry, new biology ideas from say, the 20th century. And most people probably think there aren't new things in math, right? There are breakthroughs in math all the time. One of the breakthrough ideas from the 20th century is turns out there aren't three basic three dimensional geometries. There are eight. Flat like a piece of paper, round like a sphere. And then the third one looks like a Pringle. It's this hyperbolic geometry or like saddle shape. Another one is actually instead of a single Pringle, you pass to a stack of Pringles. So like this. So we call this H2 x R. Put these all together and you get a three dimensional geometry.