The humanity of calculus | Jim Fowler | TEDxColumbus

for hundreds of years academics have thought long and hard about how to make mathematics as engaging as possible and this is what we've come up with the lecture now it has more chalkboards unfortunately I think for most people this is where they've experienced practically all of mathematics was in a classroom like like this and that probably explains why I get the reaction that I do at parties so I met some sort of event and someone comes up to me and they say what do you do and then I say I'm a mathematician and then they say I hate math or I never really liked math I can't do math and in my fantasy I'm always imagining a very different conversation you know or they they come up to me they say what you do and then I say I'm a novelist and then they say I love books I can read and I listen these are the two pillars of of elementary school you know reading and mathematics but but and ginger is totally different reactions in people and I know I get it you know I mean I I love books I love reading and I love reading rainbow as a kid you know and it's not as if you know Reading Rainbow taught me to read by watching television but Reading Rainbow taught me something about the love of reading you know you just you watch levar burton and how you see how much he loves books and you just can't help but just love them along with him and in contrast there's there's not very much love in in math classes you know most of our math classes are not really about the solution they did about getting the answer you know they're not really about the story they're just about the conclusion I mean imagine if mathematicians were tasked with with teaching Cinderella you know you could imagine that we just say theorem Cinderella lived happily ever after every be done with it you know and that that totally misses the point right I mean nobody cares about the happily ever after you know they care about the story and when mathematicians are teaching mathematics that's what they're trying to do they're trying to tell a story and that's what we've been trying to do with our calculus project mooc ulis so it's called tamuka less because it's a calculus project and cows say Moo but it's also a MOOC it's a massive open online course so anybody can sign up for free but instead of these sort of hour-long lectures MOOC ulis is built around five to ten minute videos that you know aim to tell the story of calculus these sort of narratives about the concept of of calculus and to get you an idea here's here's some screen caps so in a lot of the videos you know just writing on paper maybe we're superimposing some computer-generated graphics sometimes we're superimposing a three-dimensional model that I can move around to tell a story about the harmonic series other times i've got a number line and i'm just grabbing the number line and pulling the numbers apart to say something about about limits a lot of the arguments are done just with paper on a desk so i'm pushing around little slips of paper to group terms together to say something about a divergent series and when we're doing computations you know we're doing them with with pens so that the learner can play along at home and in every single video a very happy looking human being appears you know in order to reiterate the point that calculus is something that people do you know and I really mean do you know I don't just want Watchers of calculus videos you know I don't just want theater goers I want actors you know I want people that embody mathematics and and you know to achieve that my team and I also put together a free open-source calculus textbook and an adaptive learning platform with hundreds of calculus exercises so that anybody you know can really look at the stories of calculus you know themselves really really do it and here's an example of one of those stories so it starts with this function f of x equals x squared you can plug in values f of 2 is 4 f of 3 is 9 f of 4 is 16 you know it's not particularly exciting perhaps that f of 3 you know square three times three ends up being nine maybe that's not so exciting but the idea of calculus is to wiggle the input a little bit instead of looking at three look at 3.00 one and 3.00 one squares two 9.00 600 one and if that's not enough you wiggle the input a little bit more F of three point zero two well three point zero two squares two 9.01 200 four or F of three point zero three well 3.0 three squares two 9.01 800 nine and now you're afraid that I'm just going to keep on doing this but the point of calculus is not about numbers right the point is insight and the insight here is that F of 3.00 one is about 9.00 six and that f of 3.00 two is about 9.01 two and that f of 3.00 three is about 9.01 eight and then you look at these numbers and you're like whoa six 12 18 those are all multiples of six all right and what's happening is that when you wiggle the input the output is being affected by about six times as much so when you go from 323.00 to you go from nine to about 9.0 one to 9.0 12 because 12 is 6 times 2 you know and that's that's an insight of of calculus right and the calculus folks dress this up by saying that we've calculated the derivative of the scoring function at the point 3 now the value of F at 3 is 9 but the derivative is 6 because 6 is recording how much the output Wiggles when we wiggle the input so so this is you know this is this is one of the key insights of calculus this is the derivative you know but the goal of mathematics is not just to go around sort of making these one-off look at this pattern I mean the goal of mathematics is to try to weave all these patterns together into some you know understandable narrative so here's an example of this right here here's a number point 999 repeating and this number looks like it's less than 1 but it's not it's in fact equal to 1 and that's I think often surprising but the goal of mathematics is not just to go around muttering surprising things the goal of mathematics is to make these surprising things broadly understandable you know in one way to make something like this understandable is to step back a little bit think about a different number like 0.333 repeating of course which is equal to 1/3 and then you think wow if I take point 3 3 to be repeating and multiply it by 3 I get point 9 9 9 repeating and if I take 1/3 and I multiply it by 3 I get 1 you know and this is often how mathematics works right we've got these surprising insights but we want to make them understandable we want to walk people through the process of understanding that by starting with something easier and guiding them towards something more more exciting more more surprising a much loftier way of saying this is to make a distinction between truth and truth you know and certainly mathematicians are hopefully saying true things but that's not the goal of mathematics right the goal of mathematics is proofs to make true things broadly understandable not just believable but really understandable and the same thing you know we could have seen just thinking about Cinderella you know the truth of the Cinderella story is peasant lady gets with Prince and that's that's true right but it's totally unbelievable you know and the point of the story is to provide context to explain how is it that that surprising truth could possibly have been true you know how could that have happened right what's the proof what's the story right and that's really what math missions are trying to do how could it possibly be that point 999 repeating is equal to 1 that makes no sense you know but we can provide a proof we can provide an argument some sort of story that that explains how this conclusion can possibly come to pass and if mathematics you know is more about stories that a lot of other things follow write stories fit into sequels and prequels you know you don't just have myths you've whole methodologies and you know the really good literature creates a lot of good fanfiction so you know what's the fan fiction of mathematics right where does this go right what's the follow-up stories so here's an example of this this is a riff really on the point 99 repeating story but there's no more decimal point and I've just got 999 and instead of repeating all the way to the right now I've got 999 repeating all the way to the left and this doesn't even really look like a number you should be allowed to write down maybe it looks really big if nothing else you know but we can still play with it you know I can take this number and I can add one to this number and then I can just keep going bravely ahead and see what happens so what nine plus one is ten so I write down a zero and then I carry the 1 and then 1 plus 9 is 10 so I write down a zero and I carry the 1 and 1 plus 9 is 10 you just keep on doing this forever eventually you finish all right and at the end of this long process you've concluded that this enormous number like beast when you add 1 to it it seems that you get zero and you know maybe that tells you that this enormous number like thing is negative 1 because that's the only other thing I know that I add 1 to to get 0 and that really seems crazy you know because that thing looked enormous and now I'm telling you that it's a negative number but it's a good kind of crazy you know it's the kind of crazy that makes computers work I mean computers do store negative numbers in a way like like this and that actually raises you know I think a broader point you know it is this an important story to tell because it's useful is mathematics important primarily because it does such a good job of serving the sciences and I think asking that question is really meant to miss out on something you know people do not go around demanding real-world applications of literature you know fiction is is in fact fictional and and people don't get particularly excited about reading just because now they can finally read those instruction manuals that I've been sitting on their desk you know the the point is something bigger right I mean mathematics is not only a means to an end but it's also an end in itself you know it's not just a tool it's also a triumph you know it's an opportunity for mere mortals to join into a thousand-year-old conversation about some of the deepest things that people have ever thought about and of course it's really hard you know I'm not saying that math isn't hard for everybody but mathematics itself provides the tools to make it possible for us to think about these things I mean I think about place value you know thousands of years ago it was extremely hard to multiply large numbers and now after place value has been discovered we expect practically all of our kids to do math problems location problems that would have stumped the smartest people on earth millennia ago yes that's amazing right that's that's a real gift that we have access to those kinds of techniques of course the place that we're usually receiving those gifts from it is in those math classes you know those those math classes that are certainly imperfect and certainly be better but the problem with those classes was never how large they were you know I'm usually teaching 200 students maybe in a large calculus class but with mu-quillus you know it turns out we've now got nearly 200 thousand enrollments in mooc ulis but that's actually made the experience better perversely you know I think the result has been something that's more human more personal it's a better job of conveying the stories of calculus and it's done a better job of getting the learners to talk to each other about the stories of calculus and that's fundamentally why I'm so optimistic about all this stuff you know we've got hundreds of Lert we have hundreds of thousands of learners now in hundreds of countries and they're not paying us anything because all of our stuff is free and we're not giving them any credit you know so why on earth are they enrolling in this calculus course you know and I think they're really doing it just for the pleasure of finding things out yeah I mean that's that's a very satisfying thing so at its core you know yes mathematics is useful you know yes mathematics makes the modern world work you know but that's not really why it's so compelling you know getting numeric answers is great but what mathematics is really about is not those numbers it's about insights and it's about weaving together those insights into stories that people desperately want to tell each other and that's why for so many people all over the world the most important application of mathematics is to the human spirit thank you you you

Channel: TEDx Talks

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Keywords: millennials, Amtrak, ohio, ted x, columbus, tedx, mobility, tedx talk, English, trains, Downeaster, transportation, ted talk, boomers, asseenincolumbus, ted, high-speed rail, lifeincbus, tedx talks, TEDx, TEDxColumbus, United States, tedxcbus, ted talks, transit

Id: zOhwlYO9QNA

Length: 13min 12sec (792 seconds)

Published: Wed Nov 26 2014