# Annotated captions of Margaret Wertheim on the beautiful math of coral (and crochet) in English

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I'm here today, as June said, |

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to talk about a project |

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that my twin sister and I have been doing for the past three and half years. |

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We're crocheting a coral reef. |

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And it's a project that we've actually |

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been now joined by hundreds of people around the world, |

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who are doing it with us. Indeed thousands of people |

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have actually been involved in this project, |

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in many of its different aspects. |

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It's a project that now reaches across three continents, |

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and its roots go into the fields of mathematics, |

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marine biology, feminine handicraft |

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and environmental activism. |

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It's true. |

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It's also a project |

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that in a very beautiful way, |

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the development of this |

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has actually paralleled the evolution of life on earth, |

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which is a particularly lovely thing to be saying |

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right here in February 2009 -- |

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which, as one of our previous speakers told us, |

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is the 200th anniversary |

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of the birth of Charles Darwin. |

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All of this I'm going to get to in the next 18 minutes, I hope. |

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But let me first begin by showing you |

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some pictures of what this thing looks like. |

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Just to give you an idea of scale, |

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that installation there is about six feet across, |

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and the tallest models are about two or three feet high. |

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This is some more images of it. |

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That one on the right is about five feet high. |

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The work involves hundreds of different crochet models. |

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And indeed there are now thousands and thousands of models that people |

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have contributed all over the world as part of this. |

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The totality of this project |

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involves tens of thousands of hours |

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of human labor -- |

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99 percent of it done by women. |

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On the right hand side, that bit there is part of an installation |

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that is about 12 feet long. |

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My sister and I started this project in 2005 |

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because in that year, at least in the science press, |

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there was a lot of talk about global warming, |

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and the effect that global warming was having on coral reefs. |

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Corals are very delicate organisms, |

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and they are devastated by any rise in sea temperatures. |

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It causes these vast bleaching events |

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that are the first signs of corals of being sick. |

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And if the bleaching doesn't go away -- |

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if the temperatures don't go down -- reefs start to die. |

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A great deal of this has been happening in the Great Barrier Reef, |

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particularly in coral reefs all over the world. |

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This is our invocation in crochet of a bleached reef. |

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We have a new organization together called The Institute for Figuring, |

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which is a little organization we started |

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to promote, to do projects about the |

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aesthetic and poetic dimensions of science and mathematics. |

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And I went and put a little announcement up on our site, |

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asking for people to join us in this enterprise. |

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To our surprise, one of the first people who called |

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was the Andy Warhol Museum. |

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And they said they were having an exhibition |

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about artists' response to global warming, |

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and they'd like our coral reef to be part of it. |

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I laughed and said, "Well we've only just started it, |

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you can have a little bit of it." |

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So in 2007 we had an exhibition, |

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a small exhibition of this crochet reef. |

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And then some people in Chicago came along and they said, |

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"In late 2007, the theme of the Chicago Humanities Festival is |

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global warming. And we've got this 3,000 square-foot gallery |

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and we want you to fill it with your reef." |

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And I, naively by this stage, said, "Oh, yes, sure." |

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Now I say "naively" because actually |

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my profession is as a science writer. |

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What I do is I write books about the cultural history of physics. |

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I've written books about the history of space, |

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the history of physics and religion, |

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and I write articles for people like the New York Times and the L.A. Times. |

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So I had no idea what it meant to fill a 3,000 square-foot gallery. |

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So I said yes to this proposition. |

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And I went home, and I told my sister Christine. |

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And she nearly had a fit |

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because Christine is a professor at one of |

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L.A.'s major art colleges, CalArts, |

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and she knew exactly what it meant to fill a 3,000 square-foot gallery. |

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She thought I'd gone off my head. |

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But she went into crochet overdrive. |

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And to cut a long story short, eight months later |

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we did fill the Chicago Cultural Center's |

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3,000 square foot gallery. |

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By this stage the project had taken on |

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a viral dimension of its own, |

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which got completely beyond us. |

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The people in Chicago decided |

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that as well as exhibiting our reefs, what they wanted to do |

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was have the local people there make a reef. |

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So we went and taught the techniques. We did workshops and lectures. |

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And the people in Chicago made a reef of their own. |

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And it was exhibited alongside ours. |

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There were hundreds of people involved in that. |

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We got invited to do the whole thing |

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in New York, and in London, |

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and in Los Angeles. |

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In each of these cities, the local citizens, |

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hundreds and hundreds of them, have made a reef. |

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And more and more people get involved in this, |

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most of whom we've never met. |

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So the whole thing has sort of morphed |

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into this organic, ever-evolving creature, |

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that's actually gone way beyond Christine and I. |

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Now some of you are sitting here thinking, |

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"What planet are these people on? |

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Why on earth are you crocheting a reef? |

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Woolenness and wetness aren't exactly |

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two concepts that go together. |

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Why not chisel a coral reef out of marble? |

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Cast it in bronze." |

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But it turns out there is a very good reason |

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why we are crocheting it |

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because many organisms in coral reefs |

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have a very particular kind of structure. |

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The frilly crenulated forms that you see |

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in corals, and kelps, and sponges and nudibranchs, |

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is a form of geometry known as hyperbolic geometry. |

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And the only way that mathematicians know |

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how to model this structure |

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is with crochet. It happens to be a fact. |

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It's almost impossible to model this structure any other way, |

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and it's almost impossible to do it on computers. |

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So what is this hyperbolic geometry |

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that corals and sea slugs embody? |

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The next few minutes is, we're all going to get raised up |

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to the level of a sea slug. |

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(Laughter) |

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This sort of geometry revolutionized mathematics |

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when it was first discovered in the 19th century. |

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But not until 1997 did mathematicians actually understand |

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how they could model it. |

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In 1997 a mathematician |

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at Cornell, Daina Taimina, |

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made the discovery that this structure |

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could actually be done in knitting and crochet. |

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The first one she did was knitting. |

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But you get too many stitches on the needle. So she quickly realized |

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crochet was the better thing. |

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But what she was doing was actually making a model |

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of a mathematical structure, that many mathematicians |

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had thought it was actually impossible to model. |

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And indeed they thought that anything like this structure |

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was impossible per se. |

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Some of the best mathematicians spent hundreds of years |

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trying to prove that this structure was impossible. |

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So what is this impossible hyperbolic structure? |

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Before hyperbolic geometry, mathematicians knew |

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about two kinds of space: |

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Euclidean space, and spherical space. |

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And they have different properties. |

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Mathematicians like to characterize things by being formalist. |

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You all have a sense of what a flat space is, Euclidean space is. |

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But mathematicians formalize this in a particular way. |

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And what they do is, they do it through the concept |

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of parallel lines. |

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So here we have a line and a point outside the line. |

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And Euclid said, "How can I define parallel lines? |

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I ask the question, how many lines can I draw through |

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the point but never meet the original line?" |

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And you all know the answer. Does someone want to shout it out? |

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One. Great. Okay. |

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That's our definition of a parallel line. |

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It's a definition really of Euclidean space. |

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But there is another possibility that you all know of: |

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spherical space. |

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Think of the surface of a sphere -- |

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just like a beach ball, the surface of the Earth. |

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I have a straight line on my spherical surface. |

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And I have a point outside the line. How many straight lines |

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can I draw through the point |

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but never meet the original line? |

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What do we mean to talk about |

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a straight line on a curved surface? |

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Now mathematicians have answered that question. |

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They've understood there is a generalized concept |

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of straightness, it's called a geodesic. |

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And on the surface of a sphere, |

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a straight line is the biggest possible circle you can draw. |

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So it's like the equator or the lines of longitude. |

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So we ask the question again, |

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"How many straight lines can I draw through the point, |

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but never meet the original line?" |

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Does someone want to guess? |

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Zero. Very good. |

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Now mathematicians thought that was the only alternative. |

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It's a bit suspicious isn't it? There is two answers to the question so far, |

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Zero and one. |

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Two answers? There may possibly be a third alternative. |

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To a mathematician if there are two answers, |

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and the first two are zero and one, |

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there is another number that immediately suggests itself |

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as the third alternative. |

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Does anyone want to guess what it is? |

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Infinity. You all got it right. Exactly. |

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There is, there's a third alternative. |

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This is what it looks like. |

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There's a straight line, and there is an infinite number of lines |

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that go through the point and never meet the original line. |

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This is the drawing. |

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This nearly drove mathematicians bonkers |

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because, like you, they're sitting there feeling bamboozled. |

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Thinking, how can that be? You're cheating. The lines are curved. |

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But that's only because I'm projecting it onto a |

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flat surface. |

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Mathematicians for several hundred years |

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had to really struggle with this. |

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How could they see this? |

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What did it mean to actually have a physical model |

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that looked like this? |

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It's a bit like this: imagine that we'd only ever encountered Euclidean space. |

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Then our mathematicians come along |

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and said, "There's this thing called a sphere, |

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and the lines come together at the north and south pole." |

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But you don't know what a sphere looks like. |

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And someone that comes along and says, "Look here's a ball." |

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And you go, "Ah! I can see it. I can feel it. |

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I can touch it. I can play with it." |

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And that's exactly what happened |

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when Daina Taimina |

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in 1997, showed that you could crochet models |

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in hyperbolic space. |

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Here is this diagram in crochetness. |

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I've stitched Euclid's parallel postulate on to the surface. |

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And the lines look curved. |

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But look, I can prove to you that they're straight |

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because I can take any one of these lines, |

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and I can fold along it. |

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And it's a straight line. |

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So here, in wool, |

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through a domestic feminine art, |

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is the proof that the most famous postulate |

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in mathematics is wrong. |

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(Applause) |

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And you can stitch all sorts of mathematical |

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theorems onto these surfaces. |

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The discovery of hyperbolic space ushered in the field of mathematics |

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that is called non-Euclidean geometry. |

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And this is actually the field of mathematics |

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that underlies general relativity |

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and is actually ultimately going to show us |

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about the shape of the universe. |

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So there is this direct line |

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between feminine handicraft, |

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Euclid and general relativity. |

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Now, I said that mathematicians thought that this was impossible. |

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Here's two creatures who've never heard of Euclid's parallel postulate -- |

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didn't know it was impossible to violate, |

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and they're simply getting on with it. |

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They've been doing it for hundreds of millions of years. |

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I once asked the mathematicians why it was |

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that mathematicians thought this structure was impossible |

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when sea slugs have been doing it since the Silurian age. |

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Their answer was interesting. |

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They said, "Well I guess there aren't that many mathematicians |

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sitting around looking at sea slugs." |

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And that's true. But it also goes deeper than that. |

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It also says a whole lot of things |

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about what mathematicians thought mathematics was, |

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what they thought it could and couldn't do, |

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what they thought it could and couldn't represent. |

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Even mathematicians, who in some sense |

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are the freest of all thinkers, |

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literally couldn't see |

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not only the sea slugs around them, |

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but the lettuce on their plate -- |

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because lettuces, and all those curly vegetables, |

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they also are embodiments of hyperbolic geometry. |

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And so in some sense they literally, |

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they had such a symbolic view of mathematics, |

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they couldn't actually see what was going on |

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on the lettuce in front of them. |

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It turns out that the natural world is full of hyperbolic wonders. |

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And so, too, we've discovered |

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that there is an infinite taxonomy |

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of crochet hyperbolic creatures. |

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We started out, Chrissy and I and our contributors, |

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doing the simple mathematically perfect models. |

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But we found that when we deviated from the specific |

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setness of the mathematical code |

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that underlies it -- the simple algorithm |

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crochet three, increase one -- |

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when we deviated from that and made embellishments to the code, |

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the models immediately started to look more natural. |

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And all of our contributors, who are an amazing |

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collection of people around the world, |

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do their own embellishments. |

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As it were, we have this ever-evolving, |

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crochet taxonomic tree of life. |

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Just as the morphology |

tedtalks |
12:14 12:16 |
and the complexity of life on earth is never ending, |

tedtalks |
12:16 12:19 |
little embellishments and complexifications |

tedtalks |
12:19 12:21 |
in the DNA code |

tedtalks |
12:21 12:24 |
lead to new things like giraffes, or orchids -- |

tedtalks |
12:24 12:27 |
so too, do little embellishments in the crochet code |

tedtalks |
12:27 12:30 |
lead to new and wondrous creatures |

tedtalks |
12:30 12:33 |
in the evolutionary tree of crochet life. |

tedtalks |
12:33 12:35 |
So this project really has |

tedtalks |
12:35 12:38 |
taken on this inner organic life of its own. |

tedtalks |
12:38 12:41 |
There is the totality of all the people who have come to it. |

tedtalks |
12:41 12:43 |
And their individual visions, |

tedtalks |
12:43 12:46 |
and their engagement with this mathematical mode. |

tedtalks |
12:46 12:48 |
We have these technologies. We use them. |

tedtalks |
12:48 12:51 |
But why? What's at stake here? What does it matter? |

tedtalks |
12:51 12:54 |
For Chrissy and I, one of the things that's important here |

tedtalks |
12:54 12:56 |
is that these things suggest |

tedtalks |
12:56 12:59 |
the importance and value of embodied knowledge. |

tedtalks |
12:59 13:01 |
We live in a society |

tedtalks |
13:01 13:03 |
that completely tends to valorize |

tedtalks |
13:03 13:05 |
symbolic forms of representation -- |

tedtalks |
13:05 13:07 |
algebraic representations, |

tedtalks |
13:07 13:09 |
equations, codes. |

tedtalks |
13:09 13:11 |
We live in a society that's obsessed |

tedtalks |
13:11 13:13 |
with presenting information in this way, |

tedtalks |
13:13 13:16 |
teaching information in this way. |

tedtalks |
13:16 13:19 |
But through this sort of modality, |

tedtalks |
13:19 13:23 |
crochet, other plastic forms of play -- |

tedtalks |
13:23 13:26 |
people can be engaged with the most abstract, |

tedtalks |
13:26 13:28 |
high-powered, theoretical ideas, |

tedtalks |
13:28 13:30 |
the kinds of ideas that normally you have to go |

tedtalks |
13:30 13:33 |
to university departments to study in higher mathematics, |

tedtalks |
13:33 13:36 |
which is where I first learned about hyperbolic space. |

tedtalks |
13:36 13:40 |
But you can do it through playing with material objects. |

tedtalks |
13:40 13:42 |
One of the ways that we've come to think about this |

tedtalks |
13:42 13:45 |
is that what we're trying to do with the Institute for Figuring |

tedtalks |
13:45 13:47 |
and projects like this, we're trying to have |

tedtalks |
13:47 13:49 |
kindergarten for grown-ups. |

tedtalks |
13:49 13:51 |
And kindergarten was actually a very formalized |

tedtalks |
13:51 13:53 |
system of education, |

tedtalks |
13:53 13:55 |
established by a man named Friedrich Froebel, |

tedtalks |
13:55 13:57 |
who was a crystallographer in the 19th century. |

tedtalks |
13:57 13:59 |
He believed that the crystal was the model |

tedtalks |
13:59 14:01 |
for all kinds of representation. |

tedtalks |
14:01 14:04 |
He developed a radical alternative system |

tedtalks |
14:04 14:06 |
of engaging the smallest children |

tedtalks |
14:06 14:08 |
with the most abstract ideas |

tedtalks |
14:08 14:10 |
through physical forms of play. |

tedtalks |
14:10 14:12 |
And he is worthy of an entire talk on his own right. |

tedtalks |
14:12 14:14 |
The value of education |

tedtalks |
14:14 14:17 |
is something that Froebel championed, |

tedtalks |
14:17 14:19 |
through plastic modes of play. |

tedtalks |
14:19 14:21 |
We live in a society now |

tedtalks |
14:21 14:23 |
where we have lots of think tanks, |

tedtalks |
14:23 14:26 |
where great minds go to think about the world. |

tedtalks |
14:26 14:28 |
They write these great symbolic treatises |

tedtalks |
14:28 14:30 |
called books, and papers, |

tedtalks |
14:30 14:32 |
and op-ed articles. |

tedtalks |
14:32 14:34 |
We want to propose, Chrissy and I, |

tedtalks |
14:34 14:37 |
through The Institute for Figuring, another alternative way of doing things, |

tedtalks |
14:37 14:40 |
which is the play tank. |

tedtalks |
14:40 14:42 |
And the play tank, like the think tank, |

tedtalks |
14:42 14:44 |
is a place where people can go |

tedtalks |
14:44 14:46 |
and engage with great ideas. |

tedtalks |
14:46 14:48 |
But what we want to propose, |

tedtalks |
14:48 14:50 |
is that the highest levels of abstraction, |

tedtalks |
14:50 14:53 |
things like mathematics, computing, logic, etc. -- |

tedtalks |
14:53 14:55 |
all of this can be engaged with, |

tedtalks |
14:55 14:57 |
not just through purely cerebral algebraic |

tedtalks |
14:57 14:59 |
symbolic methods, |

tedtalks |
14:59 15:03 |
but by literally, physically playing with ideas. |

tedtalks |
15:03 15:05 |
Thank you very much. |

tedtalks |
15:05 15:10 |
(Applause) |