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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

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and the complexity of life on earth is never ending,

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little embellishments and complexifications

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in the DNA code

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lead to new things like giraffes, or orchids --

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so too, do little embellishments in the crochet code

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lead to new and wondrous creatures

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in the evolutionary tree of crochet life.

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So this project really has

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taken on this inner organic life of its own.

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There is the totality of all the people who have come to it.

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And their individual visions,

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and their engagement with this mathematical mode.

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We have these technologies. We use them.

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But why? What's at stake here? What does it matter?

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For Chrissy and I, one of the things that's important here

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is that these things suggest

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the importance and value of embodied knowledge.

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We live in a society

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that completely tends to valorize

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symbolic forms of representation --

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algebraic representations,

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equations, codes.

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We live in a society that's obsessed

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with presenting information in this way,

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teaching information in this way.

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But through this sort of modality,

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crochet, other plastic forms of play --

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people can be engaged with the most abstract,

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high-powered, theoretical ideas,

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the kinds of ideas that normally you have to go

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to university departments to study in higher mathematics,

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which is where I first learned about hyperbolic space.

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But you can do it through playing with material objects.

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One of the ways that we've come to think about this

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is that what we're trying to do with the Institute for Figuring

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and projects like this, we're trying to have

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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)