The beautiful math of coral Margaret Wertheim

and here today is June said to talk

about a project that my twin sister and

I have been doing for the past three and

a half years we’re crocheting a coral

reef and it’s a project that we’ve

actually been now joined by hundreds of

people around the world who are doing it

with us and indeed thousands of people

have actually been involved in this

project in many of its different aspects

it’s a project that now reaches across

three continents and its roots go into

the fields of mathematics marine biology

feminine handicraft

and environmental activism it’s true

it’s also a project that in a very

beautiful way the development of this

has actually paralleled the evolution of

life on Earth which is a particularly

lovely thing to be saying right here in

February 2009 which is one of our

previous speakers told us is the 200th

anniversary of the birth of Charles

Darwin all of this I’m going to get to

in the next 18 minutes I hope but let me

first begin by showing you some pictures

of what this thing looks like just to

give you an idea of scale that

installation there is about six feet

across and the tallest models are about

two or three feet high this is some more

images of it that one on the right is

about five feet high the work involves

hundreds of different crochet models and

indeed there are now thousands and

thousands of models that people have

contributed all over the world as part

of this the totality of this project

involves tens of thousands of hours of

human labor 99% of it done by women on

the right hand side that bit there as

part of an installation that is about 12

feet long my sister and I started this

project in 2005 because in that year at

least in the science press there was a

lot of talk about global warming and the

effect that global warming was having on

coral reefs corals are very delicate

organisms and they’re devastated by any

rise in sea temperatures it causes these

vast bleaching events that are the first

signs that corals are being sick and if

the Beeching doesn’t go away if the

temperatures don’t go down reef started

there’s a great deal of this has been

happening in the Great Barrier Reef

particularly in coral reefs all over the

world this is our invocation in crochet

of a bleached reef we have an

organization together called the

Institute for figuring which is a little

organization we started to promote to do

projects about the aesthetic and poetic

dimensions of Science and Mathematics

and I went and put a little announcement

up on our site asking for people to join

us in this enterprise and to our

surprise one of the first people who

called was the Andy Warhol Museum and

they said they were having an exhibition

about artists response to global warming

and they’d like our coral reef to be

part of it and I laughed and said well

we’ve only just started it you can have

a little bit of it so in 2007 we had an

exhibition a small exhibition of this

crochet reef and then some people in

Chicago came along and they said in late

2007 the theme of the Chicago humanities

festival is global warming and we’ve got

this 3,000 square-foot gallery and we

want you to fill it with your reef and I

naively by this day said oh yes sure

now I say naively because actually my

profession is as a science writer what I

do is I write books about the cultural

history of physics I’ve written books

about the history of space the history

of physics and religion and I write

articles for people like the New York

Times and the LA Times so I had no idea

what it meant to fill a 3,000

square-foot gallery so I said yes to

this proposition and I went home and I

told my sister Christine and she nearly

had a fit because Christine is a

professor at one of LA’s major art

colleges Cal arts and she knew exactly

what it meant to fill a 3,000

square-foot gallery and she thought I’d

gone off my head but she went into

crochet overdrive and to cut a long

story short eight months later we did

fill the Chicago Cultural Center the

3,000 square-foot gallery by this stage

the project had taken on a viral

dimension of its own which got

completely beyond us the people in

Chicago decided that as well as

exhibiting our reefs what they wanted to

do was have the local people there make

a reef so we went and taught the

techniques we did workshops and lectures

and the people in Chicago made a reef of

their own and it was exhibited alongside

ours and there were hundreds of people

involved in that and we got invited to

do the whole thing in New York and in

London and

Los Angeles and in each of these cities

the local citizen hundreds and hundreds

of them have made a rift and more and

more people get involved with this most

of whom we’ve never met so the whole

thing is sort of a morphed into this

organic ever-evolving creature that’s

actually got way beyond Kristen and I

now some of you are sitting here

thinking what planet are these people on

why on earth are you crocheting a reef

woollen nests and wetness aren’t exactly

two concepts that go together why not

chisel a coral reef out of marble cast

it in bronze but it turns out there’s a

very good reason why we are crocheting

it because many organisms in coral reefs

have a very particular kind of structure

that freely crenelated forms that you

see in corals and kelps and sponges and

nudibranch is a form of geometry known

as hyperbolic geometry and the only way

that mathematicians know how to model

this structure is with crochet it

happens to be a fact it’s almost

impossible to model this structure any

other way and it’s almost impossible to

do it on computers so what is this

hyperbolic geometry that corals and sea

slugs embody so we the next few minutes

is we’re all going to get raised up to

the level of a sea slug this sort of

geometry was revolutionized mathematics

when it was first discovered in the

nineteenth century but not until 1997

did mathematicians actually understand

how they could model it and in 1997 a

mathematician at Cornell Dana tamina

made the discovery that this structure

could actually be done in knitting and

crochet the first one she did was

knitting but you get too many stitches

on the needle so she quickly realized

the crochet was the better thing but

what she was doing was actually making a

model of a mathematical structure that

many mathematicians have thought it was

actually impossible to model and indeed

they thought that anything like this

structure was impossible per se some of

the best mathematicians spent hundreds

of years trying to prove that this

structure was impossible so what is this

impossible hyperbolic structure before

hyperbolic geometry mathematicians knew

about two kinds of spaced Euclidean

space and spherical space and they have

different properties and mathematicians

like to characterize things by being

formulas so you all

the sense of what a flat space is

Euclidean spaces but mathematicians

formalize it in a particular way and

what they do is they do it through the

concept of parallel lines so here we

have a line and a point outside the line

and Euclid said how can i define

parallel lines I asked the question how

many lines can I draw through the point

but never meet the original line and you

all know the answer to someone want to

shout it out one great ok that’s our

definition of a parallel line it’s a

definition really of Euclidean space but

there’s another possibility that you all

know of spherical space think of the

surface of a sphere just like a beach

ball the surface of the earth I have a

straight line on my spherical surface

and I have a point outside the line how

many let’s straight lines can I draw

through the point that never meet the

original line what do we mean to talk

about a straight line on a curved

surface now mathematicians have answered

that question and they’ve understood

there’s a generalized concept of

straightness it’s called a geodesic and

on the surface of a sphere that a

straight line is the biggest possible

circle you can draw so it’s like the

equator or the lines of longitude so we

asked the question again how many

straight lines can I draw through the

point that never meet the original line

so to someone want to guess 0 very good

now mathematicians thought that was the

only alternatives it’s a bit suspicious

isn’t it there’s two answers to the

questions so far zero and one two

answers there may possibly be a third

alternative and to a mathematician if

there are two answers and the first two

is zero and one there’s another number

that immediately suggests itself as the

third alternative does anyone want to

guess what it is infinity you all got to

right exactly there is there’s a third

alternative this is what it looks like

it is a straight line and there’s an

infinite number of lines that go through

the point and never meet the original

line this is the drawing this nearly

drove mathematicians bonkers because

like you they’re sitting there feeling

bamboozled thinking how can that be

you’re cheating the lines are curved but

that’s only because I’m projecting it on

to a flat surface and mathematicians for

several hundred years had to really

struggle with this how could they see

the

what did it mean to actually have a

physical model that looked like this and

it’s a bit like this imagine that we’d

only ever encountered Euclidean space

and then our mathematicians come along

and said this is thing called a sphere

and the lines come together at the North

and South Pole but you don’t know what a

sphere looks like and someone then comes

along and says look here’s a ball and

you are I can see it I can feel it I can

touch it I can play with it and that’s

exactly what happened when Dana came in

ER in 1997 invent in showed that you

could crochet models in hyperbolic space

here is this diagram in crochet nurse

and I’ve stitched Euclid’s parallel

postulate onto the surface and the lines

looked curved but look I can prove to

you that they’re straight because I can

take any one of these lines and I can

fold along it and it’s a straight line

so here in wool through a domestic

feminine art is the proof that the most

famous postulate in mathematics is wrong

and you can stitch all sorts of

mathematical theorems onto these

surfaces the discovery of hyperbolic

space assured in the field of

mathematics that’s called non Euclidean

geometry and this is actually the field

of mathematics that underlies general

relativity and is actually ultimately

going to show us about the shape of the

universe so there is this direct line

between feminine handicraft

Euclid and general relativity now I said

that mathematicians thought this was

impossible here is two creatures who

never heard of Euclid’s parallel

postulate didn’t know it was impossible

to violate and they’re simply getting on

with it they’ve been doing it for

hundreds of millions of years and I once

asked the mathematicians why it was that

mathematicians thought this structure

was impossible when sea slugs have been

doing it since the Silurian age and

their answer was interesting they said

well I guess there aren’t that many

mathematicians sitting around looking at

sea slugs and that’s true but it also

goes deeper than that it also says a

whole lot of things about what

mathematicians thought mathematics was

what they thought it couldn’t couldn’t

do what they thought it couldn’t

couldn’t represent and even

mathematicians who in some sense of the

freest of all thinkers literally

couldn’t see not only the sea slugs

around them but the latest on their

plate because lattices and all those

clearly vegetables they also are

embodiments of hyperbolic geometry and

so in some sense they literally they had

such a symbolic view of mathematics they

couldn’t actually see what was going on

on the lettuce in front of them it turns

out that the natural world is full of

hyperbolic wonders and so too we’ve

discovered that there is an infinite

taxonomy of crochet hyperbolic creatures

we started out crissy and I and our

contributors doing the simple

mathematically perfect models but we

found that when we deviated from the

specific setna the mathematical code

that underlies is the simple algorithm

crochet three increase one when we

deviated from that and made

embellishments to the code the models

immediately started to look more natural

and all of our contributors who are

amazing collection of people around the

world do

their own embellishments and as it were

we have this ever-evolving crochet

taxonomic tree of life and just as the

morphology and the complexity of life on

Earth is never-ending

little embellishments and

complexification zin the DNA code lead

to new things like giraffes or orchids

so two little embellishments in the

crochet code lead to new and wondrous

creatures in the evolutionary tree of

crochet life so this project really has

taken on this inner organic life of its

own that’s the totality of all the

people who’ve come to it and their

individual visions and their engagement

with this mathematical mode we have

these technologies we use them but why

what’s at stake here what does it matter

for Crissy and I one of the things

that’s important here is that these

things suggest that importance and value

of embodied knowledge we live in a

society that completely tends to

valorize symbolic forms of

representation algebraic representations

equations codes we live in a society

that’s obsessed with presenting

information in this way teaching

information in this way but through this

sort of modality crocheted other plastic

forms of play people can be engaged with

the most abstract high powered

theoretical ideas the kind of ideas that

normally you have to go to university

departments to study in higher

mathematics which is where I first

learned about hyperbolic space but you

can do it through playing with material

objects and one of the ways that we’ve

come to think about this is that what

we’re trying to do with the Institute

for figuring and projects like this

we’re trying to have kindergarten for

grown-ups

and kindergarten was actually a very

formalized system of Education

established by a man named Friedrich

Froebel who was a crystallographer in

the 19th century he believed that the

crystal was the model for all kinds of

representation and he developed a

radical alternative system of engaging

the smallest children with the most

abstract ideas through physical forms of

play and he is worthy of an entire talk

on his own right the value of education

is something that Freud championed

through plastic modes of play

we live in a society now where we have

lots of think tanks where great minds go

to think about the world and they write

these great symbolic treatises called

books and papers and op-ed articles we

want to propose Krissy and I through the

Institute of figuring another

alternative way of doing things which is

the play tank and the play tank like the

think tank is a place where people can

go and engage with great ideas but what

we want to propose is that the highest

levels of abstraction things like

mathematics computing logic etc all of

this can be engaged with not just

through purely cerebral algebraic

symbolic method methods but by literally

physically playing with ideas thank you

very much

you