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