The beautiful math of coral - Margaret Wertheim
and<00:00:16.670> here<00:00:16.940> today<00:00:17.210> is<00:00:17.390> June<00:00:17.630> said<00:00:17.900> to<00:00:18.200> talk
and here today is June said to talk
and here today is June said to talk
about<00:00:18.619> a<00:00:18.800> project<00:00:19.520> that<00:00:19.670> my<00:00:19.849> twin<00:00:19.910> sister<00:00:20.570> and
about a project that my twin sister and
about a project that my twin sister and
I<00:00:20.779> have<00:00:20.960> been<00:00:20.990> doing<00:00:21.259> for<00:00:21.529> the<00:00:21.560> past<00:00:21.740> three<00:00:22.160> and
I have been doing for the past three and
I have been doing for the past three and
a<00:00:22.340> half<00:00:22.520> years<00:00:23.000> we're<00:00:23.869> crocheting<00:00:24.410> a<00:00:24.710> coral
a half years we're crocheting a coral
a half years we're crocheting a coral
reef<00:00:25.460> and<00:00:26.829> it's<00:00:27.829> a<00:00:27.950> project<00:00:28.430> that<00:00:28.579> we've
reef and it's a project that we've
reef and it's a project that we've
actually<00:00:29.000> been<00:00:29.750> now<00:00:30.110> joined<00:00:30.470> by<00:00:30.739> hundreds<00:00:31.099> of
actually been now joined by hundreds of
actually been now joined by hundreds of
people<00:00:31.250> around<00:00:31.759> the<00:00:32.000> world<00:00:32.149> who<00:00:32.390> are<00:00:32.419> doing<00:00:32.509> it
people around the world who are doing it
people around the world who are doing it
with<00:00:32.989> us<00:00:33.200> and<00:00:33.410> indeed<00:00:33.950> thousands<00:00:34.579> of<00:00:34.670> people
with us and indeed thousands of people
with us and indeed thousands of people
have<00:00:35.270> actually<00:00:35.450> been<00:00:35.989> involved<00:00:36.320> in<00:00:36.620> this
have actually been involved in this
have actually been involved in this
project<00:00:36.980> in<00:00:37.399> many<00:00:38.210> of<00:00:38.390> its<00:00:38.540> different<00:00:38.809> aspects
project in many of its different aspects
project in many of its different aspects
it's<00:00:40.100> a<00:00:40.250> project<00:00:40.430> that<00:00:40.730> now<00:00:40.969> reaches<00:00:41.480> across
it's a project that now reaches across
it's a project that now reaches across
three<00:00:42.200> continents<00:00:42.440> and<00:00:43.070> its<00:00:43.970> roots<00:00:44.240> go<00:00:44.330> into
three continents and its roots go into
three continents and its roots go into
the<00:00:44.810> fields<00:00:45.260> of<00:00:45.380> mathematics<00:00:46.000> marine<00:00:47.000> biology
the fields of mathematics marine biology
the fields of mathematics marine biology
feminine<00:00:48.710> handicraft
feminine handicraft
feminine handicraft
and<00:00:49.960> environmental<00:00:50.960> activism<00:00:51.640> it's<00:00:52.640> true
and environmental activism it's true
and environmental activism it's true
it's<00:00:54.620> also<00:00:54.890> a<00:00:55.100> project<00:00:55.730> that<00:00:56.390> in<00:00:57.290> a<00:00:57.440> very
it's also a project that in a very
it's also a project that in a very
beautiful<00:00:57.980> way<00:00:58.400> the<00:00:59.240> development<00:00:59.810> of<00:00:59.900> this
beautiful way the development of this
beautiful way the development of this
has<00:01:00.650> actually<00:01:00.860> paralleled<00:01:01.760> the<00:01:01.940> evolution<00:01:02.660> of
has actually paralleled the evolution of
has actually paralleled the evolution of
life<00:01:03.170> on<00:01:03.410> Earth<00:01:03.590> which<00:01:04.489> is<00:01:04.519> a<00:01:04.640> particularly
life on Earth which is a particularly
life on Earth which is a particularly
lovely<00:01:05.570> thing<00:01:05.810> to<00:01:05.840> be<00:01:06.049> saying<00:01:06.320> right<00:01:06.560> here<00:01:07.040> in
lovely thing to be saying right here in
lovely thing to be saying right here in
February<00:01:07.490> 2009<00:01:08.390> which<00:01:09.229> is<00:01:09.259> one<00:01:09.530> of<00:01:09.560> our
February 2009 which is one of our
February 2009 which is one of our
previous<00:01:09.950> speakers<00:01:10.159> told<00:01:10.729> us<00:01:10.880> is<00:01:11.090> the<00:01:11.210> 200th
previous speakers told us is the 200th
previous speakers told us is the 200th
anniversary<00:01:11.720> of<00:01:12.320> the<00:01:12.680> birth<00:01:12.860> of<00:01:13.130> Charles
anniversary of the birth of Charles
anniversary of the birth of Charles
Darwin<00:01:14.360> all<00:01:15.229> of<00:01:15.650> this<00:01:15.770> I'm<00:01:15.920> going<00:01:16.070> to<00:01:16.130> get<00:01:16.280> to
Darwin all of this I'm going to get to
Darwin all of this I'm going to get to
in<00:01:16.790> the<00:01:16.909> next<00:01:17.050> 18<00:01:18.050> minutes<00:01:18.350> I<00:01:18.470> hope<00:01:18.650> but<00:01:18.920> let<00:01:19.100> me
in the next 18 minutes I hope but let me
in the next 18 minutes I hope but let me
first<00:01:19.430> begin<00:01:19.670> by<00:01:20.060> showing<00:01:20.330> you<00:01:20.630> some<00:01:21.260> pictures
first begin by showing you some pictures
first begin by showing you some pictures
of<00:01:21.710> what<00:01:22.070> this<00:01:22.250> thing<00:01:22.310> looks<00:01:22.729> like<00:01:22.850> just<00:01:23.630> to
of what this thing looks like just to
of what this thing looks like just to
give<00:01:23.930> you<00:01:24.110> an<00:01:24.290> idea<00:01:24.650> of<00:01:24.710> scale<00:01:24.950> that
give you an idea of scale that
give you an idea of scale that
installation<00:01:25.820> there<00:01:26.360> is<00:01:26.540> about<00:01:27.049> six<00:01:27.860> feet
installation there is about six feet
installation there is about six feet
across<00:01:28.370> and<00:01:28.790> the<00:01:29.270> tallest<00:01:29.690> models<00:01:30.080> are<00:01:30.290> about
across and the tallest models are about
across and the tallest models are about
two<00:01:31.310> or<00:01:31.430> three<00:01:31.460> feet<00:01:31.909> high<00:01:32.150> this<00:01:32.600> is<00:01:32.780> some<00:01:33.020> more
two or three feet high this is some more
two or three feet high this is some more
images<00:01:33.530> of<00:01:34.010> it<00:01:34.159> that<00:01:34.460> one<00:01:34.670> on<00:01:34.790> the<00:01:34.909> right<00:01:35.090> is
images of it that one on the right is
images of it that one on the right is
about<00:01:35.420> five<00:01:35.900> feet<00:01:36.260> high<00:01:36.500> the<00:01:36.920> work<00:01:37.130> involves
about five feet high the work involves
about five feet high the work involves
hundreds<00:01:38.390> of<00:01:38.540> different<00:01:38.690> crochet<00:01:39.350> models<00:01:39.799> and
hundreds of different crochet models and
hundreds of different crochet models and
indeed<00:01:40.880> there<00:01:41.240> are<00:01:41.360> now<00:01:41.560> thousands<00:01:42.560> and
indeed there are now thousands and
indeed there are now thousands and
thousands<00:01:43.159> of<00:01:43.220> models<00:01:43.580> that<00:01:43.700> people<00:01:43.820> have
thousands of models that people have
thousands of models that people have
contributed<00:01:44.299> all<00:01:44.720> over<00:01:44.990> the<00:01:45.200> world<00:01:45.409> as<00:01:45.650> part
contributed all over the world as part
contributed all over the world as part
of<00:01:46.100> this<00:01:46.310> the<00:01:46.940> totality<00:01:47.659> of<00:01:47.690> this<00:01:47.930> project
of this the totality of this project
of this the totality of this project
involves<00:01:49.190> tens<00:01:49.549> of<00:01:49.880> thousands<00:01:50.510> of<00:01:50.600> hours<00:01:51.080> of
involves tens of thousands of hours of
involves tens of thousands of hours of
human<00:01:51.890> labor<00:01:52.270> 99%<00:01:53.270> of<00:01:53.360> it<00:01:53.510> done<00:01:53.689> by<00:01:53.869> women<00:01:54.290> on
human labor 99% of it done by women on
human labor 99% of it done by women on
the<00:01:54.680> right<00:01:54.799> hand<00:01:55.100> side<00:01:55.310> that<00:01:55.340> bit<00:01:55.790> there<00:01:56.000> as
the right hand side that bit there as
the right hand side that bit there as
part<00:01:56.420> of<00:01:56.510> an<00:01:56.630> installation<00:01:57.229> that<00:01:57.380> is<00:01:57.799> about<00:01:58.100> 12
part of an installation that is about 12
part of an installation that is about 12
feet<00:01:58.790> long<00:01:58.850> my<00:01:59.630> sister<00:01:59.960> and<00:02:00.049> I<00:02:00.110> started<00:02:00.560> this
feet long my sister and I started this
feet long my sister and I started this
project<00:02:00.950> in<00:02:01.280> 2005<00:02:02.240> because<00:02:02.840> in<00:02:02.960> that<00:02:03.110> year<00:02:03.380> at
project in 2005 because in that year at
project in 2005 because in that year at
least<00:02:03.710> in<00:02:03.890> the<00:02:03.979> science<00:02:04.369> press<00:02:04.640> there<00:02:05.180> was<00:02:05.299> a
least in the science press there was a
least in the science press there was a
lot<00:02:05.510> of<00:02:05.540> talk<00:02:05.900> about<00:02:06.229> global<00:02:06.740> warming<00:02:06.770> and<00:02:07.280> the
lot of talk about global warming and the
lot of talk about global warming and the
effect<00:02:07.820> that<00:02:07.909> global<00:02:08.390> warming<00:02:08.420> was<00:02:09.200> having<00:02:09.530> on
effect that global warming was having on
effect that global warming was having on
coral<00:02:10.069> reefs<00:02:10.360> corals<00:02:11.360> are<00:02:11.480> very<00:02:11.629> delicate
coral reefs corals are very delicate
coral reefs corals are very delicate
organisms<00:02:12.769> and<00:02:12.920> they're<00:02:13.040> devastated<00:02:13.760> by<00:02:13.909> any
organisms and they're devastated by any
organisms and they're devastated by any
rise<00:02:14.360> in<00:02:14.629> sea<00:02:14.840> temperatures<00:02:15.379> it<00:02:15.650> causes<00:02:16.159> these
rise in sea temperatures it causes these
rise in sea temperatures it causes these
vast<00:02:16.849> bleaching<00:02:17.510> events<00:02:17.930> that<00:02:18.319> are<00:02:18.409> the<00:02:18.470> first
vast bleaching events that are the first
vast bleaching events that are the first
signs<00:02:19.010> that<00:02:19.159> corals<00:02:19.609> are<00:02:19.760> being<00:02:19.939> sick<00:02:20.299> and<00:02:20.480> if
signs that corals are being sick and if
signs that corals are being sick and if
the<00:02:20.959> Beeching<00:02:21.379> doesn't<00:02:21.919> go<00:02:22.069> away<00:02:22.159> if<00:02:22.549> the
the Beeching doesn't go away if the
the Beeching doesn't go away if the
temperatures<00:02:23.209> don't<00:02:23.329> go<00:02:23.569> down<00:02:23.840> reef<00:02:24.529> started
temperatures don't go down reef started
temperatures don't go down reef started
there's<00:02:25.910> a<00:02:26.000> great<00:02:26.209> deal<00:02:26.480> of<00:02:26.510> this<00:02:26.750> has<00:02:26.930> been
there's a great deal of this has been
there's a great deal of this has been
happening<00:02:27.290> in<00:02:27.620> the<00:02:27.650> Great<00:02:27.890> Barrier<00:02:28.190> Reef
happening in the Great Barrier Reef
happening in the Great Barrier Reef
particularly<00:02:29.300> in<00:02:29.420> coral<00:02:29.870> reefs<00:02:30.020> all<00:02:30.230> over<00:02:30.500> the
particularly in coral reefs all over the
particularly in coral reefs all over the
world<00:02:30.800> this<00:02:31.280> is<00:02:31.459> our<00:02:31.640> invocation<00:02:32.180> in<00:02:32.510> crochet
world this is our invocation in crochet
world this is our invocation in crochet
of<00:02:33.260> a<00:02:33.860> bleached<00:02:34.280> reef<00:02:34.670> we<00:02:35.300> have<00:02:35.480> an
of a bleached reef we have an
of a bleached reef we have an
organization<00:02:36.020> together<00:02:36.740> called<00:02:36.980> the
organization together called the
organization together called the
Institute<00:02:37.550> for<00:02:37.700> figuring<00:02:38.060> which<00:02:38.300> is<00:02:38.420> a<00:02:38.450> little
Institute for figuring which is a little
Institute for figuring which is a little
organization<00:02:39.290> we<00:02:39.380> started<00:02:39.860> to<00:02:39.980> promote<00:02:40.190> to<00:02:40.819> do
organization we started to promote to do
organization we started to promote to do
projects<00:02:41.480> about<00:02:41.690> the<00:02:41.870> aesthetic<00:02:42.290> and<00:02:42.410> poetic
projects about the aesthetic and poetic
projects about the aesthetic and poetic
dimensions<00:02:43.310> of<00:02:43.459> Science<00:02:43.819> and<00:02:44.000> Mathematics
dimensions of Science and Mathematics
dimensions of Science and Mathematics
and<00:02:44.720> I<00:02:45.170> went<00:02:45.470> and<00:02:45.620> put<00:02:45.770> a<00:02:45.800> little<00:02:46.010> announcement
and I went and put a little announcement
and I went and put a little announcement
up<00:02:46.730> on<00:02:46.910> our<00:02:47.060> site<00:02:47.330> asking<00:02:47.870> for<00:02:48.020> people<00:02:48.260> to<00:02:48.350> join
up on our site asking for people to join
up on our site asking for people to join
us<00:02:48.800> in<00:02:48.950> this<00:02:49.040> enterprise<00:02:49.550> and<00:02:49.850> to<00:02:49.940> our
us in this enterprise and to our
us in this enterprise and to our
surprise<00:02:50.870> one<00:02:51.440> of<00:02:51.470> the<00:02:51.590> first<00:02:51.890> people<00:02:52.310> who
surprise one of the first people who
surprise one of the first people who
called<00:02:52.670> was<00:02:52.760> the<00:02:53.000> Andy<00:02:53.300> Warhol<00:02:53.480> Museum<00:02:53.900> and
called was the Andy Warhol Museum and
called was the Andy Warhol Museum and
they<00:02:55.069> said<00:02:55.310> they<00:02:55.459> were<00:02:55.520> having<00:02:55.790> an<00:02:56.209> exhibition
they said they were having an exhibition
they said they were having an exhibition
about<00:02:57.050> artists<00:02:57.440> response<00:02:57.800> to<00:02:57.980> global<00:02:58.340> warming
about artists response to global warming
about artists response to global warming
and<00:02:58.850> they'd<00:02:59.030> like<00:02:59.239> our<00:02:59.450> coral<00:02:59.840> reef<00:03:00.019> to<00:03:00.050> be
and they'd like our coral reef to be
and they'd like our coral reef to be
part<00:03:00.590> of<00:03:00.709> it<00:03:00.860> and<00:03:01.070> I<00:03:01.519> laughed<00:03:01.820> and<00:03:02.060> said<00:03:02.180> well
part of it and I laughed and said well
part of it and I laughed and said well
we've<00:03:02.510> only<00:03:02.660> just<00:03:02.780> started<00:03:03.080> it<00:03:03.500> you<00:03:03.590> can<00:03:03.709> have
we've only just started it you can have
we've only just started it you can have
a<00:03:03.860> little<00:03:04.070> bit<00:03:04.310> of<00:03:04.340> it<00:03:04.519> so<00:03:04.700> in<00:03:05.620> 2007<00:03:06.620> we<00:03:06.800> had<00:03:07.070> an
a little bit of it so in 2007 we had an
a little bit of it so in 2007 we had an
exhibition<00:03:07.519> a<00:03:07.820> small<00:03:08.090> exhibition<00:03:08.390> of<00:03:08.750> this
exhibition a small exhibition of this
exhibition a small exhibition of this
crochet<00:03:09.320> reef<00:03:09.530> and<00:03:09.769> then<00:03:10.010> some<00:03:10.220> people<00:03:10.489> in
crochet reef and then some people in
crochet reef and then some people in
Chicago<00:03:11.120> came<00:03:11.330> along<00:03:11.600> and<00:03:11.780> they<00:03:11.870> said<00:03:12.080> in<00:03:12.200> late
Chicago came along and they said in late
Chicago came along and they said in late
2007<00:03:13.550> the<00:03:14.120> theme<00:03:14.360> of<00:03:14.390> the<00:03:14.660> Chicago<00:03:15.110> humanities
2007 the theme of the Chicago humanities
2007 the theme of the Chicago humanities
festival<00:03:15.920> is<00:03:16.569> global<00:03:17.569> warming<00:03:17.600> and<00:03:18.050> we've<00:03:18.230> got
festival is global warming and we've got
festival is global warming and we've got
this<00:03:18.440> 3,000<00:03:19.130> square-foot<00:03:19.370> gallery<00:03:19.910> and<00:03:20.120> we
this 3,000 square-foot gallery and we
this 3,000 square-foot gallery and we
want<00:03:20.450> you<00:03:20.630> to<00:03:20.810> fill<00:03:20.989> it<00:03:21.080> with<00:03:21.230> your<00:03:21.440> reef<00:03:21.650> and<00:03:22.040> I
want you to fill it with your reef and I
want you to fill it with your reef and I
naively<00:03:23.060> by<00:03:23.360> this<00:03:23.420> day<00:03:23.720> said<00:03:23.989> oh<00:03:24.019> yes<00:03:24.380> sure
naively by this day said oh yes sure
naively by this day said oh yes sure
now<00:03:25.940> I<00:03:25.970> say<00:03:26.300> naively<00:03:26.540> because<00:03:27.260> actually<00:03:27.739> my
now I say naively because actually my
now I say naively because actually my
profession<00:03:28.430> is<00:03:28.519> as<00:03:28.670> a<00:03:28.700> science<00:03:29.209> writer<00:03:29.420> what<00:03:30.019> I
profession is as a science writer what I
profession is as a science writer what I
do<00:03:30.200> is<00:03:30.440> I<00:03:30.530> write<00:03:30.709> books<00:03:31.040> about<00:03:31.160> the<00:03:31.459> cultural
do is I write books about the cultural
do is I write books about the cultural
history<00:03:32.239> of<00:03:32.360> physics<00:03:32.750> I've<00:03:32.930> written<00:03:33.500> books
history of physics I've written books
history of physics I've written books
about<00:03:33.890> the<00:03:34.130> history<00:03:34.459> of<00:03:34.549> space<00:03:34.850> the<00:03:35.060> history
about the history of space the history
about the history of space the history
of<00:03:35.480> physics<00:03:35.780> and<00:03:35.959> religion<00:03:36.410> and<00:03:36.560> I<00:03:36.829> write
of physics and religion and I write
of physics and religion and I write
articles<00:03:37.280> for<00:03:37.549> people<00:03:37.880> like<00:03:38.000> the<00:03:38.150> New<00:03:38.269> York
articles for people like the New York
articles for people like the New York
Times<00:03:38.750> and<00:03:38.930> the<00:03:39.049> LA<00:03:39.079> Times<00:03:39.500> so<00:03:40.070> I<00:03:40.100> had<00:03:40.250> no<00:03:40.400> idea
Times and the LA Times so I had no idea
Times and the LA Times so I had no idea
what<00:03:40.970> it<00:03:41.090> meant<00:03:41.239> to<00:03:41.360> fill<00:03:41.600> a<00:03:41.630> 3,000
what it meant to fill a 3,000
what it meant to fill a 3,000
square-foot<00:03:42.620> gallery<00:03:43.250> so<00:03:44.120> I<00:03:44.150> said<00:03:44.570> yes<00:03:44.810> to
square-foot gallery so I said yes to
square-foot gallery so I said yes to
this<00:03:45.110> proposition<00:03:45.410> and<00:03:45.950> I<00:03:46.400> went<00:03:46.640> home<00:03:46.790> and<00:03:46.970> I
this proposition and I went home and I
this proposition and I went home and I
told<00:03:47.120> my<00:03:47.390> sister<00:03:47.510> Christine<00:03:48.230> and<00:03:48.380> she<00:03:48.410> nearly
told my sister Christine and she nearly
told my sister Christine and she nearly
had<00:03:48.980> a<00:03:49.010> fit<00:03:49.100> because<00:03:50.060> Christine<00:03:50.959> is<00:03:51.140> a
had a fit because Christine is a
had a fit because Christine is a
professor<00:03:51.560> at<00:03:51.890> one<00:03:52.100> of<00:03:52.250> LA's<00:03:52.670> major<00:03:53.030> art
professor at one of LA's major art
professor at one of LA's major art
colleges<00:03:53.840> Cal<00:03:54.109> arts<00:03:54.560> and<00:03:54.769> she<00:03:55.160> knew<00:03:55.310> exactly
colleges Cal arts and she knew exactly
colleges Cal arts and she knew exactly
what<00:03:55.940> it<00:03:56.000> meant<00:03:56.150> to<00:03:56.390> fill<00:03:56.570> a<00:03:56.600> 3,000
what it meant to fill a 3,000
what it meant to fill a 3,000
square-foot<00:03:57.680> gallery<00:03:58.220> and<00:03:58.340> she<00:03:58.400> thought<00:03:58.670> I'd
square-foot gallery and she thought I'd
square-foot gallery and she thought I'd
gone<00:03:58.970> off<00:03:59.180> my<00:03:59.359> head<00:03:59.630> but<00:04:00.440> she<00:04:00.709> went<00:04:00.859> into
gone off my head but she went into
gone off my head but she went into
crochet<00:04:01.519> overdrive<00:04:02.269> and<00:04:02.480> to<00:04:02.570> cut<00:04:02.720> a<00:04:02.750> long
crochet overdrive and to cut a long
crochet overdrive and to cut a long
story<00:04:03.049> short<00:04:03.500> eight<00:04:04.340> months<00:04:04.790> later<00:04:04.850> we<00:04:05.299> did
story short eight months later we did
story short eight months later we did
fill<00:04:06.019> the<00:04:06.980> Chicago<00:04:07.430> Cultural<00:04:07.640> Center<00:04:08.030> the
fill the Chicago Cultural Center the
fill the Chicago Cultural Center the
3,000<00:04:08.810> square-foot<00:04:09.019> gallery<00:04:09.590> by<00:04:10.459> this<00:04:10.519> stage
3,000 square-foot gallery by this stage
3,000 square-foot gallery by this stage
the<00:04:11.450> project<00:04:11.900> had<00:04:12.019> taken<00:04:12.230> on<00:04:12.470> a<00:04:12.500> viral
the project had taken on a viral
the project had taken on a viral
dimension<00:04:13.430> of<00:04:13.549> its<00:04:13.700> own<00:04:13.910> which<00:04:14.209> got
dimension of its own which got
dimension of its own which got
completely<00:04:15.170> beyond<00:04:15.470> us<00:04:15.709> the<00:04:16.280> people<00:04:16.640> in
completely beyond us the people in
completely beyond us the people in
Chicago<00:04:17.000> decided<00:04:17.870> that<00:04:17.989> as<00:04:18.079> well<00:04:18.289> as
Chicago decided that as well as
Chicago decided that as well as
exhibiting<00:04:18.950> our<00:04:19.160> reefs<00:04:19.459> what<00:04:19.729> they<00:04:19.910> wanted<00:04:20.239> to
exhibiting our reefs what they wanted to
exhibiting our reefs what they wanted to
do<00:04:20.570> was<00:04:20.780> have<00:04:20.930> the<00:04:21.079> local<00:04:21.500> people<00:04:21.829> there<00:04:21.979> make
do was have the local people there make
do was have the local people there make
a<00:04:22.280> reef<00:04:22.580> so<00:04:23.210> we<00:04:23.390> went<00:04:23.630> and<00:04:23.720> taught<00:04:23.930> the
a reef so we went and taught the
a reef so we went and taught the
techniques<00:04:24.710> we<00:04:24.860> did<00:04:25.010> workshops<00:04:25.490> and<00:04:25.669> lectures
techniques we did workshops and lectures
techniques we did workshops and lectures
and<00:04:26.090> the<00:04:26.390> people<00:04:26.720> in<00:04:26.840> Chicago<00:04:26.990> made<00:04:27.950> a<00:04:27.979> reef<00:04:28.280> of
and the people in Chicago made a reef of
and the people in Chicago made a reef of
their<00:04:28.610> own<00:04:28.760> and<00:04:29.060> it<00:04:29.120> was<00:04:29.240> exhibited<00:04:29.720> alongside
their own and it was exhibited alongside
their own and it was exhibited alongside
ours<00:04:30.560> and<00:04:30.770> there<00:04:30.860> were<00:04:30.919> hundreds<00:04:31.310> of<00:04:31.370> people
ours and there were hundreds of people
ours and there were hundreds of people
involved<00:04:32.180> in<00:04:32.300> that<00:04:32.330> and<00:04:32.800> we<00:04:33.800> got<00:04:33.979> invited<00:04:34.280> to
involved in that and we got invited to
involved in that and we got invited to
do<00:04:34.820> the<00:04:34.970> whole<00:04:35.150> thing<00:04:35.180> in<00:04:35.690> New<00:04:36.260> York<00:04:36.530> and<00:04:36.800> in
do the whole thing in New York and in
do the whole thing in New York and in
London<00:04:37.909> and
London and
London and
Los<00:04:38.750> Angeles<00:04:38.960> and<00:04:39.470> in<00:04:39.800> each<00:04:40.010> of<00:04:40.220> these<00:04:40.370> cities
Los Angeles and in each of these cities
Los Angeles and in each of these cities
the<00:04:41.270> local<00:04:41.690> citizen<00:04:42.080> hundreds<00:04:42.470> and<00:04:42.590> hundreds
the local citizen hundreds and hundreds
the local citizen hundreds and hundreds
of<00:04:43.040> them<00:04:43.190> have<00:04:43.430> made<00:04:43.670> a<00:04:43.700> rift<00:04:44.000> and<00:04:44.210> more<00:04:44.390> and
of them have made a rift and more and
of them have made a rift and more and
more<00:04:44.660> people<00:04:44.900> get<00:04:45.500> involved<00:04:45.830> with<00:04:46.070> this<00:04:46.220> most
more people get involved with this most
more people get involved with this most
of<00:04:46.760> whom<00:04:46.940> we've<00:04:47.540> never<00:04:47.810> met<00:04:48.140> so<00:04:48.770> the<00:04:48.920> whole
of whom we've never met so the whole
of whom we've never met so the whole
thing<00:04:49.430> is<00:04:49.460> sort<00:04:49.820> of<00:04:49.880> a<00:04:50.000> morphed<00:04:50.510> into<00:04:50.690> this
thing is sort of a morphed into this
thing is sort of a morphed into this
organic<00:04:51.440> ever-evolving<00:04:52.340> creature<00:04:53.060> that's
organic ever-evolving creature that's
organic ever-evolving creature that's
actually<00:04:53.750> got<00:04:53.900> way<00:04:54.170> beyond<00:04:54.590> Kristen<00:04:55.010> and<00:04:55.460> I
actually got way beyond Kristen and I
actually got way beyond Kristen and I
now<00:04:57.290> some<00:04:58.130> of<00:04:58.160> you<00:04:58.400> are<00:04:58.430> sitting<00:04:58.670> here
now some of you are sitting here
now some of you are sitting here
thinking<00:04:59.210> what<00:05:00.020> planet<00:05:00.590> are<00:05:00.710> these<00:05:00.800> people<00:05:01.280> on
thinking what planet are these people on
thinking what planet are these people on
why<00:05:02.330> on<00:05:02.510> earth<00:05:02.540> are<00:05:03.110> you<00:05:03.200> crocheting<00:05:03.920> a<00:05:04.100> reef
why on earth are you crocheting a reef
why on earth are you crocheting a reef
woollen<00:05:05.270> nests<00:05:05.480> and<00:05:05.720> wetness<00:05:05.960> aren't<00:05:06.530> exactly
woollen nests and wetness aren't exactly
woollen nests and wetness aren't exactly
two<00:05:07.130> concepts<00:05:07.670> that<00:05:07.760> go<00:05:07.820> together<00:05:08.150> why<00:05:08.840> not
two concepts that go together why not
two concepts that go together why not
chisel<00:05:09.410> a<00:05:09.470> coral<00:05:09.830> reef<00:05:09.860> out<00:05:10.250> of<00:05:10.400> marble<00:05:10.670> cast
chisel a coral reef out of marble cast
chisel a coral reef out of marble cast
it<00:05:11.810> in<00:05:11.930> bronze<00:05:11.960> but<00:05:12.770> it<00:05:12.890> turns<00:05:13.160> out<00:05:13.370> there's<00:05:13.670> a
it in bronze but it turns out there's a
it in bronze but it turns out there's a
very<00:05:13.760> good<00:05:14.180> reason<00:05:14.630> why<00:05:14.780> we<00:05:15.050> are<00:05:15.320> crocheting
very good reason why we are crocheting
very good reason why we are crocheting
it<00:05:16.190> because<00:05:16.970> many<00:05:17.180> organisms<00:05:18.020> in<00:05:18.140> coral<00:05:18.440> reefs
it because many organisms in coral reefs
it because many organisms in coral reefs
have<00:05:18.740> a<00:05:18.830> very<00:05:19.070> particular<00:05:19.430> kind<00:05:19.910> of<00:05:20.030> structure
have a very particular kind of structure
have a very particular kind of structure
that<00:05:20.870> freely<00:05:21.230> crenelated<00:05:21.980> forms<00:05:22.280> that<00:05:22.400> you
that freely crenelated forms that you
that freely crenelated forms that you
see<00:05:22.730> in<00:05:22.940> corals<00:05:23.750> and<00:05:23.990> kelps<00:05:24.770> and<00:05:24.950> sponges<00:05:25.400> and
see in corals and kelps and sponges and
see in corals and kelps and sponges and
nudibranch<00:05:26.090> is<00:05:26.300> a<00:05:26.510> form<00:05:26.840> of<00:05:26.960> geometry<00:05:27.170> known
nudibranch is a form of geometry known
nudibranch is a form of geometry known
as<00:05:27.860> hyperbolic<00:05:28.370> geometry<00:05:28.700> and<00:05:29.360> the<00:05:30.080> only<00:05:30.500> way
as hyperbolic geometry and the only way
as hyperbolic geometry and the only way
that<00:05:30.710> mathematicians<00:05:31.700> know<00:05:31.880> how<00:05:32.150> to<00:05:32.210> model
that mathematicians know how to model
that mathematicians know how to model
this<00:05:33.170> structure<00:05:33.770> is<00:05:33.920> with<00:05:34.460> crochet<00:05:34.970> it
this structure is with crochet it
this structure is with crochet it
happens<00:05:35.840> to<00:05:35.990> be<00:05:36.110> a<00:05:36.140> fact<00:05:36.410> it's<00:05:36.590> almost
happens to be a fact it's almost
happens to be a fact it's almost
impossible<00:05:37.100> to<00:05:37.400> model<00:05:37.670> this<00:05:37.880> structure<00:05:38.240> any
impossible to model this structure any
impossible to model this structure any
other<00:05:38.630> way<00:05:38.810> and<00:05:38.990> it's<00:05:39.440> almost<00:05:39.620> impossible<00:05:40.040> to
other way and it's almost impossible to
other way and it's almost impossible to
do<00:05:40.550> it<00:05:40.700> on<00:05:40.820> computers<00:05:41.360> so<00:05:42.290> what<00:05:42.530> is<00:05:42.710> this
do it on computers so what is this
do it on computers so what is this
hyperbolic<00:05:43.550> geometry<00:05:43.730> that<00:05:44.420> corals<00:05:44.900> and<00:05:45.050> sea
hyperbolic geometry that corals and sea
hyperbolic geometry that corals and sea
slugs<00:05:45.760> embody<00:05:46.760> so<00:05:47.270> we<00:05:47.420> the<00:05:47.660> next<00:05:47.870> few<00:05:48.020> minutes
slugs embody so we the next few minutes
slugs embody so we the next few minutes
is<00:05:48.350> we're<00:05:48.530> all<00:05:48.650> going<00:05:48.830> to<00:05:48.890> get<00:05:49.040> raised<00:05:49.310> up<00:05:49.550> to
is we're all going to get raised up to
is we're all going to get raised up to
the<00:05:49.850> level<00:05:50.090> of<00:05:50.150> a<00:05:50.270> sea<00:05:50.450> slug<00:05:51.880> this<00:05:52.880> sort<00:05:53.240> of
the level of a sea slug this sort of
the level of a sea slug this sort of
geometry<00:05:53.540> was<00:05:54.520> revolutionized<00:05:55.520> mathematics
geometry was revolutionized mathematics
geometry was revolutionized mathematics
when<00:05:56.420> it<00:05:56.510> was<00:05:56.600> first<00:05:56.930> discovered<00:05:57.350> in<00:05:57.590> the
when it was first discovered in the
when it was first discovered in the
nineteenth<00:05:58.100> century<00:05:58.190> but<00:05:58.670> not<00:05:59.090> until<00:05:59.380> 1997
nineteenth century but not until 1997
nineteenth century but not until 1997
did<00:06:00.680> mathematicians<00:06:01.370> actually<00:06:01.760> understand
did mathematicians actually understand
did mathematicians actually understand
how<00:06:02.840> they<00:06:03.020> could<00:06:03.080> model<00:06:03.590> it<00:06:03.710> and<00:06:03.830> in<00:06:04.190> 1997<00:06:05.180> a
how they could model it and in 1997 a
how they could model it and in 1997 a
mathematician<00:06:05.660> at<00:06:06.050> Cornell<00:06:06.440> Dana<00:06:06.860> tamina
mathematician at Cornell Dana tamina
mathematician at Cornell Dana tamina
made<00:06:07.970> the<00:06:08.120> discovery<00:06:08.360> that<00:06:08.810> this<00:06:08.960> structure
made the discovery that this structure
made the discovery that this structure
could<00:06:09.860> actually<00:06:10.040> be<00:06:10.340> done<00:06:10.550> in<00:06:10.700> knitting<00:06:10.940> and
could actually be done in knitting and
could actually be done in knitting and
crochet<00:06:11.600> the<00:06:11.840> first<00:06:11.990> one<00:06:12.290> she<00:06:12.470> did<00:06:12.650> was
crochet the first one she did was
crochet the first one she did was
knitting<00:06:13.250> but<00:06:13.610> you<00:06:13.730> get<00:06:13.850> too<00:06:14.000> many<00:06:14.120> stitches
knitting but you get too many stitches
knitting but you get too many stitches
on<00:06:14.750> the<00:06:14.870> needle<00:06:15.170> so<00:06:15.290> she<00:06:15.350> quickly<00:06:15.590> realized
on the needle so she quickly realized
on the needle so she quickly realized
the<00:06:16.250> crochet<00:06:16.640> was<00:06:16.790> the<00:06:16.880> better<00:06:17.090> thing<00:06:17.420> but
the crochet was the better thing but
the crochet was the better thing but
what<00:06:18.380> she<00:06:18.560> was<00:06:18.710> doing<00:06:19.070> was<00:06:19.430> actually<00:06:19.820> making<00:06:20.060> a
what she was doing was actually making a
what she was doing was actually making a
model<00:06:20.720> of<00:06:20.840> a<00:06:20.990> mathematical<00:06:21.920> structure<00:06:22.190> that
model of a mathematical structure that
model of a mathematical structure that
many<00:06:22.580> mathematicians<00:06:23.000> have<00:06:23.450> thought<00:06:23.750> it<00:06:23.960> was
many mathematicians have thought it was
many mathematicians have thought it was
actually<00:06:24.470> impossible<00:06:24.710> to<00:06:25.100> model<00:06:25.310> and<00:06:25.580> indeed
actually impossible to model and indeed
actually impossible to model and indeed
they<00:06:26.390> thought<00:06:26.660> that<00:06:26.900> anything<00:06:27.260> like<00:06:27.410> this
they thought that anything like this
they thought that anything like this
structure<00:06:28.040> was<00:06:28.160> impossible<00:06:28.640> per<00:06:28.820> se<00:06:29.120> some<00:06:29.810> of
structure was impossible per se some of
structure was impossible per se some of
the<00:06:29.960> best<00:06:30.140> mathematicians<00:06:30.380> spent<00:06:31.220> hundreds
the best mathematicians spent hundreds
the best mathematicians spent hundreds
of<00:06:31.850> years<00:06:32.000> trying<00:06:32.360> to<00:06:32.450> prove<00:06:32.720> that<00:06:33.110> this
of years trying to prove that this
of years trying to prove that this
structure<00:06:33.620> was<00:06:33.890> impossible<00:06:34.490> so<00:06:35.330> what<00:06:35.540> is<00:06:35.720> this
structure was impossible so what is this
structure was impossible so what is this
impossible<00:06:36.290> hyperbolic<00:06:37.130> structure<00:06:37.760> before
impossible hyperbolic structure before
impossible hyperbolic structure before
hyperbolic<00:06:38.960> geometry<00:06:39.170> mathematicians<00:06:40.070> knew
hyperbolic geometry mathematicians knew
hyperbolic geometry mathematicians knew
about<00:06:40.430> two<00:06:40.670> kinds<00:06:40.910> of<00:06:41.150> spaced<00:06:41.590> Euclidean
about two kinds of spaced Euclidean
about two kinds of spaced Euclidean
space<00:06:42.950> and<00:06:43.250> spherical<00:06:43.790> space<00:06:44.240> and<00:06:44.600> they<00:06:44.960> have
space and spherical space and they have
space and spherical space and they have
different<00:06:45.590> properties<00:06:45.830> and<00:06:46.540> mathematicians
different properties and mathematicians
different properties and mathematicians
like<00:06:47.780> to<00:06:47.990> characterize<00:06:48.350> things<00:06:48.980> by<00:06:49.160> being
like to characterize things by being
like to characterize things by being
formulas<00:06:49.970> so<00:06:50.120> you<00:06:50.300> all
formulas so you all
formulas so you all
the<00:06:51.150> sense<00:06:51.419> of<00:06:51.600> what<00:06:51.810> a<00:06:51.960> flat<00:06:52.290> space<00:06:52.650> is
the sense of what a flat space is
the sense of what a flat space is
Euclidean<00:06:53.130> spaces<00:06:53.790> but<00:06:54.510> mathematicians
Euclidean spaces but mathematicians
Euclidean spaces but mathematicians
formalize<00:06:55.770> it<00:06:55.800> in<00:06:56.070> a<00:06:56.130> particular<00:06:56.310> way<00:06:56.820> and
formalize it in a particular way and
formalize it in a particular way and
what<00:06:57.720> they<00:06:57.930> do<00:06:57.990> is<00:06:58.320> they<00:06:58.470> do<00:06:58.530> it<00:06:58.650> through<00:06:58.830> the
what they do is they do it through the
what they do is they do it through the
concept<00:06:59.130> of<00:06:59.580> parallel<00:06:59.940> lines<00:07:00.120> so<00:07:01.020> here<00:07:01.350> we
concept of parallel lines so here we
concept of parallel lines so here we
have<00:07:01.680> a<00:07:01.710> line<00:07:02.010> and<00:07:02.340> a<00:07:02.520> point<00:07:02.790> outside<00:07:03.030> the<00:07:03.330> line
have a line and a point outside the line
have a line and a point outside the line
and<00:07:03.990> Euclid<00:07:04.620> said<00:07:05.040> how<00:07:05.490> can<00:07:05.550> i<00:07:05.790> define
and Euclid said how can i define
and Euclid said how can i define
parallel<00:07:06.600> lines<00:07:06.960> I<00:07:07.260> asked<00:07:07.620> the<00:07:07.830> question<00:07:08.310> how
parallel lines I asked the question how
parallel lines I asked the question how
many<00:07:09.000> lines<00:07:09.240> can<00:07:09.540> I<00:07:09.630> draw<00:07:09.840> through<00:07:10.290> the<00:07:10.470> point
many lines can I draw through the point
many lines can I draw through the point
but<00:07:10.919> never<00:07:11.130> meet<00:07:11.370> the<00:07:11.520> original<00:07:11.940> line<00:07:12.120> and<00:07:12.360> you
but never meet the original line and you
but never meet the original line and you
all<00:07:12.570> know<00:07:12.750> the<00:07:12.900> answer<00:07:13.260> to<00:07:13.380> someone<00:07:13.620> want<00:07:13.770> to
all know the answer to someone want to
all know the answer to someone want to
shout<00:07:14.010> it<00:07:14.190> out<00:07:14.600> one<00:07:15.600> great<00:07:16.200> ok<00:07:16.830> that's<00:07:17.280> our
shout it out one great ok that's our
shout it out one great ok that's our
definition<00:07:17.700> of<00:07:18.330> a<00:07:18.810> parallel<00:07:19.230> line<00:07:19.410> it's<00:07:19.590> a
definition of a parallel line it's a
definition of a parallel line it's a
definition<00:07:20.100> really<00:07:20.490> of<00:07:20.580> Euclidean<00:07:21.060> space<00:07:21.389> but
definition really of Euclidean space but
definition really of Euclidean space but
there's<00:07:22.380> another<00:07:22.620> possibility<00:07:22.889> that<00:07:23.550> you<00:07:23.700> all
there's another possibility that you all
there's another possibility that you all
know<00:07:24.120> of<00:07:24.330> spherical<00:07:25.229> space<00:07:25.620> think<00:07:26.370> of<00:07:26.520> the
know of spherical space think of the
know of spherical space think of the
surface<00:07:27.090> of<00:07:27.270> a<00:07:27.360> sphere<00:07:27.479> just<00:07:28.020> like<00:07:28.139> a<00:07:28.169> beach
surface of a sphere just like a beach
surface of a sphere just like a beach
ball<00:07:28.470> the<00:07:28.919> surface<00:07:29.310> of<00:07:29.460> the<00:07:29.610> earth<00:07:29.639> I<00:07:30.150> have<00:07:30.570> a
ball the surface of the earth I have a
ball the surface of the earth I have a
straight<00:07:30.990> line<00:07:31.020> on<00:07:31.290> my<00:07:31.620> spherical<00:07:32.160> surface
straight line on my spherical surface
straight line on my spherical surface
and<00:07:32.790> I<00:07:32.970> have<00:07:33.060> a<00:07:33.120> point<00:07:33.360> outside<00:07:33.600> the<00:07:34.020> line<00:07:34.200> how
and I have a point outside the line how
and I have a point outside the line how
many<00:07:34.560> let's<00:07:35.040> straight<00:07:35.310> lines<00:07:35.580> can<00:07:35.850> I<00:07:35.910> draw
many let's straight lines can I draw
many let's straight lines can I draw
through<00:07:36.479> the<00:07:36.630> point<00:07:36.870> that<00:07:37.050> never<00:07:37.260> meet<00:07:37.500> the
through the point that never meet the
through the point that never meet the
original<00:07:38.160> line<00:07:38.389> what<00:07:39.389> do<00:07:39.570> we<00:07:39.690> mean<00:07:39.900> to<00:07:40.110> talk
original line what do we mean to talk
original line what do we mean to talk
about<00:07:40.560> a<00:07:40.979> straight<00:07:41.490> line<00:07:41.790> on<00:07:42.060> a<00:07:42.150> curved
about a straight line on a curved
about a straight line on a curved
surface<00:07:43.070> now<00:07:44.070> mathematicians<00:07:45.060> have<00:07:45.180> answered
surface now mathematicians have answered
surface now mathematicians have answered
that<00:07:45.780> question<00:07:46.020> and<00:07:46.590> they've<00:07:47.160> understood
that question and they've understood
that question and they've understood
there's<00:07:48.389> a<00:07:48.450> generalized<00:07:48.960> concept<00:07:49.410> of
there's a generalized concept of
there's a generalized concept of
straightness<00:07:49.889> it's<00:07:50.010> called<00:07:50.250> a<00:07:50.340> geodesic<00:07:50.940> and
straightness it's called a geodesic and
straightness it's called a geodesic and
on<00:07:51.510> the<00:07:51.630> surface<00:07:51.990> of<00:07:52.080> a<00:07:52.139> sphere<00:07:52.200> that<00:07:52.710> a
on the surface of a sphere that a
on the surface of a sphere that a
straight<00:07:53.940> line<00:07:54.210> is<00:07:54.510> the<00:07:54.570> biggest<00:07:55.080> possible
straight line is the biggest possible
straight line is the biggest possible
circle<00:07:55.919> you<00:07:55.979> can<00:07:56.100> draw<00:07:56.340> so<00:07:56.729> it's<00:07:56.880> like<00:07:57.060> the
circle you can draw so it's like the
circle you can draw so it's like the
equator<00:07:57.810> or<00:07:58.110> the<00:07:58.289> lines<00:07:58.470> of<00:07:58.740> longitude<00:07:59.419> so<00:08:00.419> we
equator or the lines of longitude so we
equator or the lines of longitude so we
asked<00:08:00.750> the<00:08:00.930> question<00:08:00.960> again<00:08:01.440> how<00:08:01.919> many
asked the question again how many
asked the question again how many
straight<00:08:02.669> lines<00:08:02.940> can<00:08:03.180> I<00:08:03.270> draw<00:08:03.510> through<00:08:03.840> the
straight lines can I draw through the
straight lines can I draw through the
point<00:08:04.229> that<00:08:04.500> never<00:08:04.710> meet<00:08:04.950> the<00:08:05.220> original<00:08:05.310> line
point that never meet the original line
point that never meet the original line
so<00:08:06.390> to<00:08:06.450> someone<00:08:06.780> want<00:08:06.960> to<00:08:07.050> guess<00:08:07.970> 0<00:08:08.970> very<00:08:09.510> good
so to someone want to guess 0 very good
so to someone want to guess 0 very good
now<00:08:10.460> mathematicians<00:08:11.460> thought<00:08:11.610> that<00:08:11.789> was<00:08:11.940> the
now mathematicians thought that was the
now mathematicians thought that was the
only<00:08:12.300> alternatives<00:08:12.870> it's<00:08:13.229> a<00:08:13.320> bit<00:08:13.440> suspicious
only alternatives it's a bit suspicious
only alternatives it's a bit suspicious
isn't<00:08:14.100> it<00:08:14.280> there's<00:08:14.490> two<00:08:14.700> answers<00:08:15.060> to<00:08:15.210> the
isn't it there's two answers to the
isn't it there's two answers to the
questions<00:08:15.630> so<00:08:15.780> far<00:08:15.960> zero<00:08:16.320> and<00:08:16.680> one<00:08:16.910> two
questions so far zero and one two
questions so far zero and one two
answers<00:08:18.419> there<00:08:18.630> may<00:08:18.750> possibly<00:08:18.780> be<00:08:19.380> a<00:08:19.410> third
answers there may possibly be a third
answers there may possibly be a third
alternative<00:08:19.889> and<00:08:20.490> to<00:08:20.550> a<00:08:20.580> mathematician<00:08:21.000> if
alternative and to a mathematician if
alternative and to a mathematician if
there<00:08:21.539> are<00:08:21.630> two<00:08:21.810> answers<00:08:22.289> and<00:08:22.500> the<00:08:22.919> first<00:08:23.160> two
there are two answers and the first two
there are two answers and the first two
is<00:08:23.490> zero<00:08:23.700> and<00:08:23.940> one<00:08:24.090> there's<00:08:24.300> another<00:08:24.360> number
is zero and one there's another number
is zero and one there's another number
that<00:08:25.050> immediately<00:08:25.530> suggests<00:08:26.039> itself<00:08:26.430> as<00:08:26.669> the
that immediately suggests itself as the
that immediately suggests itself as the
third<00:08:27.300> alternative<00:08:28.050> does<00:08:28.470> anyone<00:08:28.770> want<00:08:28.979> to
third alternative does anyone want to
third alternative does anyone want to
guess<00:08:29.220> what<00:08:29.400> it<00:08:29.550> is<00:08:30.830> infinity<00:08:31.830> you<00:08:32.339> all<00:08:32.490> got<00:08:32.700> to
guess what it is infinity you all got to
guess what it is infinity you all got to
right<00:08:33.000> exactly<00:08:33.770> there<00:08:34.770> is<00:08:34.800> there's<00:08:35.339> a<00:08:35.430> third
right exactly there is there's a third
right exactly there is there's a third
alternative<00:08:35.959> this<00:08:36.959> is<00:08:37.020> what<00:08:37.320> it<00:08:37.469> looks<00:08:37.650> like
alternative this is what it looks like
alternative this is what it looks like
it<00:08:38.459> is<00:08:38.580> a<00:08:38.610> straight<00:08:38.940> line<00:08:39.180> and<00:08:39.360> there's<00:08:39.510> an
it is a straight line and there's an
it is a straight line and there's an
infinite<00:08:40.020> number<00:08:40.050> of<00:08:40.409> lines<00:08:40.709> that<00:08:41.010> go<00:08:41.159> through
infinite number of lines that go through
infinite number of lines that go through
the<00:08:41.490> point<00:08:41.700> and<00:08:41.849> never<00:08:42.000> meet<00:08:42.240> the<00:08:42.419> original
the point and never meet the original
the point and never meet the original
line<00:08:43.020> this<00:08:43.680> is<00:08:43.860> the<00:08:44.010> drawing<00:08:44.300> this<00:08:45.300> nearly
line this is the drawing this nearly
line this is the drawing this nearly
drove<00:08:45.900> mathematicians<00:08:46.709> bonkers<00:08:47.220> because
drove mathematicians bonkers because
drove mathematicians bonkers because
like<00:08:47.820> you<00:08:48.060> they're<00:08:48.270> sitting<00:08:48.540> there<00:08:48.570> feeling
like you they're sitting there feeling
like you they're sitting there feeling
bamboozled<00:08:49.680> thinking<00:08:49.950> how<00:08:50.070> can<00:08:50.130> that<00:08:50.430> be
bamboozled thinking how can that be
bamboozled thinking how can that be
you're<00:08:50.970> cheating<00:08:51.480> the<00:08:51.900> lines<00:08:52.170> are<00:08:52.470> curved<00:08:52.740> but
you're cheating the lines are curved but
you're cheating the lines are curved but
that's<00:08:53.520> only<00:08:53.670> because<00:08:53.850> I'm<00:08:54.240> projecting<00:08:54.450> it<00:08:54.990> on
that's only because I'm projecting it on
that's only because I'm projecting it on
to<00:08:55.470> a<00:08:55.550> flat<00:08:56.550> surface<00:08:56.580> and<00:08:57.529> mathematicians<00:08:58.529> for
to a flat surface and mathematicians for
to a flat surface and mathematicians for
several<00:08:58.980> hundred<00:08:59.339> years<00:08:59.580> had<00:08:59.880> to<00:08:59.910> really
several hundred years had to really
several hundred years had to really
struggle<00:09:00.600> with<00:09:00.900> this<00:09:01.020> how<00:09:01.560> could<00:09:01.890> they<00:09:02.100> see
struggle with this how could they see
struggle with this how could they see
the
the
the
what<00:09:03.120> did<00:09:03.300> it<00:09:03.420> mean<00:09:03.660> to<00:09:04.620> actually<00:09:04.920> have<00:09:05.460> a
what did it mean to actually have a
what did it mean to actually have a
physical<00:09:06.300> model<00:09:06.510> that<00:09:06.930> looked<00:09:07.110> like<00:09:07.230> this<00:09:07.560> and
physical model that looked like this and
physical model that looked like this and
it's<00:09:08.070> a<00:09:08.160> bit<00:09:08.310> like<00:09:08.490> this<00:09:08.730> imagine<00:09:09.360> that<00:09:09.720> we'd
it's a bit like this imagine that we'd
it's a bit like this imagine that we'd
only<00:09:09.990> ever<00:09:10.290> encountered<00:09:10.800> Euclidean<00:09:11.280> space
only ever encountered Euclidean space
only ever encountered Euclidean space
and<00:09:11.880> then<00:09:12.090> our<00:09:12.240> mathematicians<00:09:12.870> come<00:09:12.990> along
and then our mathematicians come along
and then our mathematicians come along
and<00:09:13.290> said<00:09:13.440> this<00:09:13.500> is<00:09:13.650> thing<00:09:13.830> called<00:09:14.070> a<00:09:14.160> sphere
and said this is thing called a sphere
and said this is thing called a sphere
and<00:09:14.820> the<00:09:15.120> lines<00:09:15.330> come<00:09:15.660> together<00:09:15.840> at<00:09:16.170> the<00:09:16.260> North
and the lines come together at the North
and the lines come together at the North
and<00:09:16.620> South<00:09:16.800> Pole<00:09:17.130> but<00:09:17.610> you<00:09:17.730> don't<00:09:17.940> know<00:09:18.060> what<00:09:18.210> a
and South Pole but you don't know what a
and South Pole but you don't know what a
sphere<00:09:18.570> looks<00:09:19.050> like<00:09:19.290> and<00:09:19.500> someone<00:09:19.680> then<00:09:19.950> comes
sphere looks like and someone then comes
sphere looks like and someone then comes
along<00:09:20.460> and<00:09:20.610> says<00:09:20.760> look<00:09:20.940> here's<00:09:21.150> a<00:09:21.180> ball<00:09:21.420> and
along and says look here's a ball and
along and says look here's a ball and
you<00:09:22.230> are<00:09:22.530> I<00:09:22.950> can<00:09:23.190> see<00:09:23.460> it<00:09:23.610> I<00:09:23.790> can<00:09:23.940> feel<00:09:24.210> it<00:09:24.360> I<00:09:24.480> can
you are I can see it I can feel it I can
you are I can see it I can feel it I can
touch<00:09:24.990> it<00:09:25.230> I<00:09:25.380> can<00:09:25.770> play<00:09:25.980> with<00:09:26.220> it<00:09:26.370> and<00:09:26.490> that's
touch it I can play with it and that's
touch it I can play with it and that's
exactly<00:09:27.360> what<00:09:27.900> happened<00:09:28.350> when<00:09:28.860> Dana<00:09:29.160> came<00:09:29.520> in
exactly what happened when Dana came in
exactly what happened when Dana came in
ER<00:09:29.790> in<00:09:30.980> 1997<00:09:31.980> invent<00:09:32.580> in<00:09:32.760> showed<00:09:33.570> that<00:09:33.900> you
ER in 1997 invent in showed that you
ER in 1997 invent in showed that you
could<00:09:34.110> crochet<00:09:34.590> models<00:09:35.010> in<00:09:35.100> hyperbolic<00:09:35.580> space
could crochet models in hyperbolic space
could crochet models in hyperbolic space
here<00:09:36.930> is<00:09:37.140> this<00:09:37.530> diagram<00:09:37.890> in<00:09:38.430> crochet<00:09:39.030> nurse
here is this diagram in crochet nurse
here is this diagram in crochet nurse
and<00:09:39.890> I've<00:09:40.890> stitched<00:09:41.250> Euclid's<00:09:42.150> parallel
and I've stitched Euclid's parallel
and I've stitched Euclid's parallel
postulate<00:09:43.140> onto<00:09:43.830> the<00:09:43.950> surface<00:09:44.370> and<00:09:44.490> the<00:09:44.610> lines
postulate onto the surface and the lines
postulate onto the surface and the lines
looked<00:09:45.210> curved<00:09:45.570> but<00:09:46.350> look<00:09:46.560> I<00:09:46.680> can<00:09:46.890> prove<00:09:47.130> to
looked curved but look I can prove to
looked curved but look I can prove to
you<00:09:47.550> that<00:09:47.580> they're<00:09:47.910> straight<00:09:48.270> because<00:09:49.260> I<00:09:49.410> can
you that they're straight because I can
you that they're straight because I can
take<00:09:49.770> any<00:09:49.980> one<00:09:50.100> of<00:09:50.250> these<00:09:50.520> lines<00:09:50.850> and<00:09:51.120> I<00:09:51.660> can
take any one of these lines and I can
take any one of these lines and I can
fold<00:09:52.230> along<00:09:52.680> it<00:09:52.860> and<00:09:53.120> it's<00:09:54.120> a<00:09:54.210> straight<00:09:54.540> line
fold along it and it's a straight line
fold along it and it's a straight line
so<00:09:56.250> here<00:09:56.700> in<00:09:57.290> wool<00:09:58.290> through<00:09:58.890> a<00:09:58.920> domestic
so here in wool through a domestic
so here in wool through a domestic
feminine<00:09:59.970> art<00:10:00.150> is<00:10:00.450> the<00:10:01.320> proof<00:10:01.620> that<00:10:01.890> the<00:10:02.010> most
feminine art is the proof that the most
feminine art is the proof that the most
famous<00:10:02.540> postulate<00:10:03.540> in<00:10:03.630> mathematics<00:10:04.320> is<00:10:04.530> wrong
and<00:10:11.739> you<00:10:12.739> can<00:10:12.919> stitch<00:10:13.129> all<00:10:13.339> sorts<00:10:13.699> of
and you can stitch all sorts of
and you can stitch all sorts of
mathematical<00:10:14.539> theorems<00:10:14.929> onto<00:10:15.259> these
mathematical theorems onto these
mathematical theorems onto these
surfaces<00:10:16.069> the<00:10:16.789> discovery<00:10:17.329> of<00:10:17.449> hyperbolic
surfaces the discovery of hyperbolic
surfaces the discovery of hyperbolic
space<00:10:18.229> assured<00:10:19.129> in<00:10:19.279> the<00:10:19.369> field<00:10:19.639> of
space assured in the field of
space assured in the field of
mathematics<00:10:20.419> that's<00:10:20.600> called<00:10:20.809> non<00:10:21.019> Euclidean
mathematics that's called non Euclidean
mathematics that's called non Euclidean
geometry<00:10:21.649> and<00:10:22.399> this<00:10:22.669> is<00:10:22.819> actually<00:10:23.119> the<00:10:23.269> field
geometry and this is actually the field
geometry and this is actually the field
of<00:10:23.660> mathematics<00:10:24.259> that<00:10:24.319> underlies<00:10:24.439> general
of mathematics that underlies general
of mathematics that underlies general
relativity<00:10:25.970> and<00:10:26.209> is<00:10:26.660> actually<00:10:26.989> ultimately
relativity and is actually ultimately
relativity and is actually ultimately
going<00:10:27.559> to<00:10:27.649> show<00:10:27.859> us<00:10:28.009> about<00:10:28.129> the<00:10:28.429> shape<00:10:28.939> of<00:10:29.119> the
going to show us about the shape of the
going to show us about the shape of the
universe<00:10:29.569> so<00:10:30.410> there<00:10:30.619> is<00:10:30.769> this<00:10:30.949> direct<00:10:31.369> line
universe so there is this direct line
universe so there is this direct line
between<00:10:32.269> feminine<00:10:33.189> handicraft
between feminine handicraft
between feminine handicraft
Euclid<00:10:34.970> and<00:10:35.119> general<00:10:35.899> relativity<00:10:36.639> now<00:10:37.639> I<00:10:37.879> said
Euclid and general relativity now I said
Euclid and general relativity now I said
that<00:10:38.209> mathematicians<00:10:38.989> thought<00:10:39.199> this<00:10:39.410> was
that mathematicians thought this was
that mathematicians thought this was
impossible<00:10:40.220> here<00:10:40.879> is<00:10:41.029> two<00:10:41.299> creatures<00:10:41.689> who
impossible here is two creatures who
impossible here is two creatures who
never<00:10:42.229> heard<00:10:42.499> of<00:10:42.679> Euclid's<00:10:43.189> parallel
never heard of Euclid's parallel
never heard of Euclid's parallel
postulate<00:10:44.239> didn't<00:10:44.899> know<00:10:45.079> it<00:10:45.199> was<00:10:45.319> impossible
postulate didn't know it was impossible
postulate didn't know it was impossible
to<00:10:46.100> violate<00:10:46.549> and<00:10:46.699> they're<00:10:47.149> simply<00:10:47.569> getting<00:10:47.779> on
to violate and they're simply getting on
to violate and they're simply getting on
with<00:10:48.199> it<00:10:48.229> they've<00:10:48.829> been<00:10:48.859> doing<00:10:49.129> it<00:10:49.339> for
with it they've been doing it for
with it they've been doing it for
hundreds<00:10:49.819> of<00:10:49.910> millions<00:10:50.089> of<00:10:50.389> years<00:10:50.689> and<00:10:51.039> I<00:10:52.039> once
hundreds of millions of years and I once
hundreds of millions of years and I once
asked<00:10:52.729> the<00:10:52.759> mathematicians<00:10:53.660> why<00:10:53.989> it<00:10:54.049> was<00:10:54.499> that
asked the mathematicians why it was that
asked the mathematicians why it was that
mathematicians<00:10:55.699> thought<00:10:56.089> this<00:10:56.359> structure
mathematicians thought this structure
mathematicians thought this structure
was<00:10:56.899> impossible<00:10:57.499> when<00:10:57.649> sea<00:10:57.889> slugs<00:10:58.220> have<00:10:58.369> been
was impossible when sea slugs have been
was impossible when sea slugs have been
doing<00:10:58.789> it<00:10:58.879> since<00:10:58.910> the<00:10:59.239> Silurian<00:10:59.869> age<00:11:00.049> and
doing it since the Silurian age and
doing it since the Silurian age and
their<00:11:01.129> answer<00:11:01.489> was<00:11:01.579> interesting<00:11:01.999> they<00:11:02.119> said
their answer was interesting they said
their answer was interesting they said
well<00:11:02.449> I<00:11:02.479> guess<00:11:02.689> there<00:11:02.899> aren't<00:11:03.079> that<00:11:03.199> many
well I guess there aren't that many
well I guess there aren't that many
mathematicians<00:11:03.889> sitting<00:11:04.489> around<00:11:04.669> looking<00:11:04.999> at
mathematicians sitting around looking at
mathematicians sitting around looking at
sea<00:11:05.299> slugs<00:11:05.629> and<00:11:05.929> that's<00:11:06.470> true<00:11:06.889> but<00:11:07.459> it<00:11:07.609> also
sea slugs and that's true but it also
sea slugs and that's true but it also
goes<00:11:08.209> deeper<00:11:08.600> than<00:11:08.749> that<00:11:08.779> it<00:11:09.259> also<00:11:09.499> says<00:11:09.859> a
goes deeper than that it also says a
goes deeper than that it also says a
whole<00:11:10.160> lot<00:11:10.399> of<00:11:10.549> things<00:11:10.819> about<00:11:11.029> what
whole lot of things about what
whole lot of things about what
mathematicians<00:11:12.289> thought<00:11:12.859> mathematics<00:11:13.639> was
mathematicians thought mathematics was
mathematicians thought mathematics was
what<00:11:14.179> they<00:11:14.299> thought<00:11:14.329> it<00:11:14.720> couldn't<00:11:15.019> couldn't
what they thought it couldn't couldn't
what they thought it couldn't couldn't
do<00:11:15.589> what<00:11:16.100> they<00:11:16.220> thought<00:11:16.459> it<00:11:16.639> couldn't
do what they thought it couldn't
do what they thought it couldn't
couldn't<00:11:17.149> represent<00:11:17.449> and<00:11:18.159> even
couldn't represent and even
couldn't represent and even
mathematicians<00:11:19.879> who<00:11:19.970> in<00:11:20.089> some<00:11:20.299> sense<00:11:20.600> of<00:11:20.720> the
mathematicians who in some sense of the
mathematicians who in some sense of the
freest<00:11:21.139> of<00:11:21.439> all<00:11:21.589> thinkers<00:11:22.159> literally
freest of all thinkers literally
freest of all thinkers literally
couldn't<00:11:23.539> see<00:11:23.959> not<00:11:24.649> only<00:11:24.679> the<00:11:25.129> sea<00:11:25.339> slugs
couldn't see not only the sea slugs
couldn't see not only the sea slugs
around<00:11:25.999> them<00:11:26.179> but<00:11:26.509> the<00:11:26.659> latest<00:11:26.869> on<00:11:27.169> their
around them but the latest on their
around them but the latest on their
plate<00:11:27.739> because<00:11:28.639> lattices<00:11:29.149> and<00:11:29.329> all<00:11:29.449> those
plate because lattices and all those
plate because lattices and all those
clearly<00:11:29.959> vegetables<00:11:30.619> they<00:11:30.799> also<00:11:31.069> are
clearly vegetables they also are
clearly vegetables they also are
embodiments<00:11:32.209> of<00:11:32.479> hyperbolic<00:11:33.379> geometry<00:11:33.589> and
embodiments of hyperbolic geometry and
embodiments of hyperbolic geometry and
so<00:11:35.149> in<00:11:35.389> some<00:11:35.749> sense<00:11:36.079> they<00:11:36.259> literally<00:11:36.649> they<00:11:37.309> had
so in some sense they literally they had
so in some sense they literally they had
such<00:11:37.789> a<00:11:37.819> symbolic<00:11:38.299> view<00:11:38.689> of<00:11:38.899> mathematics<00:11:39.529> they
such a symbolic view of mathematics they
such a symbolic view of mathematics they
couldn't<00:11:40.249> actually<00:11:40.429> see<00:11:40.939> what<00:11:41.269> was<00:11:41.299> going<00:11:41.779> on
couldn't actually see what was going on
couldn't actually see what was going on
on<00:11:42.229> the<00:11:42.499> lettuce<00:11:42.679> in<00:11:42.949> front<00:11:43.159> of<00:11:43.309> them<00:11:44.079> it<00:11:45.079> turns
on the lettuce in front of them it turns
on the lettuce in front of them it turns
out<00:11:45.679> that<00:11:45.859> the<00:11:46.009> natural<00:11:46.459> world<00:11:46.669> is<00:11:46.909> full<00:11:47.119> of
out that the natural world is full of
out that the natural world is full of
hyperbolic<00:11:47.899> wonders<00:11:48.499> and<00:11:48.739> so<00:11:49.609> too<00:11:49.669> we've
hyperbolic wonders and so too we've
hyperbolic wonders and so too we've
discovered<00:11:50.749> that<00:11:51.019> there<00:11:51.589> is<00:11:51.619> an<00:11:51.829> infinite
discovered that there is an infinite
discovered that there is an infinite
taxonomy<00:11:52.819> of<00:11:53.229> crochet<00:11:54.229> hyperbolic<00:11:54.889> creatures
taxonomy of crochet hyperbolic creatures
taxonomy of crochet hyperbolic creatures
we<00:11:55.909> started<00:11:56.449> out<00:11:56.600> crissy<00:11:57.019> and<00:11:57.139> I<00:11:57.229> and<00:11:57.470> our
we started out crissy and I and our
we started out crissy and I and our
contributors<00:11:58.159> doing<00:11:58.429> the<00:11:58.519> simple
contributors doing the simple
contributors doing the simple
mathematically<00:11:59.629> perfect<00:11:59.839> models<00:12:00.499> but<00:12:00.949> we
mathematically perfect models but we
mathematically perfect models but we
found<00:12:01.309> that<00:12:01.549> when<00:12:01.669> we<00:12:01.729> deviated<00:12:02.659> from<00:12:02.689> the
found that when we deviated from the
found that when we deviated from the
specific<00:12:03.909> setna<00:12:04.909> the<00:12:05.299> mathematical<00:12:06.109> code
specific setna the mathematical code
specific setna the mathematical code
that<00:12:07.129> underlies<00:12:07.309> is<00:12:07.970> the<00:12:08.089> simple<00:12:08.539> algorithm
that underlies is the simple algorithm
that underlies is the simple algorithm
crochet<00:12:09.979> three<00:12:10.249> increase<00:12:10.669> one<00:12:10.939> when<00:12:11.779> we
crochet three increase one when we
crochet three increase one when we
deviated<00:12:12.439> from<00:12:12.619> that<00:12:12.889> and<00:12:13.069> made
deviated from that and made
deviated from that and made
embellishments<00:12:14.209> to<00:12:14.299> the<00:12:14.419> code<00:12:14.629> the<00:12:14.989> models
embellishments to the code the models
embellishments to the code the models
immediately<00:12:15.979> started<00:12:16.429> to<00:12:16.549> look<00:12:16.729> more<00:12:16.759> natural
immediately started to look more natural
immediately started to look more natural
and<00:12:17.659> all<00:12:18.379> of<00:12:18.589> our<00:12:18.769> contributors<00:12:19.399> who<00:12:19.549> are
and all of our contributors who are
and all of our contributors who are
amazing<00:12:20.209> collection<00:12:20.720> of<00:12:20.809> people<00:12:21.019> around<00:12:21.439> the
amazing collection of people around the
amazing collection of people around the
world<00:12:21.859> do
world do
world do
their<00:12:22.589> own<00:12:22.769> embellishments<00:12:23.189> and<00:12:23.759> as<00:12:24.209> it<00:12:24.359> were
their own embellishments and as it were
their own embellishments and as it were
we<00:12:24.779> have<00:12:24.989> this<00:12:25.139> ever-evolving<00:12:25.729> crochet
we have this ever-evolving crochet
we have this ever-evolving crochet
taxonomic<00:12:27.509> tree<00:12:27.539> of<00:12:27.959> life<00:12:28.199> and<00:12:28.559> just<00:12:29.219> as<00:12:29.429> the
taxonomic tree of life and just as the
taxonomic tree of life and just as the
morphology<00:12:29.969> and<00:12:30.359> the<00:12:30.419> complexity<00:12:31.079> of<00:12:31.109> life<00:12:31.439> on
morphology and the complexity of life on
morphology and the complexity of life on
Earth<00:12:31.829> is<00:12:32.069> never-ending
Earth is never-ending
Earth is never-ending
little<00:12:33.529> embellishments<00:12:34.529> and
little embellishments and
little embellishments and
complexification<00:12:35.279> zin<00:12:35.789> the<00:12:35.879> DNA<00:12:36.359> code<00:12:36.689> lead
complexification zin the DNA code lead
complexification zin the DNA code lead
to<00:12:37.559> new<00:12:37.739> things<00:12:38.129> like<00:12:38.459> giraffes<00:12:38.969> or<00:12:39.449> orchids
to new things like giraffes or orchids
to new things like giraffes or orchids
so<00:12:40.709> two<00:12:40.769> little<00:12:41.339> embellishments<00:12:42.029> in<00:12:42.119> the
so two little embellishments in the
so two little embellishments in the
crochet<00:12:42.449> code<00:12:43.019> lead<00:12:43.679> to<00:12:43.889> new<00:12:44.159> and<00:12:44.399> wondrous
crochet code lead to new and wondrous
crochet code lead to new and wondrous
creatures<00:12:46.229> in<00:12:46.409> the<00:12:46.559> evolutionary<00:12:47.189> tree<00:12:47.489> of
creatures in the evolutionary tree of
creatures in the evolutionary tree of
crochet<00:12:48.329> life<00:12:49.069> so<00:12:50.069> this<00:12:50.339> project<00:12:50.999> really<00:12:51.179> has
crochet life so this project really has
crochet life so this project really has
taken<00:12:52.259> on<00:12:52.379> this<00:12:52.499> inner<00:12:52.859> organic<00:12:53.459> life<00:12:53.699> of<00:12:53.879> its
taken on this inner organic life of its
taken on this inner organic life of its
own<00:12:54.209> that's<00:12:54.689> the<00:12:54.929> totality<00:12:55.379> of<00:12:55.709> all<00:12:56.009> the
own that's the totality of all the
own that's the totality of all the
people<00:12:56.699> who've<00:12:56.909> come<00:12:57.179> to<00:12:57.419> it<00:12:57.569> and<00:12:57.749> their
people who've come to it and their
people who've come to it and their
individual<00:12:58.829> visions<00:12:59.249> and<00:12:59.429> their<00:12:59.549> engagement
individual visions and their engagement
individual visions and their engagement
with<00:13:00.689> this<00:13:00.839> mathematical<00:13:01.769> mode<00:13:01.979> we<00:13:02.669> have
with this mathematical mode we have
with this mathematical mode we have
these<00:13:03.149> technologies<00:13:03.839> we<00:13:04.019> use<00:13:04.049> them<00:13:04.499> but<00:13:04.829> why
these technologies we use them but why
these technologies we use them but why
what's<00:13:05.639> at<00:13:05.849> stake<00:13:06.149> here<00:13:06.179> what<00:13:06.599> does<00:13:06.749> it<00:13:06.809> matter
what's at stake here what does it matter
what's at stake here what does it matter
for<00:13:07.469> Crissy<00:13:08.129> and<00:13:08.249> I<00:13:08.429> one<00:13:08.759> of<00:13:08.789> the<00:13:09.029> things
for Crissy and I one of the things
for Crissy and I one of the things
that's<00:13:09.569> important<00:13:10.139> here<00:13:10.409> is<00:13:10.619> that<00:13:10.769> these
that's important here is that these
that's important here is that these
things<00:13:11.309> suggest<00:13:11.639> that<00:13:12.029> importance<00:13:12.659> and<00:13:12.839> value
things suggest that importance and value
things suggest that importance and value
of<00:13:13.499> embodied<00:13:14.429> knowledge<00:13:14.599> we<00:13:15.599> live<00:13:15.779> in<00:13:15.899> a
of embodied knowledge we live in a
of embodied knowledge we live in a
society<00:13:16.139> that<00:13:16.889> completely<00:13:17.519> tends<00:13:17.909> to
society that completely tends to
society that completely tends to
valorize<00:13:19.009> symbolic<00:13:20.009> forms<00:13:20.399> of
valorize symbolic forms of
valorize symbolic forms of
representation<00:13:21.499> algebraic<00:13:22.519> representations
representation algebraic representations
representation algebraic representations
equations<00:13:24.269> codes<00:13:24.719> we<00:13:25.349> live<00:13:25.529> in<00:13:25.649> a<00:13:25.709> society
equations codes we live in a society
equations codes we live in a society
that's<00:13:26.939> obsessed<00:13:27.449> with<00:13:27.689> presenting
that's obsessed with presenting
that's obsessed with presenting
information<00:13:28.739> in<00:13:29.459> this<00:13:29.609> way<00:13:29.669> teaching
information in this way teaching
information in this way teaching
information<00:13:30.539> in<00:13:31.169> this<00:13:31.289> way<00:13:31.349> but<00:13:32.220> through<00:13:32.629> this
information in this way but through this
information in this way but through this
sort<00:13:33.959> of<00:13:34.049> modality<00:13:35.329> crocheted<00:13:36.329> other<00:13:37.159> plastic
sort of modality crocheted other plastic
sort of modality crocheted other plastic
forms<00:13:38.579> of<00:13:38.759> play<00:13:38.999> people<00:13:39.869> can<00:13:40.079> be<00:13:40.259> engaged<00:13:40.619> with
forms of play people can be engaged with
forms of play people can be engaged with
the<00:13:41.039> most<00:13:41.249> abstract<00:13:41.970> high<00:13:42.329> powered
the most abstract high powered
the most abstract high powered
theoretical<00:13:43.559> ideas<00:13:43.949> the<00:13:44.279> kind<00:13:44.549> of<00:13:44.699> ideas<00:13:45.089> that
theoretical ideas the kind of ideas that
theoretical ideas the kind of ideas that
normally<00:13:45.689> you<00:13:45.809> have<00:13:45.839> to<00:13:46.199> go<00:13:46.409> to<00:13:46.859> university
normally you have to go to university
normally you have to go to university
departments<00:13:48.269> to<00:13:48.389> study<00:13:48.659> in<00:13:48.869> higher
departments to study in higher
departments to study in higher
mathematics<00:13:49.409> which<00:13:49.919> is<00:13:50.009> where<00:13:50.159> I<00:13:50.189> first
mathematics which is where I first
mathematics which is where I first
learned<00:13:50.819> about<00:13:50.879> hyperbolic<00:13:51.599> space<00:13:51.689> but<00:13:52.379> you
learned about hyperbolic space but you
learned about hyperbolic space but you
can<00:13:52.529> do<00:13:52.949> it<00:13:53.129> through<00:13:53.429> playing<00:13:53.909> with<00:13:54.179> material
can do it through playing with material
can do it through playing with material
objects<00:13:55.559> and<00:13:55.709> one<00:13:56.519> of<00:13:56.699> the<00:13:56.789> ways<00:13:56.970> that<00:13:56.999> we've
objects and one of the ways that we've
objects and one of the ways that we've
come<00:13:57.599> to<00:13:57.629> think<00:13:57.989> about<00:13:58.259> this<00:13:58.470> is<00:13:58.679> that<00:13:58.829> what
come to think about this is that what
come to think about this is that what
we're<00:13:59.220> trying<00:13:59.339> to<00:13:59.549> do<00:13:59.789> with<00:13:59.999> the<00:14:00.119> Institute
we're trying to do with the Institute
we're trying to do with the Institute
for<00:14:00.720> figuring<00:14:00.899> and<00:14:01.259> projects<00:14:01.799> like<00:14:01.829> this
for figuring and projects like this
for figuring and projects like this
we're<00:14:02.609> trying<00:14:02.759> to<00:14:03.029> have<00:14:03.179> kindergarten<00:14:03.779> for
we're trying to have kindergarten for
we're trying to have kindergarten for
grown-ups
grown-ups
grown-ups
and<00:14:05.449> kindergarten<00:14:06.449> was<00:14:06.569> actually<00:14:06.959> a<00:14:06.989> very
and kindergarten was actually a very
and kindergarten was actually a very
formalized<00:14:07.799> system<00:14:08.039> of<00:14:08.369> Education
formalized system of Education
formalized system of Education
established<00:14:09.119> by<00:14:09.809> a<00:14:09.839> man<00:14:10.109> named<00:14:10.379> Friedrich
established by a man named Friedrich
established by a man named Friedrich
Froebel<00:14:11.009> who<00:14:11.249> was<00:14:11.369> a<00:14:11.399> crystallographer<00:14:11.939> in
Froebel who was a crystallographer in
Froebel who was a crystallographer in
the<00:14:12.389> 19th<00:14:12.839> century<00:14:12.899> he<00:14:13.499> believed<00:14:13.829> that<00:14:13.859> the
the 19th century he believed that the
the 19th century he believed that the
crystal<00:14:14.489> was<00:14:14.639> the<00:14:14.759> model<00:14:15.119> for<00:14:15.239> all<00:14:15.629> kinds<00:14:16.349> of
crystal was the model for all kinds of
crystal was the model for all kinds of
representation<00:14:17.399> and<00:14:17.549> he<00:14:17.909> developed<00:14:18.569> a
representation and he developed a
representation and he developed a
radical<00:14:19.379> alternative<00:14:20.009> system<00:14:20.729> of<00:14:20.879> engaging
radical alternative system of engaging
radical alternative system of engaging
the<00:14:21.719> smallest<00:14:22.079> children<00:14:22.529> with<00:14:23.069> the<00:14:23.189> most
the smallest children with the most
the smallest children with the most
abstract<00:14:23.909> ideas<00:14:24.419> through<00:14:24.869> physical<00:14:25.379> forms<00:14:25.769> of
abstract ideas through physical forms of
abstract ideas through physical forms of
play<00:14:26.309> and<00:14:26.489> he<00:14:26.639> is<00:14:26.699> worthy<00:14:27.059> of<00:14:27.089> an<00:14:27.209> entire<00:14:27.479> talk
play and he is worthy of an entire talk
play and he is worthy of an entire talk
on<00:14:27.989> his<00:14:28.199> own<00:14:28.379> right<00:14:28.709> the<00:14:29.219> value<00:14:29.549> of<00:14:29.879> education
on his own right the value of education
on his own right the value of education
is<00:14:30.839> something<00:14:31.319> that<00:14:31.679> Freud<00:14:32.129> championed
is something that Freud championed
is something that Freud championed
through<00:14:33.419> plastic<00:14:34.049> modes<00:14:34.499> of<00:14:34.709> play
through plastic modes of play
through plastic modes of play
we<00:14:35.829> live<00:14:36.069> in<00:14:36.189> a<00:14:36.279> society<00:14:36.639> now<00:14:36.939> where<00:14:37.629> we<00:14:37.720> have
we live in a society now where we have
we live in a society now where we have
lots<00:14:38.110> of<00:14:38.230> think<00:14:38.529> tanks<00:14:38.949> where<00:14:39.339> great<00:14:39.610> minds<00:14:39.999> go
lots of think tanks where great minds go
lots of think tanks where great minds go
to<00:14:40.449> think<00:14:41.170> about<00:14:41.439> the<00:14:41.619> world<00:14:41.829> and<00:14:42.129> they<00:14:42.550> write
to think about the world and they write
to think about the world and they write
these<00:14:43.089> great<00:14:43.449> symbolic<00:14:43.899> treatises<00:14:44.589> called
these great symbolic treatises called
these great symbolic treatises called
books<00:14:45.339> and<00:14:45.670> papers<00:14:46.180> and<00:14:46.329> op-ed<00:14:46.629> articles<00:14:47.550> we
books and papers and op-ed articles we
books and papers and op-ed articles we
want<00:14:48.819> to<00:14:48.939> propose<00:14:49.329> Krissy<00:14:49.869> and<00:14:49.990> I<00:14:50.079> through<00:14:50.410> the
want to propose Krissy and I through the
want to propose Krissy and I through the
Institute<00:14:50.860> of<00:14:50.949> figuring<00:14:51.339> another
Institute of figuring another
Institute of figuring another
alternative<00:14:52.569> way<00:14:52.839> of<00:14:53.019> doing<00:14:53.379> things<00:14:53.679> which<00:14:53.949> is
alternative way of doing things which is
alternative way of doing things which is
the<00:14:55.059> play<00:14:55.329> tank<00:14:55.720> and<00:14:56.050> the<00:14:57.040> play<00:14:57.249> tank<00:14:57.610> like<00:14:57.879> the
the play tank and the play tank like the
the play tank and the play tank like the
think<00:14:58.300> tank<00:14:58.540> is<00:14:58.689> a<00:14:58.720> place<00:14:59.019> where<00:14:59.529> people<00:14:59.740> can
think tank is a place where people can
think tank is a place where people can
go<00:15:00.369> and<00:15:00.610> engage<00:15:00.910> with<00:15:01.389> great<00:15:01.629> ideas<00:15:02.199> but<00:15:02.470> what
go and engage with great ideas but what
go and engage with great ideas but what
we<00:15:03.279> want<00:15:03.550> to<00:15:03.670> propose<00:15:04.029> is<00:15:04.449> that<00:15:04.779> the<00:15:05.230> highest
we want to propose is that the highest
we want to propose is that the highest
levels<00:15:06.189> of<00:15:06.309> abstraction<00:15:06.939> things<00:15:07.179> like
levels of abstraction things like
levels of abstraction things like
mathematics<00:15:08.079> computing<00:15:08.709> logic<00:15:09.189> etc<00:15:09.309> all<00:15:09.730> of
mathematics computing logic etc all of
mathematics computing logic etc all of
this<00:15:10.269> can<00:15:10.540> be<00:15:10.689> engaged<00:15:11.019> with<00:15:11.290> not<00:15:11.800> just
this can be engaged with not just
this can be engaged with not just
through<00:15:12.399> purely<00:15:12.850> cerebral<00:15:13.240> algebraic
through purely cerebral algebraic
through purely cerebral algebraic
symbolic<00:15:14.499> method<00:15:14.829> methods<00:15:15.699> but<00:15:15.999> by<00:15:16.179> literally
symbolic method methods but by literally
symbolic method methods but by literally
physically<00:15:17.589> playing<00:15:18.009> with<00:15:18.339> ideas<00:15:19.110> thank<00:15:20.110> you
physically playing with ideas thank you
physically playing with ideas thank you
very<00:15:20.350> much
you
TEDEducation TED-Ed TED Ed, Margaret, Wertheim, mathematics, coral, reefs
