Symmetry, reality's riddle - Marcus du Sautoy
on<00:00:16.380> the<00:00:16.530> 30th<00:00:16.950> of<00:00:17.160> May<00:00:17.690> 1832<00:00:18.690> a<00:00:19.220> gunshot<00:00:20.220> was
on the 30th of May 1832 a gunshot was
on the 30th of May 1832 a gunshot was
heard<00:00:20.580> ringing<00:00:21.420> out<00:00:21.570> across<00:00:22.080> the<00:00:22.350> 13th
heard ringing out across the 13th
heard ringing out across the 13th
arrondissement<00:00:23.010> in<00:00:23.700> Paris<00:00:24.710> peasant<00:00:25.800> who<00:00:26.310> was
arrondissement in Paris peasant who was
arrondissement in Paris peasant who was
walking<00:00:26.730> to<00:00:26.849> market<00:00:27.240> that<00:00:27.360> morning<00:00:27.779> ran
walking to market that morning ran
walking to market that morning ran
towards<00:00:29.130> where<00:00:29.310> the<00:00:29.400> gunshot<00:00:29.790> had<00:00:29.880> come<00:00:30.060> from
towards where the gunshot had come from
towards where the gunshot had come from
and<00:00:30.540> found<00:00:30.930> a<00:00:31.020> young<00:00:31.200> man<00:00:31.850> writhing<00:00:32.850> in<00:00:32.940> agony
and found a young man writhing in agony
and found a young man writhing in agony
on<00:00:33.480> the<00:00:33.510> floor<00:00:33.930> clearly<00:00:34.470> shot<00:00:34.860> by<00:00:35.250> a<00:00:35.280> dueling
on the floor clearly shot by a dueling
on the floor clearly shot by a dueling
wound<00:00:36.380> the<00:00:37.380> young<00:00:37.500> man's<00:00:37.739> name<00:00:37.860> was<00:00:38.790> ever<00:00:39.090> East
wound the young man's name was ever East
wound the young man's name was ever East
galois<00:00:39.960> he<00:00:40.920> was<00:00:41.070> a<00:00:41.100> well-known<00:00:41.510> revolutionary
galois he was a well-known revolutionary
galois he was a well-known revolutionary
in<00:00:42.690> Paris<00:00:43.109> at<00:00:43.350> the<00:00:43.590> time
in Paris at the time
in Paris at the time
Galois<00:00:45.300> was<00:00:45.480> taken<00:00:45.840> to<00:00:45.960> the<00:00:46.079> local<00:00:46.199> hospital
Galois was taken to the local hospital
Galois was taken to the local hospital
where<00:00:47.370> he<00:00:47.519> died<00:00:47.730> the<00:00:48.090> next<00:00:48.239> day<00:00:48.420> in<00:00:48.870> the<00:00:49.079> arms
where he died the next day in the arms
where he died the next day in the arms
of<00:00:49.500> his<00:00:49.590> brother<00:00:49.910> and<00:00:50.910> the<00:00:50.969> last<00:00:51.179> words<00:00:51.480> he
of his brother and the last words he
of his brother and the last words he
said<00:00:51.660> to<00:00:51.929> his<00:00:52.050> brother<00:00:52.289> where<00:00:53.160> don't<00:00:53.370> cry<00:00:53.609> for
said to his brother where don't cry for
said to his brother where don't cry for
me<00:00:53.850> Alfred<00:00:54.300> I<00:00:54.539> need<00:00:55.230> all<00:00:55.469> the<00:00:55.679> courage<00:00:55.980> I<00:00:56.100> can
me Alfred I need all the courage I can
me Alfred I need all the courage I can
muster<00:00:56.519> to<00:00:56.879> die<00:00:57.149> at<00:00:57.449> the<00:00:57.480> age<00:00:57.600> of<00:00:58.140> 20<00:00:59.359> that
muster to die at the age of 20 that
muster to die at the age of 20 that
wasn't<00:01:00.690> in<00:01:00.750> fact<00:01:00.899> revolutionary<00:01:01.649> politics
wasn't in fact revolutionary politics
wasn't in fact revolutionary politics
for<00:01:02.429> which<00:01:02.550> Galois<00:01:02.999> was<00:01:03.210> famous<00:01:03.920> but<00:01:04.920> a<00:01:04.980> few
for which Galois was famous but a few
for which Galois was famous but a few
years<00:01:05.430> earlier<00:01:05.820> while<00:01:06.090> still<00:01:06.480> at<00:01:06.720> school<00:01:07.110> he'd
years earlier while still at school he'd
years earlier while still at school he'd
actually<00:01:07.890> cracked<00:01:08.370> one<00:01:08.670> of<00:01:08.760> the<00:01:08.850> big
actually cracked one of the big
actually cracked one of the big
mathematical<00:01:09.750> problems<00:01:10.200> at<00:01:10.470> the<00:01:10.590> time<00:01:10.800> and<00:01:11.760> he
mathematical problems at the time and he
mathematical problems at the time and he
wrote<00:01:12.180> to<00:01:12.420> the<00:01:12.510> academicians<00:01:13.230> in<00:01:13.409> Paris
wrote to the academicians in Paris
wrote to the academicians in Paris
trying<00:01:14.100> to<00:01:14.190> explain<00:01:14.610> his<00:01:14.940> theory<00:01:15.300> but<00:01:16.170> the
trying to explain his theory but the
trying to explain his theory but the
academicians<00:01:16.830> couldn't<00:01:17.190> understand
academicians couldn't understand
academicians couldn't understand
anything<00:01:17.880> that<00:01:18.180> he<00:01:18.300> wrote<00:01:18.510> this<00:01:19.140> is<00:01:19.320> how<00:01:19.560> he
anything that he wrote this is how he
anything that he wrote this is how he
wrote<00:01:19.950> most<00:01:20.490> of<00:01:20.670> his<00:01:20.730> mathematics<00:01:21.860> so<00:01:22.860> the
wrote most of his mathematics so the
wrote most of his mathematics so the
night<00:01:23.100> before<00:01:23.310> that<00:01:23.670> Joule<00:01:23.940> he<00:01:24.270> realized<00:01:24.690> that
night before that Joule he realized that
night before that Joule he realized that
this<00:01:24.990> possibly<00:01:25.470> is<00:01:25.680> his<00:01:25.920> last<00:01:26.190> chance<00:01:26.460> to<00:01:27.420> try
this possibly is his last chance to try
this possibly is his last chance to try
and<00:01:27.750> explain<00:01:28.110> his<00:01:28.470> great<00:01:28.740> breakthrough<00:01:29.340> so<00:01:30.000> he
and explain his great breakthrough so he
and explain his great breakthrough so he
stayed<00:01:30.390> up<00:01:30.540> the<00:01:30.690> whole<00:01:30.720> night<00:01:30.960> writing<00:01:31.680> away
stayed up the whole night writing away
stayed up the whole night writing away
trying<00:01:32.670> to<00:01:32.760> explain<00:01:33.180> his<00:01:33.450> ideas<00:01:33.900> and<00:01:34.230> as<00:01:34.710> the
trying to explain his ideas and as the
trying to explain his ideas and as the
dawn<00:01:35.010> came<00:01:35.760> up<00:01:36.000> and<00:01:36.210> he<00:01:36.270> went<00:01:36.360> to<00:01:36.480> meet<00:01:36.660> his
dawn came up and he went to meet his
dawn came up and he went to meet his
destiny<00:01:37.290> he<00:01:37.740> left<00:01:37.950> this<00:01:38.070> pile<00:01:38.310> of<00:01:38.520> papers<00:01:38.940> on
destiny he left this pile of papers on
destiny he left this pile of papers on
the<00:01:39.660> table<00:01:40.080> for<00:01:40.710> the<00:01:40.800> next<00:01:40.830> generation<00:01:41.610> maybe
the table for the next generation maybe
the table for the next generation maybe
the<00:01:42.240> fact<00:01:42.360> these<00:01:42.480> stayed<00:01:42.690> up<00:01:42.780> all<00:01:42.900> night<00:01:42.960> doing
the fact these stayed up all night doing
the fact these stayed up all night doing
mathematics<00:01:43.740> was<00:01:43.920> the<00:01:44.010> fact<00:01:44.490> that<00:01:44.550> he<00:01:44.700> was
mathematics was the fact that he was
mathematics was the fact that he was
such<00:01:45.000> a<00:01:45.030> bad<00:01:45.270> shot<00:01:45.600> that<00:01:45.810> morning<00:01:46.170> I<00:01:46.230> got
such a bad shot that morning I got
such a bad shot that morning I got
killed<00:01:46.650> and<00:01:46.980> but<00:01:47.640> contained<00:01:48.030> inside<00:01:48.210> those
killed and but contained inside those
killed and but contained inside those
documents<00:01:49.110> was<00:01:49.950> a<00:01:50.010> new<00:01:50.250> language<00:01:50.490> a<00:01:51.030> language
documents was a new language a language
documents was a new language a language
to<00:01:51.720> understand<00:01:52.140> whether<00:01:52.350> the<00:01:52.500> most
to understand whether the most
to understand whether the most
fundamental<00:01:53.340> concepts<00:01:53.940> of<00:01:54.210> science<00:01:54.860> namely
fundamental concepts of science namely
fundamental concepts of science namely
symmetry<00:01:56.550> now<00:01:57.480> symmetry<00:01:57.990> is<00:01:58.080> almost<00:01:58.410> nature's
symmetry now symmetry is almost nature's
symmetry now symmetry is almost nature's
language<00:01:59.880> it<00:02:00.060> helps<00:02:00.330> us<00:02:00.510> to<00:02:00.600> understand<00:02:01.020> so
language it helps us to understand so
language it helps us to understand so
many<00:02:01.590> different<00:02:02.070> bits<00:02:02.310> of<00:02:02.490> the<00:02:02.550> scientific
many different bits of the scientific
many different bits of the scientific
world<00:02:03.180> for<00:02:04.140> example<00:02:04.590> molecular<00:02:05.130> structure
world for example molecular structure
world for example molecular structure
what<00:02:05.940> crystals<00:02:06.510> are<00:02:06.690> possible<00:02:07.140> we<00:02:07.560> can
what crystals are possible we can
what crystals are possible we can
understand<00:02:08.129> through<00:02:08.879> the<00:02:08.970> mathematics<00:02:09.450> of
understand through the mathematics of
understand through the mathematics of
symmetry<00:02:10.140> in<00:02:10.730> microbiology<00:02:11.730> you<00:02:12.150> really
symmetry in microbiology you really
symmetry in microbiology you really
don't<00:02:12.540> want<00:02:12.750> to<00:02:12.840> get<00:02:12.989> a<00:02:13.019> symmetrical<00:02:13.560> object
don't want to get a symmetrical object
don't want to get a symmetrical object
because<00:02:14.099> they're<00:02:14.250> generally<00:02:14.430> rather<00:02:14.790> nasty
because they're generally rather nasty
because they're generally rather nasty
the<00:02:15.840> swine<00:02:16.170> flu<00:02:16.470> virus<00:02:16.680> at<00:02:17.010> the<00:02:17.099> moment<00:02:17.430> is<00:02:17.519> a
the swine flu virus at the moment is a
the swine flu virus at the moment is a
symmetrical<00:02:18.060> object<00:02:18.510> and<00:02:18.690> it<00:02:18.930> uses<00:02:19.170> the
symmetrical object and it uses the
symmetrical object and it uses the
efficiency<00:02:20.070> of<00:02:20.190> symmetry<00:02:20.940> to<00:02:21.210> be<00:02:21.330> able<00:02:21.450> to
efficiency of symmetry to be able to
efficiency of symmetry to be able to
propagate<00:02:21.810> itself<00:02:22.380> so<00:02:22.680> well
propagate itself so well
propagate itself so well
but<00:02:24.599> a<00:02:24.629> larger-scale<00:02:25.020> of<00:02:25.319> biology<00:02:25.739> actually
but a larger-scale of biology actually
but a larger-scale of biology actually
symmetry<00:02:26.520> is<00:02:26.610> very<00:02:26.790> important<00:02:27.270> because
symmetry is very important because
symmetry is very important because
actually<00:02:27.750> communicates<00:02:28.379> genetic
actually communicates genetic
actually communicates genetic
information<00:02:29.220> I've<00:02:30.090> taken<00:02:30.390> two<00:02:30.660> pictures<00:02:31.050> here
information I've taken two pictures here
information I've taken two pictures here
and<00:02:31.290> I've<00:02:31.470> made<00:02:31.650> them<00:02:31.800> artificially
and I've made them artificially
and I've made them artificially
symmetrical<00:02:33.269> and<00:02:33.870> if<00:02:33.959> I<00:02:34.019> ask<00:02:34.260> you<00:02:34.500> which<00:02:34.680> of
symmetrical and if I ask you which of
symmetrical and if I ask you which of
these<00:02:34.980> you<00:02:35.220> find<00:02:35.459> more<00:02:35.670> beautiful<00:02:36.239> you'll
these you find more beautiful you'll
these you find more beautiful you'll
probably<00:02:36.840> be<00:02:37.050> drawn<00:02:37.410> to<00:02:37.590> the<00:02:37.709> lower<00:02:37.920> two
probably be drawn to the lower two
probably be drawn to the lower two
because<00:02:39.330> it's<00:02:39.510> hard<00:02:39.810> to<00:02:39.989> make<00:02:40.110> symmetry<00:02:40.800> and
because it's hard to make symmetry and
because it's hard to make symmetry and
if<00:02:41.370> you<00:02:41.459> can<00:02:41.580> make<00:02:41.760> yourself<00:02:41.880> symmetrical
if you can make yourself symmetrical
if you can make yourself symmetrical
you're<00:02:42.780> sending<00:02:43.110> out<00:02:43.200> a<00:02:43.230> sign<00:02:43.590> that<00:02:43.620> you've
you're sending out a sign that you've
you're sending out a sign that you've
got<00:02:44.220> good<00:02:44.730> genes<00:02:45.030> you've<00:02:45.540> got<00:02:45.750> a<00:02:45.959> good
got good genes you've got a good
got good genes you've got a good
upbringing<00:02:46.500> and<00:02:47.010> therefore<00:02:47.340> you'll<00:02:47.489> make<00:02:47.700> a
upbringing and therefore you'll make a
upbringing and therefore you'll make a
good<00:02:48.030> mate<00:02:48.330> so<00:02:48.780> symmetry<00:02:49.080> is<00:02:49.260> a<00:02:49.290> language
good mate so symmetry is a language
good mate so symmetry is a language
which<00:02:50.160> can<00:02:50.340> help<00:02:50.459> to<00:02:50.640> communicate<00:02:51.049> genetic
which can help to communicate genetic
which can help to communicate genetic
information<00:02:52.970> symmetry<00:02:53.970> can<00:02:54.090> also<00:02:54.269> help<00:02:54.690> us<00:02:54.810> to
information symmetry can also help us to
information symmetry can also help us to
explain<00:02:55.230> what's<00:02:55.500> happening<00:02:55.950> in<00:02:56.129> the<00:02:56.220> Large
explain what's happening in the Large
explain what's happening in the Large
Hadron<00:02:56.610> Collider<00:02:56.819> in<00:02:57.450> CERN<00:02:57.900> or<00:02:58.230> what's<00:02:58.650> not
Hadron Collider in CERN or what's not
Hadron Collider in CERN or what's not
happening<00:02:59.069> in<00:02:59.459> the<00:02:59.549> Large<00:02:59.730> Hadron<00:02:59.940> Collider
happening in the Large Hadron Collider
happening in the Large Hadron Collider
in<00:03:00.720> CERN<00:03:00.959> to<00:03:01.650> be<00:03:01.739> able<00:03:01.830> to<00:03:01.920> make<00:03:02.099> predictions
in CERN to be able to make predictions
in CERN to be able to make predictions
about<00:03:02.849> the<00:03:03.090> fundamental<00:03:03.569> particles<00:03:03.900> we<00:03:04.200> might
about the fundamental particles we might
about the fundamental particles we might
see<00:03:04.680> there<00:03:04.980> it<00:03:05.700> seems<00:03:06.030> that<00:03:06.180> there<00:03:06.329> are<00:03:06.390> all
see there it seems that there are all
see there it seems that there are all
facets<00:03:07.110> of<00:03:07.290> some<00:03:07.500> strange<00:03:07.980> symmetrical<00:03:08.610> shape
facets of some strange symmetrical shape
facets of some strange symmetrical shape
in<00:03:09.090> a<00:03:09.360> higher<00:03:09.599> dimensional<00:03:10.319> space<00:03:10.670> and<00:03:11.670> I
in a higher dimensional space and I
in a higher dimensional space and I
think<00:03:11.790> Galileo<00:03:12.329> summed<00:03:12.810> up<00:03:12.959> very<00:03:13.200> nicely<00:03:13.470> the
think Galileo summed up very nicely the
think Galileo summed up very nicely the
power<00:03:14.099> of<00:03:14.220> mathematics<00:03:14.400> to<00:03:15.209> understand<00:03:15.780> the
power of mathematics to understand the
power of mathematics to understand the
scientific<00:03:16.709> world<00:03:17.010> around<00:03:17.280> us
scientific world around us
scientific world around us
he<00:03:18.120> wrote<00:03:18.299> the<00:03:18.599> universe<00:03:18.989> cannot<00:03:19.319> be<00:03:19.470> read
he wrote the universe cannot be read
he wrote the universe cannot be read
until<00:03:20.250> we<00:03:20.370> have<00:03:20.459> learned<00:03:20.700> a<00:03:20.849> language<00:03:21.269> and
until we have learned a language and
until we have learned a language and
become<00:03:21.750> familiar<00:03:22.019> with<00:03:22.530> the<00:03:22.769> characters<00:03:23.220> in
become familiar with the characters in
become familiar with the characters in
which<00:03:23.459> it<00:03:23.640> is<00:03:23.730> written<00:03:23.910> it<00:03:24.299> is<00:03:24.690> written<00:03:24.989> in
which it is written it is written in
which it is written it is written in
mathematical<00:03:25.829> language<00:03:25.980> and<00:03:26.519> the<00:03:26.819> letters
mathematical language and the letters
mathematical language and the letters
are<00:03:27.360> triangles<00:03:27.810> circles<00:03:28.230> and<00:03:29.010> other
are triangles circles and other
are triangles circles and other
geometric<00:03:29.760> figures<00:03:30.359> without<00:03:31.019> which<00:03:31.319> means<00:03:31.560> it
geometric figures without which means it
geometric figures without which means it
is<00:03:31.859> humanly<00:03:32.310> impossible<00:03:32.340> to<00:03:33.239> comprehend<00:03:33.750> a
is humanly impossible to comprehend a
is humanly impossible to comprehend a
single<00:03:34.260> word<00:03:35.120> but<00:03:36.120> it's<00:03:36.239> not<00:03:36.359> just<00:03:36.540> scientists
single word but it's not just scientists
single word but it's not just scientists
who<00:03:37.230> interested<00:03:37.590> in<00:03:37.739> symmetry<00:03:38.040> artists<00:03:38.940> to
who interested in symmetry artists to
who interested in symmetry artists to
love<00:03:39.540> to<00:03:39.720> play<00:03:39.750> around<00:03:40.109> with<00:03:40.319> symmetry<00:03:40.680> they
love to play around with symmetry they
love to play around with symmetry they
also<00:03:41.670> have<00:03:41.880> a<00:03:41.910> slightly<00:03:42.180> more<00:03:42.420> ambiguous
also have a slightly more ambiguous
also have a slightly more ambiguous
relationship<00:03:43.470> with<00:03:44.220> it<00:03:44.370> here's<00:03:44.970> Thomas<00:03:45.209> Mann
relationship with it here's Thomas Mann
relationship with it here's Thomas Mann
talking<00:03:46.049> about<00:03:46.170> symmetry<00:03:46.530> in<00:03:46.769> the<00:03:46.859> magic
talking about symmetry in the magic
talking about symmetry in the magic
mountain<00:03:47.370> he<00:03:47.910> has<00:03:48.000> a<00:03:48.030> character<00:03:48.540> describing
mountain he has a character describing
mountain he has a character describing
the<00:03:49.200> snowflake<00:03:49.739> and<00:03:49.980> he<00:03:50.760> says<00:03:50.970> he<00:03:51.269> shuddered
the snowflake and he says he shuddered
the snowflake and he says he shuddered
at<00:03:51.930> its<00:03:52.109> perfect<00:03:52.590> precision<00:03:52.950> he<00:03:53.370> added
at its perfect precision he added
at its perfect precision he added
deathly<00:03:54.150> the<00:03:54.450> very<00:03:54.630> marrow<00:03:54.959> of<00:03:55.079> death<00:03:55.670> but
deathly the very marrow of death but
deathly the very marrow of death but
what<00:03:56.819> I<00:03:56.850> just<00:03:57.150> like<00:03:57.269> to<00:03:57.359> do<00:03:57.480> is<00:03:57.600> to<00:03:57.690> set<00:03:57.930> up
what I just like to do is to set up
what I just like to do is to set up
expectations<00:03:58.440> of<00:03:59.069> symmetry<00:03:59.519> and<00:03:59.549> then<00:03:59.700> break
expectations of symmetry and then break
expectations of symmetry and then break
them<00:04:00.269> and<00:04:00.450> a<00:04:00.959> beautiful<00:04:01.380> example<00:04:01.859> of<00:04:01.920> this<00:04:02.040> I
them and a beautiful example of this I
them and a beautiful example of this I
found<00:04:02.910> actually<00:04:03.299> when<00:04:03.420> I<00:04:03.450> visited<00:04:03.840> a
found actually when I visited a
found actually when I visited a
colleague<00:04:04.440> of<00:04:04.530> mine<00:04:04.739> in<00:04:04.950> Japan<00:04:05.310> professor
colleague of mine in Japan professor
colleague of mine in Japan professor
Cora<00:04:05.970> Kawa<00:04:06.420> and<00:04:06.569> he<00:04:07.139> took<00:04:07.290> me<00:04:07.440> up<00:04:07.560> to<00:04:07.590> the
Cora Kawa and he took me up to the
Cora Kawa and he took me up to the
temples<00:04:08.250> in<00:04:08.400> Nikko<00:04:08.760> and<00:04:09.060> just<00:04:09.540> after<00:04:09.810> this
temples in Nikko and just after this
temples in Nikko and just after this
photo<00:04:10.170> was<00:04:10.530> taken<00:04:10.560> we<00:04:11.250> walked<00:04:11.489> up<00:04:11.670> the<00:04:11.819> stairs
photo was taken we walked up the stairs
photo was taken we walked up the stairs
and<00:04:12.389> the<00:04:12.900> Gateway<00:04:13.109> you<00:04:13.349> see<00:04:13.590> behind<00:04:13.950> has<00:04:14.190> eight
and the Gateway you see behind has eight
and the Gateway you see behind has eight
columns<00:04:14.940> with<00:04:15.480> beautiful<00:04:15.989> symmetrical
columns with beautiful symmetrical
columns with beautiful symmetrical
designs<00:04:16.769> on<00:04:17.070> sever<00:04:17.729> them<00:04:18.000> them<00:04:18.209> are<00:04:18.419> exactly
designs on sever them them are exactly
designs on sever them them are exactly
the<00:04:19.169> same<00:04:19.200> and<00:04:19.739> the<00:04:20.070> eighth<00:04:20.220> one<00:04:20.579> is<00:04:20.760> turned
the same and the eighth one is turned
the same and the eighth one is turned
upside<00:04:21.539> down<00:04:21.810> and<00:04:22.470> I<00:04:22.590> said<00:04:22.770> to<00:04:22.860> professor
upside down and I said to professor
upside down and I said to professor
Kurokawa<00:04:23.820> Wow<00:04:24.360> the<00:04:24.419> architects<00:04:24.990> must<00:04:25.200> have
Kurokawa Wow the architects must have
Kurokawa Wow the architects must have
been<00:04:25.380> really<00:04:25.530> kicking<00:04:25.950> themselves<00:04:26.099> and<00:04:26.490> they
been really kicking themselves and they
been really kicking themselves and they
realized<00:04:26.910> that<00:04:27.120> you<00:04:27.270> know<00:04:27.479> they<00:04:27.599> made<00:04:27.810> the
realized that you know they made the
realized that you know they made the
mistake<00:04:28.200> and<00:04:28.229> put<00:04:28.530> this<00:04:28.650> one<00:04:28.800> upside<00:04:29.010> down<00:04:29.430> he
mistake and put this one upside down he
mistake and put this one upside down he
said<00:04:30.150> no<00:04:30.330> no<00:04:30.479> no<00:04:30.510> it<00:04:30.840> was<00:04:30.960> a<00:04:30.990> very<00:04:31.229> deliberate
said no no no it was a very deliberate
said no no no it was a very deliberate
act<00:04:31.919> and<00:04:32.250> he<00:04:32.580> refer<00:04:32.849> me<00:04:33.060> to<00:04:33.090> this<00:04:33.240> lovely<00:04:33.690> quote
act and he refer me to this lovely quote
act and he refer me to this lovely quote
from<00:04:34.169> the<00:04:34.289> Japanese<00:04:34.710> essays<00:04:35.070> in<00:04:35.250> idleness
from the Japanese essays in idleness
from the Japanese essays in idleness
from<00:04:35.940> the<00:04:36.030> 14th<00:04:36.450> century<00:04:36.900> in<00:04:37.260> which<00:04:37.560> the<00:04:37.620> SAS
from the 14th century in which the SAS
from the 14th century in which the SAS
in<00:04:38.770> everything<00:04:39.720> uniformity<00:04:40.720> is<00:04:40.900> undesirable
in everything uniformity is undesirable
in everything uniformity is undesirable
leaving<00:04:42.640> something<00:04:42.880> incomplete<00:04:43.300> makes<00:04:43.960> it
leaving something incomplete makes it
leaving something incomplete makes it
interesting<00:04:44.440> and<00:04:44.800> gives<00:04:45.130> one<00:04:45.280> the<00:04:45.310> feeling
interesting and gives one the feeling
interesting and gives one the feeling
that<00:04:45.790> there<00:04:45.940> is<00:04:46.060> room<00:04:46.240> for<00:04:46.390> growth<00:04:46.560> even<00:04:47.560> when
that there is room for growth even when
that there is room for growth even when
building<00:04:48.130> the<00:04:48.370> imperial<00:04:48.820> palace<00:04:49.030> they<00:04:49.750> always
building the imperial palace they always
building the imperial palace they always
leave<00:04:50.320> one<00:04:50.530> place<00:04:50.850> unfinished<00:04:52.320> but<00:04:53.320> if<00:04:53.440> I<00:04:53.470> had
leave one place unfinished but if I had
leave one place unfinished but if I had
to<00:04:53.710> choose<00:04:54.030> one<00:04:55.030> building<00:04:55.840> in<00:04:55.930> the<00:04:56.020> world<00:04:56.140> to
to choose one building in the world to
to choose one building in the world to
be<00:04:56.620> cast<00:04:56.890> out<00:04:57.130> on<00:04:57.190> the<00:04:57.430> desert<00:04:57.760> island<00:04:57.910> to<00:04:58.180> live
be cast out on the desert island to live
be cast out on the desert island to live
the<00:04:58.420> rest<00:04:58.570> of<00:04:58.690> my<00:04:58.810> life<00:04:58.990> being<00:04:59.290> an<00:04:59.410> addict<00:04:59.740> of
the rest of my life being an addict of
the rest of my life being an addict of
symmetry<00:05:00.340> I<00:05:00.490> would<00:05:00.850> probably<00:05:01.000> choose<00:05:01.390> the
symmetry I would probably choose the
symmetry I would probably choose the
Alhambra<00:05:02.170> in<00:05:02.380> Granada<00:05:02.440> this<00:05:03.280> is<00:05:03.370> a<00:05:03.400> palace
Alhambra in Granada this is a palace
Alhambra in Granada this is a palace
celebrating<00:05:04.690> symmetry<00:05:05.230> recently<00:05:06.070> I<00:05:06.100> took<00:05:06.250> my
celebrating symmetry recently I took my
celebrating symmetry recently I took my
family<00:05:06.760> we<00:05:07.270> do<00:05:07.390> this<00:05:07.510> rather<00:05:07.810> kind<00:05:08.140> of<00:05:08.230> nerdy
family we do this rather kind of nerdy
family we do this rather kind of nerdy
mathematical<00:05:09.280> trips<00:05:09.550> so<00:05:09.850> which<00:05:10.060> my<00:05:10.180> family
mathematical trips so which my family
mathematical trips so which my family
love<00:05:10.750> this<00:05:10.960> is<00:05:11.110> my<00:05:11.140> son<00:05:11.560> Tamir<00:05:12.010> you<00:05:12.130> can<00:05:12.280> see
love this is my son Tamir you can see
love this is my son Tamir you can see
he's<00:05:12.610> really<00:05:12.940> enjoying<00:05:13.060> our<00:05:13.540> mathematical
he's really enjoying our mathematical
he's really enjoying our mathematical
trip<00:05:14.590> to<00:05:14.740> the<00:05:14.830> Alhambra<00:05:15.840> but<00:05:16.840> I<00:05:16.870> wanted<00:05:17.230> to<00:05:17.290> try
trip to the Alhambra but I wanted to try
trip to the Alhambra but I wanted to try
and<00:05:17.740> enrich<00:05:17.860> him<00:05:18.220> I<00:05:18.310> think<00:05:18.520> one<00:05:18.640> of<00:05:18.670> the
and enrich him I think one of the
and enrich him I think one of the
problems<00:05:18.940> about<00:05:19.300> school<00:05:19.600> mathematics<00:05:19.840> is
problems about school mathematics is
problems about school mathematics is
it's<00:05:20.410> it's<00:05:20.590> it<00:05:21.160> doesn't<00:05:21.460> look<00:05:21.610> at<00:05:21.730> how
it's it's it doesn't look at how
it's it's it doesn't look at how
mathematics<00:05:22.360> is<00:05:22.450> embedded<00:05:22.930> in<00:05:23.050> the<00:05:23.140> world<00:05:23.350> we
mathematics is embedded in the world we
mathematics is embedded in the world we
live<00:05:23.770> in<00:05:23.800> so<00:05:24.670> I<00:05:24.700> wanted<00:05:24.970> to<00:05:25.060> open<00:05:25.270> up<00:05:25.390> his<00:05:25.750> eyes
live in so I wanted to open up his eyes
live in so I wanted to open up his eyes
up<00:05:26.290> to<00:05:26.470> how<00:05:26.620> much<00:05:26.740> symmetry<00:05:27.220> is<00:05:27.340> running
up to how much symmetry is running
up to how much symmetry is running
through<00:05:28.210> the<00:05:28.450> Alhambra<00:05:28.990> and<00:05:29.560> you<00:05:29.650> see<00:05:29.800> it<00:05:29.860> all
through the Alhambra and you see it all
through the Alhambra and you see it all
really<00:05:30.130> immediately<00:05:30.700> you<00:05:30.820> go<00:05:31.000> in<00:05:31.180> the
really immediately you go in the
really immediately you go in the
reflective<00:05:31.930> symmetry<00:05:32.500> in<00:05:32.680> the<00:05:33.070> water<00:05:33.310> but
reflective symmetry in the water but
reflective symmetry in the water but
it's<00:05:34.150> on<00:05:34.240> the<00:05:34.330> walls<00:05:34.540> where<00:05:34.930> all<00:05:35.050> the<00:05:35.170> exciting
it's on the walls where all the exciting
it's on the walls where all the exciting
things<00:05:35.680> are<00:05:36.040> happening<00:05:36.490> the<00:05:36.820> Moorish<00:05:37.150> artists
things are happening the Moorish artists
things are happening the Moorish artists
would<00:05:37.750> deny<00:05:38.020> the<00:05:38.080> possibility<00:05:38.800> to<00:05:38.830> draw
would deny the possibility to draw
would deny the possibility to draw
things<00:05:39.370> with<00:05:39.550> Souls
things with Souls
things with Souls
so<00:05:40.360> they<00:05:40.480> explored<00:05:41.200> a<00:05:41.290> more<00:05:41.440> geometric<00:05:41.620> art
so they explored a more geometric art
so they explored a more geometric art
and<00:05:42.610> so<00:05:43.210> what<00:05:43.390> is<00:05:43.570> symmetry<00:05:44.170> and<00:05:44.560> the<00:05:44.800> Alhambra
and so what is symmetry and the Alhambra
and so what is symmetry and the Alhambra
somehow<00:05:45.670> asks<00:05:46.180> all<00:05:46.360> of<00:05:46.480> these<00:05:46.600> questions<00:05:46.810> what
somehow asks all of these questions what
somehow asks all of these questions what
is<00:05:47.560> symmetry<00:05:47.890> when<00:05:48.880> a<00:05:48.910> two<00:05:49.120> of<00:05:49.210> these<00:05:49.330> walls<00:05:49.600> do
is symmetry when a two of these walls do
is symmetry when a two of these walls do
they<00:05:49.900> have<00:05:50.080> the<00:05:50.200> same<00:05:50.470> symmetries<00:05:51.370> can<00:05:52.060> we<00:05:52.150> say
they have the same symmetries can we say
they have the same symmetries can we say
whether<00:05:52.600> they<00:05:52.780> discovered<00:05:53.260> all<00:05:53.410> of<00:05:53.920> the
whether they discovered all of the
whether they discovered all of the
symmetries<00:05:54.520> in<00:05:54.700> the<00:05:54.790> Alhambra<00:05:55.240> and<00:05:55.620> it<00:05:56.620> was
symmetries in the Alhambra and it was
symmetries in the Alhambra and it was
Galois<00:05:57.160> who<00:05:57.400> produced<00:05:57.730> a<00:05:57.850> language<00:05:58.330> to<00:05:58.510> be
Galois who produced a language to be
Galois who produced a language to be
able<00:05:58.720> to<00:05:58.930> answer<00:05:59.170> some<00:05:59.530> of<00:05:59.800> these<00:05:59.980> questions
able to answer some of these questions
able to answer some of these questions
the<00:06:01.660> Galois<00:06:02.760> symmetry<00:06:03.760> unlike<00:06:04.150> for<00:06:04.330> Thomas
the Galois symmetry unlike for Thomas
the Galois symmetry unlike for Thomas
Mann<00:06:04.780> which<00:06:05.020> was<00:06:05.140> something<00:06:05.350> still<00:06:05.860> and
Mann which was something still and
Mann which was something still and
deadly<00:06:06.580> the<00:06:07.000> Galois<00:06:07.420> symmetry<00:06:07.990> was<00:06:08.140> all<00:06:08.320> about
deadly the Galois symmetry was all about
deadly the Galois symmetry was all about
motion<00:06:08.980> what<00:06:09.610> can<00:06:09.820> you<00:06:09.910> do<00:06:10.210> to<00:06:10.630> a<00:06:10.660> symmetrical
motion what can you do to a symmetrical
motion what can you do to a symmetrical
object<00:06:11.650> move<00:06:12.070> it<00:06:12.250> in<00:06:12.370> some<00:06:12.580> way<00:06:12.760> so<00:06:13.210> it<00:06:13.300> looks
object move it in some way so it looks
object move it in some way so it looks
the<00:06:13.570> same<00:06:13.750> as<00:06:14.020> before<00:06:14.080> you<00:06:14.620> moved<00:06:14.860> it<00:06:15.100> I<00:06:15.280> like
the same as before you moved it I like
the same as before you moved it I like
to<00:06:15.910> describe<00:06:16.120> it<00:06:16.480> as<00:06:16.600> the<00:06:16.690> magic<00:06:17.110> trick<00:06:17.320> moves
to describe it as the magic trick moves
to describe it as the magic trick moves
what<00:06:17.920> can<00:06:18.040> you<00:06:18.130> do<00:06:18.310> to<00:06:18.490> something<00:06:18.940> you<00:06:19.180> close
what can you do to something you close
what can you do to something you close
your<00:06:19.570> eyes<00:06:19.750> I<00:06:20.020> do<00:06:20.200> something<00:06:20.680> put<00:06:20.830> it<00:06:20.950> back
your eyes I do something put it back
your eyes I do something put it back
down<00:06:21.250> again
down again
down again
and<00:06:21.670> it<00:06:21.910> looks<00:06:22.060> like<00:06:22.240> it<00:06:22.390> did<00:06:22.540> before<00:06:22.840> it
and it looks like it did before it
and it looks like it did before it
started<00:06:23.380> so<00:06:24.130> for<00:06:24.250> example<00:06:24.670> the<00:06:24.730> walls<00:06:24.940> in<00:06:25.150> the
started so for example the walls in the
started so for example the walls in the
Alhambra<00:06:25.270> I<00:06:25.870> can<00:06:26.110> take<00:06:26.320> all<00:06:26.500> of<00:06:26.530> these<00:06:26.710> tiles
Alhambra I can take all of these tiles
Alhambra I can take all of these tiles
and<00:06:27.490> fix<00:06:27.910> them<00:06:28.120> at<00:06:28.240> the<00:06:28.300> yellow<00:06:28.540> place<00:06:28.780> rotate
and fix them at the yellow place rotate
and fix them at the yellow place rotate
them<00:06:29.830> by<00:06:30.280> 90<00:06:31.120> degrees<00:06:31.420> put<00:06:31.780> them<00:06:31.900> all<00:06:31.990> back
them by 90 degrees put them all back
them by 90 degrees put them all back
down<00:06:32.320> again<00:06:32.590> and<00:06:32.620> they<00:06:32.740> fit<00:06:33.010> perfectly<00:06:33.610> down
down again and they fit perfectly down
down again and they fit perfectly down
there<00:06:34.150> and<00:06:34.510> if<00:06:34.600> you<00:06:34.690> open<00:06:34.930> your<00:06:35.050> eyes<00:06:35.140> again
there and if you open your eyes again
there and if you open your eyes again
you<00:06:35.500> wouldn't<00:06:35.680> know<00:06:35.890> that<00:06:35.920> they've<00:06:36.250> moved<00:06:36.490> but
you wouldn't know that they've moved but
you wouldn't know that they've moved but
it's<00:06:37.420> the<00:06:37.600> motion<00:06:38.140> that<00:06:38.290> really
it's the motion that really
it's the motion that really
characterizes<00:06:39.400> the<00:06:39.700> symmetry<00:06:40.180> inside<00:06:40.690> the
characterizes the symmetry inside the
characterizes the symmetry inside the
Alhambra<00:06:41.440> but<00:06:42.310> it's<00:06:42.430> also<00:06:42.580> about<00:06:42.790> producing<00:06:43.210> a
Alhambra but it's also about producing a
Alhambra but it's also about producing a
language<00:06:43.900> to<00:06:44.110> describe<00:06:44.140> this<00:06:44.680> and<00:06:44.920> the<00:06:44.980> power
language to describe this and the power
language to describe this and the power
of<00:06:45.370> mathematics<00:06:45.610> is<00:06:46.060> often<00:06:46.419> to<00:06:46.570> change<00:06:47.560> one
of mathematics is often to change one
of mathematics is often to change one
thing<00:06:48.160> into<00:06:48.460> another<00:06:48.490> to<00:06:49.150> change<00:06:49.450> geometry
thing into another to change geometry
thing into another to change geometry
into<00:06:50.530> language
into language
into language
take<00:06:51.880> you<00:06:52.000> through<00:06:52.300> perhaps<00:06:53.110> push<00:06:53.440> you<00:06:53.560> a
take you through perhaps push you a
take you through perhaps push you a
little<00:06:53.680> bit<00:06:53.890> mathematically<00:06:54.730> so<00:06:54.940> brace
little bit mathematically so brace
little bit mathematically so brace
yourselves<00:06:55.690> push<00:06:56.650> you<00:06:56.770> a<00:06:56.800> little<00:06:56.860> bit<00:06:57.070> to
yourselves push you a little bit to
yourselves push you a little bit to
understand<00:06:57.940> how<00:06:58.150> this<00:06:58.330> language<00:06:58.540> works<00:06:59.020> which
understand how this language works which
understand how this language works which
enables<00:06:59.860> us<00:06:59.920> to<00:06:59.980> capture<00:07:00.310> what<00:07:00.670> is<00:07:00.850> symmetry
enables us to capture what is symmetry
enables us to capture what is symmetry
so<00:07:02.170> let's<00:07:02.350> take<00:07:02.530> these<00:07:02.680> two<00:07:02.740> symmetrical
so let's take these two symmetrical
so let's take these two symmetrical
objects<00:07:03.700> here<00:07:04.000> let's<00:07:04.600> take<00:07:04.720> the<00:07:04.930> twisted<00:07:05.320> six
objects here let's take the twisted six
objects here let's take the twisted six
pointed<00:07:05.950> star<00:07:06.010> fish<00:07:06.490> what<00:07:06.850> can<00:07:07.000> I<00:07:07.090> do<00:07:07.150> to<00:07:07.720> this
pointed star fish what can I do to this
pointed star fish what can I do to this
starfish<00:07:08.380> which<00:07:08.830> makes<00:07:09.010> it<00:07:09.130> look<00:07:09.280> the<00:07:09.400> same
starfish which makes it look the same
starfish which makes it look the same
well<00:07:10.120> there<00:07:10.270> I<00:07:10.300> rotated<00:07:10.870> it<00:07:10.990> by<00:07:11.020> a<00:07:11.170> sixth<00:07:11.650> of<00:07:11.800> a
well there I rotated it by a sixth of a
well there I rotated it by a sixth of a
turn<00:07:12.130> and<00:07:12.610> still<00:07:12.970> it<00:07:13.090> looks<00:07:13.180> like<00:07:13.420> it<00:07:13.540> did
turn and still it looks like it did
turn and still it looks like it did
before<00:07:13.840> I<00:07:14.020> started<00:07:14.530> I<00:07:14.770> can<00:07:15.250> rotate<00:07:15.580> by<00:07:15.790> a<00:07:15.820> third
before I started I can rotate by a third
before I started I can rotate by a third
of<00:07:16.300> a<00:07:16.360> turn<00:07:16.540> or<00:07:16.840> a<00:07:16.980> half<00:07:17.980> a<00:07:18.160> turn<00:07:18.400> and<00:07:19.300> put<00:07:19.600> it
of a turn or a half a turn and put it
of a turn or a half a turn and put it
back<00:07:19.780> down<00:07:19.840> on<00:07:20.170> its<00:07:20.290> image<00:07:20.470> or<00:07:20.850> 2/3<00:07:21.850> of<00:07:22.030> a<00:07:22.090> turn
back down on its image or 2/3 of a turn
back down on its image or 2/3 of a turn
and<00:07:22.650> a<00:07:23.650> fifth<00:07:23.890> symmetry<00:07:24.370> I<00:07:24.400> can<00:07:24.670> rotate<00:07:24.790> it<00:07:24.970> by
and a fifth symmetry I can rotate it by
and a fifth symmetry I can rotate it by
five<00:07:25.420> sixth<00:07:25.810> of<00:07:25.900> a<00:07:25.990> turn<00:07:26.020> and<00:07:26.470> those<00:07:26.800> are
five sixth of a turn and those are
five sixth of a turn and those are
things<00:07:27.160> that<00:07:27.430> I<00:07:27.850> can<00:07:28.090> do<00:07:28.300> to<00:07:28.330> the<00:07:28.660> symmetrical
things that I can do to the symmetrical
things that I can do to the symmetrical
object<00:07:29.380> which<00:07:29.500> make<00:07:29.680> it<00:07:29.860> look<00:07:30.010> like<00:07:30.160> it<00:07:30.340> did
object which make it look like it did
object which make it look like it did
before<00:07:30.730> I<00:07:30.940> start<00:07:31.330> it<00:07:31.510> now<00:07:32.320> for<00:07:32.500> Galois<00:07:32.920> there
before I start it now for Galois there
before I start it now for Galois there
was<00:07:33.610> actually<00:07:33.880> a<00:07:33.940> sixth<00:07:34.450> symmetry<00:07:35.050> can
was actually a sixth symmetry can
was actually a sixth symmetry can
anybody<00:07:36.100> think<00:07:36.220> what<00:07:36.640> else<00:07:36.820> I<00:07:37.060> could<00:07:37.240> do<00:07:37.360> to
anybody think what else I could do to
anybody think what else I could do to
this<00:07:37.660> which<00:07:37.870> would<00:07:37.990> leave<00:07:38.200> it<00:07:38.350> like<00:07:38.530> it<00:07:38.560> did
this which would leave it like it did
this which would leave it like it did
before<00:07:39.070> I<00:07:39.130> started<00:07:39.190> I<00:07:40.230> can't<00:07:41.230> flip<00:07:41.530> it<00:07:41.560> because
before I started I can't flip it because
before I started I can't flip it because
I<00:07:42.070> put<00:07:42.310> a<00:07:42.340> little<00:07:42.460> twist<00:07:42.670> on<00:07:43.000> it<00:07:43.030> term<00:07:43.270> tie<00:07:43.540> it's
I put a little twist on it term tie it's
I put a little twist on it term tie it's
got<00:07:43.780> no<00:07:43.960> reflective<00:07:44.590> symmetry<00:07:45.100> but<00:07:46.030> what<00:07:46.150> I
got no reflective symmetry but what I
got no reflective symmetry but what I
could<00:07:46.480> do<00:07:46.630> is<00:07:46.750> just<00:07:46.930> leave<00:07:47.080> it<00:07:47.230> where<00:07:47.380> it<00:07:47.470> is
could do is just leave it where it is
could do is just leave it where it is
pick<00:07:48.250> it<00:07:48.280> up<00:07:48.460> and<00:07:48.640> put<00:07:49.330> it<00:07:49.420> down<00:07:49.600> again<00:07:49.830> and<00:07:50.830> for
pick it up and put it down again and for
pick it up and put it down again and for
Galois<00:07:51.340> this<00:07:51.580> was<00:07:51.700> like<00:07:51.880> the<00:07:52.150> zeroth<00:07:52.540> symmetry
Galois this was like the zeroth symmetry
Galois this was like the zeroth symmetry
actually<00:07:53.890> the<00:07:53.950> invention<00:07:54.670> of<00:07:54.730> this<00:07:54.880> number
actually the invention of this number
actually the invention of this number
zero<00:07:55.660> was<00:07:56.110> a<00:07:56.140> very<00:07:56.380> modern<00:07:56.740> concept<00:07:57.220> 7th
zero was a very modern concept 7th
zero was a very modern concept 7th
century<00:07:57.970> AD<00:07:58.180> by<00:07:58.510> the<00:07:58.570> Indians
century AD by the Indians
century AD by the Indians
it<00:07:59.800> seems<00:07:59.980> mad<00:08:00.820> to<00:08:01.090> talk<00:08:01.270> about<00:08:01.390> nothing<00:08:01.960> and
it seems mad to talk about nothing and
it seems mad to talk about nothing and
this<00:08:02.440> is<00:08:02.590> the<00:08:02.680> same<00:08:02.860> idea<00:08:03.190> this<00:08:03.340> is<00:08:03.490> a
this is the same idea this is a
this is the same idea this is a
symmetrical<00:08:04.060> to<00:08:04.240> everything<00:08:04.660> has<00:08:04.810> symmetry
symmetrical to everything has symmetry
symmetrical to everything has symmetry
where<00:08:05.380> you<00:08:05.470> just<00:08:05.620> leave<00:08:05.800> it<00:08:05.920> where<00:08:06.040> it<00:08:06.190> is<00:08:06.220> so
where you just leave it where it is so
where you just leave it where it is so
this<00:08:07.300> object<00:08:07.480> has<00:08:07.870> six<00:08:08.200> symmetries<00:08:08.770> and<00:08:09.570> what
this object has six symmetries and what
this object has six symmetries and what
about<00:08:10.720> the<00:08:10.870> triangle<00:08:11.410> well<00:08:11.800> I<00:08:11.980> can<00:08:12.220> rotate<00:08:12.370> by
about the triangle well I can rotate by
about the triangle well I can rotate by
third<00:08:13.900> of<00:08:14.050> a<00:08:14.110> turn<00:08:14.290> clockwise<00:08:14.560> or<00:08:15.550> a<00:08:15.580> third<00:08:15.790> of
third of a turn clockwise or a third of
third of a turn clockwise or a third of
a<00:08:15.970> turn<00:08:16.120> anti-clockwise<00:08:16.410> but<00:08:17.410> now<00:08:17.560> this<00:08:17.740> has
a turn anti-clockwise but now this has
a turn anti-clockwise but now this has
some<00:08:18.160> reflectional<00:08:18.700> symmetry<00:08:18.730> I<00:08:19.270> can<00:08:19.600> reflect
some reflectional symmetry I can reflect
some reflectional symmetry I can reflect
it<00:08:20.230> in<00:08:20.290> the<00:08:20.350> line<00:08:20.440> through<00:08:20.830> X<00:08:21.040> or<00:08:21.790> the<00:08:21.970> line
it in the line through X or the line
it in the line through X or the line
through<00:08:22.420> Y<00:08:22.630> or<00:08:23.500> the<00:08:23.680> line<00:08:23.830> through<00:08:24.100> Z<00:08:25.170> five
through Y or the line through Z five
through Y or the line through Z five
symmetries<00:08:26.770> and<00:08:26.920> then<00:08:27.070> of<00:08:27.160> course<00:08:27.190> the<00:08:27.760> zero
symmetries and then of course the zero
symmetries and then of course the zero
symmetry<00:08:28.600> where<00:08:28.720> I<00:08:28.750> just<00:08:28.810> pick<00:08:29.080> it<00:08:29.170> up<00:08:29.260> and
symmetry where I just pick it up and
symmetry where I just pick it up and
leave<00:08:30.280> it<00:08:30.400> where<00:08:30.520> it<00:08:30.670> is<00:08:30.700> so<00:08:31.690> both<00:08:31.870> of<00:08:31.900> these
leave it where it is so both of these
leave it where it is so both of these
objects<00:08:32.560> have<00:08:32.800> six<00:08:33.400> symmetries<00:08:34.300> now<00:08:35.080> I'm<00:08:35.200> a
objects have six symmetries now I'm a
objects have six symmetries now I'm a
great<00:08:35.440> believer<00:08:35.680> that<00:08:35.830> mathematics<00:08:36.430> is<00:08:36.550> not<00:08:36.580> a
great believer that mathematics is not a
great believer that mathematics is not a
spectator<00:08:36.880> sport<00:08:37.510> and<00:08:38.020> you<00:08:38.200> have<00:08:38.380> to<00:08:38.470> do<00:08:38.680> some
spectator sport and you have to do some
spectator sport and you have to do some
mathematics<00:08:39.460> in<00:08:39.550> order<00:08:40.060> to<00:08:40.180> really
mathematics in order to really
mathematics in order to really
understand<00:08:40.930> it<00:08:41.110> so<00:08:41.500> here's<00:08:41.710> a<00:08:41.770> little
understand it so here's a little
understand it so here's a little
question<00:08:42.190> for<00:08:42.670> you<00:08:42.820> and<00:08:43.060> I<00:08:43.450> getting<00:08:43.599> a<00:08:43.660> look<00:08:43.780> of
question for you and I getting a look of
question for you and I getting a look of
a<00:08:43.930> prize<00:08:44.260> at<00:08:44.560> the<00:08:44.650> end<00:08:44.770> of<00:08:44.860> my<00:08:44.980> talk<00:08:45.220> for<00:08:45.400> the
a prize at the end of my talk for the
a prize at the end of my talk for the
person<00:08:45.760> who<00:08:45.850> gets<00:08:45.940> closest<00:08:46.450> to<00:08:46.510> the<00:08:46.660> answer
person who gets closest to the answer
person who gets closest to the answer
the<00:08:47.920> Rubik's<00:08:48.310> Cube<00:08:48.730> how<00:08:49.600> many<00:08:49.810> symmetries
the Rubik's Cube how many symmetries
the Rubik's Cube how many symmetries
does<00:08:50.590> a<00:08:50.620> Rubik's<00:08:51.100> Cube<00:08:51.220> have<00:08:51.730> how<00:08:52.390> many<00:08:52.480> things
does a Rubik's Cube have how many things
does a Rubik's Cube have how many things
can<00:08:52.990> I<00:08:53.020> do<00:08:53.110> to<00:08:53.410> this<00:08:53.500> object<00:08:53.710> and<00:08:54.190> put<00:08:54.430> it<00:08:54.520> down
can I do to this object and put it down
can I do to this object and put it down
so<00:08:54.880> it<00:08:54.970> still<00:08:55.180> looks<00:08:55.390> like<00:08:55.570> a<00:08:55.600> cube<00:08:56.100> okay<00:08:57.100> so<00:08:57.160> I
so it still looks like a cube okay so I
so it still looks like a cube okay so I
want<00:08:57.520> you<00:08:57.580> to<00:08:57.640> think<00:08:57.820> about<00:08:57.910> that<00:08:58.150> problem<00:08:58.210> as
want you to think about that problem as
want you to think about that problem as
we<00:08:58.990> go<00:08:59.170> on<00:08:59.380> and<00:08:59.530> count<00:08:59.980> how<00:09:00.130> many<00:09:00.250> symmetries
we go on and count how many symmetries
we go on and count how many symmetries
there<00:09:01.000> are<00:09:01.180> and<00:09:01.420> there'll<00:09:01.600> be<00:09:01.630> a<00:09:01.690> prize<00:09:01.990> to<00:09:02.230> the
there are and there'll be a prize to the
there are and there'll be a prize to the
person<00:09:02.350> who<00:09:02.710> gets<00:09:02.800> closest<00:09:03.310> at<00:09:03.670> the<00:09:03.820> end
person who gets closest at the end
person who gets closest at the end
but<00:09:05.800> let's<00:09:05.980> go<00:09:06.130> back<00:09:06.310> down<00:09:06.580> to<00:09:06.610> symmetries
but let's go back down to symmetries
but let's go back down to symmetries
that<00:09:07.630> I<00:09:07.810> got<00:09:08.050> for<00:09:08.290> these<00:09:08.440> two<00:09:08.680> objects<00:09:09.220> what
that I got for these two objects what
that I got for these two objects what
Galois<00:09:10.060> I<00:09:10.090> realize<00:09:10.420> it<00:09:10.600> isn't<00:09:10.750> just<00:09:11.020> the
Galois I realize it isn't just the
Galois I realize it isn't just the
individual<00:09:11.770> symmetries<00:09:12.310> but<00:09:12.880> how<00:09:13.120> they
individual symmetries but how they
individual symmetries but how they
interact<00:09:13.930> with<00:09:14.080> each<00:09:14.350> other<00:09:14.560> which<00:09:15.010> really
interact with each other which really
interact with each other which really
characterizes<00:09:15.880> the<00:09:16.360> symmetry<00:09:16.900> of<00:09:16.930> an<00:09:17.260> object
characterizes the symmetry of an object
characterizes the symmetry of an object
if<00:09:18.460> I<00:09:18.580> do<00:09:18.640> one<00:09:18.970> magic<00:09:19.330> trick<00:09:19.360> move<00:09:19.720> followed<00:09:20.140> by
if I do one magic trick move followed by
if I do one magic trick move followed by
another<00:09:20.560> the<00:09:21.250> combination<00:09:21.820> is<00:09:21.910> a<00:09:21.940> third<00:09:22.270> magic
another the combination is a third magic
another the combination is a third magic
trick<00:09:22.960> move<00:09:23.170> and<00:09:23.470> here<00:09:24.100> we<00:09:24.310> see<00:09:24.550> Galois
trick move and here we see Galois
trick move and here we see Galois
starting<00:09:25.480> to<00:09:25.570> develop<00:09:25.930> a<00:09:26.050> language<00:09:26.440> to<00:09:27.190> see
starting to develop a language to see
starting to develop a language to see
the<00:09:27.520> substance<00:09:28.000> of<00:09:28.210> the<00:09:28.450> things<00:09:28.660> unseen<00:09:28.840> the
the substance of the things unseen the
the substance of the things unseen the
sort<00:09:29.440> of<00:09:29.500> abstract<00:09:30.010> idea<00:09:30.460> of<00:09:30.700> the<00:09:30.820> symmetry
sort of abstract idea of the symmetry
sort of abstract idea of the symmetry
underlying<00:09:32.080> this<00:09:32.440> physical<00:09:33.010> object<00:09:33.490> for
underlying this physical object for
underlying this physical object for
example<00:09:34.260> what<00:09:35.260> do<00:09:35.350> I<00:09:35.470> turn<00:09:35.530> the<00:09:36.040> starfish<00:09:36.550> by<00:09:37.060> a
example what do I turn the starfish by a
example what do I turn the starfish by a
sixth<00:09:37.750> of<00:09:37.810> a<00:09:37.900> turn<00:09:37.930> and<00:09:38.350> then<00:09:39.040> a<00:09:39.070> third<00:09:39.280> of<00:09:39.490> a
sixth of a turn and then a third of a
sixth of a turn and then a third of a
turn<00:09:39.580> so<00:09:40.330> I<00:09:40.360> given<00:09:40.660> names<00:09:40.990> the<00:09:41.830> capital
turn so I given names the capital
turn so I given names the capital
letters<00:09:42.550> ABCDE<00:09:43.210> F<00:09:43.600> are<00:09:44.020> the<00:09:44.320> names<00:09:44.560> for<00:09:44.770> the
letters ABCDE F are the names for the
letters ABCDE F are the names for the
rotations<00:09:45.550> so<00:09:46.000> be<00:09:46.240> for<00:09:46.540> example<00:09:46.600> rotates<00:09:47.350> the
rotations so be for example rotates the
rotations so be for example rotates the
little<00:09:47.650> yellow<00:09:47.890> dot<00:09:48.100> to<00:09:48.610> the<00:09:48.700> be<00:09:48.880> on<00:09:49.120> the
little yellow dot to the be on the
little yellow dot to the be on the
starfish<00:09:49.900> and<00:09:50.080> so<00:09:50.560> on<00:09:50.740> so<00:09:50.920> what<00:09:51.040> if<00:09:51.130> I<00:09:51.190> do<00:09:51.250> B
starfish and so on so what if I do B
starfish and so on so what if I do B
which<00:09:52.300> is<00:09:52.450> a<00:09:52.480> sixth<00:09:53.110> of<00:09:53.170> a<00:09:53.260> turn<00:09:53.290> followed<00:09:54.010> by<00:09:54.130> C
which is a sixth of a turn followed by C
which is a sixth of a turn followed by C
which<00:09:54.850> is<00:09:55.000> a<00:09:55.030> third<00:09:55.240> of<00:09:55.420> a<00:09:55.480> turn<00:09:55.510> well<00:09:56.200> let's<00:09:56.320> do
which is a third of a turn well let's do
which is a third of a turn well let's do
that<00:09:56.650> a<00:09:56.860> sixth<00:09:57.310> of<00:09:57.370> a<00:09:57.460> turn<00:09:57.930> followed<00:09:58.930> by<00:09:59.140> a
that a sixth of a turn followed by a
that a sixth of a turn followed by a
third<00:09:59.410> of<00:09:59.560> a<00:09:59.620> turn<00:09:59.830> the<00:10:00.790> combined<00:10:01.180> effect<00:10:01.540> s<00:10:01.720> is
third of a turn the combined effect s is
third of a turn the combined effect s is
if<00:10:01.930> I<00:10:02.050> just<00:10:02.320> rotated<00:10:03.070> it<00:10:03.190> by<00:10:03.340> half<00:10:03.610> a<00:10:03.760> turn<00:10:03.940> in
if I just rotated it by half a turn in
if I just rotated it by half a turn in
one<00:10:04.270> go<00:10:04.860> so<00:10:05.860> the<00:10:06.100> little<00:10:06.310> table<00:10:06.640> here<00:10:06.670> records
one go so the little table here records
one go so the little table here records
how<00:10:07.840> the<00:10:08.380> algebra<00:10:09.070> of<00:10:09.190> these<00:10:09.490> symmetries<00:10:09.970> work
how the algebra of these symmetries work
how the algebra of these symmetries work
I<00:10:10.330> do<00:10:10.390> one<00:10:10.630> followed<00:10:10.930> by<00:10:10.960> another<00:10:11.290> the<00:10:11.470> answer
I do one followed by another the answer
I do one followed by another the answer
is<00:10:12.070> its<00:10:12.430> rotation<00:10:12.970> D<00:10:13.120> half<00:10:13.510> a<00:10:13.660> turn<00:10:13.870> what<00:10:14.440> if<00:10:14.530> I
is its rotation D half a turn what if I
is its rotation D half a turn what if I
did<00:10:14.770> it<00:10:14.860> in<00:10:14.980> the<00:10:15.070> other<00:10:15.220> order<00:10:15.310> would<00:10:16.060> it<00:10:16.210> make
did it in the other order would it make
did it in the other order would it make
any<00:10:16.360> difference<00:10:16.570> well<00:10:17.410> let's<00:10:17.560> see<00:10:17.800> let's<00:10:18.250> do
any difference well let's see let's do
any difference well let's see let's do
the<00:10:18.520> third<00:10:18.700> of<00:10:18.910> the<00:10:19.000> turn<00:10:19.180> first<00:10:19.510> and<00:10:19.930> then<00:10:20.620> the
the third of the turn first and then the
the third of the turn first and then the
sixth<00:10:21.250> of<00:10:21.280> a<00:10:21.370> turn<00:10:21.400> of<00:10:21.760> course<00:10:21.970> it<00:10:22.180> doesn't
sixth of a turn of course it doesn't
sixth of a turn of course it doesn't
make<00:10:22.780> any<00:10:22.930> difference<00:10:23.050> it<00:10:23.500> still<00:10:23.860> ends<00:10:24.100> up<00:10:24.250> at
make any difference it still ends up at
make any difference it still ends up at
half<00:10:24.790> a<00:10:24.970> turn<00:10:25.240> and<00:10:25.510> there's<00:10:25.960> some<00:10:26.110> symmetry
half a turn and there's some symmetry
half a turn and there's some symmetry
here<00:10:26.950> in<00:10:27.070> the<00:10:27.370> way<00:10:27.550> the<00:10:27.760> symmetries<00:10:28.240> interact
here in the way the symmetries interact
here in the way the symmetries interact
with<00:10:28.900> each<00:10:28.990> other<00:10:29.280> but<00:10:30.280> this<00:10:30.400> is<00:10:30.520> completely
with each other but this is completely
with each other but this is completely
different<00:10:31.330> to<00:10:31.690> the<00:10:31.930> symmetries<00:10:32.380> of<00:10:32.410> the
different to the symmetries of the
different to the symmetries of the
triangle<00:10:33.130> let's<00:10:33.520> see<00:10:33.670> what<00:10:33.820> happens<00:10:34.180> if<00:10:34.360> we
triangle let's see what happens if we
triangle let's see what happens if we
two<00:10:34.690> two<00:10:35.140> symmetries<00:10:35.560> with<00:10:35.950> a<00:10:36.010> triangle<00:10:36.460> one
two two symmetries with a triangle one
two two symmetries with a triangle one
after<00:10:36.940> the<00:10:37.030> other<00:10:37.060> do<00:10:37.690> a<00:10:37.720> rotation<00:10:37.930> by<00:10:38.350> a<00:10:38.380> third
after the other do a rotation by a third
after the other do a rotation by a third
of<00:10:38.800> a<00:10:38.860> turn<00:10:39.010> anti-clockwise<00:10:39.310> and<00:10:40.060> reflect<00:10:40.810> in
of a turn anti-clockwise and reflect in
of a turn anti-clockwise and reflect in
the<00:10:41.080> line<00:10:41.230> through<00:10:41.470> X<00:10:41.700> well<00:10:42.700> the<00:10:42.790> combined
the line through X well the combined
the line through X well the combined
effect<00:10:43.540> is<00:10:43.720> if<00:10:44.110> I<00:10:44.200> just<00:10:44.560> done<00:10:44.800> the<00:10:44.920> reflection
effect is if I just done the reflection
effect is if I just done the reflection
in<00:10:45.520> the<00:10:45.610> line<00:10:45.730> through<00:10:46.030> Z<00:10:46.360> to<00:10:46.840> start<00:10:47.110> with<00:10:47.490> now
in the line through Z to start with now
in the line through Z to start with now
let's<00:10:48.730> do<00:10:48.850> it<00:10:48.880> in<00:10:49.060> a<00:10:49.150> different<00:10:49.270> order<00:10:49.540> let's
let's do it in a different order let's
let's do it in a different order let's
do<00:10:50.680> the<00:10:50.920> reflection<00:10:51.430> in<00:10:51.520> X<00:10:51.730> first<00:10:52.120> followed<00:10:52.780> by
do the reflection in X first followed by
do the reflection in X first followed by
the<00:10:52.960> rotation<00:10:53.380> by<00:10:53.920> a<00:10:53.950> third<00:10:54.280> of<00:10:54.430> a<00:10:54.490> turn
the rotation by a third of a turn
the rotation by a third of a turn
anti-clockwise<00:10:55.350> the<00:10:56.350> combined<00:10:56.680> effect<00:10:56.980> the
anti-clockwise the combined effect the
anti-clockwise the combined effect the
triangle<00:10:57.490> ends<00:10:57.730> up<00:10:57.850> somewhere<00:10:58.090> completely
triangle ends up somewhere completely
triangle ends up somewhere completely
different<00:10:58.690> it's<00:10:59.290> as<00:10:59.560> if<00:10:59.680> it<00:10:59.800> wasn't<00:11:00.040> reflected
different it's as if it wasn't reflected
different it's as if it wasn't reflected
in<00:11:00.760> the<00:11:00.850> line<00:11:01.060> through<00:11:01.300> Y<00:11:01.510> now<00:11:02.260> it<00:11:02.470> matters
in the line through Y now it matters
in the line through Y now it matters
what<00:11:03.430> order<00:11:03.880> you<00:11:04.030> do<00:11:04.180> the<00:11:04.360> operations<00:11:04.930> in<00:11:05.170> and
what order you do the operations in and
what order you do the operations in and
this<00:11:05.950> aware<00:11:06.190> nabel's<00:11:06.640> us<00:11:06.790> to<00:11:06.910> distinguish<00:11:07.360> why
this aware nabel's us to distinguish why
this aware nabel's us to distinguish why
the<00:11:07.630> symmetries<00:11:08.230> of<00:11:08.260> these<00:11:08.500> objects<00:11:08.950> they
the symmetries of these objects they
the symmetries of these objects they
both<00:11:09.700> have<00:11:09.970> six<00:11:10.300> symmetries<00:11:10.780> so<00:11:11.140> why
both have six symmetries so why
both have six symmetries so why
shouldn't<00:11:11.650> we<00:11:11.710> say<00:11:11.740> they<00:11:12.070> have<00:11:12.220> the<00:11:12.340> same
shouldn't we say they have the same
shouldn't we say they have the same
symmetries<00:11:13.270> but<00:11:13.960> the<00:11:14.050> way<00:11:14.230> the<00:11:14.410> symmetries
symmetries but the way the symmetries
symmetries but the way the symmetries
interact<00:11:15.360> enable<00:11:16.360> us<00:11:16.480> we've<00:11:17.050> now<00:11:17.200> got<00:11:17.350> a
interact enable us we've now got a
interact enable us we've now got a
language<00:11:17.800> distinguish<00:11:18.310> why<00:11:18.580> these
language distinguish why these
language distinguish why these
trees<00:11:19.359> are<00:11:19.389> fundamentally<00:11:20.169> different<00:11:20.619> and
trees are fundamentally different and
trees are fundamentally different and
you<00:11:21.219> could<00:11:21.339> try<00:11:21.519> this<00:11:21.579> when<00:11:21.849> you<00:11:21.909> go<00:11:21.999> down<00:11:22.179> the
you could try this when you go down the
you could try this when you go down the
pub<00:11:22.479> later<00:11:22.749> on<00:11:23.079> take<00:11:23.529> a<00:11:23.559> beer<00:11:23.859> mat<00:11:24.069> and<00:11:24.339> rotate
pub later on take a beer mat and rotate
pub later on take a beer mat and rotate
it<00:11:25.419> by<00:11:25.539> third<00:11:25.839> quarter<00:11:26.439> of<00:11:26.529> a<00:11:26.589> turn<00:11:26.769> then<00:11:27.069> flip
it by third quarter of a turn then flip
it by third quarter of a turn then flip
it<00:11:27.429> and<00:11:27.789> then<00:11:27.939> do<00:11:28.029> it<00:11:28.059> in<00:11:28.239> the<00:11:28.359> other<00:11:28.479> order<00:11:28.719> and
it and then do it in the other order and
it and then do it in the other order and
the<00:11:29.229> picture<00:11:29.559> will<00:11:29.649> be<00:11:29.739> facing<00:11:29.979> in<00:11:30.309> the
the picture will be facing in the
the picture will be facing in the
opposite<00:11:30.729> direction<00:11:30.879> now<00:11:31.739> Galois<00:11:32.739> produced
opposite direction now Galois produced
opposite direction now Galois produced
some<00:11:33.609> laws<00:11:33.849> for<00:11:34.329> how<00:11:34.479> these<00:11:34.749> tables<00:11:35.289> how
some laws for how these tables how
some laws for how these tables how
symmetries<00:11:36.249> interact<00:11:36.429> it's<00:11:36.969> always<00:11:37.119> like
symmetries interact it's always like
symmetries interact it's always like
little<00:11:37.569> Sudoku<00:11:38.259> tables<00:11:38.769> you<00:11:39.159> don't<00:11:39.369> see<00:11:39.549> any
little Sudoku tables you don't see any
little Sudoku tables you don't see any
symmetry<00:11:40.089> twice<00:11:40.869> any<00:11:41.169> row<00:11:41.529> or<00:11:41.799> column<00:11:41.889> and
symmetry twice any row or column and
symmetry twice any row or column and
using<00:11:43.389> those<00:11:43.569> rules<00:11:43.839> he<00:11:44.319> was<00:11:44.439> able<00:11:44.589> to<00:11:44.739> say
using those rules he was able to say
using those rules he was able to say
that<00:11:45.669> there<00:11:45.789> are<00:11:45.939> in<00:11:46.119> fact<00:11:46.149> only<00:11:46.599> two<00:11:47.289> objects
that there are in fact only two objects
that there are in fact only two objects
with<00:11:48.549> six<00:11:48.939> symmetries<00:11:49.599> and<00:11:49.869> they'll<00:11:50.829> be<00:11:50.979> the
with six symmetries and they'll be the
with six symmetries and they'll be the
same<00:11:51.309> as<00:11:51.489> the<00:11:51.579> symmetries<00:11:51.999> of<00:11:52.029> the<00:11:52.239> triangle
same as the symmetries of the triangle
same as the symmetries of the triangle
or<00:11:52.989> the<00:11:53.319> symmetries<00:11:53.889> of<00:11:53.919> the<00:11:54.099> six<00:11:54.339> pointed
or the symmetries of the six pointed
or the symmetries of the six pointed
star<00:11:54.789> fish<00:11:55.299> I<00:11:55.539> think<00:11:56.349> this<00:11:56.469> is<00:11:56.559> an<00:11:56.649> amazing
star fish I think this is an amazing
star fish I think this is an amazing
development<00:11:57.309> it's<00:11:57.669> almost<00:11:57.819> like<00:11:57.999> the<00:11:58.149> concept
development it's almost like the concept
development it's almost like the concept
of<00:11:58.899> number<00:11:59.439> being<00:11:59.679> developed<00:12:00.159> for<00:12:00.279> symmetry
of number being developed for symmetry
of number being developed for symmetry
in<00:12:01.359> the<00:12:01.629> frontier<00:12:02.019> I've<00:12:02.169> got<00:12:02.349> one<00:12:02.559> two<00:12:02.769> three
in the frontier I've got one two three
in the frontier I've got one two three
people<00:12:03.549> sitting<00:12:04.059> on<00:12:04.149> one<00:12:04.419> two<00:12:04.599> three<00:12:04.959> chairs
people sitting on one two three chairs
people sitting on one two three chairs
the<00:12:05.949> people<00:12:06.429> and<00:12:06.639> the<00:12:07.149> chairs<00:12:07.419> are<00:12:07.659> very
the people and the chairs are very
the people and the chairs are very
different<00:12:08.139> but<00:12:08.799> the<00:12:08.889> number<00:12:09.399> the<00:12:09.609> abstract
different but the number the abstract
different but the number the abstract
idea<00:12:10.119> of<00:12:10.389> the<00:12:10.479> number<00:12:10.809> is<00:12:10.959> the<00:12:11.109> same<00:12:11.319> and<00:12:12.069> we
idea of the number is the same and we
idea of the number is the same and we
can<00:12:12.309> see<00:12:12.459> this<00:12:12.609> now<00:12:12.819> we<00:12:12.879> go<00:12:13.089> back<00:12:13.269> to<00:12:13.419> the<00:12:13.509> walls
can see this now we go back to the walls
can see this now we go back to the walls
in<00:12:13.929> the<00:12:14.019> Alhambra<00:12:14.049> here<00:12:14.949> are<00:12:15.069> two<00:12:15.249> very
in the Alhambra here are two very
in the Alhambra here are two very
different<00:12:15.729> walls<00:12:16.119> very<00:12:16.509> different<00:12:17.199> geometric
different walls very different geometric
different walls very different geometric
pictures<00:12:18.159> but<00:12:18.879> using<00:12:19.269> the<00:12:19.359> language<00:12:19.539> of
pictures but using the language of
pictures but using the language of
Galois<00:12:20.229> we<00:12:20.559> can<00:12:20.709> understand<00:12:21.129> that<00:12:21.279> the
Galois we can understand that the
Galois we can understand that the
underlying<00:12:21.879> abstract<00:12:22.629> symmetries<00:12:23.139> of<00:12:23.169> these
underlying abstract symmetries of these
underlying abstract symmetries of these
things<00:12:23.679> are<00:12:23.829> actually<00:12:24.549> the<00:12:24.669> same<00:12:24.779> for<00:12:25.779> example
things are actually the same for example
things are actually the same for example
let's<00:12:26.319> take<00:12:26.379> this<00:12:26.589> beautiful<00:12:27.069> wall<00:12:27.279> with<00:12:27.699> the
let's take this beautiful wall with the
let's take this beautiful wall with the
triangles<00:12:28.569> did<00:12:28.719> a<00:12:28.749> little<00:12:28.869> twist<00:12:29.169> on<00:12:29.349> them<00:12:29.559> you
triangles did a little twist on them you
triangles did a little twist on them you
can<00:12:30.339> rotate<00:12:30.489> them<00:12:30.849> by<00:12:31.029> a<00:12:31.059> sixth<00:12:31.419> of<00:12:31.479> a<00:12:31.569> turn<00:12:31.599> if
can rotate them by a sixth of a turn if
can rotate them by a sixth of a turn if
you<00:12:32.259> ignore<00:12:32.589> the<00:12:32.709> colors<00:12:33.069> we're<00:12:33.519> not<00:12:33.609> matching
you ignore the colors we're not matching
you ignore the colors we're not matching
up<00:12:34.269> the<00:12:34.359> colors<00:12:34.659> but<00:12:34.899> the<00:12:35.019> shapes<00:12:35.259> match<00:12:35.499> up<00:12:35.799> if
up the colors but the shapes match up if
up the colors but the shapes match up if
I<00:12:36.129> rotate<00:12:36.519> by<00:12:36.549> sixth<00:12:37.119> of<00:12:37.179> a<00:12:37.269> turn<00:12:37.299> around<00:12:37.989> the
I rotate by sixth of a turn around the
I rotate by sixth of a turn around the
point<00:12:38.229> where<00:12:38.499> all<00:12:38.649> the<00:12:38.829> triangles<00:12:39.519> meet<00:12:39.729> what
point where all the triangles meet what
point where all the triangles meet what
about<00:12:40.419> the<00:12:40.539> center<00:12:40.899> of<00:12:40.929> a<00:12:41.049> triangle<00:12:41.409> I<00:12:41.649> can
about the center of a triangle I can
about the center of a triangle I can
rotate<00:12:42.219> my<00:12:42.429> third<00:12:42.909> of<00:12:43.149> a<00:12:43.209> turn<00:12:43.389> around<00:12:43.539> the
rotate my third of a turn around the
rotate my third of a turn around the
center<00:12:44.019> of<00:12:44.109> the<00:12:44.199> triangle<00:12:44.409> and<00:12:44.799> everything
center of the triangle and everything
center of the triangle and everything
matches<00:12:45.579> up<00:12:45.609> then<00:12:46.449> there's<00:12:46.599> an<00:12:46.689> interesting
matches up then there's an interesting
matches up then there's an interesting
place<00:12:47.259> halfway<00:12:47.619> along<00:12:47.919> an<00:12:48.129> age<00:12:48.309> where<00:12:48.789> I<00:12:48.819> can
place halfway along an age where I can
place halfway along an age where I can
rotate<00:12:49.089> by<00:12:49.449> 180<00:12:49.959> degrees<00:12:50.469> and<00:12:51.039> all<00:12:51.249> the<00:12:51.369> tiles
rotate by 180 degrees and all the tiles
rotate by 180 degrees and all the tiles
match<00:12:51.909> up<00:12:52.119> again<00:12:52.389> so<00:12:53.349> rotate<00:12:53.679> along<00:12:53.829> half<00:12:54.159> way
match up again so rotate along half way
match up again so rotate along half way
along<00:12:54.489> the<00:12:54.669> edge<00:12:54.789> and<00:12:55.059> they<00:12:55.329> all<00:12:55.509> match<00:12:55.749> up<00:12:56.099> now
along the edge and they all match up now
along the edge and they all match up now
let's<00:12:57.339> move<00:12:57.489> to<00:12:57.549> the<00:12:57.759> very<00:12:57.939> different-looking
let's move to the very different-looking
let's move to the very different-looking
wall<00:12:58.869> in<00:12:59.139> the<00:12:59.229> Alhambra<00:12:59.349> and<00:12:59.949> we<00:13:00.639> find<00:13:00.879> the
wall in the Alhambra and we find the
wall in the Alhambra and we find the
same<00:13:01.239> symmetries<00:13:01.899> here<00:13:02.289> and<00:13:02.439> the<00:13:02.619> same
same symmetries here and the same
same symmetries here and the same
interaction<00:13:03.549> so<00:13:03.879> there<00:13:04.029> was<00:13:04.119> a<00:13:04.149> sixth<00:13:04.449> of<00:13:04.479> the
interaction so there was a sixth of the
interaction so there was a sixth of the
turn<00:13:04.839> a<00:13:05.049> third<00:13:05.469> of<00:13:05.589> a<00:13:05.649> turn<00:13:05.829> with<00:13:06.099> as<00:13:06.219> nth
turn a third of a turn with as nth
turn a third of a turn with as nth
pieces<00:13:06.789> meet<00:13:06.969> and<00:13:07.859> then<00:13:08.859> the<00:13:08.949> half<00:13:09.159> a<00:13:09.279> turn<00:13:09.489> is
pieces meet and then the half a turn is
pieces meet and then the half a turn is
halfway<00:13:09.969> between<00:13:10.299> the<00:13:10.599> six<00:13:10.809> pointed<00:13:11.199> stars
halfway between the six pointed stars
halfway between the six pointed stars
and<00:13:12.029> although<00:13:13.029> these<00:13:13.209> walls<00:13:13.509> look<00:13:13.779> very
and although these walls look very
and although these walls look very
different<00:13:14.529> Galois<00:13:15.129> has<00:13:15.399> produced<00:13:15.759> a<00:13:15.879> language
different Galois has produced a language
different Galois has produced a language
to<00:13:16.449> say<00:13:16.689> that<00:13:17.289> in<00:13:17.379> fact<00:13:17.499> the<00:13:17.679> symmetry<00:13:18.129> is
to say that in fact the symmetry is
to say that in fact the symmetry is
underlying<00:13:18.609> these<00:13:18.909> are<00:13:19.149> exactly<00:13:19.719> the<00:13:19.899> same
underlying these are exactly the same
underlying these are exactly the same
and<00:13:20.409> it's<00:13:20.799> a<00:13:20.889> symmetry<00:13:21.249> we<00:13:21.429> call<00:13:21.639> six<00:13:22.029> three
and it's a symmetry we call six three
and it's a symmetry we call six three
two<00:13:22.629> here's<00:13:23.619> another<00:13:23.859> example<00:13:24.039> in<00:13:24.519> the
two here's another example in the
two here's another example in the
Alhambra<00:13:24.759> this<00:13:25.539> is<00:13:25.689> a<00:13:25.809> wall<00:13:26.139> a<00:13:26.469> ceiling<00:13:27.069> and<00:13:27.189> a
Alhambra this is a wall a ceiling and a
Alhambra this is a wall a ceiling and a
floor<00:13:27.509> they<00:13:28.509> all<00:13:28.689> look<00:13:29.019> very<00:13:29.049> different<00:13:29.739> but
floor they all look very different but
floor they all look very different but
this<00:13:30.369> language<00:13:30.549> allows<00:13:31.029> us<00:13:31.239> to<00:13:31.329> say<00:13:31.509> they<00:13:31.689> are
this language allows us to say they are
this language allows us to say they are
representations<00:13:32.529> of
representations of
representations of
same<00:13:33.250> symmetrical<00:13:33.970> abstract<00:13:34.420> object<00:13:34.870> which
same symmetrical abstract object which
same symmetrical abstract object which
we<00:13:35.470> call<00:13:35.649> 4-4-2<00:13:36.250> nothing<00:13:37.149> to<00:13:37.240> do<00:13:37.329> with
we call 4-4-2 nothing to do with
we call 4-4-2 nothing to do with
football<00:13:37.630> but<00:13:38.199> because<00:13:38.440> of<00:13:38.470> the<00:13:38.649> fact<00:13:38.829> that
football but because of the fact that
football but because of the fact that
there<00:13:39.279> are<00:13:39.399> two<00:13:39.550> places<00:13:39.699> where<00:13:40.089> you<00:13:40.209> can
there are two places where you can
there are two places where you can
rotate<00:13:40.510> by<00:13:40.810> a<00:13:40.839> quarter<00:13:41.079> of<00:13:41.320> a<00:13:41.380> turn<00:13:41.560> and<00:13:41.800> one<00:13:42.250> by
rotate by a quarter of a turn and one by
rotate by a quarter of a turn and one by
half<00:13:42.730> a<00:13:42.880> turn<00:13:43.290> now<00:13:44.290> this<00:13:44.440> part<00:13:44.769> of<00:13:44.920> the
half a turn now this part of the
half a turn now this part of the
language<00:13:45.279> is<00:13:45.399> even<00:13:45.670> more<00:13:45.940> because<00:13:46.360> Galois<00:13:46.930> can
language is even more because Galois can
language is even more because Galois can
say<00:13:47.410> did<00:13:48.220> the<00:13:48.370> Moorish<00:13:49.089> artists<00:13:49.570> discover<00:13:49.899> all
say did the Moorish artists discover all
say did the Moorish artists discover all
of<00:13:50.199> the<00:13:50.529> possible<00:13:50.889> symmetries<00:13:51.339> on<00:13:51.519> the<00:13:51.730> walls
of the possible symmetries on the walls
of the possible symmetries on the walls
in<00:13:52.209> the<00:13:52.300> Alhambra<00:13:52.329> and<00:13:52.959> it<00:13:53.440> turns<00:13:53.649> out<00:13:53.769> they
in the Alhambra and it turns out they
in the Alhambra and it turns out they
almost<00:13:54.220> did<00:13:54.820> you<00:13:55.510> can<00:13:55.690> prove<00:13:55.959> using<00:13:56.230> Galois
almost did you can prove using Galois
almost did you can prove using Galois
language<00:13:57.160> there<00:13:57.339> are<00:13:57.880> actually<00:13:58.540> only<00:13:58.899> 17
language there are actually only 17
language there are actually only 17
different<00:14:00.399> symmetries<00:14:00.910> that<00:14:01.089> you<00:14:01.300> can<00:14:01.420> do<00:14:01.600> in
different symmetries that you can do in
different symmetries that you can do in
the<00:14:01.990> walls<00:14:02.199> in<00:14:02.529> the<00:14:02.680> Alhambra<00:14:02.709> and<00:14:03.370> they<00:14:04.149> if
the walls in the Alhambra and they if
the walls in the Alhambra and they if
you<00:14:04.510> try<00:14:04.750> and<00:14:04.839> produce<00:14:05.050> a<00:14:05.199> different<00:14:05.320> wall
you try and produce a different wall
you try and produce a different wall
with<00:14:05.800> its<00:14:05.920> 18th<00:14:06.370> one<00:14:06.670> it<00:14:06.880> will<00:14:07.180> have<00:14:07.389> to<00:14:07.540> have
with its 18th one it will have to have
with its 18th one it will have to have
the<00:14:07.810> same<00:14:08.019> symmetries<00:14:08.560> as<00:14:08.740> one<00:14:09.160> of<00:14:09.190> these<00:14:09.399> 17
the same symmetries as one of these 17
the same symmetries as one of these 17
but<00:14:11.560> these<00:14:11.769> are<00:14:12.070> things<00:14:12.310> that<00:14:12.430> we<00:14:12.579> can<00:14:12.760> see<00:14:13.029> and
but these are things that we can see and
but these are things that we can see and
the<00:14:13.630> power<00:14:13.959> of<00:14:14.199> Galois<00:14:14.589> mathematical
the power of Galois mathematical
the power of Galois mathematical
language<00:14:15.699> is<00:14:15.850> it<00:14:15.970> also<00:14:16.149> allows<00:14:16.570> us<00:14:16.779> to<00:14:16.899> create
language is it also allows us to create
language is it also allows us to create
symmetrical<00:14:17.769> objects<00:14:18.310> in<00:14:18.490> the<00:14:19.240> unseen<00:14:19.690> world
symmetrical objects in the unseen world
symmetrical objects in the unseen world
beyond<00:14:20.440> the<00:14:20.589> two-dimensional
beyond the two-dimensional
beyond the two-dimensional
three-dimensional<00:14:21.389> all<00:14:22.389> the<00:14:22.660> way<00:14:22.750> through<00:14:22.990> to
three-dimensional all the way through to
three-dimensional all the way through to
the<00:14:23.170> 4<00:14:23.410> 5<00:14:23.740> or<00:14:23.949> infinite<00:14:24.310> dimensional<00:14:24.820> space
the 4 5 or infinite dimensional space
the 4 5 or infinite dimensional space
and<00:14:25.389> that's<00:14:25.779> where<00:14:26.019> I<00:14:26.050> work<00:14:26.410> I<00:14:26.649> create
and that's where I work I create
and that's where I work I create
mathematical<00:14:27.820> objects<00:14:28.570> symmetrical<00:14:29.139> objects
mathematical objects symmetrical objects
mathematical objects symmetrical objects
using<00:14:29.829> Galois<00:14:30.279> z--<00:14:30.310> language<00:14:30.820> in<00:14:31.060> very<00:14:31.810> high
using Galois z-- language in very high
using Galois z-- language in very high
dimensional<00:14:32.589> spaces<00:14:32.889> so<00:14:33.730> I<00:14:33.760> think<00:14:33.910> it's<00:14:34.029> a
dimensional spaces so I think it's a
dimensional spaces so I think it's a
great<00:14:34.240> example<00:14:34.389> of<00:14:34.779> things<00:14:34.959> unseen<00:14:35.470> which<00:14:35.769> the
great example of things unseen which the
great example of things unseen which the
power<00:14:36.160> of<00:14:36.339> mathematical<00:14:36.910> language<00:14:37.029> allows
power of mathematical language allows
power of mathematical language allows
you<00:14:38.019> to<00:14:38.170> create<00:14:38.500> so<00:14:39.339> like<00:14:39.940> Galois<00:14:40.329> I<00:14:40.480> stayed<00:14:40.779> up
you to create so like Galois I stayed up
you to create so like Galois I stayed up
all<00:14:41.139> last<00:14:41.470> night<00:14:41.680> creating<00:14:42.519> a<00:14:42.610> new
all last night creating a new
all last night creating a new
mathematical<00:14:43.930> symmetrical<00:14:44.470> object<00:14:44.889> for<00:14:45.160> you
mathematical symmetrical object for you
mathematical symmetrical object for you
and<00:14:45.550> I've<00:14:45.970> got<00:14:46.000> a<00:14:46.149> picture<00:14:46.420> of<00:14:46.660> it<00:14:46.810> here<00:14:47.170> well
and I've got a picture of it here well
and I've got a picture of it here well
unfortunate<00:14:47.980> isn't<00:14:48.130> really<00:14:48.519> a<00:14:48.550> picture<00:14:48.940> if<00:14:49.060> I
unfortunate isn't really a picture if I
unfortunate isn't really a picture if I
could<00:14:49.329> have<00:14:49.510> my<00:14:49.720> board<00:14:50.050> at<00:14:50.440> the<00:14:50.649> side<00:14:50.860> here
could have my board at the side here
could have my board at the side here
great<00:14:51.610> excellent
great excellent
great excellent
here<00:14:52.569> we<00:14:52.660> are<00:14:52.750> this<00:14:52.899> is<00:14:52.959> unfortunately<00:14:53.920> I
here we are this is unfortunately I
here we are this is unfortunately I
can't<00:14:54.310> show<00:14:54.550> you<00:14:54.579> a<00:14:54.760> picture<00:14:55.360> of<00:14:55.540> this
can't show you a picture of this
can't show you a picture of this
symmetrical<00:14:56.139> object<00:14:56.589> but<00:14:57.010> here<00:14:57.399> is<00:14:57.519> the
symmetrical object but here is the
symmetrical object but here is the
language<00:14:58.120> which<00:14:58.600> describes<00:14:59.050> how<00:14:59.350> the
language which describes how the
language which describes how the
symmetries<00:15:00.010> interact<00:15:00.480> now<00:15:01.480> this<00:15:01.690> new
symmetries interact now this new
symmetries interact now this new
symmetrical<00:15:02.560> object<00:15:03.010> does<00:15:03.610> not<00:15:03.639> have<00:15:03.940> a<00:15:03.970> name
symmetrical object does not have a name
symmetrical object does not have a name
yet<00:15:05.100> now<00:15:06.100> people<00:15:06.370> like<00:15:06.490> getting<00:15:06.760> any<00:15:06.880> names<00:15:07.149> on
yet now people like getting any names on
yet now people like getting any names on
things<00:15:07.660> on<00:15:07.930> sort<00:15:08.170> of<00:15:08.199> craters<00:15:09.190> on<00:15:09.370> the<00:15:09.399> moon<00:15:09.550> or
things on sort of craters on the moon or
things on sort of craters on the moon or
new<00:15:10.180> species<00:15:10.540> of<00:15:10.750> animals<00:15:11.290> so<00:15:11.829> I'm<00:15:11.920> going<00:15:12.069> to
new species of animals so I'm going to
new species of animals so I'm going to
give<00:15:12.220> you<00:15:12.310> the<00:15:12.459> chance<00:15:12.730> to<00:15:12.880> get<00:15:13.029> your<00:15:13.180> name<00:15:13.420> on
give you the chance to get your name on
give you the chance to get your name on
a<00:15:13.690> new<00:15:14.110> symmetrical<00:15:14.889> object<00:15:15.370> which<00:15:15.819> hasn't
a new symmetrical object which hasn't
a new symmetrical object which hasn't
been<00:15:16.240> named<00:15:16.569> before<00:15:16.959> and<00:15:17.170> this<00:15:17.470> thing<00:15:17.740> species
been named before and this thing species
been named before and this thing species
died<00:15:18.819> away<00:15:19.120> and<00:15:19.480> moons<00:15:19.990> kind<00:15:20.470> of<00:15:20.589> get<00:15:20.740> hit<00:15:21.160> by
died away and moons kind of get hit by
died away and moons kind of get hit by
meteors<00:15:21.730> and<00:15:21.970> explode<00:15:22.329> but<00:15:22.750> this
meteors and explode but this
meteors and explode but this
mathematical<00:15:23.470> object<00:15:23.769> will<00:15:23.920> live<00:15:24.100> forever<00:15:24.250> it
mathematical object will live forever it
mathematical object will live forever it
will<00:15:24.790> make<00:15:25.060> you<00:15:25.269> immortal<00:15:25.660> in<00:15:26.079> order<00:15:26.529> to<00:15:26.620> win
will make you immortal in order to win
will make you immortal in order to win
your<00:15:27.010> win<00:15:27.880> this<00:15:28.060> symmetrical<00:15:28.480> object<00:15:28.959> what
your win this symmetrical object what
your win this symmetrical object what
you<00:15:29.529> have<00:15:29.680> to<00:15:29.769> do<00:15:29.889> is<00:15:30.010> to<00:15:30.100> answer<00:15:30.399> the<00:15:30.519> question
you have to do is to answer the question
you have to do is to answer the question
I<00:15:30.940> asked<00:15:31.329> you<00:15:31.360> at<00:15:31.600> the<00:15:31.690> beginning
I asked you at the beginning
I asked you at the beginning
how<00:15:33.010> many<00:15:33.220> symmetries<00:15:33.670> of<00:15:33.699> the<00:15:33.880> Rubik's<00:15:34.240> Cube
how many symmetries of the Rubik's Cube
how many symmetries of the Rubik's Cube
have<00:15:35.819> ok<00:15:36.819> I'm<00:15:36.970> going<00:15:37.120> to<00:15:37.209> sort<00:15:37.449> you<00:15:37.600> out
have ok I'm going to sort you out
have ok I'm going to sort you out
rather<00:15:38.260> than<00:15:38.410> you<00:15:38.529> all<00:15:38.709> shouting<00:15:38.889> out<00:15:39.220> I<00:15:39.370> want
rather than you all shouting out I want
rather than you all shouting out I want
you<00:15:39.670> to<00:15:39.880> count<00:15:40.120> how<00:15:40.329> many<00:15:40.389> digits<00:15:40.899> there<00:15:41.110> are
you to count how many digits there are
you to count how many digits there are
in<00:15:41.470> that<00:15:41.620> number<00:15:41.980> okay<00:15:42.550> if<00:15:43.000> you've<00:15:43.689> got<00:15:43.810> it<00:15:43.899> as
in that number okay if you've got it as
in that number okay if you've got it as
a<00:15:44.050> factorial<00:15:44.649> you<00:15:44.829> have<00:15:44.980> to<00:15:45.069> expand<00:15:45.339> the
a factorial you have to expand the
a factorial you have to expand the
factorial
factorial
factorial
okay<00:15:47.170> now<00:15:47.380> if<00:15:47.500> you<00:15:47.590> want<00:15:47.740> to<00:15:47.800> play<00:15:48.040> I<00:15:48.340> want<00:15:48.610> you
okay now if you want to play I want you
okay now if you want to play I want you
to<00:15:48.790> stand<00:15:49.000> up<00:15:49.240> okay<00:15:49.690> if<00:15:50.050> you<00:15:50.080> think<00:15:50.350> you<00:15:50.500> can
to stand up okay if you think you can
to stand up okay if you think you can
you've<00:15:51.370> got<00:15:51.490> an<00:15:51.580> estimate<00:15:51.970> for<00:15:52.060> how<00:15:52.180> many
you've got an estimate for how many
you've got an estimate for how many
digits<00:15:52.540> right<00:15:52.990> we've<00:15:53.170> already<00:15:53.320> got<00:15:53.590> one
digits right we've already got one
digits right we've already got one
competitor<00:15:54.370> here<00:15:54.700> yeah<00:15:55.480> you<00:15:55.540> all<00:15:55.900> stay<00:15:56.110> down
competitor here yeah you all stay down
competitor here yeah you all stay down
he<00:15:56.500> wins<00:15:56.680> it<00:15:56.830> automatically<00:15:57.430> okay<00:15:58.090> excellent
he wins it automatically okay excellent
he wins it automatically okay excellent
so<00:15:58.930> we've<00:15:59.020> got<00:15:59.140> four<00:15:59.380> here<00:15:59.740> five<00:16:00.040> six<00:16:00.370> great
so we've got four here five six great
so we've got four here five six great
excellent<00:16:01.300> after<00:16:01.630> that<00:16:01.750> I<00:16:01.780> should<00:16:02.080> get<00:16:02.200> us
excellent after that I should get us
excellent after that I should get us
going
going
going
all<00:16:02.800> right<00:16:04.620> anybody<00:16:05.620> with<00:16:05.950> five<00:16:06.250> or<00:16:06.460> less
all right anybody with five or less
all right anybody with five or less
digits<00:16:07.030> you've<00:16:07.240> got<00:16:07.390> to<00:16:07.510> sit<00:16:07.660> down<00:16:07.830> because
digits you've got to sit down because
digits you've got to sit down because
you've<00:16:09.070> underestimated<00:16:09.690> five<00:16:10.690> or<00:16:10.900> less
you've underestimated five or less
you've underestimated five or less
digits<00:16:11.530> so<00:16:12.100> a<00:16:12.130> hundred<00:16:12.490> thousands<00:16:13.210> of
digits so a hundred thousands of
digits so a hundred thousands of
thousands<00:16:13.810> you've<00:16:13.960> got<00:16:14.050> to<00:16:14.140> sit<00:16:14.260> down<00:16:14.550> 60
thousands you've got to sit down 60
thousands you've got to sit down 60
digits<00:16:15.850> or<00:16:16.000> more<00:16:16.210> you've<00:16:16.900> got<00:16:17.050> to<00:16:17.140> sit<00:16:17.260> down
digits or more you've got to sit down
digits or more you've got to sit down
you've<00:16:17.710> overestimated<00:16:19.350> 20<00:16:20.350> digits<00:16:20.710> or<00:16:20.860> less
you've overestimated 20 digits or less
you've overestimated 20 digits or less
sit<00:16:21.940> down<00:16:22.150> Oh<00:16:23.700> 20<00:16:24.700> how<00:16:25.570> many<00:16:25.780> digits<00:16:25.960> are<00:16:26.260> there
sit down Oh 20 how many digits are there
sit down Oh 20 how many digits are there
in<00:16:26.530> your<00:16:26.650> number<00:16:27.810> two<00:16:28.810> so<00:16:29.080> you<00:16:29.140> sort<00:16:29.380> of<00:16:29.470> sat
in your number two so you sort of sat
in your number two so you sort of sat
down<00:16:29.710> earlier<00:16:29.770> let's<00:16:30.310> have<00:16:30.430> the<00:16:30.520> other<00:16:30.640> ones
down earlier let's have the other ones
down earlier let's have the other ones
who<00:16:30.940> said<00:16:31.120> oh<00:16:31.150> they<00:16:31.870> said<00:16:32.050> the<00:16:32.170> other<00:16:32.200> ones<00:16:32.530> who
who said oh they said the other ones who
who said oh they said the other ones who
sat<00:16:32.890> sat<00:16:33.520> down<00:16:33.700> during<00:16:34.150> the<00:16:34.240> 20<00:16:34.600> up<00:16:34.840> again<00:16:35.170> okay
sat sat down during the 20 up again okay
sat sat down during the 20 up again okay
if<00:16:35.830> I<00:16:35.950> told<00:16:36.160> you<00:16:36.310> 20<00:16:36.460> or<00:16:36.700> less<00:16:36.730> stand<00:16:37.090> up
if I told you 20 or less stand up
if I told you 20 or less stand up
because<00:16:37.360> we're<00:16:37.540> this<00:16:38.080> one<00:16:38.320> I<00:16:38.470> think<00:16:38.710> there<00:16:38.890> are
because we're this one I think there are
because we're this one I think there are
a<00:16:39.010> few<00:16:39.040> here<00:16:39.460> you've<00:16:39.790> just<00:16:40.000> said<00:16:40.150> the<00:16:40.270> people
a few here you've just said the people
a few here you've just said the people
who<00:16:40.570> just<00:16:41.020> last<00:16:41.290> sat<00:16:41.560> down<00:16:41.910> okay<00:16:42.910> how<00:16:43.090> many
who just last sat down okay how many
who just last sat down okay how many
digits<00:16:43.420> do<00:16:43.660> you<00:16:43.720> have<00:16:43.870> in<00:16:43.960> your<00:16:43.990> number<00:16:44.500> ah<00:16:46.800> ha
digits do you have in your number ah ha
digits do you have in your number ah ha
ha<00:16:48.010> how<00:16:48.730> many<00:16:49.620> 21<00:16:50.620> ok<00:16:51.190> good<00:16:51.400> how<00:16:51.550> many<00:16:51.700> do<00:16:51.820> have
ha how many 21 ok good how many do have
ha how many 21 ok good how many do have
a<00:16:51.970> new<00:16:52.090> one<00:16:52.530> 18<00:16:53.530> so<00:16:54.070> it<00:16:54.340> goes<00:16:54.520> to<00:16:54.550> this<00:16:54.820> lady
a new one 18 so it goes to this lady
a new one 18 so it goes to this lady
here<00:16:55.630> 21<00:16:56.260> is<00:16:56.440> the<00:16:56.590> closest<00:16:57.070> they<00:16:57.430> actually<00:16:57.850> has
here 21 is the closest they actually has
here 21 is the closest they actually has
the<00:16:58.150> number<00:16:58.360> of<00:16:58.450> symmetries<00:16:58.900> in<00:16:59.050> the<00:16:59.320> Rubik's
the number of symmetries in the Rubik's
the number of symmetries in the Rubik's
Cube<00:16:59.830> has<00:16:59.860> 25<00:17:00.820> digits<00:17:01.420> so<00:17:01.840> now<00:17:02.020> I<00:17:02.050> need<00:17:02.200> to<00:17:02.260> name
Cube has 25 digits so now I need to name
Cube has 25 digits so now I need to name
this<00:17:02.740> object<00:17:03.010> so<00:17:03.850> what<00:17:04.000> is<00:17:04.090> your<00:17:04.210> name<00:17:04.390> I<00:17:04.860> need
this object so what is your name I need
this object so what is your name I need
your<00:17:06.010> surname<00:17:06.250> groups<00:17:06.730> the<00:17:07.210> symmetrical
your surname groups the symmetrical
your surname groups the symmetrical
objects<00:17:07.870> generally<00:17:08.250> spell<00:17:09.250> it<00:17:09.340> for<00:17:09.370> me<00:17:09.840> G<00:17:11.460> H<00:17:12.460> e
objects generally spell it for me G H e
objects generally spell it for me G H e
Z<00:17:16.890> now<00:17:17.890> so2<00:17:18.250> s<00:17:18.430> already<00:17:18.640> been<00:17:18.730> used<00:17:19.030> as<00:17:19.180> you<00:17:19.300> in
Z now so2 s already been used as you in
Z now so2 s already been used as you in
the<00:17:19.420> mathematical<00:17:19.810> language<00:17:19.930> so<00:17:20.260> you<00:17:20.290> can't
the mathematical language so you can't
the mathematical language so you can't
have<00:17:20.680> that<00:17:20.800> so<00:17:21.100> gets<00:17:21.340> there<00:17:21.730> we<00:17:21.820> go<00:17:21.970> that's
have that so gets there we go that's
have that so gets there we go that's
your<00:17:22.570> new<00:17:22.750> symmetrical<00:17:23.200> object<00:17:23.530> you<00:17:23.650> are<00:17:23.710> now
your new symmetrical object you are now
your new symmetrical object you are now
immortal
and<00:17:31.309> if<00:17:31.460> you'd<00:17:31.580> like<00:17:31.730> your<00:17:31.940> own<00:17:32.000> symmetrical
and if you'd like your own symmetrical
and if you'd like your own symmetrical
object<00:17:33.200> I<00:17:33.290> have<00:17:33.559> a<00:17:33.590> project<00:17:34.130> so<00:17:34.340> raising<00:17:34.580> money
object I have a project so raising money
object I have a project so raising money
for<00:17:35.059> a<00:17:35.120> charity<00:17:35.330> in<00:17:35.630> Guatemala<00:17:36.110> where<00:17:36.620> I<00:17:36.650> will
for a charity in Guatemala where I will
for a charity in Guatemala where I will
stay<00:17:37.100> up<00:17:37.220> all<00:17:37.370> night<00:17:37.400> and<00:17:37.760> devise<00:17:38.179> an<00:17:38.390> object
stay up all night and devise an object
stay up all night and devise an object
for<00:17:38.870> you<00:17:38.990> for<00:17:39.350> a<00:17:39.380> donation<00:17:39.650> to<00:17:39.920> this<00:17:40.010> charity
for you for a donation to this charity
for you for a donation to this charity
to<00:17:40.550> help<00:17:40.580> kids<00:17:41.179> get<00:17:41.450> into<00:17:41.660> education<00:17:41.780> in
to help kids get into education in
to help kids get into education in
Guatemala<00:17:42.830> and<00:17:43.040> I<00:17:43.809> think<00:17:44.809> what<00:17:44.929> drives<00:17:45.140> me<00:17:45.410> is
Guatemala and I think what drives me is
Guatemala and I think what drives me is
a<00:17:45.530> mathematician<00:17:45.830> are<00:17:46.250> those<00:17:46.520> things<00:17:46.730> which
a mathematician are those things which
a mathematician are those things which
are<00:17:47.059> not<00:17:47.240> seen<00:17:47.300> the<00:17:47.870> things<00:17:48.110> that<00:17:48.590> we<00:17:49.370> haven't
are not seen the things that we haven't
are not seen the things that we haven't
discovered<00:17:50.090> and<00:17:50.480> it's<00:17:51.260> all<00:17:51.410> the<00:17:51.500> unanswered
discovered and it's all the unanswered
discovered and it's all the unanswered
questions<00:17:52.370> which<00:17:52.550> make<00:17:52.760> mathematics<00:17:53.300> a
questions which make mathematics a
questions which make mathematics a
living<00:17:53.660> subject<00:17:53.840> and<00:17:54.290> I<00:17:54.679> always<00:17:54.920> come<00:17:55.130> back<00:17:55.309> to
living subject and I always come back to
living subject and I always come back to
this<00:17:55.610> quote<00:17:55.820> from<00:17:56.030> the<00:17:56.120> Japanese<00:17:56.510> essays
this quote from the Japanese essays
this quote from the Japanese essays
denying<00:17:57.230> idleness<00:17:57.559> in<00:17:57.890> everything
denying idleness in everything
denying idleness in everything
uniformity<00:17:59.330> is<00:17:59.420> undesirable<00:17:59.960> leaving
uniformity is undesirable leaving
uniformity is undesirable leaving
something<00:18:01.190> incomplete<00:18:01.550> makes<00:18:02.150> it
something incomplete makes it
something incomplete makes it
interesting<00:18:02.600> and<00:18:02.990> gives<00:18:03.559> one<00:18:03.740> the<00:18:03.770> feeling
interesting and gives one the feeling
interesting and gives one the feeling
that<00:18:04.250> there<00:18:04.370> is<00:18:04.400> room<00:18:04.640> for<00:18:04.910> growth<00:18:05.059> thank<00:18:05.960> you
Marcus du Sautoy, Oxford, Science, Ambassador, sexy, maths, Symmetry, math, mathematics, TED, TED-Ed, TED, Ed, TEDEducation
