TED2009
Margaret Wertheim: The beautiful math of coral
Margaret Wertheim govori o čudoviti matematiki koral (in kvačkanja)
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Margaret Wertheim je vodja projekta poustvarjanja bitij koralnega grebena s posebno tehniko kvačkanja, ki jo je izumila matematičarka -- z namenom ozaveščanja o čudovitih koralnih grebenih in raziskovanja hiperbolične geometrije kot osnove nastajanja koral.
Margaret Wertheim - Figurer
By masterminding a project to model a coral reef armed only with crochet hooks, Margaret Wertheim hopes to bring some of the most complicated mathematical models embodied in our universe into the minds (and hands) of the masses. Full bio
By masterminding a project to model a coral reef armed only with crochet hooks, Margaret Wertheim hopes to bring some of the most complicated mathematical models embodied in our universe into the minds (and hands) of the masses. Full bio
Double-click the English transcript below to play the video.
00:18
I'm here today, as June said,
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Kot je napovedala June, sem danes tu,
00:20
to talk about a project
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da vam predstavim projekt,
00:22
that my twin sister and I have been doing for the past three and half years.
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s katerim se s sestro dvojčico ukvarjava zadnja tri leta in pol.
00:26
We're crocheting a coral reef.
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Kvačkava namreč koralni greben.
00:29
And it's a project that we've actually
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Gre pravzaprav za projekt,
00:32
been now joined by hundreds of people around the world,
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ki je k sodelovanju pritegnil na stotine ljudi
00:35
who are doing it with us. Indeed thousands of people
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po vsem svetu. Dobesedno tisoči
00:38
have actually been involved in this project,
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so na mnogo različnih načinov
00:40
in many of its different aspects.
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sodelovali pri njem.
00:42
It's a project that now reaches across three continents,
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Projekt danes združuje tri celine,
00:45
and its roots go into the fields of mathematics,
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njegove korenine pa segajo na področje matematike,
00:49
marine biology, feminine handicraft
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morske biologije, ženskih ročnih spretnosti
00:52
and environmental activism.
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in okoljskega aktivizma.
00:55
It's true.
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Resnično.
00:57
It's also a project
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Hkrati gre za projekt,
00:59
that in a very beautiful way,
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katerega razvoj
01:01
the development of this
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se je na krasen način
01:03
has actually paralleled the evolution of life on earth,
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skladal z evolucijo življenja na zemlji,
01:07
which is a particularly lovely thing to be saying
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kar je še posebej lepo reči
01:09
right here in February 2009 --
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tu, februarja 2009,
01:11
which, as one of our previous speakers told us,
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ko, kot je povedal že en predhodnih govorcev,
01:13
is the 200th anniversary
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beležimo dvestoto obletnico
01:15
of the birth of Charles Darwin.
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rojstva Charlesa Darwina.
01:17
All of this I'm going to get to in the next 18 minutes, I hope.
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Vsega tega se bom dotaknila v naslednjih 18 minutah, upam.
01:21
But let me first begin by showing you
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A naj vam za začetek pokažem
01:23
some pictures of what this thing looks like.
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nekaj slik, kako ta stvar izgleda.
01:26
Just to give you an idea of scale,
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Da boste dobili občutek velikosti,
01:28
that installation there is about six feet across,
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ta postavitev meri slaba dva metra v dolžino,
01:31
and the tallest models are about two or three feet high.
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najvišji modeli pa od pol do enega metra višine.
01:35
This is some more images of it.
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Tu je še nekaj slik.
01:37
That one on the right is about five feet high.
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Ta na desni je visok okrog meter in pol.
01:39
The work involves hundreds of different crochet models.
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Delo vsebuje na stotine različnih vzorcev kvačkanja.
01:43
And indeed there are now thousands and thousands of models that people
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Resnično gre za tisoče modelov, ki so jih ljudje s celega sveta
01:46
have contributed all over the world as part of this.
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prispevali za ta projekt.
01:49
The totality of this project
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Njegova razsežnost
01:51
involves tens of thousands of hours
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vsebuje na desetine tisočev ur
01:53
of human labor --
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človeškega dela --
01:55
99 percent of it done by women.
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v 99 odstotkih dela ženskih rok.
01:57
On the right hand side, that bit there is part of an installation
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Na desni strani imamo delček postavitve,
02:00
that is about 12 feet long.
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dolge okrog 3 metre in pol.
02:02
My sister and I started this project in 2005
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S sestro sva se projekta lotili leta 2005,
02:05
because in that year, at least in the science press,
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saj se je tistega leta, vsaj v znanstvenem tisku,
02:07
there was a lot of talk about global warming,
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veliko govorilo o globalnem segrevanju
02:10
and the effect that global warming was having on coral reefs.
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in o njegovem vplivu na koralne grebene.
02:13
Corals are very delicate organisms,
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Korale so izjemno občutljivi organizmi,
02:15
and they are devastated by any rise in sea temperatures.
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za katere so vsaki dvigi temperature morja pogubni.
02:18
It causes these vast bleaching events
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Povzročijo ta obširni pojav beljenja,
02:20
that are the first signs of corals of being sick.
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kar je prvi znak obolelosti koral.
02:23
And if the bleaching doesn't go away --
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In če se beljenje ne ustavi,
02:25
if the temperatures don't go down -- reefs start to die.
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če se temperature ne znižajo, grebeni začnejo odmirati.
02:28
A great deal of this has been happening in the Great Barrier Reef,
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To se je v veliki meri zgodilo tudi na Velikem koralnem grebenu,
02:31
particularly in coral reefs all over the world.
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pravzaprav na grebenih po celem svetu.
02:33
This is our invocation in crochet of a bleached reef.
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Naš poziv je v obliki kvačkanega obeljenega grebena.
02:37
We have a new organization together called The Institute for Figuring,
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Skupaj sestavljamo organizacijo, imenovano Inštitut za upodabljanje,
02:40
which is a little organization we started
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skromno organizacijo, katere namen je
02:42
to promote, to do projects about the
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promovirati in ustvarjati projekte o
02:44
aesthetic and poetic dimensions of science and mathematics.
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estetskih in poetičnih razsežnostih znanosti in matematike.
02:47
And I went and put a little announcement up on our site,
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Na naši spletni strani sem objavila oglas,
02:50
asking for people to join us in this enterprise.
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da medse vabimo nove člane organizacije.
02:52
To our surprise, one of the first people who called
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Na naše presenečenje so se med prvimi oglasili
02:55
was the Andy Warhol Museum.
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iz Muzeja Andyja Warhola.
02:57
And they said they were having an exhibition
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Povedali so, da pripravljajo razstavo
02:59
about artists' response to global warming,
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pogleda umetnikov na globalno segrevanje
03:01
and they'd like our coral reef to be part of it.
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ter da želijo razstaviti tudi naš koralni greben.
03:03
I laughed and said, "Well we've only just started it,
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V smehu sem dejala, "Pravzaprav smo šele začeli,
03:05
you can have a little bit of it."
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razstavimo lahko le malo."
03:07
So in 2007 we had an exhibition,
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Leta 2007 smo tako imeli razstavo,
03:10
a small exhibition of this crochet reef.
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skromno razstavo tega koralnega grebena.
03:12
And then some people in Chicago came along and they said,
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Nato pa so v Chicagu do nas prišli neki ljudje in rekli,
03:14
"In late 2007, the theme of the Chicago Humanities Festival is
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"Konec leta 2007 bo tema čikaškega festivala humanističnih ved
03:19
global warming. And we've got this 3,000 square-foot gallery
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prav globalno segrevanje. Naša galerija meri skoraj 3 are
03:22
and we want you to fill it with your reef."
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in želeli bi, da jo napolnite s svojimi koralami."
03:25
And I, naively by this stage, said, "Oh, yes, sure."
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In jaz sem naivno rekla, "Oh, da, seveda."
03:28
Now I say "naively" because actually
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Pravim, "naivno", saj po poklicu pravzaprav
03:30
my profession is as a science writer.
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pišem znanstvene prispevke.
03:32
What I do is I write books about the cultural history of physics.
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Pišem knjige o kulturni zgodovini fizike.
03:35
I've written books about the history of space,
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Pisala sem knjige o zgodovini vesolja,
03:37
the history of physics and religion,
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o zgodovini fizike in religije,
03:39
and I write articles for people like the New York Times and the L.A. Times.
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pišem pa tudi poljudne članke v New York Timesu in L.A. Timesu.
03:42
So I had no idea what it meant to fill a 3,000 square-foot gallery.
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Zato se mi ni sanjalo, kaj pomeni napolniti skoraj 3 are veliko galerijo.
03:46
So I said yes to this proposition.
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In sem pristala na predlog.
03:48
And I went home, and I told my sister Christine.
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Doma sem o tem povedala moji sestri Christine.
03:50
And she nearly had a fit
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Skoraj je znorela,
03:52
because Christine is a professor at one of
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saj je kot profesorica na enem izmed
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L.A.'s major art colleges, CalArts,
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boljših losangeliških umetniških kolidžev, CalArtsu,
03:57
and she knew exactly what it meant to fill a 3,000 square-foot gallery.
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natanko vedela, kaj pomeni napolniti 3 are veliko galerijo.
04:00
She thought I'd gone off my head.
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Prepričana je bila, da sem ob pamet.
04:03
But she went into crochet overdrive.
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Na koncu pa je postala skoraj obsedena s kvačkanjem.
04:05
And to cut a long story short, eight months later
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Na kratko, po osmih mesecih
04:07
we did fill the Chicago Cultural Center's
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nam je uspelo napolniti 3 are veliko galerijo
04:10
3,000 square foot gallery.
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Čikaškega kulturnega centra.
04:12
By this stage the project had taken on
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Do tega trenutka se je projekt
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a viral dimension of its own,
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kot virus razširil na dimenzije,
04:16
which got completely beyond us.
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nam popolnoma nedoumljive.
04:18
The people in Chicago decided
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Odgovorni ljudje v Čikagu so sklenili,
04:20
that as well as exhibiting our reefs, what they wanted to do
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da poleg razstavljanja naših koralnih grebenov želijo še,
04:23
was have the local people there make a reef.
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da tamkajšnji prebivalci izdelajo nove.
04:25
So we went and taught the techniques. We did workshops and lectures.
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Tako smo jih na delavnicah in predavanjih naučili tehnik kvačkanja.
04:28
And the people in Chicago made a reef of their own.
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Ljudje v Čikagu so izdelali svoj lasten koralni greben,
04:31
And it was exhibited alongside ours.
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ki je bil razstavljen poleg našega.
04:33
There were hundreds of people involved in that.
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Na stotine ljudi je sodelovalo.
04:35
We got invited to do the whole thing
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Vabili so nas, da stvar ponovimo
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in New York, and in London,
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v New Yorku, Londonu
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and in Los Angeles.
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in Los Angelesu.
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In each of these cities, the local citizens,
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V vsakem od teh mest so meščani,
04:44
hundreds and hundreds of them, have made a reef.
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na stotine ljudi, izdelali koralni greben.
04:46
And more and more people get involved in this,
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In vse več ljudi sodeluje pri tem,
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most of whom we've never met.
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od katerih večine nikoli nismo spoznali.
04:51
So the whole thing has sort of morphed
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Stvar se je pravzaprav razvila
04:53
into this organic, ever-evolving creature,
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v neko organsko, stalno razvijajoče se bitje,
04:55
that's actually gone way beyond Christine and I.
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ki naju je s Christine že zdavnaj preseglo.
04:59
Now some of you are sitting here thinking,
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Najbrž se nekateri od vas sprašujete,
05:02
"What planet are these people on?
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"S katerega planeta so ti ljudje?
05:04
Why on earth are you crocheting a reef?
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Le čemu kvačkajo koralni greben?
05:07
Woolenness and wetness aren't exactly
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Volnenost in vlažnost nista ravno pojma,
05:09
two concepts that go together.
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ki sta si sorodna.
05:11
Why not chisel a coral reef out of marble?
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Zakaj koral ne izklešejo iz marmorja?
05:13
Cast it in bronze."
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Ali jih odlijejo v bron?"
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But it turns out there is a very good reason
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Pravzaprav pa obstaja zelo dober razlog,
05:17
why we are crocheting it
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zakaj je kvačkanje najprimernejše,
05:19
because many organisms in coral reefs
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in sicer, da imajo mnogi organizmi
05:21
have a very particular kind of structure.
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koralnih grebenov zelo značilno obliko strukture.
05:23
The frilly crenulated forms that you see
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Nagubane in nazobčane oblike, vidne
05:25
in corals, and kelps, and sponges and nudibranchs,
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na koralah, algah, spužvah in morskih polžih,
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is a form of geometry known as hyperbolic geometry.
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so znane kot oblike hiperbolične geometrije.
05:31
And the only way that mathematicians know
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In edini način, na katerega znajo matematiki
05:34
how to model this structure
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prikazati to strukturo,
05:36
is with crochet. It happens to be a fact.
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je kvačkanje. To je dejstvo.
05:38
It's almost impossible to model this structure any other way,
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Te strukture praktično ni mogoče prikazati na drugačen način,
05:41
and it's almost impossible to do it on computers.
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niti s pomočjo računalnika.
05:44
So what is this hyperbolic geometry
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Kaj je torej hiperbolična geometrija,
05:46
that corals and sea slugs embody?
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ki jo utelešajo korale in morski polži?
05:49
The next few minutes is, we're all going to get raised up
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V naslednjih nekaj minutah se bomo postavili
05:52
to the level of a sea slug.
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v kožo morskega polža.
05:54
(Laughter)
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(Smeh)
05:55
This sort of geometry revolutionized mathematics
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Ta veja geometrije je ob odkritju v 19. stoletju
05:58
when it was first discovered in the 19th century.
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razburkala matematično vedo.
06:01
But not until 1997 did mathematicians actually understand
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A vse do leta 1997 matematiki niso razumeli,
06:04
how they could model it.
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kako bi jo prikazali.
06:06
In 1997 a mathematician
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Leta 1997 je matematičarka
06:08
at Cornell, Daina Taimina,
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na Univerzi Cornell, Daina Taimina,
06:10
made the discovery that this structure
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odkrila, da se takšne strukture
06:12
could actually be done in knitting and crochet.
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lahko prikaže s pletenjem in kvačkanjem.
06:14
The first one she did was knitting.
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Začela je s pletenjem.
06:16
But you get too many stitches on the needle. So she quickly realized
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A kmalu je na igli nastalo preveč zank, zato je bilo
06:18
crochet was the better thing.
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kvačkanje očitno boljši način.
06:20
But what she was doing was actually making a model
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Kar je pravzaprav počela, je bilo ustvarjanje modela
06:23
of a mathematical structure, that many mathematicians
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matematične strukture, za katero so mnogi trdili,
06:25
had thought it was actually impossible to model.
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da jo je nemogoče sestaviti.
06:28
And indeed they thought that anything like this structure
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V resnici so menili, da so bila telesa s tako strukturo
06:30
was impossible per se.
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sama po sebi nemogoča.
06:32
Some of the best mathematicians spent hundreds of years
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Nekateri najboljši matematiki so se skozi stoletja
06:34
trying to prove that this structure was impossible.
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trudili dokazati, da je ta struktura nemogoča.
06:37
So what is this impossible hyperbolic structure?
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Kaj je torej ta nemogoča hiperbolična struktura?
06:40
Before hyperbolic geometry, mathematicians knew
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Pred odkritjem hiperbolične geometrije sta bili znani
06:42
about two kinds of space:
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dve vrsti prostora:
06:44
Euclidean space, and spherical space.
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evklidski prostor in sferični prostor.
06:47
And they have different properties.
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Oba imata različne lastnosti.
06:49
Mathematicians like to characterize things by being formalist.
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Matematiki radi formalistično označujejo stvari.
06:52
You all have a sense of what a flat space is, Euclidean space is.
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Vsi veste, kaj je raven, evklidski prostor.
06:56
But mathematicians formalize this in a particular way.
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A matematiki to določijo na poseben način.
06:59
And what they do is, they do it through the concept
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In sicer preko koncepta
07:01
of parallel lines.
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vzporednih premic.
07:03
So here we have a line and a point outside the line.
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Tu imamo premico in točko izven nje.
07:06
And Euclid said, "How can I define parallel lines?
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Evklid se je vprašal, "Kako določim vzporedne premice?
07:09
I ask the question, how many lines can I draw through
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Koliko premic lahko potegnem skozi točko,
07:12
the point but never meet the original line?"
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ne da bi sekal prvotno premico?"
07:14
And you all know the answer. Does someone want to shout it out?
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Vsi veste odgovor. Kdo ga bo povedal na glas?
07:17
One. Great. Okay.
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Eno. Točno. Prav.
07:19
That's our definition of a parallel line.
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To je naša definicija vzporedne premice.
07:21
It's a definition really of Euclidean space.
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Gre pravzaprav za definicijo evklidskega prostora.
07:24
But there is another possibility that you all know of:
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A tu je še ena možnost, ki jo tudi vsi poznate:
07:26
spherical space.
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sferični prostor.
07:28
Think of the surface of a sphere --
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Pomislite na površino neke krogle --
07:30
just like a beach ball, the surface of the Earth.
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napihljive žoge, površine Zemlje.
07:32
I have a straight line on my spherical surface.
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Na tej sferični površini imamo ravno premico
07:35
And I have a point outside the line. How many straight lines
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in točko izven nje. Koliko ravnih premic
07:37
can I draw through the point
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lahko potegnem skozi točko,
07:39
but never meet the original line?
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ne da bi sekala prvotno premico?
07:41
What do we mean to talk about
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Zakaj govorimo o
07:43
a straight line on a curved surface?
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ravni premici na zakrivljeni podlagi?
07:46
Now mathematicians have answered that question.
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Matematiki so odgovorili na to vprašanje.
07:49
They've understood there is a generalized concept
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Spoznali so, da obstaja posplošen koncept
07:51
of straightness, it's called a geodesic.
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ravnosti, in sicer geodetski.
07:53
And on the surface of a sphere,
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In na površini krogle
07:55
a straight line is the biggest possible circle you can draw.
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je ravna premica največji možni krog, ki ga lahko narišete.
07:58
So it's like the equator or the lines of longitude.
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Torej kot ekvator ali črte zemljepisne dolžine.
08:02
So we ask the question again,
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Vprašajmo se torej znova,
08:04
"How many straight lines can I draw through the point,
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"Koliko ravnih premic lahko potegnem skozi točko,
08:06
but never meet the original line?"
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in se hkrati izognem prvotni premici?"
08:08
Does someone want to guess?
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Kdo želi ugibati?
08:11
Zero. Very good.
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Nič. Zelo dobro.
08:13
Now mathematicians thought that was the only alternative.
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Matematiki so torej verjeli, da je to edina alternativa.
08:15
It's a bit suspicious isn't it? There is two answers to the question so far,
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Kar pa je nekoliko sumljivo, mar ne? Doslej imamo dva odgovora,
08:18
Zero and one.
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nič in ena.
08:20
Two answers? There may possibly be a third alternative.
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Le dva odgovora? Ali obstaja tudi tretja alternativa?
08:22
To a mathematician if there are two answers,
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Za matematika se ob dveh odgovorih,
08:24
and the first two are zero and one,
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ki sta nič in ena,
08:26
there is another number that immediately suggests itself
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neogibno pojavi še eno število
08:28
as the third alternative.
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kot tretja alternativa.
08:30
Does anyone want to guess what it is?
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Bi kdo želel ugibati, katero?
08:33
Infinity. You all got it right. Exactly.
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Neskončno. Vsi imate prav. Točno tako.
08:36
There is, there's a third alternative.
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Tudi tretja alternativa obstaja.
08:38
This is what it looks like.
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Videti pa je tako.
08:40
There's a straight line, and there is an infinite number of lines
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Imamo ravno premico ter neskončno število premic,
08:43
that go through the point and never meet the original line.
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ki grejo skozi točko, a se nikoli ne dotaknejo prvotne premice.
08:45
This is the drawing.
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Tu je prikaz.
08:47
This nearly drove mathematicians bonkers
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Matematike je to privedlo skoraj na rob pameti,
08:49
because, like you, they're sitting there feeling bamboozled.
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saj so ga, tako kot vi, le zmedeno opazovali.
08:52
Thinking, how can that be? You're cheating. The lines are curved.
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Gotovo mislite, da to ni možno. Da goljufam. Premice so namreč ukrivljene.
08:55
But that's only because I'm projecting it onto a
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A to je le zato, ker je prikazano na
08:57
flat surface.
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ravni podlagi.
08:59
Mathematicians for several hundred years
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Matematiki so se stoletja
09:01
had to really struggle with this.
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bojevali s tem problemom.
09:03
How could they see this?
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Kako bi lahko to videli?
09:05
What did it mean to actually have a physical model
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Kaj bi pomenilo imeti snoven model,
09:08
that looked like this?
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ki bi izgledal tako?
09:10
It's a bit like this: imagine that we'd only ever encountered Euclidean space.
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Poskusimo tako: predstavljate si, da poznamo le evklidski prostor.
09:13
Then our mathematicians come along
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Nato pridejo naši matematiki
09:15
and said, "There's this thing called a sphere,
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in rečejo, "Obstaja stvar, imenovana krogla,
09:17
and the lines come together at the north and south pole."
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in premice se stikajo na severnem in južnem tečaju."
09:19
But you don't know what a sphere looks like.
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A vi ne veste, kako sfera sploh izgleda.
09:21
And someone that comes along and says, "Look here's a ball."
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In nekdo pride in reče, "Poglejte, žoga."
09:24
And you go, "Ah! I can see it. I can feel it.
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Vi pa, "Ah! Vidim jo. Čutim jo.
09:26
I can touch it. I can play with it."
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Držim jo. Lahko se igram z njo."
09:29
And that's exactly what happened
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In točno to se je zgodilo,
09:31
when Daina Taimina
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ko je Daina Taimina
09:33
in 1997, showed that you could crochet models
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leta 1997 pokazala, da se lahko skvačka modele
09:37
in hyperbolic space.
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v hiperboličnem prostoru.
09:39
Here is this diagram in crochetness.
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Tu imamo prikaz v kvačkanju.
09:42
I've stitched Euclid's parallel postulate on to the surface.
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Šiv na površini predstavlja Evklidov postulat o vzporednosti.
09:46
And the lines look curved.
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Linije izgledajo ukrivljene.
09:48
But look, I can prove to you that they're straight
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A kot vidite, lahko dokažem, da so ravne,
09:51
because I can take any one of these lines,
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tako, da primem katerokoli od linij
09:53
and I can fold along it.
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in prepognem preko nje.
09:56
And it's a straight line.
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Imamo ravno črto.
09:58
So here, in wool,
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Tukaj, v volni
10:01
through a domestic feminine art,
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in ženskih ročnih spretnostih
10:03
is the proof that the most famous postulate
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imamo dokaz, da je najbolj znan postulat
10:05
in mathematics is wrong.
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v matematiki napačen.
10:08
(Applause)
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(Aplavz)
10:14
And you can stitch all sorts of mathematical
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In na take površine lahko všijete različne
10:16
theorems onto these surfaces.
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matematične teoreme.
10:19
The discovery of hyperbolic space ushered in the field of mathematics
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Odkritje hiperboličnega prostora je napovedalo novo področje v matematiki,
10:22
that is called non-Euclidean geometry.
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t.i. neevklidsko geometrijo.
10:24
And this is actually the field of mathematics
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To področje je pravzaprav temeljni kamen
10:26
that underlies general relativity
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splošne relativnosti,
10:28
and is actually ultimately going to show us
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ki bo nazadnje osmislilo
10:30
about the shape of the universe.
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obliko vesolja.
10:32
So there is this direct line
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Našli smo torej neposredno povezavo
10:34
between feminine handicraft,
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med ženskimi ročnimi spretnostmi,
10:36
Euclid and general relativity.
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Evklidom in splošno relativnostjo.
10:39
Now, I said that mathematicians thought that this was impossible.
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Rekla sem že, da so matematiki to smatrali za nemogoče.
10:42
Here's two creatures who've never heard of Euclid's parallel postulate --
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Tu pa imamo dve bitji, ki še nista slišali za Evklidov postulat o vzporednosti,
10:46
didn't know it was impossible to violate,
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niti nista vedeli, da ga je mogoče ovreči,
10:48
and they're simply getting on with it.
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a to kljub temu počneta.
10:50
They've been doing it for hundreds of millions of years.
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In to že stotine milijonov let.
10:54
I once asked the mathematicians why it was
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Nekoč sem matematike vprašala, zakaj
10:56
that mathematicians thought this structure was impossible
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so nekoč menili, da je taka struktura nemogoča,
10:59
when sea slugs have been doing it since the Silurian age.
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čeprav so jo morski polži utelešali že od dobe silurja.
11:02
Their answer was interesting.
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Njihov odgovor je bil zanimiv.
11:04
They said, "Well I guess there aren't that many mathematicians
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Rekli so, "Najbrž res ni veliko matematikov,
11:06
sitting around looking at sea slugs."
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ki opazujejo morske polže."
11:08
And that's true. But it also goes deeper than that.
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In niso se motili. A tu je še druga, globlja plat.
11:11
It also says a whole lot of things
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Pove nam veliko o tem,
11:13
about what mathematicians thought mathematics was,
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kako so gledali na samo matematiko,
11:16
what they thought it could and couldn't do,
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kaj lahko z njo počnejo in česa ne,
11:18
what they thought it could and couldn't represent.
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kaj lahko predstavlja in česa ne.
11:20
Even mathematicians, who in some sense
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Celo matematiki, ki so na nek načen
11:22
are the freest of all thinkers,
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najbolj svobodomiselni od vseh mislecev,
11:24
literally couldn't see
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so dejansko okrog sebe spregledali
11:26
not only the sea slugs around them,
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ne le morske polže,
11:28
but the lettuce on their plate --
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ampak tudi solato na njihovem krožniku --
11:30
because lettuces, and all those curly vegetables,
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zelena solata in vsa kodrasta zelenjava
11:32
they also are embodiments of hyperbolic geometry.
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namreč prav tako predstavljajo hiperbolično geometrijo.
11:36
And so in some sense they literally,
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In tako so nekako prav zaradi
11:39
they had such a symbolic view of mathematics,
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njihovega simbolnega pogleda na svet
11:41
they couldn't actually see what was going on
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prezrli, kar so imeli ves čas pred sabo
11:44
on the lettuce in front of them.
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v obliki zelene solate.
11:47
It turns out that the natural world is full of hyperbolic wonders.
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Izkazalo se je, da je narava polna hiperboličnih čudes.
11:51
And so, too, we've discovered
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Prav tako smo odkrili,
11:53
that there is an infinite taxonomy
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da obstaja neskončna taksonomija
11:55
of crochet hyperbolic creatures.
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kvačkanih hiperboličnih modelov.
11:57
We started out, Chrissy and I and our contributors,
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S Chrissy in sodelavci smo začeli
12:00
doing the simple mathematically perfect models.
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z izdelavo preprostih in matematično pravilnih modelov.
12:02
But we found that when we deviated from the specific
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A ko smo skrenili z določene postavitve
12:06
setness of the mathematical code
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matematične kode, ki je predstavljala
12:09
that underlies it -- the simple algorithm
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njihovo osnovo -- preprosti algoritem, ki se glasi:
12:11
crochet three, increase one --
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pokvačkaj tri in dodaj eno petljo --
12:13
when we deviated from that and made embellishments to the code,
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ko smo skrenili s poti in začeli z okraševanjem osnovne kode,
12:16
the models immediately started to look more natural.
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so ti modeli takoj izgledali bolj naravno.
12:20
And all of our contributors, who are an amazing
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In vsi od naših sodelavcev, izjemna skupina
12:22
collection of people around the world,
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ljudi z vsega sveta,
12:24
do their own embellishments.
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ustvarjajo samosvoje krasitve.
12:26
As it were, we have this ever-evolving,
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Nastalo je to stalno razvijajoče se
12:28
crochet taxonomic tree of life.
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kvačkano taksonomično drevo življenja.
12:30
Just as the morphology
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Prav tako kot sta neskončni morfologija
12:32
and the complexity of life on earth is never ending,
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in kompleksnost življenja na Zemlji,
12:34
little embellishments and complexifications
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majhna odstopanja, krasitve in zapletanja
12:37
in the DNA code
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v verigi DNK
12:39
lead to new things like giraffes, or orchids --
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pa privedejo do novih bitij, kot so žirafe ali orhideje,
12:42
so too, do little embellishments in the crochet code
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tako tudi majhna okraševanja v kvačkanem modelu
12:45
lead to new and wondrous creatures
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privedejo do novih in čudovitih struktur
12:48
in the evolutionary tree of crochet life.
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v razvojnem drevesu kvačkanega življenja.
12:51
So this project really has
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Ta projekt je torej resnično
12:53
taken on this inner organic life of its own.
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zaživel svoje notranje organsko življenje.
12:56
There is the totality of all the people who have come to it.
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Predstavljajo ga vsi ljudje, ki so pri njem sodelovali
12:59
And their individual visions,
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s svojimi lastnimi vizijami
13:01
and their engagement with this mathematical mode.
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in angažiranostjo za ta matematični način.
13:04
We have these technologies. We use them.
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Poznamo primerne tehnologije in jih uporabljamo.
13:06
But why? What's at stake here? What does it matter?
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Toda zakaj? Kaj je v igri? Kaj je pomembno?
13:09
For Chrissy and I, one of the things that's important here
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Za naju s Chrissy je en od pomembnih vidikov,
13:12
is that these things suggest
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da se s tem opozori na
13:14
the importance and value of embodied knowledge.
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pomembnost in koristnost utelešenega znanja.
13:17
We live in a society
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Živimo v družbi,
13:19
that completely tends to valorize
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ki povsem privilegira
13:21
symbolic forms of representation --
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simbolične oblike predstavitve --
13:23
algebraic representations,
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algebrski izrazi,
13:25
equations, codes.
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enačbe, kode.
13:27
We live in a society that's obsessed
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Naša družba je obsedena
13:29
with presenting information in this way,
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s takim načinom predstavitve
13:31
teaching information in this way.
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in širjenja podatkov.
13:34
But through this sort of modality,
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A preko take vrste izražanja,
13:37
crochet, other plastic forms of play --
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kvačkanja ali drugih plastičnih oblik ustvarjanja,
13:41
people can be engaged with the most abstract,
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se lahko ljudje povežejo z najbolj abstraktnimi,
13:44
high-powered, theoretical ideas,
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izjemno pomembnimi teoretičnimi idejami,
13:46
the kinds of ideas that normally you have to go
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s katerimi se ponavadi lahko srečate le
13:48
to university departments to study in higher mathematics,
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na univerzah pri študiju višje matematike,
13:51
which is where I first learned about hyperbolic space.
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kjer sem tudi sama prvič slišala za hiperbolični prostor.
13:54
But you can do it through playing with material objects.
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Lahko pa jih spoznate tudi preko fizičnih predmetov.
13:58
One of the ways that we've come to think about this
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Ena od stvari, ki se nam je pri tem utrnila,
14:00
is that what we're trying to do with the Institute for Figuring
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je, da preko Inštituta za upodabljanje
14:03
and projects like this, we're trying to have
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in projektov, kot je ta, poskušamo ustvariti
14:05
kindergarten for grown-ups.
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vrtec za odrasle.
14:07
And kindergarten was actually a very formalized
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Vrtec je pravzaprav zelo formalizirana
14:09
system of education,
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oblika izobraževanja,
14:11
established by a man named Friedrich Froebel,
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ki jo je osnoval Friedrich Fröbel,
14:13
who was a crystallographer in the 19th century.
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kristalograf iz 19. stoletja.
14:15
He believed that the crystal was the model
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Verjel je, da je kristal pravi model
14:17
for all kinds of representation.
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za najrazličnejše predstavitve.
14:19
He developed a radical alternative system
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Razvil je radikalni alternativni sistem
14:22
of engaging the smallest children
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seznanjanja najmlajših
14:24
with the most abstract ideas
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z najbolj abstraktnimi idejami,
14:26
through physical forms of play.
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in sicer preko fizičnih igrač.
14:28
And he is worthy of an entire talk on his own right.
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O njem bi lahko pripravili cel govor.
14:30
The value of education
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Koristnost izobraževanja
14:32
is something that Froebel championed,
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je Fröbel obvladal
14:35
through plastic modes of play.
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skozi plastične načine igre.
14:37
We live in a society now
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Naša družba pozna
14:39
where we have lots of think tanks,
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veliko raziskovalnih organizacij,
14:41
where great minds go to think about the world.
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kjer se misleci ukvarjajo s svetom okoli nas.
14:44
They write these great symbolic treatises
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Ustvarjajo pomembne simbolne razprave,
14:46
called books, and papers,
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ki jim pravimo knjige, referati,
14:48
and op-ed articles.
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kolumne in članki.
14:50
We want to propose, Chrissy and I,
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S Chrissy sva preko Inštituta za upodabljanje
14:52
through The Institute for Figuring, another alternative way of doing things,
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želeli predlagati alternativni način ustvarjanja,
14:55
which is the play tank.
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in sicer neke vrste igralne organizacije.
14:58
And the play tank, like the think tank,
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Te bi bile, prav tako kot raziskovalne organizacije,
15:00
is a place where people can go
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kraj, kjer bi se ljudje lahko povezali
15:02
and engage with great ideas.
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z velikimi idejami.
15:04
But what we want to propose,
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S tem želimo poudariti,
15:06
is that the highest levels of abstraction,
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da so najkompleksnejše abstrakcije,
15:08
things like mathematics, computing, logic, etc. --
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pojmi kot so matematika, računanje, logika itd,
15:11
all of this can be engaged with,
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nam na dosegu
15:13
not just through purely cerebral algebraic
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ne le preko izključno možganskih algebrskih
15:15
symbolic methods,
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simboličnih metod,
15:17
but by literally, physically playing with ideas.
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pač pa dobesedno in zelo konkretno preko igre z idejami.
15:21
Thank you very much.
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Najlepša hvala.
15:23
(Applause)
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(Aplavz)
ABOUT THE SPEAKER
Margaret Wertheim - FigurerBy masterminding a project to model a coral reef armed only with crochet hooks, Margaret Wertheim hopes to bring some of the most complicated mathematical models embodied in our universe into the minds (and hands) of the masses.
Why you should listen
Snowflakes, fractals, the patterns on a leaf -- there's beauty to be found at the intersection of nature and physics, beauty and math. Science writer Margaret Wertheim (along with her twin sister, Christine) founded the Institute for Figuring to advance the aesthetic appreciation of scientific concepts, from the natural physics of snowflakes and fractals to human constructs such as Islamic mosaics, string figures and weaving.
The IFF's latest project is perhaps its most beguilingly strange -- a coral reef constructed entirely by crochet hook, a project that takes advantage of the happy congruence between the mathematical phenomena modeled perfectly by the creatures of the reef, and repetitive tasks such as crocheting -- which, as it turns out, is perfectly adapted to model hyperbolic space. It is easy to sink into the kaleidoscopic, dripping beauty of the yarn-modeled reef, but the aim of the reef project is twofold: to draw attention to distressed coral reefs around the world, dying in droves from changing ocean saline levels, overfishing, and a myriad of threats; and to display a flavor of math that was previously almost impossible to picture. By modeling these complex equations in physical space, this technique can help mathematicians see patterns and make breakthroughs.
Wertheim is now working on a book about maverick scientist James Carter.
Margaret Wertheim | Speaker | TED.com