ABOUT THE SPEAKER
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.

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.

More profile about the speaker
Margaret Wertheim | Speaker | TED.com
TED2009

Margaret Wertheim: The beautiful math of coral

Margaret Wertheim despre frumoasa matematica a coralilor (si crosetatul)

Filmed:
1,470,540 views

Margaret Wertheim conduce un proiect pentru a recrea recifele de corali folosind o tehnica de crosetat inventata de o matematiciana -- celebrand minunatiile recifului si facand o incursiune in geometria hiperbolica ce sta la baza crearii coralilor.
- 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

Double-click the English transcript below to play the video.

00:18
I'm here todayastăzi, as JuneIunie said,
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Ma aflu astazi aici, cum a spus si June,
00:20
to talk about a projectproiect
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pentru a vorbi despre un proiect
00:22
that my twingeamăn sistersoră and I have been doing for the pasttrecut threeTrei and halfjumătate yearsani.
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la care eu si sora mea geamana lucram de trei ani si jumatate.
00:26
We're crochetingcroşetare a coralcoral reefrecif.
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Crosetam un recif de corali.
00:29
And it's a projectproiect that we'vene-am actuallyde fapt
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Este un proiect la care acum
00:32
been now joinedalăturat by hundredssute of people around the worldlume,
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ni s-au alaturat sute de oameni din toata lumea
00:35
who are doing it with us. IndeedÎntr-adevăr thousandsmii of people
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si fac asta impreuna cu noi. Intr-adevar, mii de oameni
00:38
have actuallyde fapt been involvedimplicat in this projectproiect,
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au fost implicati in acest proiect
00:40
in manymulți of its differentdiferit aspectsaspecte.
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in multe din aspectele acestuia.
00:42
It's a projectproiect that now reachesajunge acrosspeste threeTrei continentscontinente,
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Este un proiect care acum se intinde pe trei continente.
00:45
and its rootsrădăcini go into the fieldscâmpuri of mathematicsmatematică,
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Originile lui isi au radacinile in domeniul matematicii,
00:49
marinemarină biologybiologie, femininefeminin handicraftArtizanat
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biologiei marine, artizanatului feminin
00:52
and environmentalde mediu activismActivism.
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si activismului in mediul inconjurator.
00:55
It's trueAdevărat.
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Este adevarat.
00:57
It's alsode asemenea a projectproiect
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Este de asemenea un proiect
00:59
that in a very beautifulfrumoasa way,
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a carui dezvoltare minunata
01:01
the developmentdezvoltare of this
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a dus de fapt
01:03
has actuallyde fapt paralleledparalel the evolutionevoluţie of life on earthPământ,
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la un paralelism al evolutiei vietii pe pamant,
01:07
whichcare is a particularlyîn special lovelyminunat thing to be sayingzicală
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ceea ce este un lucru foarte frumos de spus
01:09
right here in FebruaryFebruarie 2009 --
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chiar aici in februarie 2009 --
01:11
whichcare, as one of our previousanterior speakersdifuzoare told us,
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avand in vedere ca, dupa cum ne spunea unul din prezentatorii anteriori,
01:13
is the 200thlea anniversaryaniversare
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este a 200-a aniversare
01:15
of the birthnaștere of CharlesCharles DarwinDarwin.
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de la nasterea lui Charles Darwin.
01:17
All of this I'm going to get to in the nextUrmător → 18 minutesminute, I hopesperanţă.
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Sper ca in urmatoarele 18 minute sa patrund in toate acestea.
01:21
But let me first beginÎNCEPE by showingarătând you
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Dar lasati-ma sa incep prin a va arata
01:23
some picturespoze of what this thing looksarată like.
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cateva imagini despre cum arata acest lucru.
01:26
Just to give you an ideaidee of scalescară,
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Ca sa va dau o idee despre marime,
01:28
that installationinstalare there is about sixşase feetpicioare acrosspeste,
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aceasta instalatie are in jur de 2 metri lungime.
01:31
and the tallestcel mai inalt modelsmodele are about two or threeTrei feetpicioare highînalt.
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Cele mai inalte modele au cam un metru inaltime.
01:35
This is some more imagesimagini of it.
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Aici sunt mai multe imagini.
01:37
That one on the right is about fivecinci feetpicioare highînalt.
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Cel din dreapta este in jur de 1.5 metri inaltime.
01:39
The work involvesimplică hundredssute of differentdiferit crochetcroşetat modelsmodele.
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Munca presupune sute de modele diferite de crosetat.
01:43
And indeedintr-adevar there are now thousandsmii and thousandsmii of modelsmodele that people
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Si intr-adevar acum sunt mii si mii de modele
01:46
have contributedcontribuit all over the worldlume as partparte of this.
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cu care au contribuit oamenii din toata lumea la acesta.
01:49
The totalitytotalitate of this projectproiect
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In total, acest proiect
01:51
involvesimplică tenszeci of thousandsmii of hoursore
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presupune zeci de mii de ore
01:53
of humanuman labormuncă --
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de munca umana --
01:55
99 percentla sută of it doneTerminat by womenfemei.
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99% facuta de femei.
01:57
On the right handmână sidelatură, that bitpic there is partparte of an installationinstalare
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Bucatica din partea dreapta face parte dintr-o instalatie
02:00
that is about 12 feetpicioare long.
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care are in jur de 4 metri lungime.
02:02
My sistersoră and I starteda început this projectproiect in 2005
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Eu si sora mea am inceput acest proiect in 2005
02:05
because in that yearan, at leastcel mai puţin in the scienceştiinţă presspresa,
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deoarece in acel an se vorbea foarte mult, cel putin in presa stiintifica,
02:07
there was a lot of talk about globalglobal warmingîncălzire,
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despre incalzirea globala
02:10
and the effectefect that globalglobal warmingîncălzire was havingavând on coralcoral reefsRecife.
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si despre efectul pe care incalzirea globala il avea asupra recifelor de corali.
02:13
CoralsCoralii are very delicatedelicat organismsorganisme,
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Coralii sunt organisme foarte delicate.
02:15
and they are devastateddevastat by any risecreştere in seamare temperaturestemperaturile.
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Si sunt devastati de orice ridicare de temperatura a apei marii.
02:18
It causescauze these vastvast bleachingalbire eventsevenimente
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Cauzeaza imense fenomene de albire
02:20
that are the first signssemne of coralscoralii of beingfiind sickbolnav.
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care sunt primele semne de imbolnavire ale coralilor.
02:23
And if the bleachingalbire doesn't go away --
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Iar daca albirea nu trece,
02:25
if the temperaturestemperaturile don't go down -- reefsRecife startstart to diea muri.
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daca temperaturile nu scad, recifele incep sa moara.
02:28
A great dealafacere of this has been happeninglucru in the Great BarrierBariera ReefRecif,
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Acest fenomen se intampla in Marea Bariera de Corali,
02:31
particularlyîn special in coralcoral reefsRecife all over the worldlume.
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respectiv in recifele de corali din toata lumea.
02:33
This is our invocationinvocarea in crochetcroşetat of a bleachedalbite reefrecif.
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Aceasta este imitatia noastra crosetata a unui recif de corali albit.
02:37
We have a newnou organizationorganizare togetherîmpreună calleddenumit The InstituteInstitutul for FiguringImaginind,
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Avem impreuna o noua organizatie numita „Institutul de Imaginatie”,
02:40
whichcare is a little organizationorganizare we starteda început
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o mica organizatie pe care am inceput-o
02:42
to promotepromova, to do projectsproiecte about the
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ca sa promovam, sa realizam proiecte despre
02:44
aestheticestetic and poeticpoetică dimensionsdimensiuni of scienceştiinţă and mathematicsmatematică.
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dimensiunile estetice si poetice ale stiintei si matematicii.
02:47
And I wenta mers and put a little announcementanunt up on our siteteren,
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Am pus un mic anunt pe site-ul nostru,
02:50
askingcer for people to joina adera us in this enterpriseIntreprindere.
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rugand oamenii sa se alature noua in acest proiect.
02:52
To our surprisesurprinde, one of the first people who calleddenumit
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Spre surpriza noastra, unul din primii care au sunat
02:55
was the AndyAndy WarholWarhol MuseumMuzeul.
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a fost Muzeul Andy Warhol.
02:57
And they said they were havingavând an exhibitionexpoziţie
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Ziceau ca organizeaza o expozitie
02:59
about artists'artiştilor responseraspuns to globalglobal warmingîncălzire,
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despre raspunsul artistilor la incalzirea globala
03:01
and they'dle-ar like our coralcoral reefrecif to be partparte of it.
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si ca ar dori ca si reciful nostru de corali sa participe.
03:03
I laughedrâs and said, "Well we'vene-am only just starteda început it,
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Eu am ras si am zis: "Abia l-am inceput,
03:05
you can have a little bitpic of it."
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puteti sa aveti doar o parte din el.”
03:07
So in 2007 we had an exhibitionexpoziţie,
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Asa ca in 2007 am avut o expozitie,
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a smallmic exhibitionexpoziţie of this crochetcroşetat reefrecif.
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o mica expozitie a acestui recif crosetat.
03:12
And then some people in ChicagoChicago camea venit alongde-a lungul and they said,
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Apoi au venit cativa oameni din Chicago si au zis:
03:14
"In latetârziu 2007, the themetemă of the ChicagoChicago HumanitiesŞtiinţe umaniste FestivalFestivalul is
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“La sfarsit de 2007 tema Festivalului Umanitatii din Chicago este
03:19
globalglobal warmingîncălzire. And we'vene-am got this 3,000 square-footpătrat-picior galleryGalerie
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incalzirea globala. Si avem o galerie de 280 de metri patrati
03:22
and we want you to fillcompletati it with your reefrecif."
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pe care vrem sa o umpleti cu reciful dumneavoastra.”
03:25
And I, naivelynaiv by this stageetapă, said, "Oh, yes, sure."
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Iar eu, naiva pe atunci, am zis: “Oh, da. Sigur.”
03:28
Now I say "naivelynaiv" because actuallyde fapt
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Am spus „naiva” pentru ca, de fapt,
03:30
my professionprofesie is as a scienceştiinţă writerscriitor.
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profesia mea este de scriitor stiintific.
03:32
What I do is I writescrie bookscărți about the culturalcultural historyistorie of physicsfizică.
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Ceea ce fac eu este sa scriu carti despre istoria culturala a fizicii.
03:35
I've writtenscris bookscărți about the historyistorie of spacespaţiu,
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Am scris carti despre istoria spatiului,
03:37
the historyistorie of physicsfizică and religionreligie,
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istoria fizicii si religiei,
03:39
and I writescrie articlesarticole for people like the NewNoi YorkYork TimesOri and the L.A. TimesOri.
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si scriu articole pentru oameni in reviste ca “New York Times” si “L.A. Times”.
03:42
So I had no ideaidee what it meanta însemnat to fillcompletati a 3,000 square-footpătrat-picior galleryGalerie.
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Deci nu am avut nici o idee ce inseamna sa umpli o galerie de 280 de metri patrati.
03:46
So I said yes to this propositionpropoziție.
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Asa ca am zis da la aceasta propunere.
03:48
And I wenta mers home, and I told my sistersoră ChristineChristine.
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Am mers acasa si i-am spus si surorii mele Christine.
03:50
And she nearlyaproape had a fitpotrivi
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Si aproape ca a avut o criza,
03:52
because ChristineChristine is a professorProfesor at one of
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deoarece Christine este profesoara
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L.A.'s„s majormajor artartă collegescolegii, CalArtsAbsolvire,
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la unul din cele mai mari colegii de arta din L.A., CalArts,
03:57
and she knewștiut exactlyexact what it meanta însemnat to fillcompletati a 3,000 square-footpătrat-picior galleryGalerie.
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si stia exact ce inseamna sa umpli o galerie de 280 de metri patrati.
04:00
She thought I'd goneplecat off my headcap.
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A crezut ca am innebunit.
04:03
But she wenta mers into crochetcroşetat overdriveOverdrive.
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Dar a crosetat pana la epuizare.
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And to cuta taia a long storypoveste shortmic de statura, eightopt monthsluni latermai tarziu
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Pe scurt, opt luni mai tarziu,
04:07
we did fillcompletati the ChicagoChicago CulturalCulturale Center'sCentrului
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am umplut galeria Centrului cultural din Chicago
04:10
3,000 squarepătrat footpicior galleryGalerie.
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de 280 de metri patrati.
04:12
By this stageetapă the projectproiect had takenluate on
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Pana in acest moment proiectul avea
04:14
a viralvirale dimensiondimensiune of its ownpropriu,
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o dimensiune virala proprie
04:16
whichcare got completelycomplet beyonddincolo us.
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care ne-a depasit.
04:18
The people in ChicagoChicago decideda decis
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Oamenii din Chicago au decis ca,
04:20
that as well as exhibitingexpozante our reefsRecife, what they wanted to do
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odata cu expunerea recifului nostru,
04:23
was have the locallocal people there make a reefrecif.
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sa convinga localnicii sa faca si ei un recif.
04:25
So we wenta mers and taughtînvățat the techniquestehnici. We did workshopsateliere de lucru and lecturesprelegeri.
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Asa ca am mers si i-am invat tehnicile. Am organizat ateliere si cursuri.
04:28
And the people in ChicagoChicago madefăcut a reefrecif of theiral lor ownpropriu.
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Iar oamenii din Chicago au facut reciful lor propriu.
04:31
And it was exhibitedexpuse alongsidealături de oursa noastra.
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Si a fost expus impreuna cu al nostru.
04:33
There were hundredssute of people involvedimplicat in that.
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Sute de oameni au fost implicati.
04:35
We got inviteda invitat to do the wholeîntreg thing
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Am fost invitati sa facem acelasi lucru
04:38
in NewNoi YorkYork, and in LondonLondra,
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in New York si in Londra,
04:40
and in LosLos AngelesAngeles.
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si in Los Angeles.
04:42
In eachfiecare of these citiesorase, the locallocal citizenscetățeni,
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In fiecare din aceste orase,
04:44
hundredssute and hundredssute of them, have madefăcut a reefrecif.
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sute si sute de localnici au facut recife.
04:46
And more and more people get involvedimplicat in this,
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Din ce in ce mai multi oameni se implica,
04:49
mostcel mai of whompe cine we'vene-am never metîntâlnit.
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iar majoritatea lor nici nu-i cunoastem.
04:51
So the wholeîntreg thing has sortfel of morphedmorphed
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Deci totul s-a transformat
04:53
into this organicorganic, ever-evolvingîn continuă evoluţie creaturecreatură,
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intr-o creatura organica in evolutie permanenta,
04:55
that's actuallyde fapt goneplecat way beyonddincolo ChristineChristine and I.
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care de fapt ne-a depasit pe mine si Christine.
04:59
Now some of you are sittingședință here thinkinggândire,
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Multi dintre voi stati si va intrebati:
05:02
"What planetplanetă are these people on?
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"Pe ce planeta se cred oamenii astia?
05:04
Why on earthPământ are you crochetingcroşetare a reefrecif?
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De ce anume sa crosetati un recif?
05:07
WoolennessWoolenness and wetnessumezeala aren'tnu sunt exactlyexact
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Lanaria si umezeala sunt doua concepte
05:09
two conceptsconcepte that go togetherîmpreună.
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care nu prea se potrivesc.
05:11
Why not chiseldalta a coralcoral reefrecif out of marblemarmura?
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De ce sa nu sculptezi un recif de corali in marmura?
05:13
CastDistributie it in bronzebronz."
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Toarna-l in bronz.”
05:15
But it turnstransformă out there is a very good reasonmotiv
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Insa avem un motiv foarte bine intemeiat
05:17
why we are crochetingcroşetare it
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pentru care il crosetam,
05:19
because manymulți organismsorganisme in coralcoral reefsRecife
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deoarece multe organisme din recifele de corali
05:21
have a very particularspecial kinddrăguț of structurestructura.
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au o structura aparte.
05:23
The frillyfrilly crenulatedcrenulated formsformulare that you see
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Formele incretite si ondulate care le vedeti
05:25
in coralscoralii, and kelpskelps, and spongesbureţi and nudibranchsNudibranhiate,
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in corali, vareci, bureti de mare si echinoderme,
05:28
is a formformă of geometrygeometrie knowncunoscut as hyperbolichiperbolică geometrygeometrie.
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sunt o forma geometrica cunoscuta ca geometrie hiperbolica.
05:31
And the only way that mathematiciansmatematicieni know
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Singura metoda prin care matematicienii stiu
05:34
how to modelmodel this structurestructura
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cum sa modeleze aceasta structura
05:36
is with crochetcroşetat. It happensse întâmplă to be a factfapt.
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este prin crosetat. Se intampla sa fie adevarat.
05:38
It's almostaproape impossibleimposibil to modelmodel this structurestructura any other way,
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Esta aproape imposibil sa modelezi aceasta structura in alt mod.
05:41
and it's almostaproape impossibleimposibil to do it on computerscalculatoare.
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Si este aproape imposibil sa o realizezi pe calculator.
05:44
So what is this hyperbolichiperbolică geometrygeometrie
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Deci ce este aceasta geometrie hiperbolica
05:46
that coralscoralii and seamare slugsLimacși embodyîntruchipa?
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pe care o incorporeaza coralii si echinodermele?
05:49
The nextUrmător → fewpuțini minutesminute is, we're all going to get raisedridicat up
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In urmatoarele minute toti vom cobori
05:52
to the levelnivel of a seamare slugmelc.
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la nivelul unei echinoderme.
05:54
(LaughterRâs)
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(Rasete)
05:55
This sortfel of geometrygeometrie revolutionizeda revoluționat mathematicsmatematică
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Acest gen de geometrie a revolutionat matematica
05:58
when it was first discovereddescoperit in the 19thlea centurysecol.
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in secolul 19 cand a fost descoperita prima data.
06:01
But not untilpana cand 1997 did mathematiciansmatematicieni actuallyde fapt understanda intelege
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Insa abia in 1997 au inteles matematicienii, cu adevarat,
06:04
how they could modelmodel it.
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cum sa il modeleze.
06:06
In 1997 a mathematicianmatematician
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In 1997, o matematiciana
06:08
at CornellCornell, DainaIuliana TaiminaTaimina,
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de la Cornell, Diana Taimina,
06:10
madefăcut the discoverydescoperire that this structurestructura
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a descoperit ca acasta structura
06:12
could actuallyde fapt be doneTerminat in knittingtricotat and crochetcroşetat.
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ar putea fi reprodusa prin tricotare si crosetare.
06:14
The first one she did was knittingtricotat.
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Primul care l-a facut a fost tricotat.
06:16
But you get too manymulți stitchescusaturi on the needleac. So she quicklyrepede realizedrealizat
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Insa se aduna prea multe ochiuri pe ac. Asa ca a inteles repede
06:18
crochetcroşetat was the better thing.
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ca era mai bine sa croseteze.
06:20
But what she was doing was actuallyde fapt makingluare a modelmodel
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Dar ceea ce facea ea era un model
06:23
of a mathematicalmatematic structurestructura, that manymulți mathematiciansmatematicieni
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al unei structuri matematice despre care multi matematicieni
06:25
had thought it was actuallyde fapt impossibleimposibil to modelmodel.
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credeau ca este imposibil de modelat.
06:28
And indeedintr-adevar they thought that anything like this structurestructura
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Chiar credeau ca orice lucru care are aceasta structura
06:30
was impossibleimposibil perpe sese.
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este imposibil in sine.
06:32
Some of the bestCel mai bun mathematiciansmatematicieni spenta petrecut hundredssute of yearsani
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De-a lungul a sute de ani, unii dintre cei mai buni matematicieni
06:34
tryingîncercat to provedovedi that this structurestructura was impossibleimposibil.
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au incercat sa demonstreze ca aceasta structura este imposibila.
06:37
So what is this impossibleimposibil hyperbolichiperbolică structurestructura?
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Deci ce este aceasta structura hiperbolica imposibila?
06:40
Before hyperbolichiperbolică geometrygeometrie, mathematiciansmatematicieni knewștiut
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Inainte de geometria hiperbolica matematicienii stiau
06:42
about two kindstipuri of spacespaţiu:
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despre doua feluri de spatii:
06:44
EuclideanLui Euclid spacespaţiu, and sphericalsferic spacespaţiu.
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spatiu Euclidian si spatiu sferic.
06:47
And they have differentdiferit propertiesproprietăţi.
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Aveau proprietati diferite.
06:49
MathematiciansMatematicieni like to characterizecaracterizează things by beingfiind formalistformalist.
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Matematicienilor le place sa caracterizeze lucrurile intr-un mod formalist.
06:52
You all have a sensesens of what a flatapartament spacespaţiu is, EuclideanLui Euclid spacespaţiu is.
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Cu totii aveti o idee despre ce este o suprafata plana, un spatiu euclidian.
06:56
But mathematiciansmatematicieni formalizeformaliza this in a particularspecial way.
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Dar matematicienii formuleaza asta intr-un mod diferit.
06:59
And what they do is, they do it throughprin the conceptconcept
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Si ceea ce fac ei este sa se foloseasca de conceptul
07:01
of parallelparalel lineslinii.
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de linii paralele.
07:03
So here we have a linelinia and a pointpunct outsidein afara the linelinia.
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Deci aici avem o linie si un punct in afara ei.
07:06
And EuclidEuclid said, "How can I definedefini parallelparalel lineslinii?
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Euclid a zis: “Cum pot eu sa definesc liniile paralele?”
07:09
I askcere the questionîntrebare, how manymulți lineslinii can I drawa desena throughprin
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Eu pun intrebarea: “Cate linii pot sa trasez
07:12
the pointpunct but never meetîntâlni the originaloriginal linelinia?"
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prin acel punct fara sa se intalneasca cu linia initiala?”
07:14
And you all know the answerRăspuns. Does someonecineva want to shoutstriga it out?
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Si stiti cu totii raspunsul. Vrea cineva sa-l spuna cu voce tare?
07:17
One. Great. Okay.
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Una. Corect. Ok.
07:19
That's our definitiondefiniție of a parallelparalel linelinia.
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Asta este definitia noastra a liniei paralele.
07:21
It's a definitiondefiniție really of EuclideanLui Euclid spacespaţiu.
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Este chiar definitia spatiului euclidian.
07:24
But there is anothero alta possibilityposibilitate that you all know of:
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Insa mai exista o posibilitate despre care stiti cu totii --
07:26
sphericalsferic spacespaţiu.
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spatiul sferic.
07:28
Think of the surfacesuprafaţă of a spheresferă --
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Ganditi-va la suprafata unei sfere --
07:30
just like a beachplajă ballminge, the surfacesuprafaţă of the EarthPământ.
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ca o minge de plaja, ca suprafata Pamantului.
07:32
I have a straightdrept linelinia on my sphericalsferic surfacesuprafaţă.
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Am o linie dreapta pe suprafata sferica.
07:35
And I have a pointpunct outsidein afara the linelinia. How manymulți straightdrept lineslinii
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Si am un punct in afara liniei. Cate linii drepte
07:37
can I drawa desena throughprin the pointpunct
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pot sa trasez prin acel punct
07:39
but never meetîntâlni the originaloriginal linelinia?
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fara sa intersectez linia initiala?
07:41
What do we mean to talk about
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Ce inseamna sa vorbim despre
07:43
a straightdrept linelinia on a curvedcurbate surfacesuprafaţă?
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o linie dreapta pe o suprafata curbata?
07:46
Now mathematiciansmatematicieni have answeredrăspuns that questionîntrebare.
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Matematicienii au raspuns la aceasta intrebare.
07:49
They'veLe-am understoodînțeles there is a generalizedgeneralizate conceptconcept
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Au inteles ca este un concept general
07:51
of straightnessRectilinitate, it's calleddenumit a geodesicgeodezică.
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al liniaritatii. Se numeste geodezie.
07:53
And on the surfacesuprafaţă of a spheresferă,
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Pe suprafata unei sfere,
07:55
a straightdrept linelinia is the biggestCea mai mare possibleposibil circlecerc you can drawa desena.
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o linie dreapta este cel mai mare cerc posibil pe care il poti trasa.
07:58
So it's like the equatorecuator or the lineslinii of longitudeLongitudine.
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Deci este ca si ecuatorul sau liniile longitudinale.
08:02
So we askcere the questionîntrebare again,
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Deci intrebam din nou:
08:04
"How manymulți straightdrept lineslinii can I drawa desena throughprin the pointpunct,
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“Cate linii drepte pot fi trasate printr-un punct
08:06
but never meetîntâlni the originaloriginal linelinia?"
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fara sa intersectez linia initiala?”
08:08
Does someonecineva want to guessghici?
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Vrea cineva sa ghiceasca?
08:11
ZeroZero. Very good.
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Zero. Foarte bine!
08:13
Now mathematiciansmatematicieni thought that was the only alternativealternativă.
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Matematicienii au crezut ca asta este singura alternativa.
08:15
It's a bitpic suspicioussuspicios isn't it? There is two answersrăspunsuri to the questionîntrebare so fardeparte,
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E putin cam suspect, nu-i asa? Sunt deja doua raspunsuri la intrebare:
08:18
ZeroZero and one.
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zero si unu.
08:20
Two answersrăspunsuri? There mayMai possiblyeventual be a thirdal treilea alternativealternativă.
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Doua raspunsuri? S-ar putea sa mai fie si o a treia alternativa.
08:22
To a mathematicianmatematician if there are two answersrăspunsuri,
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Pentru un matematician, daca exista doua raspunsuri
08:24
and the first two are zerozero and one,
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iar primele doua sunt zero si unu,
08:26
there is anothero alta numbernumăr that immediatelyimediat suggestssugerează itselfîn sine
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inseamna ca mai exista inca un numar care se autopropune imediat
08:28
as the thirdal treilea alternativealternativă.
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ca a treia alternativa.
08:30
Does anyoneoricine want to guessghici what it is?
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Vrea cineva sa-l ghiceasca?
08:33
InfinityInfinity. You all got it right. ExactlyExact.
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Infinit. Ati inteles cu totii. Exact!
08:36
There is, there's a thirdal treilea alternativealternativă.
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Exista o a treia alternativa.
08:38
This is what it looksarată like.
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Asa arata.
08:40
There's a straightdrept linelinia, and there is an infiniteinfinit numbernumăr of lineslinii
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Este o linie dreapta si un numar infinit de linii
08:43
that go throughprin the pointpunct and never meetîntâlni the originaloriginal linelinia.
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care trec prin punct fara sa intalneasca linia initiala.
08:45
This is the drawingdesen.
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Acesta este desenul.
08:47
This nearlyaproape drovea condus mathematiciansmatematicieni bonkersbonkers
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Asta aproape ca i-a innebunit pe matematicieni,
08:49
because, like you, they're sittingședință there feelingsentiment bamboozledBamboozled.
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deoarece, ca si voi, sunt dezorientati,
08:52
ThinkingGândire, how can that be? You're cheatinginseala. The lineslinii are curvedcurbate.
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gandindu-se cum poate sa existe asa ceva? Este o inselaciune. Liniile sunt curbe.
08:55
But that's only because I'm projectingproiectând it ontope a
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Insa numai datorita faptului ca sunt proiectate
08:57
flatapartament surfacesuprafaţă.
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pe o suprafata plana.
08:59
MathematiciansMatematicieni for severalmai mulți hundredsută yearsani
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De sute de ani matematicienii
09:01
had to really strugglelupta with this.
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au trebuit sa se lupte cu asta.
09:03
How could they see this?
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Cum au putut sa vada asta?
09:05
What did it mean to actuallyde fapt have a physicalfizic modelmodel
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Ce inseamna sa ai un model fizic real
09:08
that lookedprivit like this?
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care sa arate asa?
09:10
It's a bitpic like this: imagineimagina that we'dne-am only ever encounteredîntâlnite EuclideanLui Euclid spacespaţiu.
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Este cam in felul urmator: imaginati-va ca pana acum am cunoscut doar spatiul euclidian.
09:13
Then our mathematiciansmatematicieni come alongde-a lungul
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Apoi apar matematicienii nostri
09:15
and said, "There's this thing calleddenumit a spheresferă,
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si spun: “Exista un lucru care se numeste sfera,
09:17
and the lineslinii come togetherîmpreună at the northNord and southsud polepol."
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ale carei linii se intalnesc la polul sud si nord."
09:19
But you don't know what a spheresferă looksarată like.
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Dar tu nu sti cum arata o sfera.
09:21
And someonecineva that comesvine alongde-a lungul and saysspune, "Look here'saici e a ballminge."
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Si vine cineva si zice: “Uite o minge!”
09:24
And you go, "AhAh! I can see it. I can feel it.
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Tu zici: “ Ah! O vad! Pot sa o simt!
09:26
I can touchatingere it. I can playa juca with it."
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Pot sa o ating! Pot sa ma joc cu ea!”
09:29
And that's exactlyexact what happeneds-a întâmplat
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Exact asta s-a intamplat
09:31
when DainaIuliana TaiminaTaimina
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in 1997 cand Daiana Taimina
09:33
in 1997, showeda arătat that you could crochetcroşetat modelsmodele
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a demonstrat ca se pot croseta modele
09:37
in hyperbolichiperbolică spacespaţiu.
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in spatiu hiperbolic.
09:39
Here is this diagramdiagramă in crochetnesscrochetness.
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Aici este o diagrama crosetata.
09:42
I've stitchedcusute Euclid'sLui Euclid parallelparalel postulatepostulatul on to the surfacesuprafaţă.
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Am cusut postulatul lui Euclid pe suprafata ei.
09:46
And the lineslinii look curvedcurbate.
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Liniile arata curbe.
09:48
But look, I can provedovedi to you that they're straightdrept
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Insa pot sa va demonstrez ca sunt drepte,
09:51
because I can take any one of these lineslinii,
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pentru ca pot sa iau oricare din aceste linii
09:53
and I can foldplia alongde-a lungul it.
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si pot sa pliez de-a lungul ei.
09:56
And it's a straightdrept linelinia.
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Este o linie dreapta.
09:58
So here, in woollână,
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Deci aici, in lana,
10:01
throughprin a domesticintern femininefeminin artartă,
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prin arta feminina domestica,
10:03
is the proofdovadă that the mostcel mai famouscelebru postulatepostulatul
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sta dovada ca cel mai faimos postulat
10:05
in mathematicsmatematică is wronggresit.
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din matematica este gresit.
10:08
(ApplauseAplauze)
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(Aplauze)
10:14
And you can stitchcusatura all sortsfelul of mathematicalmatematic
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Se pot coase tot felul de teoreme matemetice
10:16
theoremsteoreme ontope these surfacessuprafețe.
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pe aceste suprafete.
10:19
The discoverydescoperire of hyperbolichiperbolică spacespaţiu usheredinaugurat in the fieldcamp of mathematicsmatematică
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Descoperirea sptiului hiperbolic introduce domeniul matematic
10:22
that is calleddenumit non-Euclideannon-euclidiene geometrygeometrie.
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numit geometrie non-euclidiana.
10:24
And this is actuallyde fapt the fieldcamp of mathematicsmatematică
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Acesta este de fapt un domeniu al matematicii
10:26
that underliesstă la baza generalgeneral relativityrelativitate
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care sta la baza relativitatii generale
10:28
and is actuallyde fapt ultimatelyîn cele din urmă going to showspectacol us
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si care in final ne va arata
10:30
about the shapeformă of the universeunivers.
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forma universului.
10:32
So there is this directdirect linelinia
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Deci exista aceasta legatura directa
10:34
betweenîntre femininefeminin handicraftArtizanat,
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intre mestesugul feminin,
10:36
EuclidEuclid and generalgeneral relativityrelativitate.
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Euclid si relativitatea generala.
10:39
Now, I said that mathematiciansmatematicieni thought that this was impossibleimposibil.
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Deci, am zis ca matematicienii au crezut ca este imposibil asa ceva.
10:42
Here'sAici este two creaturescreaturi who'vecare au never heardauzit of Euclid'sLui Euclid parallelparalel postulatepostulatul --
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Aici sunt doua fiinte care n-au auzit niciodata despre axioma paralelelor lui Euclid --
10:46
didn't know it was impossibleimposibil to violateviola,
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nu stiau ca este imposibil de contrazis
10:48
and they're simplypur şi simplu gettingobtinerea on with it.
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si pur si simplu supravietuiesc cu ea.
10:50
They'veLe-am been doing it for hundredssute of millionsmilioane of yearsani.
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Fac asta de sute de milione de ani.
10:54
I onceo singura data askedîntrebă the mathematiciansmatematicieni why it was
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Odata i-am intrebat pe metematicieni
10:56
that mathematiciansmatematicieni thought this structurestructura was impossibleimposibil
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de ce cred ei ca aceasta structura este imposibila
10:59
when seamare slugsLimacși have been doing it sincede cand the SilurianSilurianului agevârstă.
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cand echinodermele o au inca din era siluriana.
11:02
TheirLor answerRăspuns was interestinginteresant.
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Raspunsul lor a fost interesant.
11:04
They said, "Well I guessghici there aren'tnu sunt that manymulți mathematiciansmatematicieni
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Au zis: “Pai, banuiesc ca nu foarte multi matematicieni
11:06
sittingședință around looking at seamare slugsLimacși."
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stau si se uita la echinoderme."
11:08
And that's trueAdevărat. But it alsode asemenea goesmerge deeperMai adânc than that.
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E adevarat. Insa este mai grav de atat.
11:11
It alsode asemenea saysspune a wholeîntreg lot of things
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Spune foarte multe lucruri
11:13
about what mathematiciansmatematicieni thought mathematicsmatematică was,
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despre ceea ce credeau matematicienii ca este matematica.
11:16
what they thought it could and couldn'tnu a putut do,
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Ce credeau ca poate sau nu poate sa faca ea.
11:18
what they thought it could and couldn'tnu a putut representreprezinta.
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Ceea ce credeau ca poate sau nu poate sa reprezinte ea.
11:20
Even mathematiciansmatematicieni, who in some sensesens
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Chiar si matematicienii care, intr-un anumit mod,
11:22
are the freestFreest of all thinkersgânditori,
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sunt cei mai liberi cugetatori,
11:24
literallyliteralmente couldn'tnu a putut see
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efectiv nu au putut sa vada,
11:26
not only the seamare slugsLimacși around them,
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nu neaparat echinodermele de langa ei,
11:28
but the lettucesalata verde on theiral lor platefarfurie --
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dar nici macar salata din farfuria lor,
11:30
because lettucessalată, and all those curlycret vegetableslegume,
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deoarece salata si toate acele legume incretite,
11:32
they alsode asemenea are embodimentsîntrupare of hyperbolichiperbolică geometrygeometrie.
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sunt si ele intruchiparea geometriei hiperbolice.
11:36
And so in some sensesens they literallyliteralmente,
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Deci intr-un anumit mod
11:39
they had suchastfel de a symbolicsimbolice viewvedere of mathematicsmatematică,
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ei au avut o viziune simbolica asupra matematicii --
11:41
they couldn'tnu a putut actuallyde fapt see what was going on
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practic nu vedeau ceea ce se intampla
11:44
on the lettucesalata verde in frontfață of them.
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cu salata din fata lor.
11:47
It turnstransformă out that the naturalnatural worldlume is fulldeplin of hyperbolichiperbolică wondersminuni.
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Se pare ca lumea naturala este plina de minuni hiperbolice.
11:51
And so, too, we'vene-am discovereddescoperit
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De asemenea am descoperit
11:53
that there is an infiniteinfinit taxonomytaxonomie
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ca exista o taxonomie infinita
11:55
of crochetcroşetat hyperbolichiperbolică creaturescreaturi.
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a creaturilor hiperbolice crosetate.
11:57
We starteda început out, ChrissyGelu and I and our contributorscontribuitori,
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Eu, Chrissy si colaboratorii nostri am inceput
12:00
doing the simplesimplu mathematicallymatematic perfectperfect modelsmodele.
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cu modele matematice simple si perfecte.
12:02
But we foundgăsite that when we deviateddeviat from the specificspecific
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Insa am aflat ca, in momentul in care deviem de la forma specifica
12:06
setnesssetness of the mathematicalmatematic codecod
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a codului matematic
12:09
that underliesstă la baza it -- the simplesimplu algorithmAlgoritmul
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care sta la baza acestui simplu algoritm,
12:11
crochetcroşetat threeTrei, increasecrește one --
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adica crosetezi trei si mai adaugi unu.
12:13
when we deviateddeviat from that and madefăcut embellishmentsembellishments to the codecod,
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Cand am deviat de la asta si am infrumutesat codul,
12:16
the modelsmodele immediatelyimediat starteda început to look more naturalnatural.
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modelele au inceput imediat sa para mai naturale.
12:20
And all of our contributorscontribuitori, who are an amazinguimitor
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Toti contribuitorii nostrii care sunt
12:22
collectionColectie of people around the worldlume,
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o colectie de oameni minunati din toata lumea,
12:24
do theiral lor ownpropriu embellishmentsembellishments.
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vin cu imbunatatirile lor personale.
12:26
As it were, we have this ever-evolvingîn continuă evoluţie,
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Si avem acest copac al vietii, ca sa zicem asa,
12:28
crochetcroşetat taxonomictaxonomice treecopac of life.
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al taxonomiei in crosetaj care evolueaza permanent.
12:30
Just as the morphologymorfologie
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Asa cum morfologia
12:32
and the complexitycomplexitate of life on earthPământ is never endingfinal,
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si complexitatea vietii pe pamant este nelimitata,
12:34
little embellishmentsembellishments and complexificationscomplexifications
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si niste modificari si complexificari
12:37
in the DNAADN-UL codecod
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in codul de ADN
12:39
leadconduce to newnou things like giraffesgirafe, or orchidsorhidee --
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duc la lucruri noi, cum ar fi girafele si orhideele,
12:42
so too, do little embellishmentsembellishments in the crochetcroşetat codecod
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asa si niste mici imbunatatiri in codul de crosetare
12:45
leadconduce to newnou and wondrousminunate creaturescreaturi
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duc la fiinte noi si minunate
12:48
in the evolutionaryevolutiv treecopac of crochetcroşetat life.
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in evolutia copacului vietii in crosetaj.
12:51
So this projectproiect really has
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Deci acest proiect chiar are
12:53
takenluate on this innerinterior organicorganic life of its ownpropriu.
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o viata organica proprie.
12:56
There is the totalitytotalitate of all the people who have come to it.
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Este totalul oamenilor care au aderat la el,
12:59
And theiral lor individualindividual visionsviziuni,
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cu viziunile lor proprii,
13:01
and theiral lor engagementlogodnă with this mathematicalmatematic modemod.
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si propria lor abordare a codului matematic.
13:04
We have these technologiestehnologii. We use them.
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Avem aceste tehnologii. Le folosim.
13:06
But why? What's at stakemiză here? What does it mattermaterie?
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Dar de ce? Ce este in joc? De ce conteaza?
13:09
For ChrissyGelu and I, one of the things that's importantimportant here
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Unul din lucrurile care sunt importante pentru mine si Chrissy aici
13:12
is that these things suggestsugera
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este ca aceste lucruri sugereaza
13:14
the importanceimportanţă and valuevaloare of embodiedîncorporate knowledgecunoştinţe.
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importanta si valoarea cunoastintelor tangibile.
13:17
We livetrăi in a societysocietate
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Traim intr-o societate
13:19
that completelycomplet tendsa tinde to valorizevalorificarea
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care are tendinta sa valorifice
13:21
symbolicsimbolice formsformulare of representationreprezentare --
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forme simbolice de reprezentare --
13:23
algebraicalgebrice representationsreprezentări,
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reprezentari algebrice,
13:25
equationsecuaţiile, codescoduri.
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ecuatii, coduri.
13:27
We livetrăi in a societysocietate that's obsessedobsedat
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Traim intr-o societate obsedata
13:29
with presentingprezentarea informationinformație in this way,
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de prezentarea informatiei in acest mod,
13:31
teachingînvățătură informationinformație in this way.
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de invatarea informatiei in acest mod.
13:34
But throughprin this sortfel of modalitymodalitate,
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Insa prin aceasta modalitate,
13:37
crochetcroşetat, other plasticplastic formsformulare of playa juca --
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crosetaj, alte modalitati plastice de joaca,
13:41
people can be engagedangajat with the mostcel mai abstractabstract,
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oamenii se pot relationa cu cele mai abstracte,
13:44
high-poweredde mare putere, theoreticalteoretic ideasidei,
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puternice, idei teoretice --
13:46
the kindstipuri of ideasidei that normallyîn mod normal you have to go
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genul de idei pentru care deobicei trebuie sa mergi
13:48
to universityuniversitate departmentsdepartamente to studystudiu in highersuperior mathematicsmatematică,
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la universitate sa studiezi matematici superioare,
13:51
whichcare is where I first learnedînvățat about hyperbolichiperbolică spacespaţiu.
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loc in care am invatat si eu pentru prima data despre spatiul hiperbolic.
13:54
But you can do it throughprin playingjoc with materialmaterial objectsobiecte.
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Insa poti sa faci asta jucandu-te cu obiecte materiale.
13:58
One of the waysmoduri that we'vene-am come to think about this
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Unul din modurile in care am ajuns sa ne gandim la asta
14:00
is that what we're tryingîncercat to do with the InstituteInstitutul for FiguringImaginind
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este ceea ce incercam sa facem prin "Institutul de Imaginatie"
14:03
and projectsproiecte like this, we're tryingîncercat to have
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si proiecte ca si acesta, incercam sa facem
14:05
kindergartengradinita for grown-upsadulti.
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o gradinita pentru adulti.
14:07
And kindergartengradinita was actuallyde fapt a very formalizedformalizat
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Gradinita a fost, de fapt,
14:09
systemsistem of educationeducaţie,
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un sistem educational puternic formalizat,
14:11
establishedstabilit by a man namednumit FriedrichFriedrich FroebelFroebel,
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infiintat de Friederich Froebel,
14:13
who was a crystallographerCristalograful in the 19thlea centurysecol.
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cristalograf din secolul al 19-lea.
14:15
He believeda crezut that the crystalcristal was the modelmodel
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El credea ca modelul
14:17
for all kindstipuri of representationreprezentare.
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pentru tot felul de reprezentari este cristalul.
14:19
He developeddezvoltat a radicalradical alternativealternativă systemsistem
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A dezvoltat un sistem alternativ radical
14:22
of engagingcaptivant the smallestcel mai mic childrencopii
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pentru a implica in idei abstracte
14:24
with the mostcel mai abstractabstract ideasidei
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copii la varste foarte mici,
14:26
throughprin physicalfizic formsformulare of playa juca.
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prin forme fizice de joaca.
14:28
And he is worthyvrednic of an entireîntreg talk on his ownpropriu right.
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Merita un intreg discurs doar pentru asta.
14:30
The valuevaloare of educationeducaţie
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Valoarea educatiei
14:32
is something that FroebelFroebel championedpromovat,
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este ceea ce Froebel a sustinut
14:35
throughprin plasticplastic modesmoduri of playa juca.
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prin moduri plastice de joaca.
14:37
We livetrăi in a societysocietate now
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Acum traim intr-o societate
14:39
where we have lots of think tanksrezervoare,
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in care avem multe organizatii de cercetare,
14:41
where great mindsminți go to think about the worldlume.
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unde mintile stralucite se intalnesc spre a discuta despre lume.
14:44
They writescrie these great symbolicsimbolice treatisestratate
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Scriu minunate tratate simbolice
14:46
calleddenumit bookscărți, and papershârtii,
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numite carti si lucrari
14:48
and op-edop-ed articlesarticole.
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si articole de opinie independente.
14:50
We want to proposepropune, ChrissyGelu and I,
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Eu si Chrissy vrem sa propunem,
14:52
throughprin The InstituteInstitutul for FiguringImaginind, anothero alta alternativealternativă way of doing things,
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prin intermediul „Institutului de Imaginatie”, o alta modalitate de a face lucrurile,
14:55
whichcare is the playa juca tankrezervor.
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si anume: organizatia de joaca.
14:58
And the playa juca tankrezervor, like the think tankrezervor,
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Organizatia de joaca, la fel ca si cea de cercetare,
15:00
is a placeloc where people can go
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este un loc unde oamenii se aduna
15:02
and engageangaja with great ideasidei.
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pentru a se implica in idei marete.
15:04
But what we want to proposepropune,
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Insa ceea ce vrem noi sa propunem
15:06
is that the highestcel mai inalt levelsniveluri of abstractionabstracție,
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este ca cele mai inalte nivele ale abstractiei,
15:08
things like mathematicsmatematică, computingtehnica de calcul, logiclogică, etcetc. --
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cum ar fi matematica, informatica, logica, etc. --
15:11
all of this can be engagedangajat with,
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toate acestea sa poata fi accesate
15:13
not just throughprin purelypur cerebralcerebrală algebraicalgebrice
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nu doar prin algebra cerebrala,
15:15
symbolicsimbolice methodsmetode,
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metode simbolice,
15:17
but by literallyliteralmente, physicallyfizic playingjoc with ideasidei.
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ci si prin joaca fizica cu idei, la propriu.
15:21
Thank you very much.
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Va multumesc foarte mult.
15:23
(ApplauseAplauze)
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(Aplauze)
Translated by Anamaria Muresan
Reviewed by Laszlo Kereszturi

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ABOUT THE SPEAKER
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.

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.

More profile about the speaker
Margaret Wertheim | Speaker | TED.com