I'm here today, as June said, to talk about a project that my twin sister and I have been doing for the past three and half years. We're crocheting a coral reef. And it's a project that we've actually been now joined by hundreds of people around the world, who are doing it with us. Indeed thousands of people have actually been involved in this project, in many of its different aspects. It's a project that now reaches across three continents, and its roots go into the fields of mathematics, marine biology, feminine handicraft and environmental activism. It's true. It's also a project that in a very beautiful way, the development of this has actually paralleled the evolution of life on earth, which is a particularly lovely thing to be saying right here in February 2009 -- which, as one of our previous speakers told us, is the 200th anniversary of the birth of Charles Darwin.
Ma aflu astazi aici, cum a spus si June, pentru a vorbi despre un proiect la care eu si sora mea geamana lucram de trei ani si jumatate. Crosetam un recif de corali. Este un proiect la care acum ni s-au alaturat sute de oameni din toata lumea si fac asta impreuna cu noi. Intr-adevar, mii de oameni au fost implicati in acest proiect in multe din aspectele acestuia. Este un proiect care acum se intinde pe trei continente. Originile lui isi au radacinile in domeniul matematicii, biologiei marine, artizanatului feminin si activismului in mediul inconjurator. Este adevarat. Este de asemenea un proiect a carui dezvoltare minunata a dus de fapt la un paralelism al evolutiei vietii pe pamant, ceea ce este un lucru foarte frumos de spus chiar aici in februarie 2009 -- avand in vedere ca, dupa cum ne spunea unul din prezentatorii anteriori, este a 200-a aniversare de la nasterea lui Charles Darwin.
All of this I'm going to get to in the next 18 minutes, I hope. But let me first begin by showing you some pictures of what this thing looks like. Just to give you an idea of scale, that installation there is about six feet across, and the tallest models are about two or three feet high. This is some more images of it. That one on the right is about five feet high. The work involves hundreds of different crochet models. And indeed there are now thousands and thousands of models that people have contributed all over the world as part of this. The totality of this project involves tens of thousands of hours of human labor -- 99 percent of it done by women. On the right hand side, that bit there is part of an installation that is about 12 feet long.
Sper ca in urmatoarele 18 minute sa patrund in toate acestea. Dar lasati-ma sa incep prin a va arata cateva imagini despre cum arata acest lucru. Ca sa va dau o idee despre marime, aceasta instalatie are in jur de 2 metri lungime. Cele mai inalte modele au cam un metru inaltime. Aici sunt mai multe imagini. Cel din dreapta este in jur de 1.5 metri inaltime. Munca presupune sute de modele diferite de crosetat. Si intr-adevar acum sunt mii si mii de modele cu care au contribuit oamenii din toata lumea la acesta. In total, acest proiect presupune zeci de mii de ore de munca umana -- 99% facuta de femei. Bucatica din partea dreapta face parte dintr-o instalatie care are in jur de 4 metri lungime.
My sister and I started this project in 2005 because in that year, at least in the science press, there was a lot of talk about global warming, and the effect that global warming was having on coral reefs. Corals are very delicate organisms, and they are devastated by any rise in sea temperatures. It causes these vast bleaching events that are the first signs of corals of being sick. And if the bleaching doesn't go away -- if the temperatures don't go down -- reefs start to die. A great deal of this has been happening in the Great Barrier Reef, particularly in coral reefs all over the world. This is our invocation in crochet of a bleached reef.
Eu si sora mea am inceput acest proiect in 2005 deoarece in acel an se vorbea foarte mult, cel putin in presa stiintifica, despre incalzirea globala si despre efectul pe care incalzirea globala il avea asupra recifelor de corali. Coralii sunt organisme foarte delicate. Si sunt devastati de orice ridicare de temperatura a apei marii. Cauzeaza imense fenomene de albire care sunt primele semne de imbolnavire ale coralilor. Iar daca albirea nu trece, daca temperaturile nu scad, recifele incep sa moara. Acest fenomen se intampla in Marea Bariera de Corali, respectiv in recifele de corali din toata lumea. Aceasta este imitatia noastra crosetata a unui recif de corali albit.
We have a new organization together called The Institute for Figuring, which is a little organization we started to promote, to do projects about the aesthetic and poetic dimensions of science and mathematics. And I went and put a little announcement up on our site, asking for people to join us in this enterprise. To our surprise, one of the first people who called was the Andy Warhol Museum. And they said they were having an exhibition about artists' response to global warming, and they'd like our coral reef to be part of it. I laughed and said, "Well we've only just started it, you can have a little bit of it." So in 2007 we had an exhibition, a small exhibition of this crochet reef. And then some people in Chicago came along and they said, "In late 2007, the theme of the Chicago Humanities Festival is global warming. And we've got this 3,000 square-foot gallery and we want you to fill it with your reef." And I, naively by this stage, said, "Oh, yes, sure." Now I say "naively" because actually my profession is as a science writer. What I do is I write books about the cultural history of physics. I've written books about the history of space, the history of physics and religion, and I write articles for people like the New York Times and the L.A. Times. So I had no idea what it meant to fill a 3,000 square-foot gallery. So I said yes to this proposition. And I went home, and I told my sister Christine. And she nearly had a fit because Christine is a professor at one of L.A.'s major art colleges, CalArts, and she knew exactly what it meant to fill a 3,000 square-foot gallery. She thought I'd gone off my head. But she went into crochet overdrive. And to cut a long story short, eight months later we did fill the Chicago Cultural Center's 3,000 square foot gallery.
Avem impreuna o noua organizatie numita „Institutul de Imaginatie”, o mica organizatie pe care am inceput-o ca sa promovam, sa realizam proiecte despre dimensiunile estetice si poetice ale stiintei si matematicii. Am pus un mic anunt pe site-ul nostru, rugand oamenii sa se alature noua in acest proiect. Spre surpriza noastra, unul din primii care au sunat a fost Muzeul Andy Warhol. Ziceau ca organizeaza o expozitie despre raspunsul artistilor la incalzirea globala si ca ar dori ca si reciful nostru de corali sa participe. Eu am ras si am zis: "Abia l-am inceput, puteti sa aveti doar o parte din el.” Asa ca in 2007 am avut o expozitie, o mica expozitie a acestui recif crosetat. Apoi au venit cativa oameni din Chicago si au zis: “La sfarsit de 2007 tema Festivalului Umanitatii din Chicago este incalzirea globala. Si avem o galerie de 280 de metri patrati pe care vrem sa o umpleti cu reciful dumneavoastra.” Iar eu, naiva pe atunci, am zis: “Oh, da. Sigur.” Am spus „naiva” pentru ca, de fapt, profesia mea este de scriitor stiintific. Ceea ce fac eu este sa scriu carti despre istoria culturala a fizicii. Am scris carti despre istoria spatiului, istoria fizicii si religiei, si scriu articole pentru oameni in reviste ca “New York Times” si “L.A. Times”. Deci nu am avut nici o idee ce inseamna sa umpli o galerie de 280 de metri patrati. Asa ca am zis da la aceasta propunere. Am mers acasa si i-am spus si surorii mele Christine. Si aproape ca a avut o criza, deoarece Christine este profesoara la unul din cele mai mari colegii de arta din L.A., CalArts, si stia exact ce inseamna sa umpli o galerie de 280 de metri patrati. A crezut ca am innebunit. Dar a crosetat pana la epuizare. Pe scurt, opt luni mai tarziu, am umplut galeria Centrului cultural din Chicago de 280 de metri patrati.
By this stage the project had taken on a viral dimension of its own, which got completely beyond us. The people in Chicago decided that as well as exhibiting our reefs, what they wanted to do was have the local people there make a reef. So we went and taught the techniques. We did workshops and lectures. And the people in Chicago made a reef of their own. And it was exhibited alongside ours. There were hundreds of people involved in that. We got invited to do the whole thing in New York, and in London, and in Los Angeles. In each of these cities, the local citizens, hundreds and hundreds of them, have made a reef. And more and more people get involved in this, most of whom we've never met. So the whole thing has sort of morphed into this organic, ever-evolving creature, that's actually gone way beyond Christine and I.
Pana in acest moment proiectul avea o dimensiune virala proprie care ne-a depasit. Oamenii din Chicago au decis ca, odata cu expunerea recifului nostru, sa convinga localnicii sa faca si ei un recif. Asa ca am mers si i-am invat tehnicile. Am organizat ateliere si cursuri. Iar oamenii din Chicago au facut reciful lor propriu. Si a fost expus impreuna cu al nostru. Sute de oameni au fost implicati. Am fost invitati sa facem acelasi lucru in New York si in Londra, si in Los Angeles. In fiecare din aceste orase, sute si sute de localnici au facut recife. Din ce in ce mai multi oameni se implica, iar majoritatea lor nici nu-i cunoastem. Deci totul s-a transformat intr-o creatura organica in evolutie permanenta, care de fapt ne-a depasit pe mine si Christine.
Now some of you are sitting here thinking, "What planet are these people on? Why on earth are you crocheting a reef? Woolenness and wetness aren't exactly two concepts that go together. Why not chisel a coral reef out of marble? Cast it in bronze." But it turns out there is a very good reason why we are crocheting it because many organisms in coral reefs have a very particular kind of structure. The frilly crenulated forms that you see in corals, and kelps, and sponges and nudibranchs, is a form of geometry known as hyperbolic geometry. And the only way that mathematicians know how to model this structure is with crochet. It happens to be a fact. It's almost impossible to model this structure any other way, and it's almost impossible to do it on computers. So what is this hyperbolic geometry that corals and sea slugs embody?
Multi dintre voi stati si va intrebati: "Pe ce planeta se cred oamenii astia? De ce anume sa crosetati un recif? Lanaria si umezeala sunt doua concepte care nu prea se potrivesc. De ce sa nu sculptezi un recif de corali in marmura? Toarna-l in bronz.” Insa avem un motiv foarte bine intemeiat pentru care il crosetam, deoarece multe organisme din recifele de corali au o structura aparte. Formele incretite si ondulate care le vedeti in corali, vareci, bureti de mare si echinoderme, sunt o forma geometrica cunoscuta ca geometrie hiperbolica. Singura metoda prin care matematicienii stiu cum sa modeleze aceasta structura este prin crosetat. Se intampla sa fie adevarat. Esta aproape imposibil sa modelezi aceasta structura in alt mod. Si este aproape imposibil sa o realizezi pe calculator. Deci ce este aceasta geometrie hiperbolica pe care o incorporeaza coralii si echinodermele?
The next few minutes is, we're all going to get raised up to the level of a sea slug. (Laughter) This sort of geometry revolutionized mathematics when it was first discovered in the 19th century. But not until 1997 did mathematicians actually understand how they could model it. In 1997 a mathematician at Cornell, Daina Taimina, made the discovery that this structure could actually be done in knitting and crochet. The first one she did was knitting. But you get too many stitches on the needle. So she quickly realized crochet was the better thing. But what she was doing was actually making a model of a mathematical structure, that many mathematicians had thought it was actually impossible to model. And indeed they thought that anything like this structure was impossible per se. Some of the best mathematicians spent hundreds of years trying to prove that this structure was impossible.
In urmatoarele minute toti vom cobori la nivelul unei echinoderme. (Rasete) Acest gen de geometrie a revolutionat matematica in secolul 19 cand a fost descoperita prima data. Insa abia in 1997 au inteles matematicienii, cu adevarat, cum sa il modeleze. In 1997, o matematiciana de la Cornell, Diana Taimina, a descoperit ca acasta structura ar putea fi reprodusa prin tricotare si crosetare. Primul care l-a facut a fost tricotat. Insa se aduna prea multe ochiuri pe ac. Asa ca a inteles repede ca era mai bine sa croseteze. Dar ceea ce facea ea era un model al unei structuri matematice despre care multi matematicieni credeau ca este imposibil de modelat. Chiar credeau ca orice lucru care are aceasta structura este imposibil in sine. De-a lungul a sute de ani, unii dintre cei mai buni matematicieni au incercat sa demonstreze ca aceasta structura este imposibila.
So what is this impossible hyperbolic structure? Before hyperbolic geometry, mathematicians knew about two kinds of space: Euclidean space, and spherical space. And they have different properties. Mathematicians like to characterize things by being formalist. You all have a sense of what a flat space is, Euclidean space is. But mathematicians formalize this in a particular way. And what they do is, they do it through the concept of parallel lines. So here we have a line and a point outside the line. And Euclid said, "How can I define parallel lines? I ask the question, how many lines can I draw through the point but never meet the original line?" And you all know the answer. Does someone want to shout it out? One. Great. Okay. That's our definition of a parallel line. It's a definition really of Euclidean space.
Deci ce este aceasta structura hiperbolica imposibila? Inainte de geometria hiperbolica matematicienii stiau despre doua feluri de spatii: spatiu Euclidian si spatiu sferic. Aveau proprietati diferite. Matematicienilor le place sa caracterizeze lucrurile intr-un mod formalist. Cu totii aveti o idee despre ce este o suprafata plana, un spatiu euclidian. Dar matematicienii formuleaza asta intr-un mod diferit. Si ceea ce fac ei este sa se foloseasca de conceptul de linii paralele. Deci aici avem o linie si un punct in afara ei. Euclid a zis: “Cum pot eu sa definesc liniile paralele?” Eu pun intrebarea: “Cate linii pot sa trasez prin acel punct fara sa se intalneasca cu linia initiala?” Si stiti cu totii raspunsul. Vrea cineva sa-l spuna cu voce tare? Una. Corect. Ok. Asta este definitia noastra a liniei paralele. Este chiar definitia spatiului euclidian.
But there is another possibility that you all know of: spherical space. Think of the surface of a sphere -- just like a beach ball, the surface of the Earth. I have a straight line on my spherical surface. And I have a point outside the line. How many straight lines can I draw through the point but never meet the original line? What do we mean to talk about a straight line on a curved surface? Now mathematicians have answered that question. They've understood there is a generalized concept of straightness, it's called a geodesic. And on the surface of a sphere, a straight line is the biggest possible circle you can draw. So it's like the equator or the lines of longitude. So we ask the question again, "How many straight lines can I draw through the point, but never meet the original line?" Does someone want to guess? Zero. Very good.
Insa mai exista o posibilitate despre care stiti cu totii -- spatiul sferic. Ganditi-va la suprafata unei sfere -- ca o minge de plaja, ca suprafata Pamantului. Am o linie dreapta pe suprafata sferica. Si am un punct in afara liniei. Cate linii drepte pot sa trasez prin acel punct fara sa intersectez linia initiala? Ce inseamna sa vorbim despre o linie dreapta pe o suprafata curbata? Matematicienii au raspuns la aceasta intrebare. Au inteles ca este un concept general al liniaritatii. Se numeste geodezie. Pe suprafata unei sfere, o linie dreapta este cel mai mare cerc posibil pe care il poti trasa. Deci este ca si ecuatorul sau liniile longitudinale. Deci intrebam din nou: “Cate linii drepte pot fi trasate printr-un punct fara sa intersectez linia initiala?” Vrea cineva sa ghiceasca? Zero. Foarte bine!
Now mathematicians thought that was the only alternative. It's a bit suspicious isn't it? There is two answers to the question so far, Zero and one. Two answers? There may possibly be a third alternative. To a mathematician if there are two answers, and the first two are zero and one, there is another number that immediately suggests itself as the third alternative. Does anyone want to guess what it is? Infinity. You all got it right. Exactly. There is, there's a third alternative. This is what it looks like. There's a straight line, and there is an infinite number of lines that go through the point and never meet the original line. This is the drawing. This nearly drove mathematicians bonkers because, like you, they're sitting there feeling bamboozled. Thinking, how can that be? You're cheating. The lines are curved. But that's only because I'm projecting it onto a flat surface. Mathematicians for several hundred years had to really struggle with this. How could they see this? What did it mean to actually have a physical model that looked like this?
Matematicienii au crezut ca asta este singura alternativa. E putin cam suspect, nu-i asa? Sunt deja doua raspunsuri la intrebare: zero si unu. Doua raspunsuri? S-ar putea sa mai fie si o a treia alternativa. Pentru un matematician, daca exista doua raspunsuri iar primele doua sunt zero si unu, inseamna ca mai exista inca un numar care se autopropune imediat ca a treia alternativa. Vrea cineva sa-l ghiceasca? Infinit. Ati inteles cu totii. Exact! Exista o a treia alternativa. Asa arata. Este o linie dreapta si un numar infinit de linii care trec prin punct fara sa intalneasca linia initiala. Acesta este desenul. Asta aproape ca i-a innebunit pe matematicieni, deoarece, ca si voi, sunt dezorientati, gandindu-se cum poate sa existe asa ceva? Este o inselaciune. Liniile sunt curbe. Insa numai datorita faptului ca sunt proiectate pe o suprafata plana. De sute de ani matematicienii au trebuit sa se lupte cu asta. Cum au putut sa vada asta? Ce inseamna sa ai un model fizic real care sa arate asa?
It's a bit like this: imagine that we'd only ever encountered Euclidean space. Then our mathematicians come along and said, "There's this thing called a sphere, and the lines come together at the north and south pole." But you don't know what a sphere looks like. And someone that comes along and says, "Look here's a ball." And you go, "Ah! I can see it. I can feel it. I can touch it. I can play with it." And that's exactly what happened when Daina Taimina in 1997, showed that you could crochet models in hyperbolic space. Here is this diagram in crochetness. I've stitched Euclid's parallel postulate on to the surface. And the lines look curved. But look, I can prove to you that they're straight because I can take any one of these lines, and I can fold along it. And it's a straight line. So here, in wool, through a domestic feminine art, is the proof that the most famous postulate in mathematics is wrong. (Applause)
Este cam in felul urmator: imaginati-va ca pana acum am cunoscut doar spatiul euclidian. Apoi apar matematicienii nostri si spun: “Exista un lucru care se numeste sfera, ale carei linii se intalnesc la polul sud si nord." Dar tu nu sti cum arata o sfera. Si vine cineva si zice: “Uite o minge!” Tu zici: “ Ah! O vad! Pot sa o simt! Pot sa o ating! Pot sa ma joc cu ea!” Exact asta s-a intamplat in 1997 cand Daiana Taimina a demonstrat ca se pot croseta modele in spatiu hiperbolic. Aici este o diagrama crosetata. Am cusut postulatul lui Euclid pe suprafata ei. Liniile arata curbe. Insa pot sa va demonstrez ca sunt drepte, pentru ca pot sa iau oricare din aceste linii si pot sa pliez de-a lungul ei. Este o linie dreapta. Deci aici, in lana, prin arta feminina domestica, sta dovada ca cel mai faimos postulat din matematica este gresit. (Aplauze)
And you can stitch all sorts of mathematical theorems onto these surfaces. The discovery of hyperbolic space ushered in the field of mathematics that is called non-Euclidean geometry. And this is actually the field of mathematics that underlies general relativity and is actually ultimately going to show us about the shape of the universe. So there is this direct line between feminine handicraft, Euclid and general relativity.
Se pot coase tot felul de teoreme matemetice pe aceste suprafete. Descoperirea sptiului hiperbolic introduce domeniul matematic numit geometrie non-euclidiana. Acesta este de fapt un domeniu al matematicii care sta la baza relativitatii generale si care in final ne va arata forma universului. Deci exista aceasta legatura directa intre mestesugul feminin, Euclid si relativitatea generala.
Now, I said that mathematicians thought that this was impossible. Here's two creatures who've never heard of Euclid's parallel postulate -- didn't know it was impossible to violate, and they're simply getting on with it. They've been doing it for hundreds of millions of years. I once asked the mathematicians why it was that mathematicians thought this structure was impossible when sea slugs have been doing it since the Silurian age. Their answer was interesting. They said, "Well I guess there aren't that many mathematicians sitting around looking at sea slugs." And that's true. But it also goes deeper than that. It also says a whole lot of things about what mathematicians thought mathematics was, what they thought it could and couldn't do, what they thought it could and couldn't represent. Even mathematicians, who in some sense are the freest of all thinkers, literally couldn't see not only the sea slugs around them, but the lettuce on their plate -- because lettuces, and all those curly vegetables, they also are embodiments of hyperbolic geometry. And so in some sense they literally, they had such a symbolic view of mathematics, they couldn't actually see what was going on on the lettuce in front of them. It turns out that the natural world is full of hyperbolic wonders.
Deci, am zis ca matematicienii au crezut ca este imposibil asa ceva. Aici sunt doua fiinte care n-au auzit niciodata despre axioma paralelelor lui Euclid -- nu stiau ca este imposibil de contrazis si pur si simplu supravietuiesc cu ea. Fac asta de sute de milione de ani. Odata i-am intrebat pe metematicieni de ce cred ei ca aceasta structura este imposibila cand echinodermele o au inca din era siluriana. Raspunsul lor a fost interesant. Au zis: “Pai, banuiesc ca nu foarte multi matematicieni stau si se uita la echinoderme." E adevarat. Insa este mai grav de atat. Spune foarte multe lucruri despre ceea ce credeau matematicienii ca este matematica. Ce credeau ca poate sau nu poate sa faca ea. Ceea ce credeau ca poate sau nu poate sa reprezinte ea. Chiar si matematicienii care, intr-un anumit mod, sunt cei mai liberi cugetatori, efectiv nu au putut sa vada, nu neaparat echinodermele de langa ei, dar nici macar salata din farfuria lor, deoarece salata si toate acele legume incretite, sunt si ele intruchiparea geometriei hiperbolice. Deci intr-un anumit mod ei au avut o viziune simbolica asupra matematicii -- practic nu vedeau ceea ce se intampla cu salata din fata lor. Se pare ca lumea naturala este plina de minuni hiperbolice.
And so, too, we've discovered that there is an infinite taxonomy of crochet hyperbolic creatures. We started out, Chrissy and I and our contributors, doing the simple mathematically perfect models. But we found that when we deviated from the specific setness of the mathematical code that underlies it -- the simple algorithm crochet three, increase one -- when we deviated from that and made embellishments to the code, the models immediately started to look more natural. And all of our contributors, who are an amazing collection of people around the world, do their own embellishments. As it were, we have this ever-evolving, crochet taxonomic tree of life. Just as the morphology and the complexity of life on earth is never ending, little embellishments and complexifications in the DNA code lead to new things like giraffes, or orchids -- so too, do little embellishments in the crochet code lead to new and wondrous creatures in the evolutionary tree of crochet life. So this project really has taken on this inner organic life of its own. There is the totality of all the people who have come to it. And their individual visions, and their engagement with this mathematical mode.
De asemenea am descoperit ca exista o taxonomie infinita a creaturilor hiperbolice crosetate. Eu, Chrissy si colaboratorii nostri am inceput cu modele matematice simple si perfecte. Insa am aflat ca, in momentul in care deviem de la forma specifica a codului matematic care sta la baza acestui simplu algoritm, adica crosetezi trei si mai adaugi unu. Cand am deviat de la asta si am infrumutesat codul, modelele au inceput imediat sa para mai naturale. Toti contribuitorii nostrii care sunt o colectie de oameni minunati din toata lumea, vin cu imbunatatirile lor personale. Si avem acest copac al vietii, ca sa zicem asa, al taxonomiei in crosetaj care evolueaza permanent. Asa cum morfologia si complexitatea vietii pe pamant este nelimitata, si niste modificari si complexificari in codul de ADN duc la lucruri noi, cum ar fi girafele si orhideele, asa si niste mici imbunatatiri in codul de crosetare duc la fiinte noi si minunate in evolutia copacului vietii in crosetaj. Deci acest proiect chiar are o viata organica proprie. Este totalul oamenilor care au aderat la el, cu viziunile lor proprii, si propria lor abordare a codului matematic.
We have these technologies. We use them. But why? What's at stake here? What does it matter? For Chrissy and I, one of the things that's important here is that these things suggest the importance and value of embodied knowledge. We live in a society that completely tends to valorize symbolic forms of representation -- algebraic representations, equations, codes. We live in a society that's obsessed with presenting information in this way, teaching information in this way. But through this sort of modality, crochet, other plastic forms of play -- people can be engaged with the most abstract, high-powered, theoretical ideas, the kinds of ideas that normally you have to go to university departments to study in higher mathematics, which is where I first learned about hyperbolic space. But you can do it through playing with material objects. One of the ways that we've come to think about this is that what we're trying to do with the Institute for Figuring and projects like this, we're trying to have kindergarten for grown-ups.
Avem aceste tehnologii. Le folosim. Dar de ce? Ce este in joc? De ce conteaza? Unul din lucrurile care sunt importante pentru mine si Chrissy aici este ca aceste lucruri sugereaza importanta si valoarea cunoastintelor tangibile. Traim intr-o societate care are tendinta sa valorifice forme simbolice de reprezentare -- reprezentari algebrice, ecuatii, coduri. Traim intr-o societate obsedata de prezentarea informatiei in acest mod, de invatarea informatiei in acest mod. Insa prin aceasta modalitate, crosetaj, alte modalitati plastice de joaca, oamenii se pot relationa cu cele mai abstracte, puternice, idei teoretice -- genul de idei pentru care deobicei trebuie sa mergi la universitate sa studiezi matematici superioare, loc in care am invatat si eu pentru prima data despre spatiul hiperbolic. Insa poti sa faci asta jucandu-te cu obiecte materiale. Unul din modurile in care am ajuns sa ne gandim la asta este ceea ce incercam sa facem prin "Institutul de Imaginatie" si proiecte ca si acesta, incercam sa facem o gradinita pentru adulti.
And kindergarten was actually a very formalized system of education, established by a man named Friedrich Froebel, who was a crystallographer in the 19th century. He believed that the crystal was the model for all kinds of representation. He developed a radical alternative system of engaging the smallest children with the most abstract ideas through physical forms of play. And he is worthy of an entire talk on his own right. The value of education is something that Froebel championed, through plastic modes of play.
Gradinita a fost, de fapt, un sistem educational puternic formalizat, infiintat de Friederich Froebel, cristalograf din secolul al 19-lea. El credea ca modelul pentru tot felul de reprezentari este cristalul. A dezvoltat un sistem alternativ radical pentru a implica in idei abstracte copii la varste foarte mici, prin forme fizice de joaca. Merita un intreg discurs doar pentru asta. Valoarea educatiei este ceea ce Froebel a sustinut prin moduri plastice de joaca.
We live in a society now where we have lots of think tanks, where great minds go to think about the world. They write these great symbolic treatises called books, and papers, and op-ed articles. We want to propose, Chrissy and I, through The Institute for Figuring, another alternative way of doing things, which is the play tank. And the play tank, like the think tank, is a place where people can go and engage with great ideas. But what we want to propose, is that the highest levels of abstraction, things like mathematics, computing, logic, etc. -- all of this can be engaged with, not just through purely cerebral algebraic symbolic methods, but by literally, physically playing with ideas. Thank you very much. (Applause)
Acum traim intr-o societate in care avem multe organizatii de cercetare, unde mintile stralucite se intalnesc spre a discuta despre lume. Scriu minunate tratate simbolice numite carti si lucrari si articole de opinie independente. Eu si Chrissy vrem sa propunem, prin intermediul „Institutului de Imaginatie”, o alta modalitate de a face lucrurile, si anume: organizatia de joaca. Organizatia de joaca, la fel ca si cea de cercetare, este un loc unde oamenii se aduna pentru a se implica in idei marete. Insa ceea ce vrem noi sa propunem este ca cele mai inalte nivele ale abstractiei, cum ar fi matematica, informatica, logica, etc. -- toate acestea sa poata fi accesate nu doar prin algebra cerebrala, metode simbolice, ci si prin joaca fizica cu idei, la propriu. Va multumesc foarte mult. (Aplauze)