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.
Kot je napovedala June, sem danes tu, da vam predstavim projekt, s katerim se s sestro dvojčico ukvarjava zadnja tri leta in pol. Kvačkava namreč koralni greben. Gre pravzaprav za projekt, ki je k sodelovanju pritegnil na stotine ljudi po vsem svetu. Dobesedno tisoči so na mnogo različnih načinov sodelovali pri njem. Projekt danes združuje tri celine, njegove korenine pa segajo na področje matematike, morske biologije, ženskih ročnih spretnosti in okoljskega aktivizma. Resnično. Hkrati gre za projekt, katerega razvoj se je na krasen način skladal z evolucijo življenja na zemlji, kar je še posebej lepo reči tu, februarja 2009, ko, kot je povedal že en predhodnih govorcev, beležimo dvestoto obletnico rojstva Charlesa Darwina.
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.
Vsega tega se bom dotaknila v naslednjih 18 minutah, upam. A naj vam za začetek pokažem nekaj slik, kako ta stvar izgleda. Da boste dobili občutek velikosti, ta postavitev meri slaba dva metra v dolžino, najvišji modeli pa od pol do enega metra višine. Tu je še nekaj slik. Ta na desni je visok okrog meter in pol. Delo vsebuje na stotine različnih vzorcev kvačkanja. Resnično gre za tisoče modelov, ki so jih ljudje s celega sveta prispevali za ta projekt. Njegova razsežnost vsebuje na desetine tisočev ur človeškega dela -- v 99 odstotkih dela ženskih rok. Na desni strani imamo delček postavitve, dolge okrog 3 metre in pol.
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.
S sestro sva se projekta lotili leta 2005, saj se je tistega leta, vsaj v znanstvenem tisku, veliko govorilo o globalnem segrevanju in o njegovem vplivu na koralne grebene. Korale so izjemno občutljivi organizmi, za katere so vsaki dvigi temperature morja pogubni. Povzročijo ta obširni pojav beljenja, kar je prvi znak obolelosti koral. In če se beljenje ne ustavi, če se temperature ne znižajo, grebeni začnejo odmirati. To se je v veliki meri zgodilo tudi na Velikem koralnem grebenu, pravzaprav na grebenih po celem svetu. Naš poziv je v obliki kvačkanega obeljenega grebena.
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.
Skupaj sestavljamo organizacijo, imenovano Inštitut za upodabljanje, skromno organizacijo, katere namen je promovirati in ustvarjati projekte o estetskih in poetičnih razsežnostih znanosti in matematike. Na naši spletni strani sem objavila oglas, da medse vabimo nove člane organizacije. Na naše presenečenje so se med prvimi oglasili iz Muzeja Andyja Warhola. Povedali so, da pripravljajo razstavo pogleda umetnikov na globalno segrevanje ter da želijo razstaviti tudi naš koralni greben. V smehu sem dejala, "Pravzaprav smo šele začeli, razstavimo lahko le malo." Leta 2007 smo tako imeli razstavo, skromno razstavo tega koralnega grebena. Nato pa so v Chicagu do nas prišli neki ljudje in rekli, "Konec leta 2007 bo tema čikaškega festivala humanističnih ved prav globalno segrevanje. Naša galerija meri skoraj 3 are in želeli bi, da jo napolnite s svojimi koralami." In jaz sem naivno rekla, "Oh, da, seveda." Pravim, "naivno", saj po poklicu pravzaprav pišem znanstvene prispevke. Pišem knjige o kulturni zgodovini fizike. Pisala sem knjige o zgodovini vesolja, o zgodovini fizike in religije, pišem pa tudi poljudne članke v New York Timesu in L.A. Timesu. Zato se mi ni sanjalo, kaj pomeni napolniti skoraj 3 are veliko galerijo. In sem pristala na predlog. Doma sem o tem povedala moji sestri Christine. Skoraj je znorela, saj je kot profesorica na enem izmed boljših losangeliških umetniških kolidžev, CalArtsu, natanko vedela, kaj pomeni napolniti 3 are veliko galerijo. Prepričana je bila, da sem ob pamet. Na koncu pa je postala skoraj obsedena s kvačkanjem. Na kratko, po osmih mesecih nam je uspelo napolniti 3 are veliko galerijo Čikaškega kulturnega centra.
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.
Do tega trenutka se je projekt kot virus razširil na dimenzije, nam popolnoma nedoumljive. Odgovorni ljudje v Čikagu so sklenili, da poleg razstavljanja naših koralnih grebenov želijo še, da tamkajšnji prebivalci izdelajo nove. Tako smo jih na delavnicah in predavanjih naučili tehnik kvačkanja. Ljudje v Čikagu so izdelali svoj lasten koralni greben, ki je bil razstavljen poleg našega. Na stotine ljudi je sodelovalo. Vabili so nas, da stvar ponovimo v New Yorku, Londonu in Los Angelesu. V vsakem od teh mest so meščani, na stotine ljudi, izdelali koralni greben. In vse več ljudi sodeluje pri tem, od katerih večine nikoli nismo spoznali. Stvar se je pravzaprav razvila v neko organsko, stalno razvijajoče se bitje, ki naju je s Christine že zdavnaj preseglo.
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?
Najbrž se nekateri od vas sprašujete, "S katerega planeta so ti ljudje? Le čemu kvačkajo koralni greben? Volnenost in vlažnost nista ravno pojma, ki sta si sorodna. Zakaj koral ne izklešejo iz marmorja? Ali jih odlijejo v bron?" Pravzaprav pa obstaja zelo dober razlog, zakaj je kvačkanje najprimernejše, in sicer, da imajo mnogi organizmi koralnih grebenov zelo značilno obliko strukture. Nagubane in nazobčane oblike, vidne na koralah, algah, spužvah in morskih polžih, so znane kot oblike hiperbolične geometrije. In edini način, na katerega znajo matematiki prikazati to strukturo, je kvačkanje. To je dejstvo. Te strukture praktično ni mogoče prikazati na drugačen način, niti s pomočjo računalnika. Kaj je torej hiperbolična geometrija, ki jo utelešajo korale in morski polži?
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.
V naslednjih nekaj minutah se bomo postavili v kožo morskega polža. (Smeh) Ta veja geometrije je ob odkritju v 19. stoletju razburkala matematično vedo. A vse do leta 1997 matematiki niso razumeli, kako bi jo prikazali. Leta 1997 je matematičarka na Univerzi Cornell, Daina Taimina, odkrila, da se takšne strukture lahko prikaže s pletenjem in kvačkanjem. Začela je s pletenjem. A kmalu je na igli nastalo preveč zank, zato je bilo kvačkanje očitno boljši način. Kar je pravzaprav počela, je bilo ustvarjanje modela matematične strukture, za katero so mnogi trdili, da jo je nemogoče sestaviti. V resnici so menili, da so bila telesa s tako strukturo sama po sebi nemogoča. Nekateri najboljši matematiki so se skozi stoletja trudili dokazati, da je ta struktura nemogoča.
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.
Kaj je torej ta nemogoča hiperbolična struktura? Pred odkritjem hiperbolične geometrije sta bili znani dve vrsti prostora: evklidski prostor in sferični prostor. Oba imata različne lastnosti. Matematiki radi formalistično označujejo stvari. Vsi veste, kaj je raven, evklidski prostor. A matematiki to določijo na poseben način. In sicer preko koncepta vzporednih premic. Tu imamo premico in točko izven nje. Evklid se je vprašal, "Kako določim vzporedne premice? Koliko premic lahko potegnem skozi točko, ne da bi sekal prvotno premico?" Vsi veste odgovor. Kdo ga bo povedal na glas? Eno. Točno. Prav. To je naša definicija vzporedne premice. Gre pravzaprav za definicijo evklidskega prostora.
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.
A tu je še ena možnost, ki jo tudi vsi poznate: sferični prostor. Pomislite na površino neke krogle -- napihljive žoge, površine Zemlje. Na tej sferični površini imamo ravno premico in točko izven nje. Koliko ravnih premic lahko potegnem skozi točko, ne da bi sekala prvotno premico? Zakaj govorimo o ravni premici na zakrivljeni podlagi? Matematiki so odgovorili na to vprašanje. Spoznali so, da obstaja posplošen koncept ravnosti, in sicer geodetski. In na površini krogle je ravna premica največji možni krog, ki ga lahko narišete. Torej kot ekvator ali črte zemljepisne dolžine. Vprašajmo se torej znova, "Koliko ravnih premic lahko potegnem skozi točko, in se hkrati izognem prvotni premici?" Kdo želi ugibati? Nič. Zelo dobro.
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?
Matematiki so torej verjeli, da je to edina alternativa. Kar pa je nekoliko sumljivo, mar ne? Doslej imamo dva odgovora, nič in ena. Le dva odgovora? Ali obstaja tudi tretja alternativa? Za matematika se ob dveh odgovorih, ki sta nič in ena, neogibno pojavi še eno število kot tretja alternativa. Bi kdo želel ugibati, katero? Neskončno. Vsi imate prav. Točno tako. Tudi tretja alternativa obstaja. Videti pa je tako. Imamo ravno premico ter neskončno število premic, ki grejo skozi točko, a se nikoli ne dotaknejo prvotne premice. Tu je prikaz. Matematike je to privedlo skoraj na rob pameti, saj so ga, tako kot vi, le zmedeno opazovali. Gotovo mislite, da to ni možno. Da goljufam. Premice so namreč ukrivljene. A to je le zato, ker je prikazano na ravni podlagi. Matematiki so se stoletja bojevali s tem problemom. Kako bi lahko to videli? Kaj bi pomenilo imeti snoven model, ki bi izgledal tako?
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)
Poskusimo tako: predstavljate si, da poznamo le evklidski prostor. Nato pridejo naši matematiki in rečejo, "Obstaja stvar, imenovana krogla, in premice se stikajo na severnem in južnem tečaju." A vi ne veste, kako sfera sploh izgleda. In nekdo pride in reče, "Poglejte, žoga." Vi pa, "Ah! Vidim jo. Čutim jo. Držim jo. Lahko se igram z njo." In točno to se je zgodilo, ko je Daina Taimina leta 1997 pokazala, da se lahko skvačka modele v hiperboličnem prostoru. Tu imamo prikaz v kvačkanju. Šiv na površini predstavlja Evklidov postulat o vzporednosti. Linije izgledajo ukrivljene. A kot vidite, lahko dokažem, da so ravne, tako, da primem katerokoli od linij in prepognem preko nje. Imamo ravno črto. Tukaj, v volni in ženskih ročnih spretnostih imamo dokaz, da je najbolj znan postulat v matematiki napačen. (Aplavz)
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.
In na take površine lahko všijete različne matematične teoreme. Odkritje hiperboličnega prostora je napovedalo novo področje v matematiki, t.i. neevklidsko geometrijo. To področje je pravzaprav temeljni kamen splošne relativnosti, ki bo nazadnje osmislilo obliko vesolja. Našli smo torej neposredno povezavo med ženskimi ročnimi spretnostmi, Evklidom in splošno relativnostjo.
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.
Rekla sem že, da so matematiki to smatrali za nemogoče. Tu pa imamo dve bitji, ki še nista slišali za Evklidov postulat o vzporednosti, niti nista vedeli, da ga je mogoče ovreči, a to kljub temu počneta. In to že stotine milijonov let. Nekoč sem matematike vprašala, zakaj so nekoč menili, da je taka struktura nemogoča, čeprav so jo morski polži utelešali že od dobe silurja. Njihov odgovor je bil zanimiv. Rekli so, "Najbrž res ni veliko matematikov, ki opazujejo morske polže." In niso se motili. A tu je še druga, globlja plat. Pove nam veliko o tem, kako so gledali na samo matematiko, kaj lahko z njo počnejo in česa ne, kaj lahko predstavlja in česa ne. Celo matematiki, ki so na nek načen najbolj svobodomiselni od vseh mislecev, so dejansko okrog sebe spregledali ne le morske polže, ampak tudi solato na njihovem krožniku -- zelena solata in vsa kodrasta zelenjava namreč prav tako predstavljajo hiperbolično geometrijo. In tako so nekako prav zaradi njihovega simbolnega pogleda na svet prezrli, kar so imeli ves čas pred sabo v obliki zelene solate. Izkazalo se je, da je narava polna hiperboličnih čudes.
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.
Prav tako smo odkrili, da obstaja neskončna taksonomija kvačkanih hiperboličnih modelov. S Chrissy in sodelavci smo začeli z izdelavo preprostih in matematično pravilnih modelov. A ko smo skrenili z določene postavitve matematične kode, ki je predstavljala njihovo osnovo -- preprosti algoritem, ki se glasi: pokvačkaj tri in dodaj eno petljo -- ko smo skrenili s poti in začeli z okraševanjem osnovne kode, so ti modeli takoj izgledali bolj naravno. In vsi od naših sodelavcev, izjemna skupina ljudi z vsega sveta, ustvarjajo samosvoje krasitve. Nastalo je to stalno razvijajoče se kvačkano taksonomično drevo življenja. Prav tako kot sta neskončni morfologija in kompleksnost življenja na Zemlji, majhna odstopanja, krasitve in zapletanja v verigi DNK pa privedejo do novih bitij, kot so žirafe ali orhideje, tako tudi majhna okraševanja v kvačkanem modelu privedejo do novih in čudovitih struktur v razvojnem drevesu kvačkanega življenja. Ta projekt je torej resnično zaživel svoje notranje organsko življenje. Predstavljajo ga vsi ljudje, ki so pri njem sodelovali s svojimi lastnimi vizijami in angažiranostjo za ta matematični način.
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.
Poznamo primerne tehnologije in jih uporabljamo. Toda zakaj? Kaj je v igri? Kaj je pomembno? Za naju s Chrissy je en od pomembnih vidikov, da se s tem opozori na pomembnost in koristnost utelešenega znanja. Živimo v družbi, ki povsem privilegira simbolične oblike predstavitve -- algebrski izrazi, enačbe, kode. Naša družba je obsedena s takim načinom predstavitve in širjenja podatkov. A preko take vrste izražanja, kvačkanja ali drugih plastičnih oblik ustvarjanja, se lahko ljudje povežejo z najbolj abstraktnimi, izjemno pomembnimi teoretičnimi idejami, s katerimi se ponavadi lahko srečate le na univerzah pri študiju višje matematike, kjer sem tudi sama prvič slišala za hiperbolični prostor. Lahko pa jih spoznate tudi preko fizičnih predmetov. Ena od stvari, ki se nam je pri tem utrnila, je, da preko Inštituta za upodabljanje in projektov, kot je ta, poskušamo ustvariti vrtec za odrasle.
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.
Vrtec je pravzaprav zelo formalizirana oblika izobraževanja, ki jo je osnoval Friedrich Fröbel, kristalograf iz 19. stoletja. Verjel je, da je kristal pravi model za najrazličnejše predstavitve. Razvil je radikalni alternativni sistem seznanjanja najmlajših z najbolj abstraktnimi idejami, in sicer preko fizičnih igrač. O njem bi lahko pripravili cel govor. Koristnost izobraževanja je Fröbel obvladal skozi plastične načine igre.
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)
Naša družba pozna veliko raziskovalnih organizacij, kjer se misleci ukvarjajo s svetom okoli nas. Ustvarjajo pomembne simbolne razprave, ki jim pravimo knjige, referati, kolumne in članki. S Chrissy sva preko Inštituta za upodabljanje želeli predlagati alternativni način ustvarjanja, in sicer neke vrste igralne organizacije. Te bi bile, prav tako kot raziskovalne organizacije, kraj, kjer bi se ljudje lahko povezali z velikimi idejami. S tem želimo poudariti, da so najkompleksnejše abstrakcije, pojmi kot so matematika, računanje, logika itd, nam na dosegu ne le preko izključno možganskih algebrskih simboličnih metod, pač pa dobesedno in zelo konkretno preko igre z idejami. Najlepša hvala. (Aplavz)