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We can engage so many more students with this, and they can have a better time doing it.
より多くの学生を引き込むことで 彼らも楽しく数学を学んでくれるでしょう
en-ja
And let's understand: this is not an incremental sort of change.
Und man muss verstehen, dass das nicht eine schrittweise Veränderung sein kann.
en-de
We're trying to cross the chasm here between school math and the real-world math.
We proberen hier de kloof te overbruggen tussen school-wiskunde en echte-wereld-wiskunde.
en-nl
And you know if you walk across a chasm, you end up making it worse than if you didn't start at all -- bigger disaster.
И, как вы знаете, если вы пойдете пешком через пропасть, то -- лучше бы вы и не начинали -- случится катастрофа.
en-ru
No, what I'm suggesting is that we should leap off, we should increase our velocity so it's high, and we should leap off one side and go the other -- of course, having calculated our differential equation very carefully.
Não, o que estou sugerindo é que deveríamos saltar, deveríamos aumentar nossa velocidade para que seja alta, e deveríamos pular de um lado para o outro -- claro, tendo calculado nossa equação diferencial muito cuidadosamente.
en-pt-br
(Laughter) So I want to see a completely renewed, changed math curriculum built from the ground up, based on computers being there, computers that are now ubiquitous almost.
(Risas) Por eso quiero ver un plan de estudios matemáticos totalmente renovado, construido desde cero, basado en que las computadoras estén allí, en computadoras ahora casi omnipresentes.
en-es
Calculating machines are everywhere and will be completely everywhere in a small number of years.
macchine di calcolo che sono ovunque e che in pochi anni saranno veramente dappertutto.
en-it
Now I'm not even sure if we should brand the subject as math, but what I am sure is it's the mainstream subject of the future.
この科目を数学としていいのかどうか分かりませんが 確信をもって言えるのは 今後 重要な科目であることです
en-ja
Let's go for it, and while we're about it, let's have a bit of fun, for us, for the students and for TED here.
さあ 始めましょう 行動を起こしながら 楽しみましょう 我々のため 学生のため TEDのために
en-ja
Thanks.
شکریہ۔
en-ur
(Applause)
(Aplaus) Aitäh!
en-et
Delighted to be here and to talk to you about a subject dear to my heart, which is beauty.
Tôi rất vui được ở đây và nói với quý vị về môt chủ đề thân thuộc của tôi, đó là cái đẹp.
en-vi
I do the philosophy of art, aesthetics, actually, for a living.
Na verdade, eu trabalho com a filosofia da arte e a estética. para ganhar a vida.
en-pt
I try to figure out intellectually, philosophically, psychologically, what the experience of beauty is, what sensibly can be said about it and how people go off the rails in trying to understand it.
Provo a comprendere intellettualmente, filosoficamente, psicologicamente, cosa sia l'esperienza della bellezza, cosa possa esserne detto in maniera sensibile e come le persone vadano fuori strada nel tentativo di capirla.
en-it
Now this is an extremely complicated subject, in part because the things that we call beautiful are so different.
这是个很复杂的问题, 部分原因是因为我们认为“美”的事物 是如此的不同。
en-zh-cn
I mean just think of the sheer variety -- a baby's face, Berlioz's "Harold in Italy," movies like "The Wizard of Oz" or the plays of Chekhov, a central California landscape, a Hokusai view of Mt. Fuji, "Der Rosenkavalier," a stunning match-winning goal in a World Cup soccer match, Van Gogh's "Starry Night," a Jane Austen novel, Fred Astaire dancing across the screen.
Gândiţi-vă doar la imensa varietate-- chipul unui copil, "Harold în Italia" a lui Berlioz, filme ca "Vrajitorul din Oz". sau piesele lui Cehov, un peisaj din centrul Californiei, o imagine a Muntelui Fuji de-a lui Hokusai, "Der Rosenkavalier" un gol spectaculos care a adus victoria unei echipe la Campionatul Mondial de fotbal, "Noaptea înstelată" a lui Van Gogh, un roman a lui Jane Austen, Fred Astaire dansând pe ecranul unui cinematograf.
en-ro
This brief list includes human beings, natural landforms, works of art and skilled human actions.
Rövid listánkon szerepelnek emberek, természetes tájak, művészi alkotások és bravúros emberi teljesítmények.
en-hu
An account that explains the presence of beauty in everything on this list is not going to be easy.
Een uitleg geven die de aanwezigheid van schoonheid in alles op deze lijst verklaart zal niet eenvoudig zijn.
en-nl
I can, however, give you at least a taste of what I regard as the most powerful theory of beauty we yet have.
Но поне мога да ви дам усещането за това, което наричам най-силната теория за красота, която имаме до сега.
en-bg
And we get it not from a philosopher of art, not from a postmodern art theorist or a bigwig art critic.
És az elmélet nem egy művészetfilozófustól, nem is egy posztmodern művészettörténésztől vagy egy menő kritikustól ered.
en-hu
No, this theory comes from an expert on barnacles and worms and pigeon breeding, and you know who I mean: Charles Darwin.
Нет, эта теория предложена специалистом по ракам и червям и по разведению голубей. Вы догадываетесь, о ком я говорю - о Чарльзе Дарвине.
en-ru
Of course, a lot of people think they already know the proper answer to the question, "What is beauty?"
Di certo molte persone credono di conoscere già la giusta risposta alla domanda: "Cos'è la bellezza?
en-it
It's in the eye of the beholder.
Elle est dans l'œil de celui qui regarde.
en-fr
It's whatever moves you personally.
Bármi lehet, ami saját szempontunkból megkapó.
en-hu
Or, as some people, especially academics prefer, beauty is in the culturally conditioned eye of the beholder.
Sau, după cum unii oameni -- mai ales academicienii -- preferă frumuseţea este condiţionată cultural în ochii spectatorului.
en-ro
People agree that paintings or movies or music are beautiful because their cultures determine a uniformity of aesthetic taste.
Có những người đồng ý rằng các tranh vẽ hay bộ phim hay nhạc đều đẹp bởi vì nền văn hóa quyết định thị hiếu thẩm mỹ
en-vi
Taste for both natural beauty and for the arts travel across cultures with great ease.
Le goût pour la beauté naturelle et pour les arts voyage à travers les cultures très facilement.
en-fr
Beethoven is adored in Japan.
Музыку Бетховена ценят в Японии,
en-ru
Peruvians love Japanese woodblock prints.
祕魯人喜歡日本木刻版畫
en-zh-tw
Inca sculptures are regarded as treasures in British museums, while Shakespeare is translated into every major language of the Earth.
פסלי האינקה נחשבים לאוצרות במוזיאונים בריטיים, בעוד ששייקספיר מתורגם לכל שפה מרכזית בעולם.
en-he
Or just think about American jazz or American movies -- they go everywhere.
Sau gândiţi-vă doar la jazzul american sau la filmele americane -- sunt pretutindeni.
en-ro
There are many differences among the arts, but there are also universal, cross-cultural aesthetic pleasures and values.
Il y a de nombreuses différences parmi les arts, mais il y a aussi des plaisirs et des valeurs esthétiques universelles trans-culturelles.
en-fr
How can we explain this universality?
この普遍性は どう説明できるのでしょう?
en-ja
The best answer lies in trying to reconstruct a Darwinian evolutionary history of our artistic and aesthetic tastes.
Die beste Antwort liegt darin, zu versuchen, eine Darwin'sche Entstehungsgeschichte zu rekonstruieren von unseren künstlerischen und ästhetischen Vorlieben.
en-de
We need to reverse-engineer our present artistic tastes and preferences and explain how they came to be engraved in our minds by the actions of both our prehistoric, largely pleistocene environments, where we became fully human, but also by the social situations in which we evolved.
Нужно провести ретроспекцию наших современных предпочтений и вкусов и объяснить, каким образом они укоренились в нашем сознании. В процессе эволюции на нас оказывали влияние как доисторические природные условия эпохи плейстоцена, в которых окончательно сформировался человек разумный, так и социальные условия, в которых мы находились.
en-ru
This reverse engineering can also enlist help from the human record preserved in prehistory.
W tej analizie można się wspomóc prehistorycznym zapisem ewolucji. Chodzi o skamieliny,
en-pl
I mean fossils, cave paintings and so forth.
像是化石,洞穴壁畫
en-zh-tw
And it should take into account what we know of the aesthetic interests of isolated hunter-gatherer bands that survived into the 19th and the 20th centuries.
והיא צריכה לקחת בחשבון את מה שאנו יודעים על טעמם האסתטי של שבטי ציידים-מלקטים מבודדים שחיו עד למאות ה-19 וה-20.
en-he
Now, I personally have no doubt whatsoever that the experience of beauty, with its emotional intensity and pleasure, belongs to our evolved human psychology.
我個人 並不懷疑 美的體驗包含 強烈的情緒與歡愉 也就是屬於已進化人類的心理層面
en-zh-tw
The experience of beauty is one component in a whole series of Darwinian adaptations.
美的体验是整个达尔文主义 适应过程中的一个成份。
en-zh-cn
Beauty is an adaptive effect, which we extend and intensify in the creation and enjoyment of works of art and entertainment.
La beauté est un effet adaptatif, que nous étendons et intensifions dans la création et la jouissance des oeuvres d'art et de divertissement.
en-fr
As many of you will know, evolution operates by two main primary mechanisms.
العديد منكم يعلم بأن، نظرية التطور تعمل بآليتين أساسيتين،
en-ar
The first of these is natural selection -- that's random mutation and selective retention -- along with our basic anatomy and physiology -- the evolution of the pancreas or the eye or the fingernails.
第一个是自然选择-- 这是中是随机的基因突变和选择性保留-- 与我们基本解剖学和生理学结构一起-- 如胰腺、眼睛或指甲的进化。
en-zh-cn
Natural selection also explains many basic revulsions, such as the horrid smell of rotting meat, or fears, such as the fear of snakes or standing close to the edge of a cliff.
Die natürliche Auslese erklärt auch viele grundlegende Ekelgefühle, so wie sie der fürchterliche Geruch von verdorbenem Fleisch auslöst, oder Ängste, so wie die Angst vor Schlangen, oder davor, nahe am Rand einer Klippe zu stehen.
en-de
Natural selection also explains pleasures -- sexual pleasure, our liking for sweet, fat and proteins, which in turn explains a lot of popular foods, from ripe fruits through chocolate malts and barbecued ribs.
自然选择也解释了愉悦-- 性愉悦, 对糖、脂肪和蛋白质的喜爱, 这反过来解释了许多广受欢迎的食物, 从成熟的果实到巧克力糖 和烤排骨。
en-zh-cn
The other great principle of evolution is sexual selection, and it operates very differently.
Mekanisme evolusi yang lainnya adalah seleksi seksual, dan cara kerjanya sangat berbeda.
en-id
The peacock's magnificent tail is the most famous example of this.
De prachtige staart van de pauw is daar het meest bekende voorbeeld van.
en-nl
It did not evolve for natural survival.
Nie pomaga w przetrwaniu.
en-pl
In fact, it goes against natural survival.
фактически, он является помехой в этой борьбе.
en-ru
No, the peacock's tail results from the mating choices made by peahens.
Хвост павлина обязан своим появлением предпочтениям в выборе полового партнера, который делали самки павлина.
en-ru
It's quite a familiar story.
И это вполне естественно:
en-ru
It's women who actually push history forward.
역사를 전진시키는 건 사실 여자들입니다.
en-ko
Darwin himself, by the way, had no doubts that the peacock's tail was beautiful in the eyes of the peahen.
Bu arada Darwin'in kendisinin tavuz kuşunun kuyruğunun, dişi tavuz kuşunun gözüne güzel gözüktüğü hakkında hiçbir kuşkusu yoktur.
en-tr
He actually used that word.
הוא למעשה השתמש במילה הזו.
en-he
Now, keeping these ideas firmly in mind, we can say that the experience of beauty is one of the ways that evolution has of arousing and sustaining interest or fascination, even obsession, in order to encourage us toward making the most adaptive decisions for survival and reproduction.
Eye of the Peahen.) Şimdi, bu düşünceleri sıkıca aklımızda tutarak güzellik tecrübesinin, hayatta kalmamız ve ürememiz için en uygun kararları vermeye bizi cesaretlendirmek amacıyla, evrimin sahip olduğu canlandırıcı,harekete geçirici hatta takıntılı ve cazibeli yollardan biridir diyebiliriz.
en-tr
Beauty is nature's way of acting at a distance, so to speak.
Piękno jest narzędziem jakie ewolucja wykorzystuje na odległość.
en-pl
I mean, you can't expect to eat an adaptively beneficial landscape.
제 말은, 우린 순응적으로 이로운 대지를 먹을 순 없습니다.
en-ko
It would hardly do to eat your baby or your lover.
Tampoco funcionaría con tu bebé o tu pareja.
en-es
So evolution's trick is to make them beautiful, to have them exert a kind of magnetism to give you the pleasure of simply looking at them.
因此,进化的方式是 让他们看起来赞, 让他们散发出一种吸引力, 让你仅仅是看着他们就觉得超爽的。
en-zh-cn
Consider briefly an important source of aesthetic pleasure, the magnetic pull of beautiful landscapes.
Zamyslime sa nad dôležitým zdrojom estetického potešenia, nad tou magnetickou príťažlivosťou nádherných scenérií.
en-sk
People in very different cultures all over the world tend to like a particular kind of landscape, a landscape that just happens to be similar to the pleistocene savannas where we evolved.
אנשים מתרבויות שונות מאוד מכל קצוות תבל נוטים לאהוב סוג מסוים של נוף, נוף שדומה במקרה לזה של הסוואנה הפלאייסטוקנית בה נבררנו.
en-he
This landscape shows up today on calendars, on postcards, in the design of golf courses and public parks and in gold-framed pictures that hang in living rooms from New York to New Zealand.
Acest fel de peisaj apare azi pe calendare, pe cărţi poştale, în design-ul terenurilor de golf şi al parcurilor şi în tablourile înrămate din camerele de zi din New Tork până în Noua Zeelandă.
en-ro
It's a kind of Hudson River school landscape featuring open spaces of low grasses interspersed with copses of trees.
Нещо като пейзажи от арт движението Хъдсън ривър, включващи открити пространства с ниска трева и осеяни с дървета.
en-bg
The trees, by the way, are often preferred if they fork near the ground, that is to say, if they're trees you could scramble up if you were in a tight fix.
Дърветата често са предпочитани, ако се разклоняват близо до земята, това означава, че са дървета, които можете да изкачите, ако се намирате в тежко положение.
en-bg
The landscape shows the presence of water directly in view, or evidence of water in a bluish distance, indications of animal or bird life as well as diverse greenery and finally -- get this -- a path or a road, perhaps a riverbank or a shoreline, that extends into the distance, almost inviting you to follow it.
Die Landschaft zeigt die Anwesenheit von Wasser ganz in der Nähe, oder die Andeutung von Wasser in einer bläulichen Entfernung, Anzeichen von Tieren oder Vögeln, sowie diverses Laub und letztendlich -- sehen Sie sich das an -- einen Pfad, oder eine Straße, vielleicht ein Flussufer oder eine Küstenlinie, die in die Ferne läuft, fast wie eine Einladung, ihr zu folgen.
en-de
This landscape type is regarded as beautiful, even by people in countries that don't have it.
נוף זה נחשב ליפה, אפילו עבור אנשים במדינות בהן הוא לא קיים.
en-he
The ideal savanna landscape is one of the clearest examples where human beings everywhere find beauty in similar visual experience.
Idealny krajobraz sawanny jest jasnym przykładem tego, że wszyscy ludzie znajdują piękno w podobnych doświadczeniach.
en-pl
But, someone might argue, that's natural beauty.
Mas alguém pode argumentar que isso é beleza natural.
en-pt-br
How about artistic beauty?
那麼人工藝術品呢?
en-zh-tw
Isn't that exhaustively cultural?
Az nem kizárólag kulturálisan meghatározott?
en-hu
No, I don't think it is.
Tidak, saya pikir itu bukan seperti itu.
en-id
And once again, I'd like to look back to prehistory to say something about it.
Une fois encore, j'aimerais revenir à la préhistoire pour en parler.
en-fr
It is widely assumed that the earliest human artworks are the stupendously skillful cave paintings that we all know from Lascaux and Chauvet.
Es wird im Allgemeinen angenommen, dass die frühesten menschlichen Kunstwerke die erstaunlich fachkundig ausgeführten Höhlenmalereien sind, die wir alle aus Lascaux kennen und Chauvet.
en-de
Chauvet caves are about 32,000 years old, along with a few small, realistic sculptures of women and animals from the same period.
Gua Chauvet berusia sekitar 32.000 tahun, bersama beberapa patung realis kecil wanita dan binatang dari masa yang sama.
en-id
But artistic and decorative skills are actually much older than that.
Но в действительности художественные навыки гораздо старше.
en-ru
Beautiful shell necklaces that look like something you'd see at an arts and crafts fair, as well as ochre body paint, have been found from around 100,000 years ago.
美麗的貝殼項鍊 就像是那種你會在藝術展覽場上找到的一樣 例如赭石人體彩繪 經研究 迄今已超過十萬年
en-zh-tw
But the most intriguing prehistoric artifacts are older even than this.
Nhưng những chế tác hấp dẫn nhất của thời tiền sử thậm chí còn xưa hơn thời đó.
en-vi
I have in mind the so-called Acheulian hand axes.
是像 所謂的阿舍利手斧
en-zh-tw
The oldest stone tools are choppers from the Olduvai Gorge in East Africa.
Alat jaman batu tertua adalah alat pemotong dari Jurang Olduvai di Afrika Timur
en-id
They go back about two-and-a-half-million years.
Chúng đã có mặt khoảng 2,5 triệu năm.
en-vi
These crude tools were around for thousands of centuries, until around 1.4 million years ago when Homo erectus started shaping single, thin stone blades, sometimes rounded ovals, but often in what are to our eyes an arresting, symmetrical pointed leaf or teardrop form.
Essas ferramentas grosseiras foram usadas por milhares de séculos, até mais ou menos 1.4 milhão de anos atrás quando o Homo erectus começou a fazer lâminas finas de pedra, às vezes com formas ovais arredondadas, mas muitas vezes no que para nós parece com folhas pontudas ou formatos de lágrimas cativantes e simétricas.
en-pt-br
These Acheulian hand axes -- they're named after St. Acheul in France, where finds were made in 19th century -- have been unearthed in their thousands, scattered across Asia, Europe and Africa, almost everywhere Homo erectus and Homo ergaster roamed.
Queste amigdale acheuleane - prendono il nome da Saint-Acheul di Francia, dove sono state scoperte nel Diciannovesimo secolo - sono state portate alla luce a migliaia, disseminate per Asia, Europa e Africa, quasi dovunque abbiano vagato l'Homo erectus e l'Homo ergaster.
en-it
Now, the sheer numbers of these hand axes shows that they can't have been made for butchering animals.
Nun, die schiere Anzahl dieser Handäxte zeigt, dass sie nicht dafür geschaffen worden sein können, um Tiere zu schlachten.
en-de
And the plot really thickens when you realize that, unlike other pleistocene tools, the hand axes often exhibit no evidence of wear on their delicate blade edges.
והעלילה מסתבכת יותר כשאתם מבינים שבניגוד לכלים אחרים מהפלאייסטוקן, גרזני היד האלה לעיתים לא מראים סימן לבלאי על קצוות חודיהם העדינים.
en-he
And some, in any event, are too big to use for butchery.
De asemenea, unele sunt prea mari pentru a fi fost folosite în măcelărie.
en-ro
Their symmetry, their attractive materials and, above all, their meticulous workmanship are simply quite beautiful to our eyes, even today.
Su simetría, sus materiales atractivos y, sobre todo, su meticulosa manufactura son sencillamente muy hermosas a nuestros ojos, aún hoy.
en-es
So what were these ancient -- I mean, they're ancient, they're foreign, but they're at the same time somehow familiar.
Mik hát ezek az ősi -- úgy értem, ősiek, idegenek, de ugyanakkor valahonnan mégis ismerősek.
en-hu
What were these artifacts for?
Những đồ cổ này dùng để làm gì?
en-vi
The best available answer is that they were literally the earliest known works of art, practical tools transformed into captivating aesthetic objects, contemplated both for their elegant shape and their virtuoso craftsmanship.
Cel mai accesibil răspuns este că erau la propriu cele mai timpurii opere de artă, unelte practice transformate în obiecte estetice captivante, contemplate atât pentru forma lor elegantă, cât şi pentru măiestria cu care au fost lucrate.
en-ro
Hand axes mark an evolutionary advance in human history -- tools fashioned to function as what Darwinians call "fitness signals" -- that is to say, displays that are performances like the peacock's tail, except that, unlike hair and feathers, the hand axes are consciously cleverly crafted.
Te siekierki świadczą o postępie w historii ewolucji. Funkcjonują jako Darwinowskie świadectwo zdrowia, to pokaz, przedstawienie, jak pawi ogon, ale w przeciwieństwie do włosów i piór, siekierki są świadomie i sprytnie wytwarzane.
en-pl
Competently made hand axes indicated desirable personal qualities -- intelligence, fine motor control, planning ability, conscientiousness and sometimes access to rare materials.
Kapak tangan yang dibuat dengan cerdas menunjukkan kualitas pribadi yang baik -- kepintaran, kontrol fungsi motor yang baik, kemampuan merencanakan, sifat kehati-hatian dan terkadang akses terhadap bahan-bahan langka.
en-id
Over tens of thousands of generations, such skills increased the status of those who displayed them and gained a reproductive advantage over the less capable.
במהלך עשרות אלפי דורות, כישורים אלה הגבירו את הסטטוס של מי שהפגין אותם, ונתנו להם יתרון רבייתי על פני הפחות מוכשרים.
en-he
You know, it's an old line, but it has been shown to work -- "Why don't you come up to my cave, so I can show you my hand axes?"
É uma velha cantada, mas provou ter funcionado: "Por que você não vem na minha caverna e eu lhe mostro os meus bifaces?"
en-pt-br
(Laughter) Except, of course, what's interesting about this is that we can't be sure how that idea was conveyed, because the Homo erectus that made these objects did not have language.
(Gelach) Behalve, natuurlijk, wat er nog interessant aan is, is dat we niet zeker weten hoe dat idee werd overgebracht, omdat Homo erectus die deze objecten maakte niet over taal beschikte.
en-nl
It's hard to grasp, but it's an incredible fact.
É difícil de compreender, mas é um facto incrível.
en-pt
This object was made by a hominid ancestor, Homo erectus or Homo ergaster, between 50,000 and 100,000 years before language.
Este objeto foi feito por um ancestral hominídeo - Homo erectus ou Homo ergaster - entre 50 e 100 mil anos antes da linguagem.
en-pt-br
Stretching over a million years, the hand axe tradition is the longest artistic tradition in human and proto-human history.
Prolongando-se por mais de um milhão de anos a tradição dos bifaces é a tradição artística mais longa na história humana e proto-humana.
en-pt
By the end of the hand axe epic, Homo sapiens -- as they were then called, finally -- were doubtless finding new ways to amuse and amaze each other by, who knows, telling jokes, storytelling, dancing, or hairstyling.
עם סיום עידן גרזני היד, הומו ספייאנס -- כך קראו להם בשלב זה -- חיפשו ככל הנראה דרכים חדשות לבדר ולהדהים זה את זה על-ידי, מי יודע, סיפור בדיחות, סיפור סיפורים, ריקוד או עיצוב שיער.
en-he
Yes, hairstyling -- I insist on that.
沒錯,是頭髮造型,我堅持用這個詞
en-zh-tw
For us moderns, virtuoso technique is used to create imaginary worlds in fiction and in movies, to express intense emotions with music, painting and dance.
עבורנו, המודרניים, טכניקה וירטואוזית משמשת ליצירת עולמות דימיוניים בסרטים ובספרים, כדי לבטא רגשות עזים עם מוזיקה, ציור ומחול.
en-he