RobertLang_全新折纸【中英文对照】

1.My talk is “Flapping Birds and Space Telescopes.”
我演讲的题目是《展翅的鸟儿与太空望远镜》。
2.And you would think that should have nothing to do with one another, but I hope by the end of these 18 minutes, you’ll see a little bit of a relation.
你会觉得他们相互之间没有联系， 但我希望在18分钟以后， 你能看到一些关联。
3.It ties to origami. So let me start.
这与折纸有关。下面我就开始了。
4.What is origami?
什么是折纸？
5.Most people think they know what origami is. It’s this: flapping birds, toys, cootie catchers, that sort of thing.
很多人以为他们知道折纸是什么。它是这样的： 展翅的鸟儿、玩具、东西南北之类的东西。
6.And that is what origami used to be.
折纸术以前是这样的。
7.But it’s become something else.
但它已经改变了。
8.It’s become an art form, a form of sculpture.
它已经成为了一种艺术形式，一种雕塑形式。
9.The common theme — what makes it origami — is folding, is how we create the form.
共同的主题——折纸术的本质—— 是折叠，也是我们如何创造形态的。
10.You know, it’s very old. This is a plate from 1797.
你们知道，这非常古老。这是1797年的一幅画。
11.It shows these women playing with these toys.
上面是这些妇女们玩纸玩具的场景。
12.If you look close, it’s this shape, called a crane.
如果你靠近点看，它是这种形状的，叫做鹤。
13.Every Japanese kid learns how to fold that crane.
每个日本孩子 都学折纸鹤。
14.So this art has been around for hundreds of years, and you would think something that’s been around that long — so restrictive, folding only —
所以这种艺术已经存在了数百年， 你可能会想如果某种东西 已经存在了这么久——如此有限制性，只能折叠——
15.everything that could done has been done a long time ago.
那么所有能做出的东西应该在很久以前就做出来了。
16.And that might have been the case.
实际情况也许会是如此。
17.But in the 20th century, a Japanese folder named Yoshizawa came along, and he created tens of thousands of new designs.
但在20世纪， 一位名为吉泽的日本折纸艺术家出现了， 他创造出了数万种全新的设计。
18.But even more importantly, he created a language — a way we could communicate, a code of dots, dashes and arrows.
更重要的是，他创造了一种语言—— 一种我们可以交流的方式， 一种由点、破折号和箭头构成的代码。
19.Harkening back to Susan Blackmore’s talk, we now have a means of transmitting information with heredity and selection, and we know where that leads.
联系到苏珊·布莱克摩尔的演讲， 我们现在有了一种通过传承与选择 传递信息的方法， 我们也知道它的走向。
20.And where it has led in origami is to things like this.
而它在折纸术中产生的 是这样的东西。
21.This is an origami figure: one sheet, no cuts, folding only, hundreds of folds.
这是一个折纸作品： 一张纸，没有裁剪，只有折叠，数百次折叠。
22.This too is origami, and this shows where we’ve gone in the modern world.
而这也是折纸， 它显示出我们在现代世界中的已经走到哪了。
23.Naturalism. Detail.
自然主义。细节。
24.You can get horns, antlers — even if you look close, cloven hooves.
你可以做出犄角，鹿角—— 如果你靠近看，偶蹄。
25.And it raises a question: what changed?
这就引出一个问题：什么发生了改变？
26.And what changed is something you might not have expected in an art, which is math.
发生变化的是一种 你在艺术中可能不曾期待的东西， 那就是数学。
27.That is, people applied mathematical principles to the art, to discover the underlying laws.
也就是说，人们将数学原理应用 到艺术中， 来发现潜在的规律。
28.And that leads to a very powerful tool.
这就形成了一种强大的工具。
29.The secret to productivity in so many fields — and in origami — is letting dead people do your work for you.
在众多领域提高生产力的秘密—— 包括在折纸术中—— 是让死去的人为你工作。
30.(Laughter) Because what you can do is take your problem and turn it into a problem that someone else has solved, and use their solutions.
（笑声） 因为你所能做的 是将你的问题 转变成一个其他人已经解决的问题， 并运用他们的解决方法。
31.And I want to tell you how we did that in origami.
而我想要告诉你们，我们是如何在折纸术中做到这一点的。
32.Origami revolves around crease patterns.
折纸术是围绕折痕图进行的。
33.The crease pattern shown here is the underlying blueprint for an origami figure.
这个折痕图就是一个折纸造型 的设计图
34.And you can’t just draw them arbitrarily.
设计图可不能随便画。
35.They have to obey four simple laws.
它们必须遵循4个简单的规则。
36.And they’re very simple, easy to understand.
它们非常简单，并且很好理解。
37.The first law is two-colorability. You can color any crease pattern with just two colors without ever having the same color meeting.
第一个规则是双可着色性。你可以用两种颜色 填充你想画的的折痕图而 相同的颜色不会相邻。
38.The directions of the folds at any vertex — the number of mountain folds, the number of valley folds — always differs by two. Two more or two less.
在任何顶点的折叠方向– 凸折法的数量，凹折法的数量– 之间总是相差两下。多折或少折两下。
39.Nothing else.
就这么简单。
40.If you look at the angles around the fold, you find that if you number the angles in a circle, all the even-numbered angles add up to a straight line.
如果观察折痕周围的角， 你会发现在数围成一圈的角时， 所有列为偶数的角加起来是一条直线。
41.All the odd-numbered angles add up to a straight line.
所有列为奇数的角加起来是一个直线。
42.And if you look at how the layers stack, you’ll find that no matter how you stack folds and sheets, a sheet can never penetrate a fold.
接下来，如果观察这些纸是怎么叠加起来的， 你会发现不论怎样叠加褶层和纸片， 纸片永远不能 穿透褶层。
43.So that’s four simple laws. That’s all you need in origami.
这就是四则简单的规则。在折纸艺术中这就是全部。
44.All of origami comes from that.
所有的折纸都源于这些。
45.And you’d think, “Can four simple laws give rise to that kind of complexity?”
现在你觉得：“那些复杂的工艺 能是从四则简单的规则中衍生出来的吗？”
46.But indeed, the laws of quantum mechanics can be written down on a napkin, and yet they govern all of chemistry, all of life, all of history.
但是，事实上，量子力学的法则 可以在一张餐巾纸上写出来。 而它们可以支配所有的化学， 甚至生活和历史的全部。
47.If we obey these laws, we can do amazing things.
如果遵循这些规则， 我们能做出令人吃惊的事。
48.So in origami, to obey these laws, we can take simple patterns — like this repeating pattern of folds, called textures — and by itself it’s nothing.
所以折纸时，在遵循这些规则的情况下， 我们可以做出简单的样式– 比如这个重复的折叠样式，叫做纹理– 虽然这样单独看起来很普通。
49.But if we follow the laws of origami, we can put these patterns into another fold that itself might be something very, very simple,
但如果我们遵守折纸的规则， 我们能把这些样式加入另一种折法， 这种折法本身非常非常的简单。
50.but when we put it together, we get something a little different.
但当我们把它加进来， 会得到很不一样的东西。
51.This fish, 400 scales — again, it is one uncut square, only folding.
这条鱼有400片鱼鳞， 同样，它是一张没被剪过的正方形纸张。
52.And if you don’t want to fold 400 scales, you can back off and just do a few things, and add plates to the back of a turtle, or toes.
如果你不想折400片鱼鳞， 你可以退而求其次，做些简单的折叠 得到一只乌龟的背壳或脚趾。
53.Or you can ramp up and go up to 50 stars on a flag, with 13 stripes.
或者可以提升成为一面拥有 50颗星星和13条横条的旗子（美国国旗）。
54.And if you want to go really crazy, 1,000 scales on a rattlesnake.
如果你想做些疯狂的事情， 这有一条有1000片鳞片的响尾蛇。
55.And this guy’s on display downstairs, so take a look if you get a chance.
这个作品展示在楼下， 所以你们有机会可以看看。
56.The most powerful tools in origami have related to how we get parts of creatures.
在折纸艺术中，最有用的方法 和我们怎样构造生物的一部分有关。
57.And I can put it in this simple equation.
我可以用一个简单的等式来解释。
58.We take an idea, combine it with a square, and you get an origami figure.
我们产生了一个想法， 把它与张纸片结合，就能得到一个折纸作品。
59.(Laughter) What matters is what we mean by those symbols.
（笑声） 重要的是这些符号代表什么。
60.And you might say, “Can you really be that specific?
你们可能会问：“真的能做到那么具体吗？
61.I mean, a stag beetle — it’s got two points for jaws, it’s got antennae. Can you be that specific in the detail?”
我是说一只鹿角虫有两个点状的嘴， 和触角。你真的能做到具体到细节吗？”
62.And yeah, you really can.
是的，真的可以。
63.So how do we do that? Well, we break it down into a few smaller steps.
那该怎么做呢？我们把它分成 几个小步骤。
64.So let me stretch out that equation.
为此，让我来展开这个等式。
65.I start with my idea. I abstract it.
我先从我的构思开始，使它抽象化。
66.What’s the most abstract form? It’s a stick figure.
什么是最抽象的形式呢？线条画。
67.And from that stick figure, I somehow have to get to a folded shape that has a part for every bit of the subject.
然后从这个线条画，我得用某种方式得到折叠的式样， 并且包括想要表现对象的所有部分。
68.A flap for every leg.
一片三角形折叠对应一条腿。
69.And then once I have that folded shape that we call the base, you can make the legs narrower, you can bend them, you can turn it into the finished shape.
然后，我们称这个折叠的式样为基础。 你可以使它的腿变细，使其弯曲， 你可以把它做成成品。
70.Now the first step: pretty easy.
第一步：很简单。
71.Take an idea, draw a stick figure.
做出一个构思，画一幅线条图。
72.The last step is not so hard, but that middle step — going from the abstract description to the folded shape — that’s hard.
最后一步也不是很难，但中间的一步– 把抽象的描绘变为折叠的式样– 这很难。
73.But that’s the place where the mathematical ideas can get us over the hump.
但就是在这，数学理论让我们 翻越难关。
74.And I’m going to show you all how to do that so you can go out of here and fold something.
我要向你们展示怎样做， 这样离开这里后，你们可以叠出些东西。
75.But we’re going to start small.
但我们要先从小的开始。
76.This base has a lot of flaps in it.
这个基础有很多片状物。
77.We’re going to learn how to make one flap.
我们要学习怎样做一个片状物。
78.How would you make a single flap?
你会怎样叠一个片状物呢？
79.Take a square. Fold it in half, fold it in half, fold it again, until it gets long and narrow, and then we’ll say at the end of that, that’s a flap.
拿一张正方形的纸，把它对折再对折， 直到它变得又长又细， 然后这个的尾部就是一个片状物。
80.I could use that for a leg, an arm, anything like that.
我能用它做一条腿，一只手臂，和所有相似的东西。
81.What paper went into that flap?
在片状物中是什么样的纸呢？
82.Well, if I unfold it and go back to the crease pattern, you can see that the upper left corner of that shape is the paper that went into the flap.
如果把它展开去看它的折痕图， 你们可以看到在纸片的左上角的形状 就是构成片状物的纸。
83.So that’s the flap, and all the rest of the paper’s left over.
所以那就是一个片状物，和所有剩下的纸。
84.I can use it for something else.
我可以用剩下的部分做点别的。
85.Well, there’s other ways of making a flap.
也有另外的做片状物的方法。
86.There’s other dimensions for flaps.
也有不同形状的片状物。
87.If I make the flaps skinnier, I can use a bit less paper.
如果把片状物叠得更细一些，所用的纸会更少。
88.If I make the flap as skinny as possible, I get to the limit of the minimum amount of paper needed.
如果把片状物尽可能的叠细， 就能只用片状物所需的最少的纸。
89.And you can see there, it needs a quarter-circle of paper to make a flap.
就像你们所看到的，只需要纸上四分之一个圆就可以作出一个片状物。
90.There’s other ways of making flaps.
还有别的做片状物的方法。
91.If I put the flap on the edge, it uses a half circle of paper.
如果把片状物放在纸片边上，就需要一个半圆的纸。
92.And if I make the flap from the middle, it uses a full circle.
如果把片状物放在纸片的中心，就需要一整圆。
93.So no matter how I make a flap, it needs some part of a circular region of paper.
就是说不论怎样叠， 片状物是由 纸上圆形区域的一部分做成的。
94.So now we’re ready to scale up.
现在让我们来提升到新的水平。
95.What if I want to make something that has a lot of flaps?
如果要叠一个有很多片状物的东西该怎么办呢？
96.What do I need? I need a lot of circles.
我需要什么？我需要很多的圆。
97.And in the 1990s, origami artists discovered these principles and realized we could make arbitrarily complicated figures just by packing circles.
在二十世纪九十年代， 折纸艺术家发现了这些规则， 并了解到我们可以通过组合圆形 来叠出任意复杂的形状。
98.And here’s where the dead people start to help us out.
这就是那些死去的人能帮到我们的地方。
99.Because lots of people have studied the problem of packing circles.
因为很多人都研究过 组合圆形的问题。
100.I can rely on that vast history of mathematicians and artists looking at disc packings and arrangements.
我可以依赖那些有关圆的组合和排列的 大量的数学与艺术的历史。
101.And I can use those patterns now to create origami shapes.
然后我可以用这些式样来制造折纸的形状。
102.So we figured out these rules whereby you pack circles, you decorate the patterns of circles with lines according to more rules. That gives you the folds.
我们可以依据这些规则来组合圆形， 依据更多的规矩我们可以 用线条来装饰圆。这就有了折叠线。
103.Those folds fold into a base. You shape the base.
沿这些线折叠就可以得到大体形状。你们就做出了大体的形状。
104.You get a folded shape — in this case, a cockroach.
你们得到一个折叠的形状，在这里，是一只蟑螂。
105.And it’s so simple.
而且它非常的简单。
106.(Laughter) It’s so simple that a computer could do it.
（笑声） 因为它很简单，电脑就可以把它做出来。
107.And you say, “Well, you know, how simple is that?”
你们可能问“那能有多简单呢？”
108.But computers, you need to be able to describe things in very basic terms, and with this we could.
但是要用电脑，你们需要用最基本的方法 来描述一件事物。而这里我们可以做到。
109.So I wrote a computer program a bunch of years ago called TreeMaker, and you can download it from my website.
所以我在很多年前写了一个电脑程序， 叫做TreeMaker(造树者），你们可以在我的网页上下载它。
110.It’s free. It runs on all the major platforms — even Windows.
它是免费的。它可以在大部分的操作系统里面运行，甚至在Windows里。
111.(Laughter) And you just draw a stick figure, and it calculates the crease pattern.
（笑声） 然后你们就可以自己画一个线条图， 这个程序会根据线条图计算折痕。
112.It does the circle packing, calculates the crease pattern, and if you use that stick figure that I just showed, which you can kind of tell — it’s a deer, it’s got antlers —
这个程序可以排列圆形，计算折痕， 还有如果你们用刚才我展示的线条图， 你们可以看出它是一只有角的鹿，
113.you’ll get this crease pattern.
你们就可以得到这个折痕图。
114.And if you take this crease pattern, you fold on the dotted lines, you’ll get a base that you can then shape into a deer, with exactly the crease pattern that you wanted.
用这个折痕图，折叠有虚线的地方， 你们就能得到一个基础，然后再用 你们想用的方法 叠出一只鹿。
115.And if you want a different deer, not a white-tailed deer, you change the packing, and you can do an elk.
如果你们想要一只不同种的鹿， 而不是白尾鹿， 你们可以改变圆形的排列， 然后得到一只麋鹿。
116.Or you could do a moose.
或是一只驼鹿。