1.A great way to start, I think, with my view of simplicity, is to take a look at TED. Here you are, understanding why we’re here, what’s going on, with no difficulty at all.
要谈什么是简单,我想最好的开题方式 就是看看活跃在TED会场上的头脑 你们现在都能明白自己为何会在这里 知道现在有什么事情在发生 并且作出这样的判断都是不需费劲的
2.The best AI in the planet would find it complex and confusing, and my little dog Watson would find it simple and understandable, but would miss the point.
而世界上最厉害的人工智能则会认为这是非常复杂、茫然无绪 而我家的小狗则会认为这是简单且容易理解的 可是它却根本上歪曲了原意
3.(Laughter) He would have a great time.
(笑声) 它也许很开心
4.And of course, if you’re a speaker here, like Hans Rosling, a speaker finds this complex, tricky. But in Hans Rosling’s case, he had a secret weapon yesterday,
假如你能像汉斯·罗斯林那样讲得有趣生动 有些人可能会认为这样的复杂性很难理解 但是罗斯林却有一套秘密(来帮助你理解)
5.literally, in his sword swallowing act.
我说的是 他竟然施起口吞宝剑的绝技来了
6.And I must say I thought of quite a few objects that I might try to swallow today and finally gave up on — but he just did it and that was a wonderful thing.
这让我想到 我今天也可以玩一下吞东西的杂技 但我最终还是放弃了 但是罗斯林做了 我认为那是很了不起一件事情
7.So Puck meant not only are we fools in the pejorative sense, but that we’re easily fooled. In fact what Shakespeare was pointing out is we go to the theater in order to be fooled,
所以说 帕克说我们是傻子时不单单是带有嘲笑的口吻 我们确实很容易被愚弄 莎士比亚就曾经说过 我们上剧院 就是为了被戏弄
8.so we’re actually looking forward to it.
我们内心是有这样一种欲望的
9.We go to magic shows in order to be fooled.
我们去看魔术表演也是同样道理
10.And this makes many things fun, but it makes it difficult to actually get any kind of picture on the world we live in, or on ourselves.
这就让很多事情变得有趣 但是这样一来 我们就很难看出世界以及自身的生存状况
11.And our friend, Betty Edwards, the Drawing On the Right Side of the Brain lady, shows these two tables to her drawing class and says,
我们的朋友 贝蒂·艾伍兹 她告诉我们要用右脑来画画 并且 给她的学生展示了两张桌子 然后说
12.the problem you have with learning to draw is not that you can’t move your hand, but that the way your brain perceives images is faulty.
画画的一大难题 不是你自己不会运笔 而是在于你的大脑观察图像的方式是有错的
13.It’s trying to perceive images into objects rather than seeing what’s there.
就是把图像看成是实物 而不是单纯的只看到图像本身
14.And to prove it, she says, the exact size and shape of these tabletops is the same, and I’m going to prove it to you.
她说 这两个桌面的形状和大小都是一样的 我现在就给大家演示一下
15.She does this with cardboard, but since I have an expensive computer here, I’ll just rotate this little guy around and ….
她是用纸板做演示的 我这里有一台价格不菲的电脑 我就用电脑做吧 我把它转过来
16.Now having seen that — and I’ve seen it hundreds of times, because I use this in every talk I give — I still can’t see that they’re the same size and shape, and I doubt that you can either.
虽然我已经几百次重复这样的演示 因为我做的每一次演讲都会用到这个演示 可我还是不能相信他们是具有同样的形状和 大小的 我想你也不一定肯定的这么说
17.So what do artists do? Well, what artists do is to measure.
那么艺术家们会怎么做?他们会去测量
18.They measure very, very carefully.
他们会测量得非常非常仔细
19.And if you measure very, very carefully with a stiff arm and a straight edge, you’ll see that those two shapes are exactly the same size.
要是你非常认真的拿着一把直尺、绷紧双臂去量的话 你会发现 那两个形状是 完全一样大小的
20.And the Talmud saw this a long time ago, saying, we see things not as they are, but as we are.
《塔木德》一书很早就有这样的记载 我们看到的事物 并不是它们本身的形态 而是他们反映在我们的头脑和思维中的形态
21.I certainly would like to know what happened to the person who had that insight back then, if they actually followed it to its ultimate conclusion.
我很想知道 当初认识到这一点的人 假如他能够将这种想法付诸实践的话 最终将得到什么启示
22.So if the world is not as it seems and we see things as we are, then what we call reality is a kind of hallucination happening inside here. It’s a waking dream.
假如说世界并非如我们所观察到的那个样子 而是我们自身按照自己的理解来看待这个世界 那么我们所言的现实 就是一种幻觉 它就发生在大脑里 我们都沉醉于梦国
23.And understanding that that is what we actually exist in is one of the biggest epistemological barriers in human history.
而要意识到这样一种生存状况 就是人类历史上最大的知识论局限
24.And what that means: “simple and understandable”
那就意味着:所谓的“简单、可理解”
25.might not be actually simple or understandable, and things we think are complex might be made simple and understandable.
可能事实上既不简单 又不容易理解 而那些我们认为是复杂的事物则是由简单、可理解的事物组成的
26.Somehow we have to understand ourselves to get around our flaws.
我们需要理解自我 才能走出我们自身的一些缺陷
27.We can think of ourselves as kind of a noisy channel.
我们可以把自己当成是一种噪声信道
28.The way I think of it is, we can’t learn to see until we admit we’re blind.
我认为 除非我们承认自己是盲的 否则我们不能学会看东西
29.Once you start down at this very humble level, then you can start finding ways to see things.
一旦你从这样谦卑的位置开始做 你就可以掌握看事情的办法
30.And what’s happened over the last four hundred years in particular is that human beings have invented brainlets: little additional parts for our brain,
特别是在过去的400年里 人类发明了“脑挂”(brainlet) 就是各种对大脑的辅助装置
31.made out of powerful ideas that help us see the world in different ways.
这些装置帮助我们 去以一种不一样的眼光 去看待这个世界
32.And these are in the form of sensory apparatus — telescopes, microscopes — reasoning apparatus, various ways of thinking, and most importantly,
它们通常是作为人体感官之辅助出现 比如望远镜、显微镜 以及各种思维上的辅助工具
33.in the ability to change perspective on things.
以及更重要的 就是以全新的视角去看待同样的问题
34.I’ll talk about that a little bit.
我今天要谈的就是这个问题
35.It’s this change in perspective, and what it is we think we’re perceiving, that has helped us make more progress in the last four hundred years
恰恰是这种视野上的改变 以及我们看待事物的态度 使得我们得以在过去的400年里取得了巨大的进步
36.than we have in the rest of human history.
这是人类历史上未曾有过的
37.And yet it is not taught in any K through 12 curriculum in America that I’m aware of.
可是 这样的理念却没有在任何一间幼儿园到中学的课堂上得以呈现
38.So one of the things that goes from simple to complex is when we do more. We like more.
我们做事情做得越来越多的时候 事情就会从简单变为复杂 人喜欢更多的东西
39.If we do more in a kind of a stupid way, the simplicity gets complex.
假如我们是以一种傻乎乎的方式去做事 那么简单的事情也会变得复杂
40.And in fact, we can keep on doing it for a very long time.
事实上 我们可以长期做这样的事情
41.But Murray Gell-Mann yesterday talked about emergent properties.
默里·盖尔曼昨天就提到了一个叫“涌现”的特征
42.Another name for them could be “architecture”
其另一名字就是“建筑”
43.as a metaphor for taking the same old material and thinking about non-obvious, non-simple ways of combining it.
就是把同样的古老的材料 通过不寻常的、不简单的方式来加以组合
44.And in fact, what Murray was talking about yesterday in the fractal beauty of nature, of having the descriptions at various levels be rather similar,
事实上 盖尔曼昨天提到的自然的分形之美 就是指可以在不同的层次 存在结构类似的解释
45.all goes down to the idea that the elementary particles are both sticky and stand-offish, and they’re in violent motion.
而所有的一切皆可归结到基本粒子的解释 这些粒子既是相吸的,又是相斥的 同时又处于不断的变化状态
46.Those three things give rise to all the different levels of what seem to be complexity in our world.
在此三者之上 即可诞生出这个世界上的 千姿百态的复杂
47.But how simple?
但是何为简单?
48.So when I saw the Roslings’ Gapminder stuff a few years ago, I just thought it was the greatest thing I’d seen in conveying complex ideas simply.
几年前我看到罗斯林的Gapminder演示的时候 我认为那是我见过的最好的演示 它很好的把复杂的东西简单化了
49.But then I had a thought of, boy, maybe it’s too simple.
可是转念一想 似乎也做得太简单了
50.And I put some effort in to try and check to see how well these simple portrayals of trends over time actually matched up with some ideas and investigations from the side,
于是我决定去验证一下图上显示出来的数据走势 是否与实际相吻合 事实表明 图上的数据确实是与实际一致的
51.and I found that they matched up very well.
并且关联度非常大
52.So the Roslings have been able to do simplicity without removing what’s important about the data.
所以说 罗斯林能够在保证数据不被破坏的情况下 做出形象化的展示
53.Whereas the film yesterday that we saw of the simulation of the inside of a cell, as a former molecular biologist, I didn’t like that at all.
而在我们昨天看到的那部电影里 那是一个关于细胞内部的模拟 我曾经是一位分子生物学家 但是我不喜欢它的描述
54.Not because it wasn’t beautiful or anything, but because it misses the thing that most students fail to understand about molecular biology, and that is,
不是说它不美 而是说它没能把大多数学生关于分子生物学 感觉难以理解的东西说清楚
55.why is there any probability at all of two complex shapes finding each other just the right way so they combine together and be catalyzed?
那就是 为何两个不同的复杂形状 能够知道对方就是自己需要的伙伴 并且能够相互结合 产生化学作用?
56.And what we saw yesterday was, every reaction was fortuitous.
我们昨天看得到的就是 每一次反应都是相当随机的
57.They just swooped in the air and bound, and something happened.
他们在空中飞舞 而后奇迹就发生了
58.But in fact those molecules are spinning at the rate of about a million revolutions per second.
但事实上 这些分子是以 每秒100万次的速度在旋转
59.They’re agitating back and forth their size every two nanoseconds.
每隔一分钟 他们就会改变自身的大小
60.They’re completely crowded together. They’re jammed, they’re bashing up against each other.
它们都是笼聚在一起的 像是塞车的车龙 相互摩擦
61.And if you don’t understand that in your mental model of this stuff, what happens inside of a cell seems completely mysterious and fortuitous.
假如你不能理解这样的一个模型 简而言之 发生在细胞内部的一切事情是充满神秘感与随意的
62.And I think that’s exactly the wrong image for when you’re trying to teach science.
但这恰恰是一个错误的看法 假如你是教学生科学的话
63.So another thing that we do is to confuse adult sophistication with the actual understanding of some principle.
我们做的另一件事情 就是利用一些具体的例证 来破除成年人某些误解
64.So a kid who’s 14 in high school gets this version of the Pythagorean theorem, which is a truly subtle and interesting proof, but in fact it’s not a good way to start learning about mathematics.
一个14岁的孩子 在学校里学会了这样一套关于勾股定理的方法 这是一个非常微妙而有趣的证明 但这并非学习数学的一个很好的门路
65.So a more direct one, one that gives you more of the feeling of math, is something closer to Pythagoras’ own proof which goes like this.
有一种更直接的方式,它可以让你更好的体验到数学之乐趣 毕达哥拉斯自己采用的就是类似的证明方法
66.So here we have this triangle, and if we surround that C square with three more triangles and we copy that, notice that we can move those triangles down like this,
这里有一个三角形 假如我们在正方形周围 放几个小三角形 大家注意 我可以这样子移动这几个三角形
67.and that leaves two open areas that are kind of suspicious, and bingo. And that is all you have to do.
就在画面中留下两处空白区 看上去似乎有点奇怪 好 我们就这么做可以了
68.And this kind of proof is the kind of proof that you need to learn when you’re learning mathematics in order to get an idea of what it means
这样的证明就是你在学习数学的时候 应该学习的证明的方式 就是首先弄明白原理的实质
69.before you look into the, literally, 12 or 1500 proofs of Pythagoras’ theorem that had been discovered.
而不是首先去看前人得出的 那1500多个证明的思路
70.Now let’s go to young children.
好 我们现在谈谈青年
71.This is a very unusual teacher who was a kindergarten and first-grade teacher, but was a natural mathematician.
这是一位相当特殊的老师 她是一位幼儿园和小学一年级的老师 还是一位天生的数学家
72.So she was like that jazz musician friend you have who never studied music, but is a terrific musician.
她就像一些爵士乐音乐家一样,从未学过器乐 但却是为杰出的音乐家
73.She just had a feeling for math, and here are her six-year-olds, and she’s got them making shapes out of a shape.
她自身对于数学有一种感情 她面对的是6岁的学生 她让孩子玩拼图游戏
74.So they pick a shape they like — a diamond, or a square, or a triangle, or a trapezoid — and then they try and make the next larger shape of that same shape, and the next larger shape.
他们选了自己喜欢的一个形状 比如钻石型 比如方形 比如三角形 或平行四边形 让孩子在此基础上搭建出一个更大的形状
75.And you can see the trapezoids are a little challenging there.
对于孩子而言 平行四边形是一个极大的挑战
76.And [what] this teacher did on every project was to have the children act like first it was a creative arts project and then something like science.
这位老师所做的 就是让孩子感知到 那是一个创意艺术的项目 而后才是科学知识的学习
77.So they’d created these artifacts.
他们制作了这些仿制品
78.Now she had them look at them and do this laborious — which I thought for a long time, until she explained to me, was to slow them down so they’ll think.
老师叫学生看着他们的创作 并且让他们观察很久 我想了很久 不懂 直到她跟我说 她这么做 目的在于让孩子停下来去思考
79.So they’re cutting out the little pieces of cardboard here, and pasting them up.
他们从卡纸上把小纸片剪下来 然后贴在这里
80.But the whole point of this thing is for them to look at this chart and fill it out.
而这一切的目的在于 让他们看到这个表 并且填好它
81.What have you noticed about what you did?
你注意到了什么?
82.And so six-year-old Lauren there noticed that the first one took one, and the second one took three more, and the total was four on that one.
6岁的罗伦注意到 第一格需要一个纸片 第二格则需要额外的3个 总计需要4个
83.The third one took five more, and the total was nine on that one, and then the next one.
第三个则需要额外的5个 加起来是9个 以此类推
84.So she saw right away that the additional tiles that you had to add around the edges was always going to grow by two.
她马上就发现 所需的额外纸片数量总是以2为基准增加 到了边缘的时候就肯定是以2为基数增加
85.So she was very confident about how she made those numbers there.
她对此非常自信
86.And she could see that these were the square numbers up until about six.
她发现一直去到数字6 都会出现平方数
87.Where she wasn’t sure what six times six was, and what seven times seven was.
她还不知道6乘以6等于多少 也不知7乘以7等于多少
88.But then she was confident again.
但她马上又变得自信起来了
89.So that’s what Lauren did.
这就是罗伦的故事
90.And then the teacher, Gillian Ishijima, had the kids bring all of their projects up to the front of the room and put them on the floor.
她的老师 Gillian Ishijima 要求孩子把所有的作业拿到课室前面 扔在地板上
91.And everybody went batshit. Holy shit! They’re the same!
大家都乐了 原来大家得到的是同样的结果
92.No matter what the shapes were, the growth law is the same.
不管大家拿的是什么形状的纸片 最终得出的增长规律是一致的
93.And the mathematicians and scientists in the crowd will recognize these two progressions as a first order discrete differential equation,
在座的数学家和科学家应该知道 这两种演变之名称分别为 一阶微分方程
94.and a second order discrete differential equation.
和二阶微分方程
95.Derived by six-year-olds.
而这居然被6岁的孩子发现了
96.Well, that’s pretty amazing.
实在是妙不可言
97.That isn’t what we usually try to teach six-year-olds.
这可不是我们惯常的教6岁小孩的方法
98.So let’s take a look now at how we might use the computer for some of this.
接下来让我们看看电脑如何帮助我们实现同样的目的
99.And so the first idea here is just to show you the kind of things that children do.
首先我想给大家看看 孩子通常会怎么玩
100.I’m using the software that we’re putting on the 100 dollar laptop.
我用的是OLPC笔记本电脑上的软件
101.So I’d like to draw a little car here.
我先画一辆小小的车
102.I’ll just do this very quickly. And put a big tire on him.
我画得很快 还要加上大大的轮胎
103.And I get a little object here, and I can look inside this object.
好了 现在我有一个东西在这里了 我还能看出其内部之组成
104.I’ll call it a car. And here’s a little behavior: car forward.
我把它成为汽车 我还定义了一个行为 那就是汽车前进
105.Each time I click it, car turn.
我点击它 它就会动
106.If I want to make a little script to do this over and over again, I just drag these guys out and set them going.
要是我要通过脚本来反复实现这样的功能的话 只需要把这些东西拖出来就行了
107.And I can try steering the car here by — see the car turn by five here?
我还能让汽车转弯 看到它稍微转了个弯吗?
108.So what if I click this down to zero?
要是我把这一数值降到零呢
109.It goes straight. That’s a bit of a revelation for nine-year-olds.
汽车就会一直往前走 这对于9岁的孩子而言就是莫大的启示
110.Make it go in the other direction.
还可以让汽车走其他的方向
111.But of course that’s a little bit like kissing your sister as far as driving a car.
但是 单单会开一辆汽车跟 给你的妹妹一个亲吻没有两样
112.So the kids want to do a steering wheel.
孩子想要自己的一个方向盘
113.So they draw a steering wheel.
于是他们自己画一个
114.And we’ll call this a wheel.
我们将其命名为方向盘
115.And, see this wheel’s heading here?
看到方向盘的走势吗?
116.If I turn this wheel, you can see that number over there going minus and positive.
要是我拨弄一下这方向盘 你会看到那个数字在上下波动
117.That’s kind of an invitation to pick up this name of those numbers coming out there and to just drop it into the script here.
我们通过这样的方式 让孩子学会这些数字 他们只需要把数字拉到这里就行了
118.And now I can steer the car with the steering wheel.
现在我就能通过方向盘控制整个汽车了
119.And it’s interesting.
真的很好玩
120.You know how much trouble the children have with variables, but by learning it this way, in a situated fashion, they never forget from this single trial
孩子们对于变量这个概念很难把握 而假如他们是在类似的情景下去学习 他们永远也不会忘记自己所做的实验
121.what a variable is and how to use it.
不会忘记何为变量 也不会忘记变量的使用方法
122.And we can reflect here the way Gillian Ishijima did.
我们可以回想一下 Gillian Ishijima 的那个做法
123.So if you look at the little script here, the speed is always going to be 30.
假如你看看这一脚本 上面写 速度总是保持30英里不变
124.We’re going to move the car, according to that, over and over again.
我们将按照那个规则来驱动车子前进
125.And I’m dropping a little dot for each one of these things.
每走一段我都会让车子留下点印迹
126.They’re evenly spaced because they’re 30 apart.
每两段之间的距离是均等的 都是30