請雙擊下方英文字幕播放視頻。
譯者: Eric Chen
審譯者: Jeannie Cheng
00:18
A great way to start, I think, with my view of simplicity
0
18330
4000
要了解我對簡約的看法最佳的開場是
00:22
is to take a look at TED. Here you are, understanding why we're here,
1
22330
7000
來看看TED。你在這裡試著了解我們為何聚集一堂
00:29
what's going on with no difficulty at all.
2
29330
5000
我們輕易的就可以明白我們為何在此是為了什麼
00:34
The best A.I. in the planet would find it complex and confusing,
3
34330
4000
但是,全世界最好的人工智慧卻會認為這很複雜又令人迷惑
00:38
and my little dog Watson would find it simple and understandable
4
38330
5000
但是我的小狗華森應該覺得這簡單又容易懂
00:43
but would miss the point.
5
43330
2000
不過他可能會錯過重點
00:45
(Laughter)
6
45330
3000
(笑)
00:48
He would have a great time.
7
48330
3000
牠可能會在這裡玩得很開心
00:51
And of course, if you're a speaker here, like Hans Rosling,
8
51330
5000
誠然,你如果是這裡的演講者之一,如 Hans Rosling
00:56
a speaker finds this complex, tricky. But in Hans Rosling's case,
9
56330
5000
會感到演講的複雜與難度。但是對Hans Rosling 來說
01:01
he had a secret weapon yesterday,
10
61330
2000
他昨天啟用了一項秘密武器
01:03
literally, in his sword swallowing act.
11
63330
4000
那可以像是吞劍表演
01:07
And I must say, I thought of quite a few objects
12
67330
2000
我承認我確實想了一大堆物件
01:09
that I might try to swallow today and finally gave up on,
13
69330
5000
用來當做吞劍的道具,不過最後還是放棄了
01:14
but he just did it and that was a wonderful thing.
14
74330
4000
但是,他做到了,這真是一件妙事
01:18
So Puck meant not only are we fools in the pejorative sense,
15
78330
5000
因此 Puck 認為我們不只輕易的被耍了
01:23
but that we're easily fooled. In fact, what Shakespeare
16
83330
4000
而且我們很容易被騙。事實上莎士比亞
01:27
was pointing out is we go to the theater in order to be fooled,
17
87330
3000
曾指出,我們進戲院看戲,就是為了被戲弄
01:30
so we're actually looking forward to it.
18
90330
4000
而且,我們是很期待去經驗這樣的事情
01:34
We go to magic shows in order to be fooled.
19
94330
2000
我們看魔術也是一樣
01:36
And this makes many things fun, but it makes it difficult to actually
20
96330
8000
許多事因此而變得有趣,不過這卻令我們難於
01:44
get any kind of picture on the world we live in or on ourselves.
21
104330
4000
去理解我們所在的世界,甚至於了解自己
01:48
And our friend, Betty Edwards,
22
108330
2000
我們的朋友 Betty Edwards
01:50
the "Drawing on the Right Side of the Brain" lady, shows these two tables
23
110330
3000
在那個以右腦來繪畫的人,她展示了兩張桌子
01:53
to her drawing class and says,
24
113330
5000
她對著繪圖班的同學說
01:58
"The problem you have with learning to draw
25
118330
4000
在你們學習繪畫時碰到的困難
02:02
is not that you can't move your hand,
26
122330
2000
並不是你們不肯動手
02:04
but that the way your brain perceives images is faulty.
27
124330
6000
而是你們的大腦接收到畫面的資訊是錯的
02:10
It's trying to perceive images into objects
28
130330
2000
大腦會把圖形轉化成物件
02:12
rather than seeing what's there."
29
132330
2000
而不是真的去看物件的本身
02:14
And to prove it, she says, "The exact size and shape of these tabletops
30
134330
5000
她說:為了證明這兩張桌子的大小與形狀是一樣的
02:19
is the same, and I'm going to prove it to you."
31
139330
3000
我現在要證明給你們看
02:22
She does this with cardboard, but since I have
32
142330
3000
她當時是用卡紙板來做
02:25
an expensive computer here
33
145330
3000
不過,有鑑於我這裡有一台昂貴的電腦
02:28
I'll just rotate this little guy around and ...
34
148330
3000
旋轉一下這個小東西過去
02:34
Now having seen that -- and I've seen it hundreds of times,
35
154330
3000
現在我們證實了 -- 而我已經看了上百次
02:37
because I use this in every talk I give -- I still can't see
36
157330
4000
因為每次演講到這個議題都會舉這個例子 --
02:41
that they're the same size and shape, and I doubt that you can either.
37
161330
5000
我還是無法看出它們的大小與形狀相同,我相信你們也不行
02:46
So what do artists do? Well, what artists do is to measure.
38
166330
5000
那麼藝術家們在做什麼呢?他們測量
02:51
They measure very, very carefully.
39
171330
2000
非常、非常仔細的測量
02:53
And if you measure very, very carefully with a stiff arm and a straight edge,
40
173330
4000
如果你非常、非常小心的測量,同時手很穩、尺很直
02:57
you'll see that those two shapes are
41
177330
2000
你會發覺這兩個形狀
02:59
exactly the same size.
42
179330
3000
確實一樣大
03:02
And the Talmud saw this a long time ago, saying,
43
182330
5000
Talmud 在很久以前就發現了這個現象
03:07
"We see things not as they are, but as we are."
44
187330
3000
他說:我們看東西並不是以物件的本身,而是以我們對於它的認知
03:10
I certainly would like to know what happened to the person
45
190330
2000
我很想知道那些,在那個時代
03:12
who had that insight back then,
46
192330
3000
就可以看到這些事實的人的遭遇
03:15
if they actually followed it to its ultimate conclusion.
47
195330
4000
看看他們是否真的遵循這樣的結論
03:21
So if the world is not as it seems and we see things as we are,
48
201330
2000
如果這個世界不是我們看到的,而是按照我們的想像
03:23
then what we call reality is a kind of hallucination
49
203330
6000
那麼我們所謂的真實只是一種
03:29
happening inside here. It's a waking dream,
50
209330
3000
發生在這裡面的幻覺,它稱作白日夢
03:32
and understanding that that is what we actually exist in
51
212330
5000
要明白我們確實存在
03:37
is one of the biggest epistemological barriers in human history.
52
217330
5000
也是人類歷史上對於認知的最大障礙之一
03:42
And what that means: "simple and understandable"
53
222330
2000
也就是說:簡單而易懂的
03:44
might not be actually simple or understandable,
54
224330
3000
可能實際上並不是:簡單而易懂
03:47
and things we think are "complex" might be made simple and understandable.
55
227330
6000
我們認為複雜的也許是簡單易懂
03:53
Somehow we have to understand ourselves to get around our flaws.
56
233330
4000
有時候,我們必須了解自己而避開自己的缺陷
03:57
We can think of ourselves as kind of a noisy channel.
57
237330
2000
我們可以認為自己是一種雜訊的來源
03:59
The way I think of it is, we can't learn to see
58
239330
5000
我認為:我們無法一窺全貌
04:04
until we admit we're blind.
59
244330
2000
除非我們承認自己的盲點
04:06
Once you start down at this very humble level,
60
246330
4000
一旦你可以從一個謙卑的角度切入
04:10
then you can start finding ways to see things.
61
250330
3000
則能夠開始找到真正看東西的方法
04:13
And what's happened, over the last 400 years in particular,
62
253330
5000
特別是過去四百年來所發生的現象
04:18
is that human beings have invented "brainlets" --
63
258330
3000
就是人類開始將大腦分區
04:21
little additional parts for our brain --
64
261330
4000
我們了解大腦多一點
04:25
made out of powerful ideas that help us
65
265330
2000
就能幫助我們創造有利的創意
04:27
see the world in different ways.
66
267330
2000
去用不同的方式來看這個世界
04:29
And these are in the form of sensory apparatus --
67
269330
3000
以感官的儀器的方式展現
04:32
telescopes, microscopes -- reasoning apparatus --
68
272330
5000
望遠鏡、顯微鏡 -- 理性的儀器設備
04:37
various ways of thinking -- and, most importantly,
69
277330
4000
各式各樣的思維,而最重要的是
04:41
in the ability to change perspective on things.
70
281330
4000
有能力以不同的觀點去觀察事情
04:45
I'll talk about that a little bit.
71
285330
1000
我來深入一點
04:46
It's this change in perspective
72
286330
2000
這個觀點上的改變
04:48
on what it is we think we're perceiving
73
288330
3000
和我們所認為感知的
04:51
that has helped us make more progress in the last 400 years
74
291330
5000
已經幫助我們在過去四百年當中進步許多
04:56
than we have in the rest of human history.
75
296330
2000
相較於之前的人類歷史
04:58
And yet, it is not taught in any K through 12 curriculum in America that I'm aware of.
76
298330
8000
但是據我所知在美國的教育系統裡這並未被重視
05:11
So one of the things that goes from simple to complex
77
311330
2000
其中一件事情是,當我們把事情從簡單變成複雜
05:13
is when we do more. We like more.
78
313330
3000
是當我們想要更多。我們喜歡更多
05:16
If we do more in a kind of a stupid way,
79
316330
3000
如果我們用了笨的方法來追求更多
05:19
the simplicity gets complex
80
319330
3000
那麼簡單就複雜化了
05:22
and, in fact, we can keep on doing it for a very long time.
81
322330
5000
事實上,我們會一直持續的這樣做
05:27
But Murray Gell-Mann yesterday talked about emergent properties;
82
327330
3000
不過 Murray Gell-Mann 昨天談到了一個意外的特性
05:30
another name for them could be "architecture"
83
330330
4000
它另外的名字叫做「建築」
05:34
as a metaphor for taking the same old material
84
334330
4000
拿來當做隱喻,拿一些古老的素材
05:38
and thinking about non-obvious, non-simple ways of combining it.
85
338330
7000
想一些不明顯意見、複雜的方式去結合
05:45
And in fact, what Murray was talking about yesterday in the fractal beauty of nature --
86
345330
8000
事實上, Murray 昨天談到的是大自然不規則的美
05:53
of having the descriptions
87
353330
2000
它的描述
05:55
at various levels be rather similar --
88
355330
4000
在不同的層次下可以如此相似
05:59
all goes down to the idea that the elementary particles
89
359330
5000
歸根究底就是分子元素
06:04
are both sticky and standoffish,
90
364330
3000
既能結合又可以獨力
06:07
and they're in violent motion.
91
367330
4000
而他們都在劇烈的活動
06:11
Those three things give rise to all the different levels
92
371330
3000
以上三點將我們的世界提升到了
06:14
of what seem to be complexity in our world.
93
374330
4000
所有看似繁雜的層次
06:20
But how simple?
94
380330
2000
哪究竟有多簡單?
06:22
So, when I saw Roslings' Gapminder stuff a few years ago,
95
382330
5000
幾年前當我看見 Roslings' Gapminder 概念時
06:27
I just thought it was the greatest thing I'd seen
96
387330
2000
認為是我見過最好的東西
06:29
in conveying complex ideas simply.
97
389330
5000
將複雜的概念簡單化
06:34
But then I had a thought of, "Boy, maybe it's too simple."
98
394330
3000
但是,我又想到~天啊!這會不會太簡單了
06:37
And I put some effort in to try and check
99
397330
5000
於是我試著去體驗與檢查
06:42
to see how well these simple portrayals of trends over time
100
402330
4000
看看這些簡單的模式如何經過時間
06:46
actually matched up with some ideas and investigations from the side,
101
406330
5000
去確切的與其他的概念和調查配合在一起
06:51
and I found that they matched up very well.
102
411330
2000
我發現它們非常的相符
06:53
So the Roslings have been able to do simplicity
103
413330
5000
因此 Roslings 的概念可以將事情簡單化
06:58
without removing what's important about the data.
104
418330
4000
同時不會失去重要的資訊
07:02
Whereas the film yesterday that we saw
105
422330
4000
如同我們昨天看到的影片
07:06
of the simulation of the inside of a cell,
106
426330
2000
模仿細胞內部
07:08
as a former molecular biologist, I didn't like that at all.
107
428330
6000
身為一個前生物學家來說,我並不喜歡
07:14
Not because it wasn't beautiful or anything,
108
434330
2000
並不是因為它不美麗或其他因素
07:16
but because it misses the thing that most students fail to understand
109
436330
5000
而是他缺少了些讓大部分學生都不容易理解的部份
07:21
about molecular biology, and that is:
110
441330
3000
對於分子生物學來說
07:24
why is there any probability at all of two complex shapes
111
444330
5000
沒有解釋了為什麼要有兩個複雜的形狀的機率
07:29
finding each other just the right way
112
449330
2000
以正確的方式找到對方
07:31
so they combine together and be catalyzed?
113
451330
3000
而相互的結合與催化
07:34
And what we saw yesterday was
114
454330
2000
然而我們昨天所看到的是
07:36
every reaction was fortuitous;
115
456330
3000
所有的反應都是偶然的。
07:39
they just swooped in the air and bound, and something happened.
116
459330
4000
它們就那麼分散到空氣中結合在一起,然後發生了反應
07:43
But in fact, those molecules are spinning at the rate of
117
463330
4000
然而,那些分子以一定的速度旋轉
07:47
about a million revolutions per second;
118
467330
3000
將近每秒一百萬轉
07:50
they're agitating back and forth their size every two nanoseconds;
119
470330
6000
它們以兩毫微秒的速度相互攪動
07:56
they're completely crowded together, they're jammed,
120
476330
3000
它們完全的擠在一起,它們卡住了
07:59
they're bashing up against each other.
121
479330
3000
它們撲向對方
08:02
And if you don't understand that in your mental model of this stuff,
122
482330
3000
如果你不能理智地明白這些事
08:05
what happens inside of a cell seems completely mysterious and fortuitous,
123
485330
5000
在細胞裡所發生的事就全然是神秘和偶然
08:10
and I think that's exactly the wrong image
124
490330
2000
而我認為這就是個完全錯誤的圖像
08:12
for when you're trying to teach science.
125
492330
3000
如果你試著去教科學
08:18
So, another thing that we do is to confuse adult sophistication
126
498330
5000
另外,我們常常做出令人混淆的世故
08:23
with the actual understanding of some principle.
127
503330
5000
即使我們只懂得其中的一些道理
08:28
So a kid who's 14 in high school
128
508330
2000
一個14歲上中學的孩子
08:30
gets this version of the Pythagorean theorem,
129
510330
6000
他拿到畢氏定理課本的時候
08:36
which is a truly subtle and interesting proof,
130
516330
3000
也是個有趣又微妙的證明
08:39
but in fact it's not a good way to start learning about mathematics.
131
519330
7000
不過這不是個開始學數學的好方法
08:46
So a more direct one, one that gives you more of the feeling of math,
132
526330
5000
最好的方法應該是更直接的,一個可以給你關於數學更直觀的感覺
08:51
is something closer to Pythagoras' own proof, which goes like this:
133
531330
4000
就畢達哥拉斯自己所用的版本,它就像螢幕所顯示的一樣
08:55
so here we have this triangle, and if we surround that C square with
134
535330
6000
當我們拿到這個三角形,如果我們用一個C正方形圍繞它
09:01
three more triangles and we copy that,
135
541330
3000
多出三個三角形,然後我們複製它
09:04
notice that we can move those triangles down like this.
136
544330
5000
發現我們可以把這三角形像這樣移下
09:09
And that leaves two open areas that are kind of suspicious ...
137
549330
3000
留下了兩個開放的空間讓我們思考
09:12
and bingo. That is all you have to do.
138
552330
7000
對了,這就是你所要做的
09:19
And this kind of proof is the kind of proof
139
559330
2000
而這樣的證據就是我們要的證明
09:21
that you need to learn when you're learning mathematics
140
561330
3000
也是你學習數學的時候所需要學習到的
09:24
in order to get an idea of what it means
141
564330
3000
讓你明瞭它真正的意涵
09:27
before you look into the, literally, 1,200 or 1,500 proofs
142
567330
4000
在你進入這12到1500個證明
09:31
of Pythagoras' theorem that have been discovered.
143
571330
3000
在已被發現的畢達哥拉斯定律之前
09:37
Now let's go to young children.
144
577330
3000
現在我們來看看小朋友們
09:40
This is a very unusual teacher
145
580330
2000
一位非比尋常的老師
09:42
who was a kindergarten and first-grade teacher,
146
582330
4000
教導幼稚園和一年級新生
09:46
but was a natural mathematician.
147
586330
2000
但是天生就是個數學家
09:48
So she was like that jazz musician friend you have who never studied music
148
588330
5000
她就像你的爵士音樂家朋友卻從來沒有上過音樂學院
09:53
but is a terrific musician;
149
593330
2000
不過卻是傑出的樂手
09:55
she just had a feeling for math.
150
595330
2000
她就是對數學有天份
09:57
And here are her six-year-olds,
151
597330
3000
在這裡有她才六歲的學生
10:00
and she's got them making shapes out of a shape.
152
600330
5000
她著他們拿著形狀創作出更多的形狀
10:05
So they pick a shape they like -- like a diamond, or a square,
153
605330
2000
他們拿起他們喜愛的形狀 -- 菱形或是一個方形
10:07
or a triangle, or a trapezoid -- and then they try and make
154
607330
3000
或三角形,或梯形,然後他們就常試著去創作
10:10
the next larger shape of that same shape, and the next larger shape.
155
610330
4000
然後從一個形狀嘗試更大的一個形狀,然後再試另一個大形狀
10:14
You can see the trapezoids are a little challenging there.
156
614330
4000
而你會發現不規則多邊形更具挑戰性
10:18
And what this teacher did on every project
157
618330
3000
這位老師「所做」出的每到題
10:21
was to have the children act like first it was a creative arts project,
158
621330
5000
就像是讓小朋友參與一個新的藝術創作一樣
10:26
and then something like science.
159
626330
2000
然後才是像是科學這樣的東西
10:28
So they had created these artifacts.
160
628330
2000
而創作出了這些手工藝品
10:30
Now she had them look at them and do this ... laborious,
161
630330
4000
老師要他們注視這些形狀,然後動手做
10:34
which I thought for a long time, until she explained to me was
162
634330
4000
這讓我思考了很長的時間,直到她解釋給我聽
10:38
to slow them down so they'll think.
163
638330
3000
是讓他們慢下來以利他們的思考
10:41
So they're cutting out the little pieces of cardboard here
164
641330
3000
然後他們切下這些小紙板
10:44
and pasting them up.
165
644330
2000
將他們貼好
10:46
But the whole point of this thing is
166
646330
4000
然而這整個的行動的意義是
10:50
for them to look at this chart and fill it out.
167
650330
3000
讓他們看懂這些表格並將它填滿
10:53
"What have you noticed about what you did?"
168
653330
4000
你注意到了你會做什麼嗎?
10:57
And so six-year-old Lauren there noticed that the first one took one,
169
657330
4000
六歲的 Lauren 發覺第一個用掉了一個
11:01
and the second one took three more
170
661330
5000
然後第二個多用了三個
11:06
and the total was four on that one,
171
666330
2000
而整個用掉了四個
11:08
the third one took five more and the total was nine on that one,
172
668330
4000
第三個多用了五個,整體的數量是九個
11:12
and then the next one.
173
672330
1000
然後繼續下一個
11:13
She saw right away that the additional tiles that you had to add
174
673330
5000
因此她馬上得到啟發而知道她必須學會加上去
11:18
around the edges was always going to grow by two,
175
678330
4000
沿著邊緣總是要加上2
11:22
so she was very confident about how she made those numbers there.
176
682330
3000
接下來她很有自信的知道她可以將數字放在哪裡
11:25
And she could see that these were the square numbers up until about six,
177
685330
5000
而且她可以看出這些數字直到6都是平方數
11:30
where she wasn't sure what six times six was
178
690330
3000
但她卻不是很確定六乘以六是什麼
11:33
and what seven times seven was,
179
693330
2000
也不確定七乘以七是什麼
11:35
but then she was confident again.
180
695330
3000
不過她再次感覺信心
11:38
So that's what Lauren did.
181
698330
2000
這就是 Lauren 所做的
11:40
And then the teacher, Gillian Ishijima, had the kids
182
700330
4000
之後這位老師 Gillian Ishijima 帶著孩子們
11:44
bring all of their projects up to the front of the room and put them on the floor,
183
704330
3000
帶著所有的作品來到房屋的前面,將他們放在地板上
11:47
and everybody went batshit: "Holy shit! They're the same!"
184
707330
8000
而每個人都十分驚訝,天啊!他們是一樣的!
11:55
No matter what the shapes were, the growth law is the same.
185
715330
4000
無論是什麼樣的形狀,增長的規律卻是一樣的
11:59
And the mathematicians and scientists in the crowd
186
719330
3000
就群眾中的數學家與科學家而言
12:02
will recognize these two progressions
187
722330
2000
他們發現了這兩個方程式
12:04
as a first-order discrete differential equation
188
724330
3000
第一個就是一組微分方程式
12:07
and a second-order discrete differential equation,
189
727330
5000
和另一個第二組微分方程式
12:12
derived by six-year-olds.
190
732330
4000
被一位六歲的小朋友所執行
12:16
Well, that's pretty amazing.
191
736330
1000
這~實在非常令人吃驚
12:17
That isn't what we usually try to teach six-year-olds.
192
737330
3000
這的確不是我們平常教導六歲的小朋友的知識
12:20
So, let's take a look now at how we might use the computer for some of this.
193
740330
7000
現在讓我們看看,如何運用在電腦上運用這些
12:27
And so the first idea here is
194
747330
4000
第一個想法是
12:31
just to show you the kind of things that children do.
195
751330
4000
單純的展示小朋友所做的
12:35
I'm using the software that we're putting on the $100 laptop.
196
755330
5000
我將這個軟體安裝在這一百美金的電腦上
12:40
So I'd like to draw a little car here --
197
760330
6000
現在我想來畫一部小車
12:46
I'll just do this very quickly -- and put a big tire on him.
198
766330
7000
我就快快的畫一下,然後給他加上大輪胎
12:59
And I get a little object here and I can look inside this object,
199
779330
4000
現在我得到了一個小物件,然後我可以從內部檢視這個物件
13:03
I'll call it a car. And here's a little behavior: car forward.
200
783330
5000
我把它稱作是一台車,而在這裡給這個車子一個前進的動作
13:08
Each time I click it, car turn.
201
788330
3000
我每按一下,車轉
13:11
If I want to make a little script to do this over and over again,
202
791330
2000
如果我要寫個程式不斷的重複這樣的動作
13:13
I just drag these guys out and set them going.
203
793330
5000
我只需要把它拉過來設定他怎麼走
13:20
And I can try steering the car here by ...
204
800330
3000
然後我想從這裡駕駛它
13:23
See the car turn by five here?
205
803330
2000
你們可以看到車子轉了五度
13:25
So what if I click this down to zero?
206
805330
3000
如果我把這裡的數字設為零?
13:28
It goes straight. That's a big revelation for nine-year-olds.
207
808330
5000
它就會向前,這是受到一位九歲大的小朋友啟發而來
13:33
Make it go in the other direction.
208
813330
2000
讓它走想另一個方向
13:35
But of course, that's a little bit like kissing your sister
209
815330
2000
當然,這有點像在親你妹妹
13:37
as far as driving a car,
210
817330
3000
當你駕駛這輛車
13:40
so the kids want to do a steering wheel;
211
820330
3000
小孩子都想要一個方向盤
13:43
so they draw a steering wheel.
212
823330
3000
因此畫了一個方向盤
13:46
And we'll call this a wheel.
213
826330
5000
我們就稱之為方向盤
13:51
See this wheel's heading here?
214
831330
4000
所以,看到這個方向盤帶領我們去那兒嗎?
13:55
If I turn this wheel, you can see that number over there going minus and positive.
215
835330
5000
如果我轉一下這個方向盤,你可以看到上面的數字增多或減少
14:00
That's kind of an invitation to pick up this name of
216
840330
2000
這就像是一個邀請函
14:02
those numbers coming out there
217
842330
3000
請你在數字中挑出一個來
14:05
and to just drop it into the script here,
218
845330
2000
然後將它丟到程式碼當中
14:07
and now I can steer the car with the steering wheel.
219
847330
5000
現在我就可以用方向盤駕駛車子了
14:12
And it's interesting.
220
852330
2000
這是很有趣的
14:14
You know how much trouble the children have with variables,
221
854330
3000
你知道這些變數帶給小朋友多大的困擾嗎
14:17
but by learning it this way, in a situated fashion,
222
857330
2000
但是這樣的學習方法,在這種的潮流,
14:19
they never forget from this single trial
223
859330
3000
他們絕對不會忘記這個實驗
14:22
what a variable is and how to use it.
224
862330
3000
變數是怎麼使用的
14:25
And we can reflect here the way Gillian Ishijima did.
225
865330
2000
我們也可以對照 Gillian Ishijima 的作法
14:27
So if you look at the little script here,
226
867330
2000
請你看一下這個小程式
14:29
the speed is always going to be 30.
227
869330
2000
速度持續著在30
14:31
We're going to move the car according to that over and over again.
228
871330
5000
我們將按照這個數字重複的來操控這車
14:36
And I'm dropping a little dot for each one of these things;
229
876330
4000
我在每一段中留下一個點
14:40
they're evenly spaced because they're 30 apart.
230
880330
3000
它們將有相同的間隔因為它們相距30
14:43
And what if I do this progression that the six-year-olds did
231
883330
3000
但如果我也像之前六歲小孩一樣做級數
14:46
of saying, "OK, I'm going to increase the speed by two each time,
232
886330
5000
我會說:好吧,每一段的速度都會翻兩倍
14:51
and then I'm going to increase the distance by the speed each time?
233
891330
3000
而我將每段速度增加距離
14:54
What do I get there?"
234
894330
4000
我會得到什麼樣的結果呢
14:58
We get a visual pattern of what these nine-year-olds called acceleration.
235
898330
7000
我們會得到一個九歲大的孩子所看見的視覺模式並稱之為加速
15:05
So how do the children do science?
236
905330
2000
那麼小孩子如何去面對科學呢?
15:08
(Video) Teacher: [Choose] objects that you think will fall to the Earth at the same time.
237
908330
3000
(影片)老師:這些你以為會同時掉落到地面的物件
15:11
Student 1: Ooh, this is nice.
238
911330
3000
這很有意思
15:18
Teacher: Do not pay any attention
239
918330
2000
老師:請別管
15:20
to what anybody else is doing.
240
920330
3000
其他人在做什麼
15:35
Who's got the apple?
241
935330
2000
誰得到那個蘋果
15:37
Alan Kay: They've got little stopwatches.
242
937330
2000
Alan Kay:他們拿著一個小碼錶
15:44
Student 2: What did you get? What did you get?
243
944330
2000
老師:你得到了什麼?你得到了什麼?
15:46
AK: Stopwatches aren't accurate enough.
244
946330
3000
AK:碼錶並不夠精準
15:49
Student 3: 0.99 seconds.
245
949330
2000
女孩:0.99秒
15:52
Teacher: So put "sponge ball" ...
246
952330
3000
老師:那放「海綿球」
15:56
Student 4l: [I decided to] do the shot put and the sponge ball
247
956330
3000
女孩:那裡有一個鉛球和一個海綿球
15:59
because they're two totally different weights,
248
959330
3000
這兩個物件擁有完全不同的重量
16:02
and if you drop them at the same time,
249
962330
2000
如果你同時間扔下他們
16:04
maybe they'll drop at the same speed.
250
964330
2000
也許他們會以相同的速度下降
16:06
Teacher: Drop. Class: Whoa!
251
966330
2000
老師:扔下
16:10
AK: So obviously, Aristotle never asked a child
252
970330
3000
顯然的 Aristotle (亞里斯多德)從未問過一個小孩
16:13
about this particular point
253
973330
3000
在這個特別的範疇
16:16
because, of course, he didn't bother doing the experiment,
254
976330
2000
因為顯然的他不會去做這樣的實驗
16:18
and neither did St. Thomas Aquinas.
255
978330
2000
而 St. Thomas Aquinas (聖安東尼.阿魁那斯)也不會這麼做
16:20
And it was not until Galileo actually did it
256
980330
2000
直到 Galileo (伽利略)做了一些
16:22
that an adult thought like a child,
257
982330
3000
讓成人像小孩一般思考
16:25
only 400 years ago.
258
985330
3000
距今已有四百年
16:28
We get one child like that about every classroom of 30 kids
259
988330
4000
現在我們可以從30個孩子一班裡面發覺一個這樣的孩子
16:32
who will actually cut straight to the chase.
260
992330
3000
會不斷的去探索
16:35
Now, what if we want to look at this more closely?
261
995330
3000
現在,假設我們要繼續深入探討
16:38
We can take a movie of what's going on,
262
998330
3000
我們可以透過拍攝影像來觀察
16:41
but even if we single stepped this movie,
263
1001330
2000
不過就算是我們慢格放映這影片
16:43
it's tricky to see what's going on.
264
1003330
2000
也很難得看得出怎麼一回事
16:45
And so what we can do is we can lay out the frames side by side
265
1005330
3000
因此我們能做的就是一格、一格畫面慢慢放來看
16:48
or stack them up.
266
1008330
2000
或者是把他們堆疊起來
16:50
So when the children see this, they say, "Ah! Acceleration,"
267
1010330
5000
而孩子們看到這個現象就會說:阿~加速
16:55
remembering back four months when they did their cars sideways,
268
1015330
3000
讓他們回憶起幾個月前他們做的車子圖片
16:58
and they start measuring to find out what kind of acceleration it is.
269
1018330
6000
他們開始測量試著找出是那一種加速的模式
17:04
So what I'm doing is measuring from the bottom of one image
270
1024330
6000
而我所做的就是從底層開始測量一個圖片
17:10
to the bottom of the next image, about a fifth of a second later,
271
1030330
5000
約五分一秒後在下一個圖片的底部測量
17:15
like that. And they're getting faster and faster each time,
272
1035330
2000
就像這樣,就會逐次加快速度
17:17
and if I stack these guys up, then we see the differences; the increase
273
1037330
10000
如果我把這些都堆疊起來,那我們就可以看出分別,增加
17:27
in the speed is constant.
274
1047330
3000
而速度則是一致的
17:30
And they say, "Oh, yeah. Constant acceleration.
275
1050330
2000
然他們就會說:喔~這是等速的加速
17:32
We've done that already."
276
1052330
2000
這樣我們就成功啦
17:34
And how shall we look and verify that we actually have it?
277
1054330
8000
那麼我們該怎麼樣去確認我們做的對不對?
17:42
So you can't tell much from just making the ball drop there,
278
1062330
5000
我們的確不可以像丟一個球到目標一般決定
17:47
but if we drop the ball and run the movie at the same time,
279
1067330
4000
但如果我們我們同時間丟一個球和放映影片
17:53
we can see that we have come up with an accurate physical model.
280
1073330
5000
我們就可以發覺我們創造了一個準確的物理模型
18:00
Galileo, by the way, did this very cleverly
281
1080330
4000
伽利略,順便提一下,他用很聰明的方式做到這一點
18:04
by running a ball backwards down the strings of his lute.
282
1084330
3000
他用他的魯特琴(lute)弦反彈他的球
18:07
I pulled out those apples to remind myself to tell you that
283
1087330
5000
我把這些蘋果拿出來是要提醒我自己別忘了告訴你們
18:12
this is actually probably a Newton and the apple type story,
284
1092330
5000
這可以說是一個牛頓與蘋果式的故事
18:17
but it's a great story.
285
1097330
2000
而且是一個偉大的故事
18:19
And I thought I would do just one thing
286
1099330
2000
我想我還要再做一件事情
18:21
on the $100 laptop here just to prove that this stuff works here.
287
1101330
10000
利用我這一百元美金的筆電證明這些東西是行得通的
18:31
So once you have gravity, here's this --
288
1111330
3000
你擁有地心引力,像是地球這兒
18:34
increase the speed by something,
289
1114330
2000
用某種東西增加速度
18:36
increase the ship's speed.
290
1116330
3000
加速一個船的速度
18:39
If I start the little game here that the kids have done,
291
1119330
3000
如果我摹擬孩子們所做的去弄個小遊戲
18:42
it'll crash the space ship.
292
1122330
2000
這太空船會墜毀
18:44
But if I oppose gravity, here we go ... Oops!
293
1124330
4000
不過如果我有地心引力~讓我們來~哎呀
18:48
(Laughter)
294
1128330
2000
(笑聲)
18:50
One more.
295
1130330
1000
我們再來一次
18:54
Yeah, there we go. Yeah, OK?
296
1134330
5000
好極了,我們來吧~Yeah,OK?
18:59
I guess the best way to end this is with two quotes:
297
1139330
7000
我想引用兩段名言來結束今天的演講
19:06
Marshall McLuhan said,
298
1146330
2000
Marshall McLuhan 說
19:08
"Children are the messages that we send to the future,"
299
1148330
4000
『兒童是我們向未來發出的訊息』
19:12
but in fact, if you think of it,
300
1152330
2000
不過事實上,如果你想一想
19:14
children are the future we send to the future.
301
1154330
2000
是兒童將我們送向未來
19:16
Forget about messages;
302
1156330
3000
忘記訊息這事情
19:19
children are the future,
303
1159330
3000
兒童就是未來
19:22
and children in the first and second world
304
1162330
2000
在第一和第二世界裡的孩童
19:24
and, most especially, in the third world
305
1164330
3000
特別是第三世界的孩童
19:27
need mentors.
306
1167330
2000
都需要導師引領
19:29
And this summer, we're going to build five million of these $100 laptops,
307
1169330
5000
在這個夏天,我們將製做五百萬台百元美金筆記型電腦
19:34
and maybe 50 million next year.
308
1174330
2000
然後下一年是五千萬台
19:36
But we couldn't create 1,000 new teachers this summer to save our life.
309
1176330
7000
但是我們不能在這個夏天創造出一千個新的老師來拯救我們的未來
19:43
That means that we, once again, have a thing where we can put technology out,
310
1183330
6000
這代表了再一次我們有需要利用科技來傳播重要的訊息
19:49
but the mentoring that is required to go
311
1189330
3000
不過導師才是我們的需求
19:52
from a simple new iChat instant messaging system
312
1192330
5000
從一個簡單的 iChat 即時通系統
19:57
to something with depth is missing.
313
1197330
2000
到一些具有深度的訊息中缺少了一部份
19:59
I believe this has to be done with a new kind of user interface,
314
1199330
3000
我相信這可能引導至一個新的使用者介面
20:02
and this new kind of user interface could be done
315
1202330
4000
而這樣的使用者介面是可以做得到的
20:06
with an expenditure of about 100 million dollars.
316
1206330
5000
大約花費一億元美金
20:11
It sounds like a lot, but it is literally 18 minutes of what we're spending in Iraq --
317
1211330
7000
這聽起來好像很多,但是只是我們在伊拉克18分鐘的花費
20:18
we're spending 8 billion dollars a month; 18 minutes is 100 million dollars --
318
1218330
5000
我們每個月花費八十億美金,十八分鐘剛好是一億美金
20:23
so this is actually cheap.
319
1223330
2000
因此這實在是很便宜
20:25
And Einstein said,
320
1225330
4000
正如愛因斯坦所說
20:29
"Things should be as simple as possible, but not simpler."
321
1229330
3000
『事情可以越簡單越好,但是人不可以簡單』
20:32
Thank you.
322
1232330
1000
謝謝你
New videos
關於本網站
本網站將向您介紹對學習英語有用的 YouTube 視頻。 您將看到來自世界各地的一流教師教授的英語課程。 雙擊每個視頻頁面上顯示的英文字幕,從那裡播放視頻。 字幕與視頻播放同步滾動。 如果您有任何意見或要求,請使用此聯繫表與我們聯繫。