TED2004
Steven Strogatz: The science of sync
Steven Strogats談同步
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數學家Steven Strogats談生物（如：鳥類、螢火蟲、魚類）如何在無人發號司令的情況下同步成一個群體。這個有力的同步化傾向也延伸到非生物體上。
Steven Strogatz - Mathematician
In his work in applied mathematics, Steven Strogatz studies the way math and biology intersect. Full bio
In his work in applied mathematics, Steven Strogatz studies the way math and biology intersect. Full bio
Double-click the English transcript below to play the video.
00:19
I was trying to think, how is sync connected to happiness,
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我試著想，同步跟快樂有什麼關連，
00:21
and it occurred to me that for some reason we take pleasure in synchronizing.
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然後我想到因為某些原因，我們在同步時感到愉悅。
00:28
We like to dance together, we like singing together.
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我們喜歡一起跳舞、一起歌唱。
00:31
And so, if you'll put up with this, I would like to enlist your help
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所以，如果你們願意的話，我想要請你們幫忙
00:36
with a first experiment today. The experiment is --
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今天的第一個實驗。實驗是這樣的：
00:40
and I notice, by the way, that when you applauded,
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我發現當你們拍手時，
00:43
that you did it in a typical North American way,
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你們以一個典型的北美方式拍手。
00:45
that is, you were raucous and incoherent.
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也就是說你們是喧鬧且沒有規則的。
00:49
You were not organized. It didn't even occur to you to clap in unison.
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你們是沒有規律的。你們根本沒有想到要一致的拍手。
00:54
Do you think you could do it? I would like to see if this audience would --
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你們覺得你們做得到嗎？我想要看看在座的各位，
00:58
no, you haven't practiced, as far as I know --
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且據我所知你們沒有練習過，
01:00
can you get it together to clap in sync?
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是否可以一致地拍手。
01:04
(Clapping)
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（拍手）
01:14
Whoa! Now, that's what we call emergent behavior.
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哇嗚！那是我們叫做意外的行為。
01:16
(Laughter)
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（笑聲）
01:18
So I didn't expect that, but -- I mean, I expected you could synchronize.
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我沒有預期會如此，應該說，我預期你們可以一致地拍手。
01:22
It didn't occur to me you'd increase your frequency.
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但我沒想到你們會越拍越快。
01:25
It's interesting.
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這很有趣。
01:27
(Laughter)
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（笑聲）
01:30
So what do we make of that? First of all, we know that you're all brilliant.
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我們從中得到什麼？首先，我們都知道各位是非常聰明的。
01:34
This is a room full of intelligent people, highly sensitive.
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這是一個充滿高智商人們的房間，非常敏銳。
01:38
Some trained musicians out there.
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在座有一些受過訓練的音樂家。
01:41
Is that what enabled you to synchronize?
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這是讓你們能夠同步的原因嗎？
01:43
So to put the question a little more seriously,
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或者稍微認真點來說，
01:46
let's ask ourselves what are the minimum requirements for what you just did,
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讓我們問問自己，你們剛剛做的事，也就是自發的同步，
01:50
for spontaneous synchronization.
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最基本上需要甚麼。
01:53
Do you need, for instance, to be as smart as you are?
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你們需要，舉例來說，像你們這樣聰明嗎？
01:57
Do you even need a brain at all just to synchronize?
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又或你們需要有腦袋才能達成同步嗎？
02:04
Do you need to be alive? I mean, that's a spooky thought, right?
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你需要活著嗎？我的意思是，這是有點恐怖的想法，對吧？
02:09
Inanimate objects that might spontaneously synchronize themselves.
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無生命物體間可以自發同步。
02:14
It's real. In fact, I'll try to explain today that sync is maybe one of,
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這是真的。事實上，我今天想要試著解釋同步化有可能是一種，
02:21
if not one of the most, perhaps the most pervasive drive in all of nature.
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甚至可能是主要的自然力量。
02:25
It extends from the subatomic scale to the farthest reaches of the cosmos.
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它從次原子尺度延伸到天文尺度。
02:31
It's a deep tendency toward order in nature
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它是大自然趨於規律的推手，
02:35
that opposes what we've all been taught about entropy.
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與我們所學關於亂度的概念相反。
02:38
I mean, I'm not saying the law of entropy is wrong -- it's not.
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我的意思是，我沒有說亂度定律是錯的，它沒有錯。
02:41
But there is a countervailing force in the universe --
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但有個跟它抗衡的力量--
02:43
the tendency towards spontaneous order. And so that's our theme.
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趨動自發規律的傾向，也就是我們的主題。
02:48
Now, to get into that, let me begin with what might have occurred to you immediately
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現在，進入主題，讓我從你們一開始聽到
02:52
when you hear that we're talking about synchrony in nature,
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要談自然界同步化可能想到的東西開始講起，
02:56
which is the glorious example of birds that flock together,
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也就是壯觀的例子當鳥兒們一同飛
03:02
or fish swimming in organized schools.
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或是魚群整齊地游動。
03:06
So these are not particularly intelligent creatures,
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他們不是特別聰明的動物，
03:10
and yet, as we'll see, they exhibit beautiful ballets.
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但我們等下可以看到他們呈現美妙的芭蕾。
03:15
This is from a BBC show called "Predators,"
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這是從BBC的節目Predators（獵食者）中擷取的，
03:17
and what we're looking at here are examples of synchrony that have to do with defense.
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我們看到的是跟防禦有關的同步化的例子。
03:23
When you're small and vulnerable, like these starlings,
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當你很小很容易受傷害的時候，就像那些歐掠鳥，
03:26
or like the fish, it helps to swarm to avoid predators, to confuse predators.
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或是像魚時，跟同伴一同移動可以避開掠食者，或使掠食者困惑。
03:35
Let me be quiet for a second because this is so gorgeous.
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讓我安靜一下因為這實在是太美麗了。
03:53
For a long time, biologists were puzzled by this behavior,
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有很長的一段時間，生物學家為這種行為感到困惑，
03:56
wondering how it could be possible.
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不了解這怎麼可能。
03:59
We're so used to choreography giving rise to synchrony.
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我們很習慣編舞能創造同步。
04:03
These creatures are not choreographed.
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但這些動物沒有被編舞。
04:05
They're choreographing themselves.
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他們是為自己編舞。
04:09
And only today is science starting to figure out how it works.
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直到今天科學才開始瞭解這是如何進行的。
04:13
I'll show you a computer model made by Iain Couzin, a researcher at Oxford,
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我會給你們看一個由Ian Kuzan，一個牛津的科學家做的電腦模擬，
04:19
that shows how swarms work.
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模擬成群活動是怎麼運作的。
04:21
There are just three simple rules.
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有三個簡單的規則。
04:24
First, all the individuals are only aware of their nearest neighbors.
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第一，所有個體只感受到離他們最近的個體。
04:29
Second, all the individuals have a tendency to line up.
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第二，所有個體會對齊。
04:33
And third, they're all attracted to each other,
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第三，他們之間會互相吸引，
04:36
but they try to keep a small distance apart.
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但之間也會保有一些距離。
04:39
And when you build those three rules in,
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當你把這些規則設定進去，
04:42
automatically you start to see swarms
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就可以看到集體活動的現象，
04:44
that look very much like fish schools or bird flocks.
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與魚群和鳥群活動非常類似。
04:48
Now, fish like to stay close together, about a body length apart.
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魚兒們喜歡緊密的在一起，個體之間大約一個身體遠。
04:52
Birds try to stay about three or four body lengths apart.
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鳥兒們個體之間則有三到四個身體遠。
04:55
But except for that difference, the rules are the same for both.
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但除了距離不同外，規則是一樣的。
05:04
Now, all this changes when a predator enters the scene.
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但當獵食者加進來時，一切都改變了。
05:09
There's a fourth rule: when a predator's coming, get out of the way.
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所以有第四個規則：當獵食者來時，閃開。
05:23
Here on the model you see the predator attacking.
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在這個模擬中，你看到獵食者攻擊。
05:28
The prey move out in random directions,
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被捕食者往各個方向散開，
05:30
and then the rule of attraction brings them back together again,
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然後個體間的吸引力又把他們帶回來，
05:33
so there's this constant splitting and reforming.
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所以有分開又重新形成的現象。
05:37
And you see that in nature.
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這在自然界中是看得到的。
05:47
Keep in mind that, although it looks as if each individual is acting to cooperate,
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記住，雖然看起來每個個體互相幫忙，
05:53
what's really going on is a kind of selfish Darwinian behavior.
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但事實上只是個自私的達爾文行為。
05:57
Each is scattering away at random to try to save its scales or feathers.
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每個個體只是為了保護自己的鱗片或羽毛而逃走。
06:03
That is, out of the desire to save itself,
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也就是說，為了要救自己，
06:06
each creature is following these rules,
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每個個體遵循這些規律，
06:09
and that leads to something that's safe for all of them.
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然後達成可以救整個群體的目的。
06:11
Even though it looks like they're thinking as a group, they're not.
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雖然看起來他們是以一個群裡來思考，但他們不是的。
06:32
You might wonder what exactly is the advantage to being in a swarm,
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你可能會想他們群裡行動的好處到底是什麼？
06:35
so you can think of several.
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你可以想到好幾個。
06:37
As I say, if you're in a swarm, your odds of being the unlucky one
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就像我說的，如果是群體行動，你是那個不幸被獵食的個體機會
06:41
are reduced as compared to a small group.
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相對於一小群體大大降低。
06:45
There are many eyes to spot danger.
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有很多眼睛可以看到危險。
06:48
And you'll see in the example with the starlings, with the birds,
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你看這個歐掠鳥的例子
06:55
when this peregrine hawk is about to attack them,
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當遊隼鷹要攻擊他們時，
06:57
that actually waves of panic can propagate,
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恐懼波可以向外延伸，
07:00
sending messages over great distances.
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將訊息傳遞到很遠的地方。
07:03
You'll see -- let's see, it's coming up possibly at the very end -- maybe not.
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你會看到--我看看，應該是在最後面會出現--好像沒有。
07:12
Information can be sent over half a kilometer away
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利用這個方法，訊息可以在很短的時間內
07:15
in a very short time through this mechanism.
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被傳到超過半公里遠的地方。
07:20
Yes, it's happening here.
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是的，在這裡發生。
07:22
See if you can see those waves propagating through the swarm.
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看你是不是可以看到那些波在群體中傳播。
07:26
It's beautiful. The birds are, we sort of understand, we think,
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很漂亮的。這些鳥兒，從電腦模擬中，
07:30
from that computer model, what's going on.
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我們覺得我們有點瞭解發生了什麼事。
07:32
As I say, it's just those three simple rules,
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就像我說的，就是那三個規則，
07:34
plus the one about watch out for predators.
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再加上小心掠食者。
07:36
There doesn't seem to be anything mystical about this.
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感覺沒有任何神祕的地方。
07:39
We don't, however, really understand at a mathematical level.
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但在數學的層面上，我們沒有辦法完全理解。
07:42
I'm a mathematician. We would like to be able to understand better.
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我是個數學家。我們想要更深入的瞭解。
07:46
I mean, I showed you a computer model, but a computer is not understanding.
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我的意思是，我給你們看了一個電腦模擬，但電腦不會理解。
07:49
A computer is, in a way, just another experiment.
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電腦，在某方面來說，也只是另一個實驗。
07:52
We would really like to have a deeper insight into how this works
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我們很想要更深入理解這怎麼運作的，
07:55
and to understand, you know, exactly where this organization comes from.
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你知道的，就是這樣的組織結構是哪裡來的。
08:00
How do the rules give rise to the patterns?
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怎麼由規律形成模式？
08:02
There is one case that we have begun to understand better,
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有一個例子使我們開始去瞭解多一點，
08:05
and it's the case of fireflies.
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這個例子是螢火蟲。
08:08
If you see fireflies in North America,
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如果你在北美看到螢火蟲，
08:10
like so many North American sorts of things,
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就像北美的很多其他東西一樣，
08:12
they tend to be independent operators. They ignore each other.
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他們是互不相干的個體。他們忽略其他個體。
08:16
They each do their own thing, flashing on and off,
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他們自己做自己的，自己亮自己暗，
08:18
paying no attention to their neighbors.
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跟鄰居沒有任何關係。
08:20
But in Southeast Asia -- places like Thailand or Malaysia or Borneo --
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但在東南亞，像是泰國或馬來西亞或婆羅州，
08:25
there's a beautiful cooperative behavior that occurs among male fireflies.
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公螢火蟲會美妙地合作。
08:30
You can see it every night along the river banks.
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你每晚都可以在河畔看到。
08:33
The trees, mangrove trees, are filled with fireflies communicating with light.
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在這些樹叢、紅樹林中，充滿著用光來溝通的螢火蟲。
08:38
Specifically, it's male fireflies who are all flashing in perfect time together,
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更明確的說，公螢火蟲會一起閃爍，
08:43
in perfect synchrony, to reinforce a message to the females.
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完全同步化的，來增強傳給母螢火蟲的訊息。
08:47
And the message, as you can imagine, is "Come hither. Mate with me."
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這個訊息，就像你想像的，是「來這裡，跟我交配。」
08:52
(Music)
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（音樂）
08:59
In a second I'm going to show you a slow motion of a single firefly
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等一下我要給你們看僅包含一隻螢火蟲的慢速影片，
09:03
so that you can get a sense. This is a single frame.
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來讓你們更加瞭解。這是單一鏡頭。
09:06
Then on, and then off -- a 30th of a second, there.
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然後亮，然後暗--在三十分之一秒中達成。
09:11
And then watch this whole river bank, and watch how precise the synchrony is.
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然後看整個河畔的影片，看整個同步化有多精準。
09:18
On, more on and then off.
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亮、更多亮、然後暗。
09:27
The combined light from these beetles -- these are actually tiny beetles --
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這些小蟲發出的光亮相加起來--而且他們只是小蟲--
09:30
is so bright that fishermen out at sea can use them
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足以讓在外海的打魚人
09:33
as navigating beacons to find their way back to their home rivers. It's stunning.
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利用這些光亮來作為回家指路的燈塔。這是非常驚奇的。
09:37
For a long time it was not believed
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當西方旅遊者，像是Sir Francis Drake，
09:39
when the first Western travelers, like Sir Francis Drake,
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第一次從泰國帶回這不可置信的故事時，
09:42
went to Thailand and came back with tales of this unbelievable spectacle.
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沒有人相信這樣的事情。
09:46
No one believed them.
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沒有人相信他們。
09:48
We don't see anything like this in Europe or in the West.
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在歐洲或是在西方我們看不到任何類似的現象。
09:51
And for a long time, even after it was documented,
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而且很長的一段時間，就算這已經被建檔，
09:54
it was thought to be some kind of optical illusion.
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大部份的人認為是視覺幻象。
09:56
Scientific papers were published saying it was twitching eyelids
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一些發表的科學文獻說這是眼皮震顫，
09:59
that explained it, or, you know, a human being's tendency
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也就是說，人類傾向看到一些
10:03
to see patterns where there are none.
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不存在的模式。
10:05
But I hope you've convinced yourself now, with this nighttime video,
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但我希望你們看了這段影片後會相信
10:08
that they really were very well synchronized.
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這些螢火蟲真的是同步化了。
10:11
Okay, well, the issue then is, do we need to be alive
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好，現在的問題是，我們需要活著
10:14
to see this kind of spontaneous order,
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才能有這樣的自發性規律嗎？
10:16
and I've already hinted that the answer is no.
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我已經暗示了答案是否定的。
10:21
Well, you don't have to be a whole creature.
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恩，你不需要是一整個生命體。
10:23
You can even be just a single cell.
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你可以只是一個單細胞。
10:25
Like, take, for instance, your pacemaker cells in your heart right now.
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就像是，打個比方來說，你心臟的節律細胞。
10:28
They're keeping you alive.
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他們讓你活著。
10:30
Every beat of your heart depends on this crucial region, the sinoatrial node,
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每一個心跳都跟節律點這個重要的地方有關。
10:35
which has about 10,000 independent cells that would each beep,
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這個區域包括了一萬個獨立的細胞，每個有自己的
10:39
have an electrical rhythm -- a voltage up and down --
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電波規律--電壓上升及下降--
10:42
to send a signal to the ventricles to pump.
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來傳遞訊號使心室加壓輸血。
10:45
Now, your pacemaker is not a single cell.
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好，你們的節律點不是一個單一的細胞。
10:48
It's this democracy of 10,000 cells that all have to fire in unison
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是一個一萬個細胞組成的民主社會，其中每個細胞需要同時激發
10:51
for the pacemaker to work correctly.
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才能使整個節律點運作正常。
10:54
I don't want to give you the idea that synchrony is always a good idea.
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我不想讓你們覺得同步化永遠是好的。
10:57
If you have epilepsy, there is an instance of billions of brain cells, or at least millions,
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如果你有癲癇，你腦中就有幾十億個細胞，或至少幾百萬的細胞，
11:02
discharging in pathological concert.
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以一個病態的方式同步放電。
11:06
So this tendency towards order is not always a good thing.
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所以這個傾向規律的現象不一定是好事。
11:10
You don't have to be alive. You don't have to be even a single cell.
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你不需要有生命。你也不需要是個細胞。
11:13
If you look, for instance, at how lasers work,
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舉例來說，如果你們看雷射如何運作，
11:16
that would be a case of atomic synchrony.
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這會是個原子間的同步。
11:19
In a laser, what makes laser light so different from the light above my head here
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在雷射光中，讓雷射光跟我頭頂上的這個光不一樣的就是
11:23
is that this light is incoherent --
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我頭上的光是不同相的，
11:25
many different colors and different frequencies,
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有很多不同的顏色和不同的頻率，
11:28
sort of like the way you clapped initially --
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有點像是你們一開始拍手的樣子。
11:31
but if you were a laser, it would be rhythmic applause.
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但雷射光就好像是你們有規律的拍手。
11:34
It would be all atoms pulsating in unison,
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所有的原子一起同步震動，
11:36
emitting light of one color, one frequency.
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發出同一個顏色的光，一種頻率。
11:40
Now comes the very risky part of my talk,
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接下來是我的演講中最大膽的一部份，
11:43
which is to demonstrate that inanimate things can synchronize.
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就是我要示範無生命物體如何同步。
11:47
Hold your breath for me.
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請為我屏住呼吸。
11:49
What I have here are two empty water bottles.
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我這裡有兩個空的水瓶。
11:56
This is not Keith Barry doing a magic trick.
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這不是Keith Barry做魔術表演。
11:58
This is a klutz just playing with some water bottles.
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這是一個笨手笨腳的人在玩幾個水瓶。
12:03
I have some metronomes here.
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我這有一些節拍器。
12:08
Can you hear that?
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你們可以聽到嗎？
12:12
All right, so, I've got a metronome,
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好，所以我有一個節拍器，
12:14
and it's the world's smallest metronome, the -- well, I shouldn't advertise.
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而且它是世界上最小的節拍器。好，我不該打廣告。
12:18
Anyway, so this is the world's smallest metronome.
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不論如何，這是世界上最小的節拍器。
12:21
I've set it on the fastest setting, and I'm going to now take
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我把它設定在最快的地方，然後我要拿
12:24
another one set to the same setting.
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另外一個節拍器也在最快的設定。
12:28
We can try this first. If I just put them on the table together,
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我們可以先試這個。如果我只是把這兩個同時放在桌上，
12:33
there's no reason for them to synchronize, and they probably won't.
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沒有什麼原因會讓他們同步，且他們應該不會。
12:42
Maybe you'd better listen to them. I'll stand here.
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或許你應該要聽聽他們。我來站到這裡。
12:49
What I'm hoping is that they might just drift apart
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我希望他們會慢慢變成不同步
12:51
because their frequencies aren't perfectly the same.
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因為它們的頻率沒有完全相同。
13:01
Right? They did.
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是吧？他們不同步了。
13:03
They were in sync for a while, but then they drifted apart.
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他們同步了一陣子，然後慢慢分開了。
13:07
And the reason is that they're not able to communicate.
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這是因為他們沒有溝通。
13:09
Now, you might think that's a bizarre idea.
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現在，你們可能會覺得這是個奇怪的想法。
13:11
How can metronomes communicate?
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節拍器怎麼會溝通？
13:14
Well, they can communicate through mechanical forces.
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好，他們可以透過機械力量溝通。
13:17
So I'm going to give them a chance to do that.
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所以我要給他們一個這麼做的機會。
13:19
I also want to wind this one up a bit. How can they communicate?
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我也要把這個上緊發條。他們要如何溝通呢？
13:22
I'm going to put them on a movable platform,
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我要把他們放在一個可以移動的平面上，
13:24
which is the "Guide to Graduate Study at Cornell." Okay? So here it is.
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就是「康乃爾研究生手冊」。好嗎？就是這樣。
13:33
Let's see if we can get this to work.
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我們來看看這樣有沒有用。
13:37
My wife pointed out to me that it will work better if I put both on at the same time
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我太太告訴我把兩個同時放上去比較會成功，
13:41
because otherwise the whole thing will tip over.
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因為不這樣的話，整個架構會翻倒。
13:43
All right. So there we go. Let's see. OK, I'm not trying to cheat --
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好，就是這樣。讓我們看看。我沒有試圖作弊，
13:50
let me start them out of sync. No, hard to even do that.
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讓我讓它們一開始不同步。不行，連這樣都很難。
14:08
(Applause)
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（掌聲）
14:12
All right. So before any one goes out of sync, I'll just put those right there.
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好。在任何一個不同步之前，我還是把它們放在那裡。
14:17
(Laughter)
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（笑聲）
14:18
Now, that might seem a bit whimsical,
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現在，這看起來可能有點不切實際，
14:20
but this pervasiveness of this tendency towards spontaneous order
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但這樣具影響力地傾向同步化的力量，
14:25
sometimes has unexpected consequences.
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有時會有一些無法預期的結果。
14:29
And a clear case of that,
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且一個明確的例子是
14:31
was something that happened in London in the year 2000.
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2000年在倫敦發生的事。
14:34
The Millennium Bridge was supposed to be the pride of London --
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千禧橋本來應該是倫敦的驕傲--
14:37
a beautiful new footbridge erected across the Thames,
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泰晤士河上一座美麗的天橋，
14:41
first river crossing in over 100 years in London.
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倫敦百年來第一座橫過泰晤士河的橋。
14:45
There was a big competition for the design of this bridge,
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那時為了這座橋的設計有一個很大的比賽。
14:48
and the winning proposal was submitted by an unusual team --
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最後得獎的是一組不尋常的組合：
14:52
in the TED spirit, actually -- of an architect --
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是TED精神--一個建築家，
14:55
perhaps the greatest architect in the United Kingdom, Lord Norman Foster --
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有可能是英國最棒的建築家：Lord Norman Foster--
14:59
working with an artist, a sculptor, Sir Anthony Caro,
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和一個藝術家兼雕刻家：Sir Anthony Caro；
15:04
and an engineering firm, Ove Arup.
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和一個工程公司：Ove Arup。
15:08
And together they submitted a design based on Lord Foster's vision,
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他們一起以Lord Foster的願景為基礎送出一份設計案，
15:13
which was -- he remembered as a kid reading Flash Gordon comic books,
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就是--他記得當他還是個小孩時，他看了Flash Gorden的漫畫書，
15:17
and he said that when Flash Gordon would come to an abyss,
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他說Flash Goder從深淵中出來時，
15:20
he would shoot what today would be a kind of a light saber.
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他會射出一個現在應該叫做光劍的東西。
15:23
He would shoot his light saber across the abyss, making a blade of light,
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他會從深淵中射出光劍，形成一道光，
15:27
and then scamper across on this blade of light.
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然後尋著這道光爬出來。
15:29
He said, "That's the vision I want to give to London.
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他說：「那是我想要給倫敦的意像。
15:31
I want a blade of light across the Thames."
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我想要在泰晤士河上造一道光。」
15:35
So they built the blade of light,
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所以他們建造了這道光，
15:37
and it's a very thin ribbon of steel, the world's --
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且那是一條很細的鋼鐵，
15:43
probably the flattest and thinnest suspension bridge there is,
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有可能是世界上最平最細的吊橋，
15:46
with cables that are out on the side.
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僅有兩條在兩旁的鋼索。
15:49
You're used to suspension bridges with big droopy cables on the top.
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你們很習慣看到吊橋上面有粗大的鋼索。
15:52
These cables were on the side of the bridge,
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但這座橋的鋼索是在旁邊，
15:55
like if you took a rubber band and stretched it taut across the Thames --
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有點像是拿條橡皮筋拉開在泰晤士河兩側，
15:59
that's what's holding up this bridge.
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成為這座橋。
16:01
Now, everyone was very excited to try it out.
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好，大家都很興奮要試試看。
16:03
On opening day, thousands of Londoners came out, and something happened.
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啓用日當天，好幾千倫敦人來到這裡，但某件事發生了。
16:08
And within two days the bridge was closed to the public.
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兩天之內，這座橋就不對外開放了。
16:12
So I want to first show you some interviews with people
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我想要先給你們看一些訪問，
16:17
who were on the bridge on opening day, who will describe what happened.
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訪問啓用日當天在場的人們，他們會告訴你發生了什麼事。
16:20
Man: It really started moving sideways and slightly up and down,
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男：他開始橫向移動，有一點上下搖晃，
16:25
rather like being on the boat.
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像是在坐船一樣。
16:28
Woman: Yeah, it felt unstable, and it was very windy,
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女：是的，感覺不穩定，而且那時風很大，
16:31
and I remember it had lots of flags up and down the sides, so you could definitely --
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我記得當時有很多旗子在橋邊，所以可以感覺到風。
16:35
there was something going on sideways, it felt, maybe.
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當時也有橫向移動，感覺上有。
16:38
Interviewer: Not up and down? Boy: No.
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記者：沒有上下嗎？男孩：沒有。
16:40
Interviewer: And not forwards and backwards? Boy: No.
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記者：也沒有前後擺動？男孩：沒有。
16:42
Interviewer: Just sideways. About how much was it moving, do you think?
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記者：就只有橫向的。大約移動多少，你覺得？
16:45
Boy: It was about --
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男孩：大概是--
16:47
Interviewer: I mean, that much, or this much?
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記者：我的意思是，這麼多？還是這麼多？
16:49
Boy: About the second one.
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男孩：大概第二個。
16:51
Interviewer: This much? Boy: Yeah.
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記者：這麼多？男孩：是阿。
16:53
Man: It was at least six, six to eight inches, I would have thought.
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男：至少有六到八英寸，我覺得。
16:56
Interviewer: Right, so, at least this much? Man: Oh, yes.
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記者：是的，所以，至少這麼多？男：喔是的。
16:58
Woman: I remember wanting to get off.
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女：我記得很想要離開。
17:00
Interviewer: Oh, did you? Woman: Yeah. It felt odd.
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記者：是嗎？女：是的，感覺很奇怪。
17:02
Interviewer: So it was enough to be scary? Woman: Yeah, but I thought that was just me.
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記者：所以是夠強讓人感到害怕的？女：是的，但我當時覺得只是我而已。
17:08
Interviewer: Ah! Now, tell me why you had to do this?
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記者：喔！那麼告訴我為什麼你要這麼做？
17:11
Boy: We had to do this because, to keep in balance
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男孩：我們需要這麼做才能保持平衡。
17:13
because if you didn't keep your balance,
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因為如果你沒有保持平衡，
17:15
then you would just fall over about, like, to the left or right, about 45 degrees.
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你有可能摔倒，就是說向左向右，大概45度這樣。
17:21
Interviewer: So just show me how you walk normally. Right.
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記者：那麼示範給我看你怎麼正常走路。好。
17:26
And then show me what it was like when the bridge started to go. Right.
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然後再示範給我看當時在橋上怎麼走路的。好。
17:31
So you had to deliberately push your feet out sideways and --
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所以你必須刻意把腳往旁邊踩而且
17:35
oh, and short steps?
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喔，很小的步伐？
17:37
Man: That's right. And it seemed obvious to me
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男：是的，而且感覺是理所當然的，
17:40
that it was probably the number of people on it.
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有可能是因為在上面有很多人。
17:44
Interviewer: Were they deliberately walking in step, or anything like that?
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記者：那他們有刻意這樣走嗎？或是像這樣嗎？
17:48
Man: No, they just had to conform to the movement of the bridge.
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男：沒有，他們就是要配合橋的晃動。
17:52
Steven Strogatz: All right, so that already gives you a hint of what happened.
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Steven Strogats:好，所以那稍微地告訴你們發生了什麼事。
17:55
Think of the bridge as being like this platform.
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想像這座橋就是我們剛剛用的平面。
17:59
Think of the people as being like metronomes.
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想像這些人就是剛剛的節拍器。
18:02
Now, you might not be used to thinking of yourself as a metronome,
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現在，你可能不習慣想像自己是節拍器，
18:05
but after all, we do walk like -- I mean, we oscillate back and forth as we walk.
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但無論如何，我們走路像--我的意思是，我們在走路時前後震動。
18:09
And especially if we start to walk like those people did, right?
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而且尤其是我們開始像那些人那樣走路。
18:12
They all showed this strange sort of skating gait
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他們都有那種奇怪的溜冰步伐
18:16
that they adopted once the bridge started to move.
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且只要橋一開始晃動他們就會那樣走。
18:19
And so let me show you now the footage of the bridge.
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讓我給你們看那座橋影片片段。
18:22
But also, after you see the bridge on opening day, you'll see an interesting clip
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而且，在我給你們看過啓用那天橋的樣子，你們會看一段有趣的影片，
18:26
of work done by a bridge engineer at Cambridge named Allan McRobie,
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裡面述說一個劍橋的造橋工程師叫做艾倫馬洛畢做的工作，
18:31
who figured out what happened on the bridge,
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他解釋了橋發生了什麼事，
18:33
and who built a bridge simulator to explain exactly what the problem was.
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且建造了模擬橋來解釋問題在哪。
18:37
It was a kind of unintended positive feedback loop
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這有點像是人走路的樣子和橋移動的樣子間
18:41
between the way the people walked and the way the bridge began to move,
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一個非刻意的正向回饋，
18:44
that engineers knew nothing about.
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這是工程師們不知道的。
18:46
Actually, I think the first person you'll see
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事實上，我想你會看到的第一個人
18:48
is the young engineer who was put in charge of this project. Okay.
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是一個負責這個計劃的年輕工程師。好。
18:53
(Video) Interviewer: Did anyone get hurt? Engineer: No.
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（影帶）：記者？有任何人受傷嗎？工程師：沒有。
18:55
Interviewer: Right. So it was quite small -- Engineer: Yes. Interviewer: -- but real?
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記者：好。所以它很小。工程師：是的。記者：但是真實的？
18:58
Engineer: Absolutely. Interviewer: You thought, "Oh, bother."
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工程師：當然。記者：你想「喔，糟糕」
19:01
Engineer: I felt I was disappointed about it.
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工程師：我當時覺得很沮喪。
19:04
We'd spent a lot of time designing this bridge, and we'd analyzed it,
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我們花了很多時間設計這座橋，且我們有分析它，
19:08
we'd checked it to codes -- to heavier loads than the codes --
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我們確認它符合建築設計規範--比規範還能承受更多重量--
19:11
and here it was doing something that we didn't know about.
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但它卻這樣做了我們不知道的事。
19:14
Interviewer: You didn't expect. Engineer: Exactly.
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記者：你沒有預期會這樣。工程師：完全沒有。
19:16
Narrator: The most dramatic and shocking footage
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旁白：最戲劇化且最驚人的片段
19:19
shows whole sections of the crowd -- hundreds of people --
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是看到一整個群體，幾百人，
19:22
apparently rocking from side to side in unison,
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明顯地一同左右搖擺，
19:24
not only with each other, but with the bridge.
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不是只跟旁邊的人，而是跟著整座橋。
19:27
This synchronized movement seemed to be driving the bridge.
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這樣的同步化動作似乎是讓整座橋晃動的原因。
19:31
But how could the crowd become synchronized?
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但群眾怎麼會變成同步化呢？
19:34
Was there something special about the Millennium Bridge that caused this effect?
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這千禧橋有什麼特別的因素讓它產生這樣的效果嗎？
19:38
This was to be the focus of the investigation.
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這是調查的重點。
19:42
Interviewer: Well, at last the simulated bridge is finished, and I can make it wobble.
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記者：恩，至少模擬橋已經做好了，且我可以讓它擺動。
19:49
Now, Allan, this is all your fault, isn't it? Allan McRobie: Yes.
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現在，艾倫，這是你的錯對吧？艾倫馬羅畢：是的。
19:53
Interviewer: You designed this, yes, this simulated bridge,
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記者：你設計了這個，對吧，這座模擬橋，
19:55
and this, you reckon, mimics the action of the real bridge?
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而且你認為它可以模擬真正的橋？
19:58
AM: It captures a lot of the physics, yes.
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艾：它包含了大部份的物理現象。是的。
20:00
Interviewer: Right. So if we get on it, we should be able to wobble it, yes?
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記者：好，所以如果我們到上面去，它應該也會擺動，對吧？
20:06
Allan McRobie is a bridge engineer from Cambridge who wrote to me,
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艾倫馬羅畢是一位來自劍橋的造橋工程師，他寫信給我
20:09
suggesting that a bridge simulator ought to wobble
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說一座模擬橋
20:12
in the same way as the real bridge --
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應該要和真實的橋一樣會擺動--
20:14
provided we hung it on pendulums of exactly the right length.
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只要我們把它掛在一樣長的擺錘。
20:16
AM: This one's only a couple of tons, so it's fairly easy to get going.
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艾：這個只有幾頓重，所以應該很容易讓它動起來。
20:19
Just by walking. Interviewer: Well, it's certainly going now.
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只要走一走就行。記者：是的，它的確在動了。
20:22
AM: It doesn't have to be a real dangle. Just walk. It starts to go.
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艾：不需要是什麼擺盪，只要走路，它就會開始動。
20:25
Interviewer: It's actually quite difficult to walk.
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記者：其實走路挺難的。
20:28
You have to be careful where you put your feet down, don't you,
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你需要很小心你的每一個步子，
20:31
because if you get it wrong, it just throws you off your feet.
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因為如果你踩錯了，你就會跌倒。
20:34
AM: It certainly affects the way you walk, yes. You can't walk normally on it.
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艾：他當然影響到你如何走路。是的，你沒有辦法正常走路。
20:39
Interviewer: No. If you try and put one foot in front of another,
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記者：沒錯，如果你試圖將一隻腳放在另一隻前面，
20:41
it's moving your feet away from under you. AM: Yes.
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它就會把你的腳從你下面移開。艾：是的。
20:44
Interviewer: So you've got to put your feet out sideways.
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記者：所以你一定要把腳放在旁邊。
20:47
So already, the simulator is making me walk in exactly the same way
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所以，這個模擬已經讓你跟在橋上一樣的方式行走，
20:50
as our witnesses walked on the real bridge.
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而且我們的見證者是在真的橋上走過的人。
20:52
AM: ... ice-skating gait. There isn't all this sort of snake way of walking.
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艾：...滑冰式步伐。不像我們平常的走路方式。
20:55
Interviewer: For a more convincing experiment,
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記者：更真實一點的模擬，
20:57
I wanted my own opening-day crowd, the sound check team.
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我要模擬開放日的人群，音控小組。
21:00
Their instructions: just walk normally.
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它們的指令：照正常走路。
21:12
It's really intriguing because none of these people is trying to drive it.
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很有趣的是這些人中沒有一個試著去擺動它。
21:16
They're all having some difficulty walking.
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他們在上面走路都有困難。
21:19
And the only way you can walk comfortably is by getting in step.
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唯一可以舒適地走法就是一同踏出步伐。
21:22
But then, of course, everyone is driving the bridge.
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但如果這樣，所有人就會對橋用力。
21:27
You can't help it. You're actually forced by the movement of the bridge to get into step,
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你沒有辦法阻止的。你被橋的動作控制住，
21:32
and therefore to drive it to move further.
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且走路的同時也讓橋移動更大。
21:38
SS: All right, well, with that from the Ministry of Silly Walks,
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SS:好，最後留一個「踩八字步的部委」的東西，
21:42
maybe I'd better end. I see I've gone over.
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或許我應該結束。我已經超時了。
21:45
But I hope that you'll go outside and see the world in a new way,
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但我希望你們會走出這裡然後以新的眼光看世界，
21:48
to see all the amazing synchrony around us. Thank you.
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看我們周圍這些美妙的同步現象。謝謝。
21:51
(Applause)
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（掌聲）
ABOUT THE SPEAKER
Steven Strogatz - MathematicianIn his work in applied mathematics, Steven Strogatz studies the way math and biology intersect.
Why you should listen
Steven Strogatz studies some of the most interesting problems in applied mathematics -- such as the intersection of math and biology, looking for patterns in the human sleep-wake cycle or in swarms of blinking fireflies.
He's been looking at nonlinear dynamics and chaos applied to physics, engineering and biology, and branching out into new areas, such as explorating of the small-world phenomenon in social networks (popularly known as "six degrees of separation"), and its generalization to other complex networks in nature and technology.
Strogatz' work has been in the news as British engineers released the definitive paper on the Millenium Bridge wobble, and its roots in how people walk on an unpredictable surface.
In 2012, he re-examined the "birthday problem" >>
Steven Strogatz | Speaker | TED.com