神秘的混沌理论（2009）

It was as if the lightest breath of wind one day could make the
就好像今日的一缕微风也能决定
difference a month later between a snowstorm and a perfectly sunny day.
一个月后暴雪肆虐还是风和日丽
How can a simple system that works in the regular clockwork manner
像星象仪一样按钟表工作机理工作的
of my orrery become unpredictable?
简单系统怎会如此难料呢
It's all down to how it's configured, how the gears are connected.
这取决于系统的设定 齿轮的衔接
In essence, under certain circumstances,
在既定的环境下
the tiniest difference in the starting positions of the cogs,
初始时 齿轮上哪怕最微小的差别
differences that are too small to measure,
小到无法衡量的差别
can get bigger and bigger with each turn of the handle.
也在运作中会越变越大
With each step in the process the system then moves
随着系统一步步运作
further and further away from where you thought it was going.
结果就会离原先的设想越来越远
Lorenz captured this radical idea
洛伦斯在一次颇有影响的演讲中
in an influential talk he gave called,
提出了这个激进的想法
"Does a flap of a butterfly's wings in Brazil
一只蝴蝶在巴西轻扇翅膀
set off a tornado in Texas? "
会导致德州的龙♥卷♥风♥吗
It was a powerful and evocative image
那是清晰而富有感召力的一幕
and within months a new phrase had entered our language.
几个月内 一个新的短语诞生了
"The butterfly effect. "
蝴蝶效应
And the butterfly effect, the hallmark of all chaotic systems,
蝴蝶效应 这个混沌系统的典型
started turning up everywhere.
在生活中比比皆是
In the early '70s, a young Australian called Robert May,
70年代初 有位澳洲青年罗伯特·梅
was investigating a mathematical equation
想通过一个数学方程 来建立
that modelled how animal populations changed over time.
动物种群数量如何随时间变化的模型
But here too lurked the dreaded butterfly effect.
但他不知道 这其中也暗含着令人畏惧的蝴蝶效应
Immeasurably small changes to the rates at which the animals reproduced
任何一种动物繁殖比例上 细不可测的变化
could sometimes have huge consequences on their overall population.
都可能导致整个种群数量巨大变化
Numbers could go up and down wildly for no obvious reason.
测算结果变动极大 根本查不到原因
The idea that a mathematical equation gave you the power
想通过一个数学方程 预测整个系统的变化
to predict how a system will behave, was dead.
这个想法没有出路
In some sense this is the end of the Newtonian dream.
某种意义上 这也是牛顿学说的终点
When I was a graduate student, the belief was,
当我还是研究生时 大家相信
as we got more and more computer power,
随着电脑计算能力的不断提升
we'd be able to solve ever more complicated sets of equations.
我们必然能够解出更加复杂的方程
But this said that's not necessarily true.
混沌理论认为这种想法不一定对
You could have the simplest equations you can think of,
哪怕是你能想到的最简单的方程式
with nothing random in them, you know everything.
不含任何随机因子 一切可知
And yet, if they have behaviour that gives you chaotic solutions,
只要运行过程中出现一点点偏差
then you can never know the starting point accurately enough.
结果也会跟最初的设想 大相径庭
Centuries of scientific certainty
历经数个世纪的科学确定性
dissolved in just a few short years.
在短短几年之内就被瓦解了
The truth of the clockwork universe turned out to be just an illusion.
认为宇宙像钟表装置的观点 被证明是错的
Something which had seemed a logical certainty,
而某些看似有其逻辑必然性的
revealed itself merely as an act of faith.
可能只因对牛顿的盲目崇拜
And what's worse,
更糟的是
the truth had been staring us in the face all the time.
真♥相♥一直在我们眼前
Because chaos is everywhere.
因为混乱无处不在
It seemed unpredictability was hard-wired
看起来无法预测性存在于
into every aspect of the world we live in.
我们生活的每一方面
The global climate could dramatically change
全球气候会在短短几年间
in the course of a few short years.
巨幅变动
The stock markets could crash without warning.
股票市场可能毫无预警地崩溃
We could be wiped from the face of the planet overnight
我们可能一夜之间在地球上灭绝
and there is nothing anyone could do about it.
却对此无能为力
Unfortunately, I have to tell you that all of this is true.
很不幸 我不得不承认这些都是事实
And yet to be scared of chaos is pointless.
但是惧怕混沌也是毫无意义的
It's woven into the basic laws of physics.
它是基本物理定律的一部分
And we really all have to accept it as a fact of life.
我们不得不接受它 因为这就是生活
The idea of chaos really did have a big impact
混沌理论在近二三十年间
over a period of about 20 or 30 years,
影响巨大
because it changed the way everyone thought about
它改变了所有人对
what they were doing in science.
科学研究的看法
It changed it to the point
让人们接受了
that they forgot that they'd ever believed otherwise.
这与之前截然不同的理论
What chaos did was to show us
混沌理论说明
that the possibilities inherent in the simple mathematics
简单数学所具有的内在可能性
are much broader and much more general than you might imagine.
比你想象的要广泛而普遍得多
And so a clockwork universe can
所以即使宇宙真如钟表装置
nonetheless behave in the rich, complex way that we experience.
也可能带给我们纷繁复杂的体验
The discovery of chaos
混沌理论的发现
was a real turning point in the history of science.
是科学史上真正的转折点
As it tore down the Newtonian dream,
它撕碎了牛顿学说的美梦
scientists began to look more favourably at Turing and
科学家们开始偏好图灵和
Belousov's work on spontaneous pattern formation.
别洛乌索夫的关于自发模式形成的学说
And perhaps more importantly, as they did so,
更重要的是 他们也着手研究此理论
they realised something truly astonishing.
他们发现了真正惊人的东西
That there was a very deep and unexpected link.
就是有一种出乎意料的深深联♥系♥
A truly cosmic connection
一种真正无尽的联♥系♥
between nature's strange power to self-organise
存在于自然界自组织的神奇力量
and the chaotic consequences of the butterfly effect.
和蝴蝶效应的混沌结果之间
Between them, Turing, Belousov, May and Lorenz,
图灵 别洛乌索夫 梅和洛伦斯
had all discovered different faces of just one really big idea.
各自发现了这个大思想体系中的不同方面
They discovered that the natural world
他们发现了自然界的
could be deeply, profoundly unpredictable.
深不可测
But the very same things that make it unpredictable
但正是使自然界难料的事物
also allow it to create pattern and structure.
促使它创造了模式和结构
Order and chaos.
有序与混沌
It seems the two are more deeply linked
这两者的联♥系♥ 似乎比我们
than we could have ever imagined.
想象中更紧密
So how is this possible?
这怎么可能呢
What do phenomena as apparently different as the patterns in
明显不一样的别洛乌索夫溶液的模式和
Belousov's chemicals and the weather, have in common?
气象问题之间到底有什么共同之处呢
First, though both systems behave in very complicated ways,
其一 尽管两个系统的运行方式都很复杂
they are both based on surprisingly simple mathematical rules.
却都以极其简单的数学规则为基础
Secondly, these rules have a unique property.
其次 这些规则都有个独一无二的性质
A property that's often referred to as coupling, or feedback.
通常称作耦合或反馈
To show you what I mean,
为了更好地理解
to show you both order and chaos can emerge
我要向大家展示有序和混沌如何
on the their own from a simple system with feedback, I'm going to do
自发地通过反馈从一个简单系统中产生
what seems at first glance like a rather trivial experiment.
我要做的实验乍看似乎没什么价值
This screen behind me is connected up to the camera that's filming me.
我背后的屏幕连接着拍摄着我的摄像机
But the camera in turn is filming me with the screen.
它也同时在拍摄着我和大屏幕
This creates a loop with multiple copies of me
这就在屏幕上形成了
appearing on the screen.
我的多重循环影像
This is a classic example of a feedback loop.
这是一个反馈回路的经典实例
We get a picture, in a picture, in a picture.
一幅图在一幅图中 它们又在另一幅图中
At first it seems fairly predictable.
起初 它看起来是可预测的
But as we zoom the camera in
但是当我们把镜头拉近
some pretty strange things begin to happen.
十分奇怪的事情发生了
The first thing I notice is that the object I'm filming
我首先看到的是拍摄的东西
stops bearing much resemblance to what now appears on the screen.
在屏幕上看起来不如之前相似了
Small changes in the movement of the match become rapidly amplified
火柴细小的动作变化通过摄像机
as they loop round from the camera to the screen and back to the camera.
和屏幕之间的反复回路被迅速放大了
So even though I can describe each step in the process mathematically,
即使我能用数学来描述此过程下的每一步
I still have no way of predicting how tiny changes
火苗闪烁的细微变化
in the flickering of the flame will end up in the final image.
对屏幕上成像的影响也仍然无法预测
This is the butterfly effect in action.
这就是蝴蝶效应在动作中的体现
But now here comes the spooky bit.
接下来就有点让人毛骨悚然了
With just a slight tweak to the system,
系统轻微的调整
these strange and rather beautiful patterns begin to emerge.
就产生了这些奇异而美丽的图案
The same system, one that's based on simple rules with feedback,
建立在简单反馈上的同一系统
produces chaos and order.
同时创造了混沌与有序
The same mathematics is generating chaotic behaviour
同一数学原理同时引起了混沌行为
and patterned behaviour.
和模式行为
This changes completely how you think about all of this.
这完全改变了你的观念
The idea that there are regularities in nature and then,
自然界包含规律
totally separately from them,
同时又包含无规律
are irregularities, and these are just two different things,
这是完全不同的两样东西
is just not true.
这样的想法是不对的
These are two ends of a spectrum of behaviour
它们只是同一数学表达
which can be generated by the same kind of mathematics.
产生的两个极端