神秘的混沌理论（2009）

And it's the closest thing we have at the moment
这是我们现今拥有的
to the kind of true mathematics of nature.
最接近真正自然数学的观念
I think one of the great take home messages from Turing's work and from
图灵的工作及其化学生物等方面的发现
the discoveries in chemistry and biology and so on, is that
所传递的最伟大的信息之一是
ultimately, pattern formation seems to be woven, very, very deeply
模式形成已经彻底渗透到了
into the fabric of the universe.
宇宙整个构造之中
And it actually takes some very simple
事实上它只是通过一些非常简单
and familiar processes, like diffusion,
而熟悉的步骤 比如扩散
like the rates of chemical reactions,
比如化学反应的速率
and the interplay between them naturally gives rise to pattern.
以及它们之间的相互作用自发形成模式
So pattern is everywhere, it's just waiting to happen.
模式无所不在 只是有待形成
From the '70s on, more and more scientists
从70年代起 越来越多的科学家
began to embrace the concept that chaos and pattern
开始接受混沌与模式是
are built into nature's most basic rules.
自然界最基本规则这一观念
But one scientist more than any other
其中有位科学家与众不同地
brought a fundamentally new understanding
对这个令人震惊和迷惑的观念
to this astonishing and often puzzling idea.
进行了全新的奠基性的诠释
He was a colourful character and something of a maverick.
他性格活跃 喜欢标新立异
His name is Benoit Mandelbrot.
名叫伯努瓦·曼德勃罗
Benoit Mandelbrot wasn't an ordinary child.
伯努瓦·曼德勃罗的幼年经历很不寻常
He skipped the first two years of school
一入学就连跳两级
and as a Jew in war-torn Europe
身为一个犹太人在战乱的欧洲
his education was very disrupted.
学业经常被迫中断
He was largely self-taught or tutored by relatives.
大部分时间都是自学或由亲戚辅♥导♥
He never formally learned the alphabet,
他从未正式学过字母表
or even multiplication beyond the five times table.
或者5以上的乘法表
But, like Alan Turing,
但是 就像阿兰·图灵
Mandelbrot had a gift for seeing nature's hidden patterns.
曼德勃罗具有发现自然界潜在模式的天赋
He could see rules where the rest of us see anarchy.
别人看到的是混乱 而他看到了规则
He could see form and structure,
别人看到得是毫无形状的杂乱
where the rest of us just see a shapeless mess.
他却看到了形式与结构
And above all, he could see that a strange new kind of
最重要的是他看到了全新而奇异的
mathematics underpinned the whole of nature.
能够支撑整个自然界的数学科学
Mandelbrot's lifelong quest was to find a simple mathematical basis
他终其一生找寻一种简单的数学依据
for the rough and irregular shapes of the real world.
来解释现实中粗糙而无规则的形状
Mandelbrot was working for IBM
他是在IBM工作
and he was not in the normal academic environment.
并不在一般的学术环境里
And he was working on a pile of different problems about irregularities
他研究有关自然界 金融市场等
in nature, in the financial markets, all over the place.
各方面的种种无规则问题
And I think at some point it dawned on him that everything
我觉得他一定程度上认识到了
he was doing seem to be really parts of the same big picture.
自己所做的正是未来蓝图的一部分
And he was a sufficiently original and unusual person that he realised
他是个有独创精神的不同寻常的人
that pursuing this big picture was what he really wanted to do.
知道自己真正想做的就是实现这个蓝图
To Mandelbrot, it seemed perverse
对曼德勃罗而言 这有点荒谬
that mathematicians had spent centuries contemplating
数学家们花费数个世纪思索
idealised shapes like straight lines or perfect circles.
直线或圆这类理想化的图形
And yet had no proper or systematic way of describing
却没有合适的系统化的方式来记录
the rough and imperfect shapes that dominate the real world.
主宰真实世界的粗糙而不完美的图形
Take this pebble.
比如这鹅卵石
Is it a sphere or a cube?
它是圆是方
Or maybe a bit of both?
或者两者兼有
And what about something much bigger?
再举个大点的例子
Look at the arch behind me.
看我后面的拱门
From a distance, it looks like a semi-circle.
远看 它像个半圆
But up close, we see that it's bent and crooked.
但近看 就看到了其凹凸的表面
So what shape is it?
那它到底是什么形状呢
Mandelbrot asked if there's something unique
曼德勃罗想知道是否有种独一无二的东西
that defines all the varied shapes in nature.
能够定义自然界中这些不规则形状
Do the fluffy surfaces of clouds, the branches in trees
云朵蓬松的表面 树的枝干
and rivers, the crinkled edges of shorelines,
河的支流 蜿蜒的海岸线
share a common mathematical feature?
它们是否拥有共同的数学特征呢
Well, they do.
确实是有的
Underlying nearly all the shapes in the natural world
隐含在自然界所有形状下
is a mathematical principle known as self-similarity.
有一数学原理 称为自相似性
This describes anything in which the same shape
它描述的是相同形状
is repeated over and over again at smaller and smaller scales.
不断在越来越小的水平上复♥制♥
A great example are the branches of trees.
最明显的一个例子就是树的枝干
They fork and fork again, repeating that simple process
他们不停地在越来越小的水平下
over and over at smaller and smaller scales.
重复分叉这一简单过程
The same branching principle applies in the structure of our lungs
同样的分支原理也适用于我们的肺部结构
and the way our blood vessels are distributed throughout our bodies.
以及血管遍布全身的分布方式
It even describes how rivers split into ever smaller streams.
甚至可以描述江河支流的产生
And nature can repeat all sorts of shapes in this way.
自然界就是这样重复着各种形状
Look at this Romanesco broccoli.
看这棵罗马花椰菜
Its overall structure is made up of a series of
它整个结构由一系列圆锥
repeating cones at smaller and smaller scales.
在越来越小的水平上重复而组成
Mandelbrot realised self-similarity
曼德勃罗意识到自相似性
was the basis of an entirely new kind of geometry.
是一种全新几何学的基础
And he even gave it a name - fractal.
甚至给它命名为分形体
Now, that's a pretty neat observation.
这观察起来着实简洁
But what if you could represent this property of nature in mathematics?
但如果你能将这一自然性质用数学表示呢
What if you could capture its essence to draw a picture?
如果你能把其本质绘成图
What would that picture look like?
那这图看起来是什么样的呢
Could you use a simple set of mathematical rules
你能够用简单的一组数学规则
to draw an image that didn't look man-made?
画出不像人工合成的图像吗
The answer would come from Mandelbrot.
曼德勃罗给出了答案
Who had taken a job at IBM in the late 1950s
20世纪50年代的后期他在IBM工作
to gain access to its incredible computing power
利用大量的电脑辅助
and pursue his obsession with the mathematics of nature.
追求着自己迷恋的自然数学
Armed with a new breed of super-computer,
在一种新的超级计算机的帮助下
he began investigating a rather curious
他开始研究一个分外奇妙
and strangely simple-looking equation
却相当简单的方程式
that could be used to draw a very unusual shape.
根据此方程式可以画出极不寻常的图形
What I'm about to show you is one of the most remarkable
我将要讲述的是至今发现的
mathematical images ever discovered.
最著名的数学图形之一
Epic doesn't really do it justice.
史诗并没有公平对待它
This is the Mandelbrot set.
这就是曼德勃罗集
It's been called the thumbprint of god.
曾被誉为上帝的指纹
And when we begin to explore it,
当我们深入探索之后
you'll understand why.
就会明白这赞誉是实至名归的
Just as with the tree or the broccoli,
就像观察树木或者甘蓝
The closer you study this picture, the more detail you see.
靠得越近 就能看到越多的细节
Each shape within the set
集♥合♥里的每个图形
contains an infinite number of smaller shapes.
都包含了无限个更小的图形
Baby Mandelbrots that go on for ever.
子曼德勃罗集们会无限循环下去
Yet all this complexity stems from
但所有复杂都来源于
just one incredibly simple equation.
一个简单得难以置信的方程
This equation has a very important property.
它有一个非常重要的性质
It feeds back on itself.
就是反馈到自身
Like a video loop,
类似于那个循环摄像
each output becomes the input for the next go.
每一步的输出是下一步的输入
This feedback means that an incredibly simple mathematical
这种反馈意味着一个极其简单的
equation can produce a picture of infinite complexity.
数学公式可以产生无限复杂的图片
The really fascinating thing
真正神奇的地方在于
is that the Mandelbrot set isn't just a bizarre mathematical quirk.
曼德勃罗集不只是一个数学奇观
Its fractal property of being similar at all scales
它在所有水平上相似的分形性质
mirrors a fundamental ordering principle in nature.
反映了自然界一个基本的次序原理
Turing's patterns, Belousov's reaction
图灵的图案 别洛乌索夫的反应
and Mandelbrot's fractals
和曼德勃罗的分形体
are all signposts pointing to a deep underlying natural principle.
都是指向深层次自然原理的路标
When we look at complexities in nature, we tend to ask,
我们目睹了自然界的复杂后 不禁会问
"where did they come from? "
"复杂是从何而来的"
There is something in our heads that says
我们的思维定式认为
complexity does not arise out of simplicity.
复杂不可能来源于简单
It must arise from something complicated.
它必然脱胎于同样复杂的事物
We conserve complexity.
我们让复杂守恒了
But what the mathematics in this whole area is telling us
但这个领域的数学研究告诉我们的就是
is that very simple rules naturally give rise to very complex objects.
十分简单的规则自发地♥产♥生了复杂的事物
And so if you look at the object, it looks complex,
因此 你面对一件看来复杂的事物时
and you think about the rule that generates it, it's simple.
想想触发它的规则 其实很简单