1
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双摆证明

2
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命运既不随机也不注定

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两根棍子

4
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用一个铰链连在一起

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挂在支架上

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松手

7
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就这么简单的东西

8
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你猜它会怎么动

9
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如果只有一根摆

10
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就是你中学物理课上学过的那个单摆

11
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答案无聊到不值得讨论

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来回摆

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越摆越小

14
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最后停下来

15
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你可以精确预测它三分钟后的位置

16
00:00:25,871 --> 00:00:28,523
也可以精确预测它三小时后的位置

17
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牛顿力学完美适用

18
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世界清晰可控

19
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但你在它下面再接一根棍子

20
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奇迹就发生了

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双摆的运动像发了疯一样

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第二根棍子翻转 甩动

23
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画出的轨迹

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让任何人第一眼都会以为

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这东西坏了

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你以为它在胡来

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不

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它严格遵守牛顿力学

29
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每一个瞬间的运动都可以用拉格朗日方程精确描述

30
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方程写出来

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高中生都能看懂

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然后你做一个实验

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把两个一模一样的双摆放在一起

34
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初始角度只差零点一度

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松手

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前两秒

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它们的运动几乎完全一致

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第三秒

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轨迹开始分离

40
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第五秒

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两个摆已经完全不相干了

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像两个素不相识的陌生人

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物理学家欣布罗特团队在实验中测量了这个分离速度

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他们发现

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两个双摆之间的差异以指数速度增长

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增长指数大约是每秒七点五

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这个数字叫李亚普诺夫指数

48
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它意味着什么呢

49
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你的测量精度每提高十倍

50
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你能多预测的时间只延长大约零点三秒

51
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你就是把全世界最精密的仪器搬来

52
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也不过多预测几秒钟而已

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哈喽

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大家好

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我是王利杰

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如果想看真实的双摆混沌模拟动画

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可以在任何视频网站搜索

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双摆混沌

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非常有趣

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今天这个话题来自一位观众

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她发给我一段她和 AI 的长对话

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从双摆的混沌图案开始

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一路聊到了涌现 递归因果 计算不可约性

64
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最后她说了一句话

65
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让我停下来想了很久

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她说

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大概二十年前

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我就觉得宇宙是一台大计算机

69
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那时候还不知道量子计算机这个概念

70
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现在知道了

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宇宙就是一套量子算法

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让一切都在最初的设计中

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有规律而又在不可预测中发展着

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这句话不完全精确

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但她的直觉触碰到了一个很深的东西

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今天我想从双摆混沌出发

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带你走进去看看

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我们先说清楚一个概念

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这个概念极度反直觉

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但极度重要

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它叫 确定性混沌

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你平时说混沌

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脑子里想的大概是乱七八糟 没有规律 随机

84
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但物理学里的混沌

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跟随机完全不是一回事

86
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双摆系统里没有任何随机成分

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没有骰子

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没有量子涨落

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没有外部噪声

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它百分之百遵守经典力学

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百分之百确定性

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给定完全精确的初始条件

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它的运动轨迹在理论上是唯一的

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确定的

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没有第二种可能

96
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但问题在于

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完全精确 这四个字

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在物理世界里永远做不到

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你的测量仪器永远有误差

100
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哪怕你测到小数点后一百位

101
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第一百零一位的偏差仍然会在足够长的时间之后

102
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被系统放大成天壤之别

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这种放大不是线性的

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是指数级的

105
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今天差一毫米

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三天后差一公里

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这种现象有一个通俗的名字 蝴蝶效应

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但蝴蝶效应这个说法太浪漫了

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浪漫到遮蔽了它最震撼的地方

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最震撼的地方不是蝴蝶扇翅膀能引发龙卷风

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最震撼的地方是 这个系统的每一步都有因果

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每一步都有因果

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不是随机的

114
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每一个瞬间的运动

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都严格地 毫无例外地

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由前一个瞬间决定

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因果链条没有任何断裂

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但长期行为不可预测

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这两件事同时成立

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这才是双摆真正让人头皮发麻的地方

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它告诉你

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因果和可预测

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是两回事

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你以为有因果就能预测

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不

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因果只保证每一步都有来路

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但不保证你能看见终点

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沃尔弗拉姆给这种现象取了一个名字

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叫计算不可约性

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意思是

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有些系统

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你没法走捷径去知道它的未来

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没有公式能让你跳过中间过程直达答案

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你唯一能做的

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就是让系统自己运行

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一步一步地走

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走到哪算哪

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宇宙本身的演化

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很可能就是这样一次不可压缩的计算过程

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没有谁在运行结束之前就知道结局 包括宇宙自己

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你可能觉得这是物理学家的抽象游戏

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其实不是

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天气预报就是最日常的例子

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气象学家拥有地球大气的完整方程组

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拥有遍布全球的传感器网络

146
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拥有超级计算机

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但他们仍然只能预测大约十天后的天气

148
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不是因为方程不对

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不是因为计算机不够快

150
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是因为大气本身就是一个混沌系统

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初始条件的微小误差

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会在十天左右

153
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被放大到覆盖整个预测范围

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这就是计算不可约性

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最直接的体现

156
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你明天要不要带伞

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气象局能告诉你

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但你下个月某一天要不要带伞

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没有任何力量能回答

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那位观众在对话里说过一段话

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我觉得说得特别好

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她说

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每一个微小的因果都是可预测的

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但所有因果放在一起就变成了无常的现实

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而这种无常却在宇宙层面有规律地运转

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她用自己的语言

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无意中精准地描述了确定性混沌的核心特征

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但还有一层更深的东西

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她的对话没有展开

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我想问你一个问题

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如果混沌是世界的底层机制

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那你的大脑

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你用来理解混沌的这个器官

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它自己在什么状态下运行

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答案可能会让你意外

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二零二二年

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神经科学家奥伯恩在一篇综述中汇总了大量证据

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指向一个结论

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人类大脑

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在接近一个叫混沌边缘的状态下运行

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想象一条光谱

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一端是完全有序

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所有神经元步调一致地放电

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像一支军队齐步走

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这种状态叫癫痫

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另一端是完全混沌

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所有神经元各干各的

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毫无协调

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这种状态叫昏迷

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大脑既不在这一端

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也不在那一端

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它精确地悬在两者之间

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在这个临界点上

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大脑同时拥有两种看似矛盾的能力

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有序带来的记忆和稳定性

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你昨天学的东西今天还在

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混沌带来的灵活性和创造力

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你能处理从未见过的新情况

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00:07:23,086 --> 00:07:26,699
莫拉莱斯团队在二零二一年的研究进一步发现

200
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当人工神经网络被训练去处理复杂的视觉任务时

201
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表现最优的状态恰好也在混沌边缘

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太稳定

203
00:07:35,925 --> 00:07:37,324
网络就僵死了

204
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像一台只会背答案的考试机器

205
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太混沌

206
00:07:40,925 --> 00:07:42,805
信息就像写在水面上

207
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瞬间消散

208
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只有在边缘

209
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系统才能同时做到记住过去和适应未来

210
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这让我不得不想到一个更大的问题

211
00:07:53,074 --> 00:07:55,153
如果大脑在混沌边缘运行

212
00:07:55,155 --> 00:07:56,747
那你每天体验到的那个 我

213
00:07:57,114 --> 00:08:01,588
那个感觉连续 稳定 坚实的自我 到底是什么

214
00:08:02,275 --> 00:08:03,367
二零二四年

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00:08:03,475 --> 00:08:07,567
神经生理学家费舍提出了一个很值得咀嚼的观点

216
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他说

217
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自我 的感觉不是某个大脑区域的产物

218
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大脑在处理外部信号和自身动作时

219
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面临一个根本问题 感觉信号是延迟的

220
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运动指令是提前的

221
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你看到一个球飞过来

222
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视觉信号到达大脑需要时间

223
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你要接住它

224
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运动指令必须提前发出

225
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为了协调这种时间差

226
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大脑必须建立一个区分 我 和 非我 的计算模型

227
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不是为了哲学

228
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不是为了自尊

229
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只是为了协调时间差

230
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而这个计算模型本身

231
00:08:43,774 --> 00:08:46,526
就涌现出了我们所体验的 自我感

232
00:08:47,482 --> 00:08:48,414
换句话说

233
00:08:48,482 --> 00:08:51,015
我 不是一个坐在大脑某处的小人

234
00:08:51,562 --> 00:08:52,655
我 是大脑

235
00:08:52,682 --> 00:08:55,454
在混沌边缘维持动态平衡时

236
00:08:55,482 --> 00:08:56,974
产生的一种模式

237
00:08:57,401 --> 00:08:59,054
一种暂时的同步

238
00:08:59,362 --> 00:09:00,635
这不是哲学猜想

239
00:09:00,842 --> 00:09:02,334
这是可以验证的

240
00:09:02,401 --> 00:09:03,535
你喝了一杯酒

241
00:09:03,602 --> 00:09:05,735
大脑的混沌特征发生改变

242
00:09:05,761 --> 00:09:07,474
你的 自我感 就会松动

243
00:09:07,881 --> 00:09:09,640
这就是为什么微醺的人

244
00:09:09,641 --> 00:09:11,495
觉得世界变得不一样了

245
00:09:11,761 --> 00:09:13,214
你深度冥想的时候

246
00:09:13,362 --> 00:09:15,655
默认模式网络的活动模式改变

247
00:09:15,802 --> 00:09:18,414
自我 的边界感会暂时消融

248
00:09:18,641 --> 00:09:20,895
很多冥想者报告的 无我 体验

249
00:09:20,921 --> 00:09:25,135
神经科学已经可以在脑扫描中观察到对应的动态变化

250
00:09:26,121 --> 00:09:26,714
我 这个东西

251
00:09:27,241 --> 00:09:29,414
比你以为的脆弱得多

252
00:09:29,562 --> 00:09:31,364
也灵活得多

253
00:09:31,710 --> 00:09:34,403
你身体里有很多细胞都在不断更新

254
00:09:34,791 --> 00:09:37,324
你的神经连接每天都在重组

255
00:09:37,671 --> 00:09:41,204
你今天的信念和十年前可能截然相反

256
00:09:41,510 --> 00:09:43,624
但你仍然觉得 我还是我

257
00:09:44,350 --> 00:09:47,484
这种连续感不是来自某个不变的核心

258
00:09:47,870 --> 00:09:49,883
它来自模式的连续性

259
00:09:50,311 --> 00:09:53,324
就像河流 河水每秒都在更换

260
00:09:53,551 --> 00:09:55,563
但河的形状保持着

261
00:09:55,990 --> 00:09:56,663
你不是水

262
00:09:56,990 --> 00:09:58,004
你是河道

263
00:09:58,271 --> 00:10:01,131
但河道本身也在缓慢改变

264
00:10:01,438 --> 00:10:02,072
说到这里

265
00:10:02,239 --> 00:10:03,491
我不得不想到

266
00:10:03,519 --> 00:10:05,871
佛陀在两千五百年前说的那个词

267
00:10:06,438 --> 00:10:07,131
无常

268
00:10:07,519 --> 00:10:08,971
大多数人听到无常

269
00:10:09,039 --> 00:10:11,638
第一反应是消极的 什么都靠不住

270
00:10:11,639 --> 00:10:12,812
什么都会失去

271
00:10:13,039 --> 00:10:15,918
但如果你用双摆的视角重新看这个概念

272
00:10:15,918 --> 00:10:18,651
你会发现无常根本不消极

273
00:10:18,718 --> 00:10:21,487
它是宇宙运行的底层代码

274
00:10:21,755 --> 00:10:24,408
佛陀从来没说过世界是随机的

275
00:10:24,515 --> 00:10:28,808
他说的是缘起 一切现象都由条件聚合而生

276
00:10:28,914 --> 00:10:30,408
这恰恰是因果

277
00:10:30,554 --> 00:10:33,127
佛陀也没说过命运是写死的

278
00:10:33,194 --> 00:10:34,347
他说条件会变

279
00:10:34,715 --> 00:10:35,673
条件变了

280
00:10:35,674 --> 00:10:37,048
结果就跟着变

281
00:10:37,314 --> 00:10:37,707
无常

282
00:10:38,074 --> 00:10:40,353
用现代物理学的语言翻译过来

283
00:10:40,355 --> 00:10:43,553
就是确定性混沌 每一步都有因果

284
00:10:43,554 --> 00:10:45,367
但长期不可预测

285
00:10:45,554 --> 00:10:48,447
每一个瞬间都是前一个瞬间的结果

286
00:10:48,515 --> 00:10:51,415
但你没法跳过时间去预知未来

287
00:10:51,763 --> 00:10:52,895
你仔细想想

288
00:10:52,923 --> 00:10:55,255
这里面有一个极其微妙的含义

289
00:10:55,482 --> 00:10:57,881
它意味着你此刻的每一个选择

290
00:10:57,883 --> 00:10:59,096
都是真实的

291
00:10:59,163 --> 00:11:01,336
不是被命运剧本写好的表演

292
00:11:01,442 --> 00:11:03,696
也不是毫无意义的随机噪声

293
00:11:04,003 --> 00:11:06,216
你的选择进入了因果链条

294
00:11:06,283 --> 00:11:08,295
成为下一步的初始条件

295
00:11:08,562 --> 00:11:10,521
而那个下一步会走向哪里

296
00:11:10,523 --> 00:11:12,775
没有人提前知道 包括你自己

297
00:11:13,163 --> 00:11:14,361
这不是无力感

298
00:11:14,362 --> 00:11:15,076
恰恰相反

299
00:11:15,283 --> 00:11:16,216
这是自由

300
00:11:16,403 --> 00:11:18,836
真正的自由不是 我想去哪就去哪

301
00:11:19,283 --> 00:11:23,163
真正的自由是 下一步是真实开放的

302
00:11:23,350 --> 00:11:24,923
我在之前的视频里

303
00:11:24,949 --> 00:11:26,183
详细讲过涌现

304
00:11:26,549 --> 00:11:29,242
秩序如何从简单规则中诞生

305
00:11:29,390 --> 00:11:31,783
但今天我想把视角倒过来

306
00:11:32,189 --> 00:11:34,683
不是秩序如何从混沌中诞生

307
00:11:34,750 --> 00:11:38,482
而是为什么混沌本身就是生命的必需品

308
00:11:39,189 --> 00:11:40,869
如果宇宙完全有序

309
00:11:40,870 --> 00:11:42,523
像一块完美的晶体

310
00:11:42,549 --> 00:11:44,482
那什么新东西都不会出现

311
00:11:44,510 --> 00:11:45,183
没有变化

312
00:11:45,390 --> 00:11:46,102
没有进化

313
00:11:46,309 --> 00:11:47,323
没有创造

314
00:11:47,510 --> 00:11:49,188
如果宇宙完全随机

315
00:11:49,189 --> 00:11:51,228
那什么结构都维持不住

316
00:11:51,230 --> 00:11:51,903
没有记忆

317
00:11:52,110 --> 00:11:52,823
没有形状

318
00:11:53,150 --> 00:11:54,163
没有意识

319
00:11:54,789 --> 00:11:56,962
生命选择了中间地带

320
00:11:57,150 --> 00:11:58,828
或者更准确地说

321
00:11:58,829 --> 00:12:01,770
生命只能在中间地带出现

322
00:12:02,357 --> 00:12:06,209
你的心跳不是完美的节拍器 那反而是病态的

323
00:12:06,396 --> 00:12:09,130
健康的心脏有微妙的不规则性

324
00:12:09,196 --> 00:12:11,489
医学上叫心率变异性

325
00:12:11,637 --> 00:12:15,569
这种混沌特征恰恰是心脏健康的标志

326
00:12:15,877 --> 00:12:19,689
你的脑波不是整齐的正弦波 那是癫痫

327
00:12:20,036 --> 00:12:21,630
正常脑波是混沌的

328
00:12:21,916 --> 00:12:23,841
但混沌中有结构

329
00:12:24,189 --> 00:12:26,601
甚至艺术也在验证这件事

330
00:12:26,949 --> 00:12:29,841
完全规整的节拍机械而死板

331
00:12:29,949 --> 00:12:32,402
完全随机的声音就是噪音

332
00:12:32,788 --> 00:12:34,402
真正打动人的音乐

333
00:12:34,508 --> 00:12:36,762
活在规律和意外之间

334
00:12:37,069 --> 00:12:39,402
爵士乐手管它叫摇摆感

335
00:12:39,508 --> 00:12:41,922
画家管它叫笔触的呼吸

336
00:12:42,069 --> 00:12:43,961
舞者管它叫气息

337
00:12:44,189 --> 00:12:45,782
它们都在利用同一件东西

338
00:12:46,268 --> 00:12:47,402
混沌边缘

339
00:12:47,548 --> 00:12:50,388
那个让一切活过来的临界区

340
00:12:50,975 --> 00:12:52,707
所以如果你问我

341
00:12:52,774 --> 00:12:55,734
宇宙到底是一台写死了结局的机器

342
00:12:55,735 --> 00:12:57,808
还是一场纯粹的随机骰子

343
00:12:58,255 --> 00:12:59,008
我的回答是

344
00:12:59,335 --> 00:13:00,187
都不是

345
00:13:00,735 --> 00:13:02,628
宇宙更像一个双摆

346
00:13:02,975 --> 00:13:05,827
规则简单到中学生都能写出方程

347
00:13:06,095 --> 00:13:08,467
但从这几条简单规则出发

348
00:13:08,495 --> 00:13:09,987
它生成的复杂性

349
00:13:10,054 --> 00:13:12,247
超出了所有观察者的预测能力

350
00:13:12,495 --> 00:13:14,109
包括宇宙自己

351
00:13:14,576 --> 00:13:14,969
而你

352
00:13:15,296 --> 00:13:16,910
就是这个双摆系统

353
00:13:16,936 --> 00:13:19,056
在混沌边缘涌现出来的

354
00:13:19,056 --> 00:13:20,749
一次暂时的同步

355
00:13:21,257 --> 00:13:22,690
你不是被设计出来的

356
00:13:22,897 --> 00:13:24,310
你是长出来的

357
00:13:24,456 --> 00:13:25,489
你不是永恒的

358
00:13:25,737 --> 00:13:26,910
你是动态的

359
00:13:27,377 --> 00:13:28,830
你的存在本身

360
00:13:28,857 --> 00:13:31,374
就是混沌生出秩序的证据

361
00:13:31,640 --> 00:13:34,614
这才是双摆真正告诉我们的事情

362
00:13:34,921 --> 00:13:36,413
不是世界有多乱

363
00:13:36,841 --> 00:13:39,374
而是 在混沌的最深处

364
00:13:39,441 --> 00:13:42,790
有什么东西正在试图成形

365
00:13:43,217 --> 00:13:45,329
你觉得双摆画出的轨迹美吗

366
00:13:45,816 --> 00:13:46,530
如果觉得美

367
00:13:46,857 --> 00:13:49,030
想想那种美感来自哪里

368
00:13:49,656 --> 00:13:51,589
也许是因为你认出了自己

369
00:13:51,977 --> 00:13:53,589
因为你也是那个图案

370
00:13:54,017 --> 00:13:55,496
从确定的规则中

371
00:13:55,497 --> 00:13:57,936
长出了不可预测的生命

372
00:13:58,473 --> 00:13:59,148
我是王利杰

373
00:13:59,427 --> 00:14:00,323
我们下期见