复杂系统：整体无法由平均个体线性推导

知道一个消费者怎样选择，不能直接推出整个市场；知道一个神经元怎样工作，也不能直接推出大脑怎样工作。个体会彼此影响，前一个人的选择改变后一个人的处境，反应又回头改变前者。整体的行为因此还取决于连接方式和互动顺序。

平均值在这里尤其容易误导。平均消费者可能并不存在，平均意见也可能没有任何人真正持有。把每个部分的典型行为相加，会漏掉少数关键节点、反馈和极端事件。

以上讲的是整体为什么不能从个体平均值推出。复杂系统的预测误差会随时间迅速放大 讨论的是另一个问题：即使已经有了模型，初始误差仍会在非线性系统里不断放大。两者都涉及非线性，推理失败的位置不同。

《Skin in the Game》原文：

Understanding how the subparts of the brain (say, neurons) work will never allow us to understand how the brain works. A group of neurons or genes, like a group of people, differs from the individual components—because the interactions are not necessarily linear.

Understanding the genetic makeup of a unit will never allow us to understand the behavior of the unit itself.

ntifragile has been about the failure of the average to represent anything in the presence of nonlinearities and asymmetries similar to the minority rule. So let us go beyond: The average behavior of the market participant will not allow us to understand the general behavior of the market. You can examine markets as markets and individuals as individuals, but markets are not sums of average individuals

Groups are units on their own. There are qualitative differences between a group of ten and a group of, say, 395,435. Each is a different animal, in the literal sense

The higher the dimension, in other words, the higher the number of possible interactions, and the more disproportionally difficult it is to understand the macro from the micro, the general from the simple units. This disproportionate increase of computational demands is called the curse of dimensionality.

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