Leon 的文章推荐过几次了，真是厉害，这篇是我的年度最佳

我试着用我的话简单解释一下

1，各态历经是一个数学概念，运用到实际场景可以理解为，个体的趋势和群体的趋势一致

2，符合这一规律的便是各态历经的（ergodic），否则便是non-ergodic

3，人生轨迹，投资等，都属于 non-ergodic，作者用实验证明

4，如果你觉得好好学习努力工作能实现圆满人生，如果你觉得价值投资可以慢慢变富，sorry，绝大部分人都不会实现

5，在non-ergodic的事情上，我们要把理想的可能性去除掉，才会有奇迹发生

Knowing whether a process is ergodic or non-ergodic is critical in knowing how much risk to take. Investing and wealth are non-ergodic processes, which imply that our first thoughts on expected values are very wrong.

I've heard about ergodicity before, but wasn't quite able to understand it until I watched this video by Ergodicity TV. It's an important concept but seems more widely known in physics than in finance. I want to try explaining it in my own words below.

We're familiar with different types of "averages" - mean, median, mode 1. Let's focus on mean for today, and take it as the expected value of some random event 2. **How we define expected value can give us dramatically different results, changing our mindset on the attractiveness of bets and how much to bet.**

**Ergodicity means that the ensemble average is the same as the time average.** Something being non-ergodic means the opposite, that the ensemble average is not the time average.

Yeah, I'm not sure what ensemble and time here mean 3 either, so let's look at an example of tossing a coin.

Suppose some random dude tosses a coin 5 times, getting some heads and some tails. We can calculate the time average for this simulation by getting the average number of heads for one person across a period of time. There are 3 heads out of 5 tosses, so that's 0.6 heads (3 divided by 5).

Suppose we get a few more people to toss coins. We get something like below, where I'm representing heads as 1 and tails as 0 for convenience:

There are two types of averages we can use here. The first is the time average from before, where we get the **average over some period of time for one person.**

The second is the ensemble average, where we get the **average over one period of time for multiple people.**