I was reading this book, a compilation of essays about bitcoin and capitalism, and I was struggling to understand the concept of ergodicity.
So I asked ChatGPT to explain it with a simple analogy, and I thought the explanation was good enough to share. If it’s wrong in some way, let me know:
Imagine a vast, sprawling amusement park with many different attractions and rides. Each ride represents a different state or condition that a system (like an economy, a molecule in a gas, or even a person’s life) can experience.
Now, imagine two ways to experience this park. One way is as a single visitor: you spend the whole day going from ride to ride, trying each one. Over time, you experience everything the park has to offer. Your single journey through the park represents a time average; that is, you’re sampling all the possible states over a period of time.
The other way to experience the park is by looking at a snapshot of all the visitors at one moment. Instead of one person experiencing all the rides, you see thousands of people, each on a different ride. This snapshot represents a space average, where you see all the possible states (rides) at one instant through the experiences of many different visitors.
A system (or park) is ergodic when the long-term time average (your full day at the park) is the same as the average experience of many people at a single moment (the snapshot of everyone). In other words, what you experience over time is the same as what everyone experiences collectively at one point.
In practical terms, if a system is ergodic, studying a single part of it over time can give you a good understanding of the whole system at any given moment. If it’s not ergodic, then the individual experience might be quite different from the average experience, and more complex methods are needed to understand the whole system.
I like to ask ChatGPT to generate simple analogies and metaphors for complex concepts, because I find them easier to grasp and if needed, explain to others. This method misses some details and nuances, but 75% understanding is better than whatever it was prior…
Unfortunately, I couldn’t get dalle3 to generate an appropriate corresponding image (though that capability *has* to be possible in the near future). Midjourney was slightly better so I’m including here:
