Pragma #7 — Non-Ergodicity
“The important point is that complexity, and the non-ergodic nature of many of the systems we deal with can lead to extreme outcomes that we cannot predict.” — Richard Bookstaber
Picture a gambler at a roulette table versus an investor in the stock market. The gambler plays a game where each spin is a fresh start, while the investor rides the wave of market trends. It’s impossible that the roulette yields 101, as that’s not included in the set of possible outcomes. But it’s possible for a wave to turn into a devastating tsunami.
The Theory: Ergodicity vs. Non-Ergodicity
In an ergodic system, the average outcome of a group is equal to the average outcome of an individual over time. Don’t panic, let’s go through an example.
Imagine a group of 100 people tossing a coin at the same time. On average, 50% will land on heads.
Now compare this to one person tossing a coin 100 times. On average, this person will get heads 50% of the time too.
This is property is known as ergodicity. We are taught that most systems are ergodic, but most of them are not.
A trick to identify an ergodic system is to do the following:
look at one individual’s trajectory across time
look at a bunch of individual’s trajectories at a single point in time
If if the average outcome is the same: ergodic.
If not: non-ergodic.
Non-Ergodic systems
Non-ergodic systems are everywhere. Here you can find some common characteristics:
Path dependence: The outcomes depend heavily on the specific path taken or the decisions made. Different individuals may experience vastly different results based on their choices, circumstances, or timing.
Cumulative effects: In non-ergodic systems, decisions and events can compound over time. A tiny initial difference can lead to significant divergence in outcomes later, which allows for a wide range of possible futures. This ties into non-linear systems.
Risk of ruin (and chance of moonshot): Non-ergodic systems can lead to extreme outcomes (both positive and negative) due to the accumulation of risk or favourable conditions. An example would be the fall of Lehman Brothers.
Some examples of non-ergodic systems include the stock market, entrepreneurship, health outcomes, or natural disasters.
The Practice
Think long-term: In a non-ergodic world, outcomes build over time. Rather than sweating the small stuff or panicking at temporary setbacks, zoom out and focus on the bigger picture. Keep an eye on the horizon.
Rethink averages: averages are most useful in ergodic systems, but they’re useless when it comes to non-ergodicity. The fact that 1 out of 2 businesses fail after 5 years doesn’t mean yours will, too.
Be Adaptive: Non-ergodic systems thrive on unpredictability. What worked yesterday might not hold true tomorrow. Embrace flexibility and adjust your approach as you get more information.
Just for fun…
“Now compare this to one person tossing a coin 100 times. On average, this person will get heads 50% of the time too.”
Turns out to be more complicated. https://www.newscientist.com/article/2397248-coin-flips-dont-truly-have-a-50-50-chance-of-being-heads-or-tails/#:~:text=Researchers%20who%20flipped%20coins%20350%2C757,per%20cent%20of%20the%20time.