Explaining Ergodicity Without Mathematical Jargon

Perhaps I am reaching beyond my grasp, but here is ergodicity simply explained.

In the most basic terms I can manage. An ergodic scenario, whose phenomenon extracted would then be explained as ergodicity – is when the average outcome of a group is the same as the average outcome of an individual, over time.

Let’s take the most baseline example to explain. The tossing of a fair coin.

If 100 people toss a coin once, or if 1 person tosses a coin 100 times, probabilistically, you will have the same set of results. Over time, the single actor will turn in similar results to a randomly distributed set of other coin tossers.

This rule is a reality of the narrow confines of coin tossing 50/50 chance outcomes. This is an example of an ergodic system. Had the individual over time had results that differed significantly from the randomly distributed set of other coin tossers then in fact this system would be non-ergodic.

However, since we know the 50/50 toss can’t be (realistically) gamed. If the results differed we could assert confidently that this coin was in fact loaded, and therefore conclude that someone is taking us out to lunch – to echo Nassim Taleb’s terrifically poignant Skin In The Game.

Finding non-ergodicity in what are otherwise supposedly ‘ergodic’ systems will typically nudge in the direction of a steaming pile of BS.

What Ergodicity Teaches Us About Randomness

The key to a simplified explanation of ergodicity, that doesn’t rely on stochastic process, hyperbolic manifold and statistical physics, is understanding that systems containing defined variables are typically ergodic while systems without (most of human life) are non-ergoditc.

This echoes again, Nassim Taleb and the Ludic Fallacy, an attempt to understand real life phenomena via explanations of statistical games whose variables and well known and defined. A casino is in fact the least random place on earth.

— A terrific way to think about ergodicity (borrowed from taylorpearson.me)

A way to identify an ergodic situation is to ask, do I get the same result if I:

  • look at one individual’s trajectory across time?
  • look at a bunch of individual’s trajectories at a single point in time?

If not: non-ergodic.

If yes: ergodic.

Humanity & Why Stakes Matter

Ergodic systems are best measured in those systems absent the variable of human behaviour.

For example, within the seemingly random pattern of smoke filling a room ergodicity can be found or how heat distribution might be ergodic on a heating plate of metal. These are the complex building blocks of explaining ‘ergodicity’ which can then be abstracted by thick heads like me to be able to claim whether ergodicity is or isn’t.

But as soon as the human variable is entered, the chance of ruin, collapse, complete failure, death or what Nassim Taleb calls the ‘absorbing barrier’ arrive. Systems that otherwise might seem ergodic (say, financial markets) can turn out to be, in fact, non-ergodic.

Path dependence matters, measure an individuals trajectory over time. Should one meet the absorbing barrier they are removed from the game.

Conclusion

Well, I hope you got something out of that.

I am not a physicist, mathematician, statistician or any of the technical ician’s one might have ascribed to them as a measure of authority. I am but a man keen on ‘The Incerto‘ and fascinated by the works and lessons Nassim Taleb.

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