Ergodicity

From him, I learned that the skiers that you see on TV, the fastest racers in the world, didn’t get there because they were the fastest. They got there because they were the fastest of those who didn’t get injured into retirement.

Ref. C706-A

In skiing, and life in general, it is not the best ones who succeed. It is the best ones of those who survive.

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In theory, performance determines success. The fastest skier wins the race, and the most performing employee becomes the most successful one. In practice, performance is subordinate to survival. It is the fastest racer of those who survive that wins races, it is the highest performing employee who doesn’t burn out that becomes the most successful, and so on.

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I’m not just making the banal point that survival matters. I’m saying that it matters more than performance.[4]

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The point is, in a single instant of time, pure performance is all that matters. Instead, over a prolonged period of time, survival dwarfs performance.

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Over the short term, consequences that apply beyond the short-term do not matter. Over the long term, they do.

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In my cousin’s case, the broken leg preventing him from competing in future races is a “phantom consequence” that is not observable in the short term but affects the long term. If we make decisions based on what happens over narrow intervals and forget about these “phantom consequences,” we will make bad decisions.[8] Ergodicity is the study of these phantom consequences.[9]

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The explanation for the skier paradox is that, whereas my cousin had a chance to win each race, he is not guaranteed to race all of them. Any major injury prevents him from participating, causing him to forego expected future gains.

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In general, we can say that in any repeated activity, irreversibility absorbs future gains. This means that you cannot extrapolate future outcomes from solely the expected outcomes of the activity performed once. You also need to consider the impact of irreversible consequences.

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For children, falls, fights, and mistakes in general tend to have more reversible consequences than for adults.  Sometimes I wonder if part of the nostalgy that many have for childhood is nostalgy for reversibility.

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Too often, we observe a snapshot of someone’s life and believe that we witnessed a piece of short-term performance. But if practice is required to get to a place where one can attempt that, then what we are really observing is long-term performance. A professional skier in his 30s successfully managed risk in the previous decades – no matter what he seems doing in this one race we’re observing.

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If you practice yoga, do not attempt to reach the maximum amount of stretch per session.[10] Instead, maximize the amount you can achieve without risking any major injury.[11] A single trauma is enough to prevent you from practicing effectively for months or even years.

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If you have a job, do not attempt to work as hard as possible. Instead, work as hard as you can without risking your health, marriage, or mental sanity. These three are damn hard to recover once lost.[12]

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More in general, in any endeavor in which success depends on you accumulating some kind of resource (money, skill, connections, trust[13], etc.), do not maximize growth regardless of survival. Instead, maximize growth that conserves survival.

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Rather, the above is an invitation to distinguish between calculated risks whose consequences you can recover from and recklessness whose consequences might permanently debilitate you. There is a sweet spot where you expose yourself to the former but not the latter[14], and that’s a good place to aim.

Ref. 34DA-O

People who replied “$500,000” to the previous question assumed that death in one round just means that no winnings are collected during that round, but future rounds are still winnable. In Russian Roulette, however, one loss means that you also forego all future gains. Losses are irreversible and extend in the future.

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For example, relationships are like Russian Roulette – in the sense that they grow stronger over time, but only if you get to spend time with your partner. If, one day, you break their trust, they might decide not to see you again. You will lose all chances to rebuild the relationship. Similarly, in investing, losing your capital means that you lost both your capital and all future returns that it could have generated.

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Whenever an activity cannot be assumed repeatable at infinity, we should be wary of expecting to achieve its average outcome.[17]

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Any form of “game-over” nullifies future gains, bringing the average down. Hence, we can say that possible game-overs are a cause of non-ergodicity.

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Similarly, in my cousin’s example, breaking his leg is a form of game-over (the damage is irreversible, at least during the championship). It implies losing the race in which the injury took place and all the following ones. This causes his average number of wins during a championship to be lower than expected (his chances of winning a race multiplied by the number of races).

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Game-overs are common. They include bankruptcies, injuries, severe depressions, burnouts, and break-ups of all kinds (between romantic partners, business partners, or friends). The next chapter analyzes some of them.

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Sports. The harder you practice, the faster you progress. However, if you try too hard, you might injure yourself. Irrecoverable damage at your joints might end your ability to perform the sport well, or at all.

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A single negative event can render short-term maximization irrelevant.

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A system is ergodic[22] if its population outcome coincides with the lifetime outcome of each of its components. Otherwise, it is non-ergodic.

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For example, Russian Roulette is non-ergodic because the lifetime outcome differs from the population outcome. If you keep playing it because you fail to grasp its non-ergodicity and mistakenly believe that your lifetime outcome equals your population one, you will end up dead instead of rich.

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Sadly, when we observe someone’s success, our automatic reaction is often to desire it for ourselves, without asking ourselves if we would actually like it – both its pros and its cons, without cherry-picking.

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“The part of the person that we envy doesn’t exist without the rest of that person,” he writes. “If we aren’t willing to trade places with them completely – their life, their body, their thoughts – then there is nothing to be envious about.”

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Too often, when we look at the winner, we fail to see all his clones in the parallel universes in which he lost his bets. Any serious decision-making process cannot neglect them.

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Whenever we desire an outcome because we see those that benefited from it, it is good practice asking yourself, do you want the outcome, or do you want the opportunity to take the gamble that produced the outcome? If you only want the former but not the latter, you might be unprepared for what’s to come.

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What’s the take-away? That payoffs depend on time horizons.

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That you cannot base your decisions on a payoff computed on a time horizon that isn’t yours. This is one of the big lessons of ergodicity: the study of how payoffs scale over time and space.

Ref. 3E6C-E

Here are a few key points covered so far: - Irreversibility absorbs future gains. - We call “population outcome” the outcome of many people performing an action once, and “lifetime outcome” the outcome of one person performing an action many times. If they differ, the system that produces them is non-ergodic. - You can only rely on expected outcomes if you are guaranteed a large number of repetitions. Otherwise, they are misleading. (The law of large numbers requires a large number of repetitions). - Risk aversion is rational in the presence of non-ergodicity.

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Be wary of centralization, especially when there is no skin in the game[34] ensuring that the incentives of the center coincide with those of the peripheries.

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