WHY IS ERGODICITY IMPORTANT? AN EXAMPLE
My cousin was born in a mountain village in the French Alps. Like many there, he learned to ski before reading.
I am a good skier, but I remember the humiliation when I was 14 and he was 6, seeing him surpass me, swift as a bullet.
My cousin was born in a mountain village in the French Alps. Like many there, he learned to ski before reading.
I am a good skier, but I remember the humiliation when I was 14 and he was 6, seeing him surpass me, swift as a bullet.
2/ At a young age, he made it into the World Championships for his age bracket. Boy, he was fast.
His career came to an abrupt end a decade later, one injury at a time. First, he injured his ankle. Then, he broke his knee. A few more injuries later, he retired, too young.
His career came to an abrupt end a decade later, one injury at a time. First, he injured his ankle. Then, he broke his knee. A few more injuries later, he retired, too young.
3/ 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.
They got there because they were the fastest of those who didn’t get injured into retirement.
4/ In skiing, and life in general, it is not the best ones who succeed. It is the best ones of those who survive.
5/ In theory, performance determines success. The most performing employee becomes the most successful one.
In practice, performance is subordinate to survival. It is the most performing employee who doesn’t burn out that becomes the most successful, and so on.
In practice, performance is subordinate to survival. It is the most performing employee who doesn’t burn out that becomes the most successful, and so on.
6/ I’m not just making the banal point that survival matters. I’m saying that it matters more than performance. Let’s run the numbers.
7/ Let’s imagine that every time my cousin participates in a skiing race, he has a two-in-ten chance of winning it, and a two-in-ten chance of breaking his knee.
How many races will he have won, on average, at the end of a championship consisting of 10 races?
How many races will he have won, on average, at the end of a championship consisting of 10 races?
8/ The naïve answer is two races. That is the product of the number of races, 10, times the probability of winning each, two-in-ten.
This would be correct if the races were independent of each other.
In reality, if he breaks his knee during a race, he misses the following ones.
This would be correct if the races were independent of each other.
In reality, if he breaks his knee during a race, he misses the following ones.
9/ So, he can participate in the second race only if he didn’t break his knee during the first one. He can participate in the third race only if he didn’t break his knee in the previous two ones, and so on.
His chances of completing all ten races are pretty slim – only 11%.
His chances of completing all ten races are pretty slim – only 11%.
10/ If we take the time to compute his chances to participate in each race, we discover that his expected number of wins is less than one.
This is fewer than the two wins we would expect if breaking a knee didn’t prevent him from participating in subsequent races.
This is fewer than the two wins we would expect if breaking a knee didn’t prevent him from participating in subsequent races.
11/ 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.
Instead, over a prolonged period of time, survival
dwarfs performance.
12/ There is a difference between what matters when we consider narrow intervals and what does when we consider broader ones.
Over the short term, consequences that apply beyond the short-term do not matter.
Over the long term, they do.
Over the short term, consequences that apply beyond the short-term do not matter.
Over the long term, they do.
13/ In my cousin's case, the broken leg preventing him from competing in future races is the “phantom consequence” that is not observable in the short term but affects the long term.
14/ If we make decisions based on what happens over narrow intervals and forget about these “phantom consequences,” we will make bad decisions.
Ergodicity is the study of these phantom consequences.
Ergodicity is the study of these phantom consequences.
15/ This was an excerpt of the first chapter of my book, "Ergodicity: Definition, Examples, And Implications, As Simple As Possible."
You can read the full book on gum.co/ergodicity
You can read the full book on gum.co/ergodicity
16/ 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 future gains.
Any major injury prevents him from participating, causing him to forego future gains.
17/ 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.
This means that you cannot extrapolate future outcomes from solely the expected outcomes of the activity performed once.
18/ Of course, what I mentioned so far is about long-term performance, not short-term one.
However, in many venues of life, the two are more similar than apparent.
However, in many venues of life, the two are more similar than apparent.
19/ For example, winning a single race is an instance of short-term performance.
A good racer can just “risk it all” and win, with a bit of luck.
However, to become good enough a racer to do it, long-term performance is necessary too.
A good racer can just “risk it all” and win, with a bit of luck.
However, to become good enough a racer to do it, long-term performance is necessary too.
20/ Too often, we observe a snapshot of someone’s life and believe that we witnessed a piece of short-term performance.
But if skills are required even to attempt performing that, then what we are really observing is long-term performance.
But if skills are required even to attempt performing that, then what we are really observing is long-term performance.
21/ Therefore, in any endeavor in which success depends on you accumulating some kind of resource (money, skill, connections, trust, etc.), do not maximize growth regardless of survival.
Instead, maximize growth that conserves survival.
Instead, maximize growth that conserves survival.
22/ The above is not an invitation to excessive prudence.
Yes, until you experience pain, you do not know where the boundary is.
And yes, going too slowly comes with problems too.
Yes, until you experience pain, you do not know where the boundary is.
And yes, going too slowly comes with problems too.
23/ Rather, it's an invitation to distinguish between calculated risks whose consequences you can recover from & recklessness whose consequences can permanently debilitate you
There's a sweet spot where you expose yourself to the former but not the latter – a good place to aim
There's a sweet spot where you expose yourself to the former but not the latter – a good place to aim
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