every branch has high-value leaves: Nonlinear Function
Created: January 09, 2021
Modified: February 25, 2022

every branch has high-value leaves

This page is from my personal notes, and has not been specifically reviewed for public consumption. It might be incomplete, wrong, outdated, or stupid. Caveat lector.

Events that seem really terrible---closing off good outcomes and potentially leading to bad outcomes---often refine into a fine path that mostly sticks to the good parts and avoids the bad parts. The good outcomes that you were attached to aren't the only good outcomes, and we have more agency than we think to make the best of seemingly bad situations.It would be useful to think this even if it weren't true, in the sense that optimism is an important ethic, but it's also clearly true in many cases.

For example, consider the question of whether you get into the college of your dreams. Choosing a college is clearly a major life event: it determines the friends you make, the people you learn from, the first place you live, and the opportunities that you will have for the rest of your life. On the other hand, plenty of people go to their first choice college and end up being miserable, either then or afterwards, and many people go to a college that wasn't their first choice and end up having an amazing experience. Admissions decisions are important, and it's reasonable to suppose that your dream college has better outcomes in expectation, and to make decisions accordingly. But your expectations are necessarily quite coarse. Once the reality is determined, you have a chance to plan more closely, and things that seemed less desirable on average can still be quite good.

This is a positive spin on the fact that nothing matters: most bad things don't matter as much as you think they do; even things that seem really big don't affect your ability to be happy nearly as much as you think they will. People adapt, preferences change, and you learn to look on the bright side. For example, if you asked me, do I think a global pandemic would be a good thing, I'd obviously have said no. If you'd asked if I'd enjoy being shut in my apartment for a year, I'd also have said no; it'd feel like prison. But in the actual reality, I was happier during the COVID pandemic than before; I found ways to make it into a good experience.

Churchill:

"One must never forget when misfortunes come that it is quite possible they are saving one from something much worse; or that when you make some great mistake, it may very easily serve you better than the best-advised decision."

Relatedly, it is important to actually get to the leaves. Starting the 'right' projects has no value if you never finish them. Don't let analysis paralysis keep you stuck clinging to the trunk of the tree, afraid to venture out on a branch.

To continue the analogy: the tree is bigger than you think it is, and it's not really a graph-theoretic tree. The branches overlap. Even if do you end up at a leaf that isn't great on its own, you've still learned something about the tree, about climbing, and you're often in a position to jump to another branch. Sometimes this can get you into a position you would never have been able to reach directly. If you think about climbing with a growth mindset, there are always steps worth taking.