Spud Infinity

What’s the deal with so-called necessary mistakes?

For example: “I know it’s a bad idea to go to law school, but I guess it’s just a mistake I need to make,” or “I probably shouldn’t take my cats along on this road trip, but maybe this is a mistake I need to make.”

Usually people say this to justify departing from someone’s advice or from conventional wisdom.

Reason 1: Euphemism

They doubt the advice but don’t want to come out and say it directly.

Reason 2: Learning

“I believe this won’t work, but I want to know why.”

Maybe the advice doesn’t account for the information value you’d get from making the mistake.

For instance, you might say, “I know it would probably be uncomfortable to put my right shoe on my left foot, but I don’t actually know what it would feel like, so I’m going to find out.” I’m willing to pay the price of discomfort in order to learn something.

Analogy: in reinforcement learning, sometimes the best approach is to explore using a policy different from the one you think is optimal. Q-learning is one such approach. This is called “off-policy” learning.

Objection: this reason explains how “mistakes” can be useful. But what makes them necessary?

Reason 2.1: Developing your own model

“My model predicts that this is the best course of action. I need to take it to develop a better model.”

Example: You advise me not to take my cats on my trip. You point out some reasons it will be a pain. I trust your judgment but I don’t understand the reasons. I need to take my cats so I can find out where my model is wrong. I’m willing to pay the cost of doing the wrong thing to learn something valuable.

Bad advisors only know Reason 1

Advisors—teachers, managers, coaches, etc.—often discourage you from making your own mistakes, probably in part because they only know about Reason 1. If you reject their advice, they conclude you must be doubting them. (I too only knew about Reason 1 for a long time. Oops.)

If you can convince them that you’re making a mistake for Reason 2 or 2.1, they may be more inclined to go along.

Doing things your own way

If you depart from someone’s advice without believing it, you’re not making your own mistake, you’re just doing things your own way.

Sometimes in those cases it’s convenient to pretend that you’re making a mistake. This may be more palatable to the advisor.

Example: “Of course, teacher, you in your infinite wisdom must be correct that I should never start a sentence with a conjunction. But this is just one of those mistakes I have to make.”

Bad advisors will still grumble about your way

Regardless of your reasons for doing things your own way, bad advisors will grumble about it. Other people’s ways are weird, alien ways, and it takes strenuous thinking to get into someone else’s frame of mind and help them sort out their own mistakes. Bad advisors aren’t interested in all that hard work.

Example: The C programmer doesn’t want to debug your Haskell code.

Great advisors, on the other hand, understand the benefits of doing things your own way and are excited to learn something new.

I thought about this today because I heard Agnes Callard talk about how she wants to learn from her students:

[My students] always want more instruction from me. They’re like, but tell us what you’re expecting, and tell us what you want, and tell us how to write a paper, and how do I avoid this problem, and how do I do this? And what I tell them is like, I want you to teach me something new that I don’t know yet. So I can’t tell you how to do that. Because if I told you what to say, then I would already know it. And then you wouldn’t be surprising me. I can’t teach you how to surprise me.