Self Curiosity

Hi everyone,

I was talking to a friend the other day about difficulty debugging feelings, and they talked about how one of the problems they have with it is that it is difficult, and so it felt like failure when they spent some time trying to figure out what they were feeling and didn’t come up with a good answer.

I thought this was interesting, because it was a problem that made total sense but that I didn’t have, and I think a large part of that is a different stance to investigation and problem solving which ultimately boils down to “Yeah, sometimes problems are hard and you’re not going to solve them in one sitting”.

I think this is something I learned as a mathematician. I’m always a bit wary of this as an explanation because I find that I often use it and then people point out to me that actually typically mathematicians are just as bad as everyone else at this and I have to acknowledge that this is true and that what I really mean is not that mathematicians learn this but that I learned this as a mathematician, and that mathematicians who didn’t need to go read Thinking through the implications.

But in this case I really did learn it as a mathematician, and I do think it is a mathematician’s skill suitably generalised. In The State of Being Stuck, Ben Orlin quotes Andrew Wiles as saying that one of the key traits of being good at mathematics is “accepting the state of being stuck.” - avoiding getting frustrated just because you haven’t solved the problem.

“What you have to handle when you start doing mathematics as an older child or as an adult is accepting the state of being stuck,” Wiles said. “People don’t get used to that. They find it very stressful.”

He used another word, too: “afraid.” “Even people who are very good at mathematics sometimes find this hard to get used to. They feel they’re failing.”

But being stuck, Wiles said, isn’t failure. “It’s part of the process. It’s not something to be frightened of.”

Catch me and my teacher colleagues any afternoon, and—if you can get past the “sine” puns and fraction jokes—you’ll likely find us griping about precisely this phenomenon. Our students lack persistence. Give them a recipe, and they settle into monotonous productivity; give them an open-ended puzzle, and they panic.

Students want the Method, the panacea, the answer key. Accustomed to automaticity, they can’t accept being stuck.

Wiles recognizes this fear, and knows that it’s misplaced. “For people who carry on,” he said, “it’s really an enjoyable experience. It’s exciting.”

I really like this article because I don’t think people pay enough attention to the emotions of doing mathematics (or any other skill) and they are actually key to the experience, and I think it gets to one half of the experience very well: Key to doing mathematics well is avoiding having negative emotions when you haven’t solved the problem yet. If trying and not succeeding (yet) feels like failure, and failure feels bad, you’ll end up with a very negative experience of doing mathematics.

(I think a lot of people end up with this very negative experience of mathematics because of how it’s taught).

This is also how all problem solving works: If not solving a problem will cause you to feel bad, you’ll learn to avoid problems that are “too hard” - ones where you have a decent chance of getting stuck.

This is bad for two reasons: The first is that hard problems exist, and sometimes you’re going to have to solve them. This sort of aversion makes it much more likely that you will fail to solve important problems. The second is that working on problems that are too hard for you is how you get better at solving problems like that - if you never challenge yourself, your skill at problem solving will tend to stagnate, because you have no real reason to improve.

One way out of this is self-compassion. Self-compassion is a cornerstone of a lot of healthy working with emotions: Rather than beating yourself up about your failings, treat yourself like you would treat a good friend. If you can’t imagine saying “You’re such an idiot for not solving this problem” to someone you loved, why say it to yourself?

(A common answer here is “It’s OK to hold myself to higher standards than I do to other people”, but this problem demonstrates that you’re not doing that: Self-compassion allows you to tackle harder problems than you otherwise would, so in fact raises your standards. Also cf. Being an Example to Others: The standards you hold yourself to also impact other people because they become the standards they hold themselves to)

Self-compassion is good and important and you should aim for it, but I think it’s actually not quite enough. Even if you don’t beat yourself up for failing to solve a problem, you just run into the issue that repeatedly failing to achieve something is just really frustrating and not much fun. It’s all very well to not be afraid of being stuck, but that doesn’t mean you’re suddenly going to enjoy it.

I think the solution to this is to switch away from quite such a goal directed mindset and more to one of open curiosity. Rather than just treating the problem as important and thus worth solving, treat it as interesting and thus worth thinking about. The goal is not just to solve the problem, it is to become the sort of person who can solve the problem, and any interesting thoughts you have in that space (even if they conclude that something you tried didn’t work!) are a positive outcome. There is still of course a problem that you need to solve, and your thoughts are directed towards it, but your goal is more to explore the problem space than to solve the problem.

The nice thing about this approach is that it’s fun in a way that relentlessly grinding on a single problem won’t be. It lets you play with ideas, go off on tangents if they seem interesting, and generally build a much more complete understanding of the problem and its surroundings.

Approaching it this way has a couple of major advantages. Firstly, it actually makes you much more likely to the solve the problem, because working on it is now fun and so you’re more likely to put in the effort. Secondly, it makes you much better at solving other problems like it in future - rather than making a beeline for the solution and doing whatever works, you are more invested in understanding and fleshing out your knowledge for future, which strengthens your abilities in this area.

This also ties into the model I laid out in Safety as an enabler of growth and Desire as a driver of growth. If you have some area you want to get better at, you need to feel safe to experiment, and you need to want to get better at it. Self-compassion is what provides safety (because failing is no longer terrible), but curiosity is what provides desire because it makes you actually want to explore the area and get better at it.

Which brings me back to the original problem: Figuring out your feelings in a situation can be hard, and won’t always produce useful results. No matter how much self compassion you have, that can’t really make the experience of trying to sit with your feelings less frustrating.

But the same solution applies: Rather than trying to just figure out what your specific feelings in the moment are, instead try to cultivate curiosity about your thoughts and feelings more broadly. Specific incidents and questions (“What do I want?” “Why am I reacting this way?”) are useful problems to guide your investigation, and it is important to be able to solve them, but the more important thing is to be good at the general process of understanding and relating to your feelings.

This suggests that as well as an attitude of self compassion, it’s also useful to adopt one of self curiosity. A general attitude that your own thoughts and feelings are interesting and worth investigating in their own right. Feelings are not, first and foremost, a problem to be solved, but an interesting area to investigate further.