Problems worth solving

Do you sometimes feel like you're spending time on the wrong problems?

Cover for Problems worth solving

the drift

Most people drift through life solving whatever problems happen to fall in front of them. Like a log floating on a river, drifting wherever it takes you. Failing to spend energy on choosing problems worth solving surrenders you to the entropy of the world. I frequently notice this drift myself too. Sometimes I realize none of the problems I’m working on were deliberately chosen. Other times I might have several interesting projects, yet find myself forced to choose one over the others. This passivity might seem harmless, natural even. But it’s actually quite dangerous. We just fail to observe its effects properly.

The fact is, time is limited, and some problems are more important than others. But how are we supposed to know which ones are worth solving? I wonder then, could there be a universal model for choosing important problems? A way of thinking that considers the full spectrum of human problems: choosing one’s life’s work — what shirt to wear — what problems your startup should solve — what skills to learn — which language to learn — where to spend your time. There might be. I’ve been thinking about a few ideas that together form a coherent model to help you choose problems worth solving. One that is both analytical and intuitive. And one I hope to return to whenever I find myself drifting too much.

So, every single person would benefit from asking:

which problems are worth solving?

Simplified, it’s about maximizing the ratio of output to input. Your time and energy are limited; you cannot solve all problems. Look for problems where solving them produces the most value relative to the resources you use. Choosing worthwhile problems becomes a simple equation, something like:

y = 2.5a + 1.2b + 0.1c

Where y represents the value you aim to maximize. Variables a, b, and c represent potential problems to solve, while their coefficients represent their impact potential. You can choose only one variable, obviously you go for option a. as it has the highest impact potential.

But reality is messier. You rarely know the exact values. You might not even know all the variables. Worse, you might not realize there’s a choice to be made at all. So to most people choosing problems to solve, the equation looks more like:

y = … + xb + zc + …

Revealing the unknown variables and their impact potential becomes a problem worth solving in itself. The first step towards choosing problems worth solving: a deliberate decision to actively find better problems.1

conscious analysis

Start by asking whether you are solving important problems. That is, will they have an outsized impact on whatever you care about? Fact is, you probably have a pretty good picture of what problems are worth solving. You just haven’t bothered to ask or look carefully enough.

Here’s Richard Hamming while he was at Bell Labs:

Over on the other side of the dining hall was a chemistry table. I had worked with one of the fellows, Dave McCall; furthermore he was courting our secretary at the time. I went over and said, “Do you mind if I join you?” They can’t say no, so I started eating with them for a while. And I started asking, “What are the important problems of your field?” And after a week or so, “What important problems are you working on?” And after some more time I came in one day and said, “If what you are doing is not important, and if you don’t think it is going to lead to something important, why are you at Bell Labs working on it?” I wasn’t welcomed after that; I had to find somebody else to eat with! That was in the spring.

In the fall, Dave McCall stopped me in the hall and said, “Hamming, that remark of yours got underneath my skin. I thought about it all summer, i.e. what were the important problems in my field. I haven’t changed my research,” he says, “but I think it was well worthwhile.” And I said, “Thank you Dave,” and went on. I noticed a couple of months later he was made the head of the department. I noticed the other day he was a Member of the National Academy of Engineering. I noticed he has succeeded. I have never heard the names of any of the other fellows at that table mentioned in science and scientific circles. They were unable to ask themselves, “What are the important problems in my field?”

Everyone needs someone like Hamming in their life. Or at the very least a frequent visit every three months at your front door to ask you whether you’re solving important problems. It’s not fun, and definitely not easy. Especially when your commitment bias has locked in already to whatever you’ve started. Easier to go with the default option than to exert cognitive efforts just to find a new problem to solve! But, it’s necessary to stop drifting.

What makes a problem important though? Here’s Hamming:

It’s not the consequence that makes a problem important, it is that you have a reasonable attack. That is what makes a problem important.

A problem worth solving, needs a reasonable attack, in addition to a high impact potential. Let’s say you care about money, like a lot, and you want to become rich, like super rich. Winning the lottery would certainly have a huge impact potential. But no matter how smart you are, you don’t really have a reasonable attack, your odds of winning are effectively zero.2

You could distill this combination of impact potential and having a reasonable attack into a simple formula — expected value. For any problem, multiply the impact potential of each outcome by its probability, then sum the results. This yields expected value, and you should go for any problem with a positive, and ideally highest, expected value. The probabilities of positive outcomes represent your reasonable attack: how likely you are to succeed given your current capabilities. The impact potential represents the value of each outcome. The beauty of expected value is that it can make different outcomes with varying levels of uncertainty equally comparable.

Intuitively thinking about the expected value of decisions is surprisingly useful. Don’t get too caught up in the math. Few things are so precise as to allow you to calculate precise numbers. That’s not the point anyways. The point is to build intuition and confidence on whether a problem is worth pursuing.3

You’ll quickly begin to form a mental habit for estimating ballpark figures that anchor your expectations more rationally.4 It’s especially good with outlier cases. Take for example asking someone you like out for a date, talking to a stranger on the first day of school, or applying for your dream job. A moment’s reflection shows the upside from success could easily be 100x better than any downside from failure. So even a 1% chance makes it worth it. We have a habit of irrationally overweighting short-term negative outcomes. This should help alleviate for that bias.5

At this point you might say “thanks for the reminder, but this stuff is pretty obvious, anything else?”

Yes, a few more thoughts.

taste & curiosity

“Taste in Science is very important. To distinguish what’s a good problem and what’s a problem that no one’s going to care about the answer to anyway—that’s taste. And I think I have good taste.”
– Jim Simons, Renaissance Technologies.6

In an ideal world you’d have perfect information and could choose the optimal problem through a simple chain of thoughts. But that’s not how it works in practice. Rarely, if ever, do you have that quality of information.

Your taste will guide you in the direction where the light of your consciousness cannot reach. Turns out, it’s actually pretty dark wherever you go. I previously wrote about cultivating taste. It’s quite powerful in determining which problems might be worth solving. Choosing problems is a creative act, and your subconscious is better equipped for this than your conscious mind.

Of course, this only works if your taste is actually good. You also need to be confident in your own taste too. You have to be able to tell whether a problem feels good because it’s genuinely worth solving, or because your biases are playing tricks on your mind.

The usefulness of taste depends on what you’re trying to achieve. It’s the most useful when you’re solving problems close to the essence of your soul — your life’s work, your happiness, anything creative. They come from the same place, so there are fewer layers of conscious thought blurring what’s important or biasing your judgement.

When it comes to taste and how you feel, curiosity gets you a step closer to understanding problems worth solving. Consider it a subset of taste, originating from the same place. Ask yourself, do you feel like you must push yourself to work on the problem? Or does it pull you in? If it fails to pull you in, it’s probably not worth solving.7

Choosing problems shouldn’t be too analytical, especially problems that occupy large chunks of your time. Your conscious mind is much more prone to deception; it has a flawed understanding of what you truly value, influenced by social pressures, and biased by your desire for pleasure. Curiosity instead comes from a place less tainted by society’s programming or the desires of your conscious mind.

While you shouldn’t be too analytical, you should avoid being excessively primal as well. Find a good balance where you lean into the primal instincts you trust, while using your conscious and analytical brain to ensure you’re not being fooled. Jumping from a shiny new problem to another without considering long-term consequences isn’t really smart, even if each new thing feels exciting at first. You’ll only satisfy your short-term curiosity without reaping the true benefits of solving the problem itself. There is great value in completion.

I’m not sure if curiosity is better at evaluating the impact potential of a problem, but it’s definitely better at knowing whether you have a reasonable attack. You feel it instantly when you do. By virtue, if a problem is driven by curiosity, you gain inherent satisfaction from working on it. This allows you to work longer and harder, improving your attack.

hard problems

Hard problems make up a great heuristic for choosing which problems are worth solving. Curiosity will help you solve hard problems — hard problems tend to be important problems. This isn’t a coincidence. Remember, our resources are limited, so we try to optimize time and energy relative to the value we gain. Sure, go for easy problems with high impact if you can find them. But everyone’s looking for those, not just because of their input-output ratio, but because they’re, well, easy.

Not surprising, everyone has a reasonable attack on easy problems. Easy problems become quickly overcrowded: the easier it is, the more people can solve it, and the less valuable solving it becomes. This prices them out and they stop rewarding any extra premiums for solving them. The best problems are otherwise hard problems that are only easy because of your unique ability that gives you a reasonable attack.

Caution. Not all hard problems are important. Human tendency to avoid difficult stuff makes hard problems undervalued and important, but difficulty is just a shorthand for finding important stuff. The markets for problems are not perfect.

will you remain a drifting log?

Not actively scanning for potential problems to solve can lead you into a canyon that’s hard to climb out of. When you go for the option that the world puts in front of you, you let your external environment determine the problems you spend all your time solving, starting from when you’re child. Maybe its the sports or instruments your parents put you in, or the subjects they expect you to study. Later you pursue the careers and achievements other expect of you. At no point do you stop to really think about which problems are worth solving.

In the end, it’s your choice. You can be the log in the river, flowing wherever the river takes you. But remember, the sea at the end of the river might not be your desired destination. There might not be a sea at all! You might end up in a desert, like the Okavango river, or underground, like the Reka river. It should be pretty obvious that the circumstances handed to us by the entropy of the universe won’t align with our internal view of what the world should be. Steering your own course feels a lot better. Especially when it creates a flywheel effect together with your confidence.

Choosing problems worth solving doesn’t mean that you have to be ultra-ambitious or try to change the world, even if anything out of Hollywood might make you think otherwise. I think it’s more about choosing problems that align with your internal values; understanding what you value the most; finding the problems that lead you closest to it. If that means cleaning toilets in Tokyo, then so be it.

Just be more intentional about it.

Space River Drifting through space

Notes

  1. Extend this logic, and your life can be simplified to a sum of bunch of y values. Imagine the compounding effect on your life when you begin a simple habit of scanning for optimal problems. ↳︎

  2. Oddly, a survey found that 39%?! of Finnish people believe winning the lottery is their most likely path to wealth. Maybe I’m wrong after all.. ↳︎

  3. Great paper by Michael Mauboussin & Dan Callahan on confidence and probabilities in decision-making. ↳︎

  4. It’s like weaponizing your intuition through deliberate practice. ↳︎

  5. It’s funny how economists have long modelled humans as perfectly rational beings that maximize expected value. We’ll never be perfectly rational, but it doesn’t hurt to be slightly more rational, a bit less biased. I don’t mind contributing to making their models slightly less wrong. ↳︎

  6. From the The New Yorker profile on Jim Simons. ↳︎

  7. Derek Sivers has a great rule of thumb: “hell yeah, or no” . Only do things that feel like a hell yeah, no inbetweens. Skip anything remotely “meh”. Otherwise you’ll say yes to a bunch of mediocre things that stop you from doing the hell yeah things. ↳︎