I used to solve problems with the following, inferior algorithm:

Read the problem statement.

Read other things (textbooks, e.g.).

Repeat 1-2 until understanding materializes.

It’s the grade-school formula for approaching problems, and it’s deeply reinforced in us because *it works in school*. Tests are often filled with questions that require only direct regurgitation of content. If you don’t something, the best thing you can do is look it up — the answers are all in the textbook, after all. And so the patterning becomes reinforced until calcification. Reading becomes the only way your brain learns to unblock itself.

Even in more quantitative fields (often heralded as natural catalysts for exceptional thought), problems often simply become **composites** of the lower-level fundamentals. You can still find the answer in a textbook, you just need to have seen the concept before in the textbook. And so the solution is ultimately still can be approached as a matter of building up the fundamentals, then recombining them to find a solution. At least, one can hobble through graduate-level physics and mathematics like this (I, for one, did).

### This fails because most important answers aren’t simply *found*

The reason why this is so painfully ineffective in the real world is because many of the most important problems in the real world are not solvable by this method. Of course, you can still happily get through life Googling everything, you’re restricting yourself to solving only the most shallow of problems: those that have precisely been solved before. And there are a few canonical problems that cannot be solved in this way:

**Important problems**. The problems that*no one*has solved.**Malformed problems**. Problems that are stated poorly, obscuring the main problem you’re trying to solve.**Internal problems**. The problems that heterogeneously plague you and your specific internal state.

For these problems, the reason why you can’t solve a problem is often not because you simply haven’t stumbled upon the answer. It’s usually because you *don’t understand something*, either about the way the problem fits into a unifying objective, something specific about a particular concept, or something about the way your mind is getting caught in some sort of discouraging feedback loop.

Unfortunately, we are poorly equipped to handle these roadblocks. Instead, we are raised with a single brute force method at our disposal — read more, read more, read more. And so we get trapped in a loop where, as we try to read, we fail to diagnose our misunderstanding, we fail to see the forest from the trees, and we get battered by our own internal loop of frustration and insecurity — “I must not be smart enough”, “this is so hard”, “I’m so tired” — with our only method of recourse being to grind it out.

### The solution: the three eigenvectors of unblocking

Everything that happens in your head when you can’t solve a problem can be untangled by asking three questions:

Not always necessary, but important to start here first, in case you have the objective implicitly wrong. E.g. “to get good grades” vs. “to understand physics” — generally try to focus on the latter, though that’s a topic for another post I suppose.

**What’s happening inside of me as I struggle through this?**Recognize the feeling tone — feeling discouraged, feeling pressured, feeling bored — so you can deal with them in light of your established objective.

**What don’t I understand, and what’s the best way to solve that?**Finally, you can try to dissect your failure into the highly specific sub-points that you don’t understand, then figure out a step to take that gives you the best chance at solving that more clearly defined problem.

(LLMs are exceptional for pushing you to do this, btw)

Every single blocker to solving a problem can be categorized as insufficient scrutiny against one of these three questions. And, while, I’ve written about the first two before, I’d like to talk a bit more about the last — while it might sound obvious, this is the core unblocking method that stands in opposition to the method of simply reading and regurgitating.

Reading is quite difficult to beat as a method of answer-finding, because it’s pretty painless. It’s completely straightforward — anyone can read one more sentence. And, as a result, it can be almost entirely *passive, *particularly when leveraging it to solve a problem. Just keep going until you get to an answer. Unfortunately, the problem is that this also reinforces you to read the wrong way — skimming towards the particular aim of unblocking yourself.

Of course, this is not to say that reading isn’t valuable — *deeply* reading something, I would argue, is one of the best ways to truly know a subject. But the habit of *dissecting your misunderstanding* has to exist beneath. Without answering the question “what don’t I understand” repeatedly, the best you’ll achieve from any problem set or coursework is a patchwork set of facts and formulae, not a deep intuition that can form a foundation for flexible problem-solving.

### Final comments

There are a couple unfortunate things about this whole unblocking yourself thing. The first is that it’s kind of hard to realize you need it until you *really* need it. In general, it doesn’t help that, if you read enough, you can still be extremely successful. Almost all questions that are asked of a person have been solved before, so you can race along in life regurgitating the solutions of others. But here are a couple examples of where this methodology can confer unfair advantage:

This is what makes

*incredible*employees, because:When everyone is regurgitating existing solutions, establishing an objective, dissecting a problems into basic components, then reasoning through the solution space from first principles will find you constructing something asymmetrically better. You’ll have the capacity to jump from one local maxima to another, which few employees have.

Nothing will be out of reach of your understanding, so your slope will often exceed that of your colleagues.

This is a necessary (though not sufficient) condition to start a successful company, because your situation will be so heterogeneous and pace of iteration so rapid that you need a way to rapidly traverse the maze comprised of the parameters of your business and your own internal state.

The second unfortunate thing is that, while this is a sufficient system to unblock yourself, it’s not sufficient to spell success. That, in my experience, is usually about building systems and habits that point to where you want to go, not about instantaneous skill. But that’s also another post.