How to do hard things

This is a system I only somewhat tongue in cheek refer to as “The Fully General System For Learning To Do Hard Things”. It’s a useful conceptual framework for how to get better at things that you currently find difficult.

I don’t always explicitly follow it, but I often find that when I’ve succeeded my success comes from implicitly following it, and almost every time someone asks me for advice on learning to do things I just describe a specialised version of the system to them.

The system “always” works in the sense that “eventually” either you will find out why the objective is impossible for you or you will succeed, but it’s very much the unhelpful kind of eventually where there’s no guarantee that it won’t take an interminably long time. The more likely outcome is that either you will succeed relatively quickly or get bored and give up, but that’s OK – the system is designed so that you will have gained benefit from following it at every step along the way even if you do not achieve your final goal.

I should also note that this system is not in any way a short cut. It’s a lot of work. The goal of the system is not to save you work, it’s to ensure that the work you do is useful.

The Single-Loop System

When you know what success looks like but cannot currently achieve it, the system works as follows:

  1. Find something that is like the hard thing but is easy.
  2. Modify the easy thing so that it is like the hard thing in exactly one way that you find hard.
  3. Do the modified thing until it is no longer hard.
  4. If you get stuck, do one of the following:
    1. Go back to step 3 and pick a different way in which the problem is hard.
    2. Recursively apply the general system for learning to do hard things to the thing you’re stuck on.
    3. Go ask an expert or a rubber duck for advice.
    4. If you’re still stuck after trying the first three, it’s possible that you may have hit some sort of natural difficulty limit and may not be able to make progress.
  5. If the original hard thing is now easy, you’re done. If not, go back to step 2.

The reason this works much better than just practicing the hard thing is because it gives you a much more direct feedback loop. There is exactly one aspect of the problem at any time that you are trying to get better at, and you can focus on that aspect to the exclusion of all else. When you are practicing something that is difficult in multiple ways, you will be bad at it in all of those ways. More, you will be worse at it in all of those ways than you would be if you’d tried them on their own. Additionally, when you fail you have to do a complicated root cause analysis to figure out why.

Instead, by isolating one aspect of the problem that is difficult, you will fairly rapidly improve, or hit the limits of your ability.

The Double-Loop System

If you don’t know what success looks like, you need to do double loop learning, where you mix improving your understanding of the problem with your ability to execute the solution.

  1. Apply the single loop system to the problem of improving your understanding of the problem space (e.g. consume lots of examples and learn to distinguish good from bad) in order to acquire a sense of good taste.
  2. Apply the single loop system to the problem of doing well according to your own sense of good taste.
  3. Get feedback on the result from others. Do they think you did it well? If yes, great! You’re good at the thing. If no, either improve your sense of taste or theirs. If you choose yours, go back to step 1 with the new example. If you choose theirs, apply the single loop system to the hard problem of convincing others that your thing is good.

Is this all a horrible oversimplification? Well, yes, of course it is. It is however a very useful horrible oversimplification that is very good for getting you unstuck when problems seem intractable.

How To Identify Points of Difficulty

Sometimes it will be obvious what you need to improve, sometimes it won’t. When it doesn’t, here are some things that can help you figure it out:

  • Try to do the thing as best you can. Don’t worry about failing, failing is expected, but try to pay attention to how you’re doing it. Write down a list of things you thought you did badly, and things you did adequately but struggled with. Also if at some point you got stuck, note where you got stuck.
  • Look for beginners exercises for the area you want to work on and try a variety of those. Observe which ones are hard.
  • Talk to an expert on the subject (ideally one who is used to teaching) and ask them to help you identify some areas you need to work on.
  • Rather than starting from the easy thing, work in the other direction. Try taking the hard thing and removing one hard aspect of it at a time until you get it to a point where removing any hard aspect would make it easy.

Worked Example: Learning to Write Better

This is particularly good as a mechanism for improving your writing (and writing about it is a good lead in to the mechanism on a particular area, so I’d encourage everyone to work on improving their writing).

Writing can be hard in a wide variety of ways. Some common ones (in roughly the order I think it’s worth tackling them) are:

  • The actual physical process of writing.
  • Finding a good writing voice.
  • Perfectionism and/or fear of showing others your work and/or not being sure what to write about stopping you from the process of starting to write about it.
  • Editing and structure.

And that’s even before you get into specific forms of writing. You could also struggle with e.g. dialogue, description, etc.

Set against this is the fact that if you’re reading this you definitely can write. I promise. You might not be able to write a novel (I can’t at the moment), but you can certainly write a tweet, and it’s just a series of incremental steps to get from there to wherever you want to be.

Here’s some examples:

  1. Learn to touch type if you can’t already. If you can’t touch type you will get blocked on the basic mechanics of writing. This makes the feedback loop for everything harder. Maybe try ztype, typesy, or Mavis Beacon1
  2. Learn to write in your speaking voice. If you can’t figure out how to write about a topic, try speaking about it into your phone (get a recorder app). Once you’ve started writing, try to read it out loud. This isn’t the only writing voice worth using, but it’s an important one.
  3. Practice writing without any expectation of quality. e.g. write in a private file or google doc, or create a blog with an explicit disclaimer that it’s for writing experiments. Some good writing experiments:
    • Observational writing. Pick an object (a lit candle is an interesting one) and write down everything you notice about it.
    • Pick a subject you are reasonably familiar with and set yourself a word count of, say, a thousand words. You can write whatever you want as long as you hit that goal. Feel free to write a stream of consciousness.
    • Pick an opinion of yours and write a 500 word case for it.
  4. Rather than worrying about the general problem of editing, start thinking about editing with specific goals. e.g.
    • This ties in well with getting a good writing voice. Read it out loud, figure out where good pauses are and put paragraph breaks in where natural pauses occur. Fix language that sounds awkward.
    • Try editing purely based on word count. Can you express the same thing with fewer words? What would you do if you had to cut the length of the piece in half?
    • Try editing ot remove specific words. Can you write the whole thing in up goer five? (Note: The result of doing so will be terrible, but the goal here is to practice editing more than produce a good piece)

There are plenty of other things to try, but these are some good starting points.

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The One Weird Word Rule

Here is a writing trick I find useful (though am not always good at following): You are only allowed one1 weird word2 per article, and you have to explain the meaning of that word.

If you have more than that, you’ll almost certainly lose the reader because they will not be able to keep track of the multiple new words.

What makes a word weird? Familiarity for the audience. If I’m writing for a monolingual French audience then they have my sympathies because my French is somewhere between appalling and non-existent and every English word is weird to them. Similarly, if I use a technical term, that term is weird for anyone outside that technical speciality.

If you wanted to ensure your audience is fully general (among English speakers) you could go full up goer five3 in the article, restricting yourself to only the thousand most common words in the English language. This is a useful exercise but I think it’s going a bit far.4. Use your judgement – it’s generally reasonable to assume that the reader is fairly literate, it’s generally not reasonable to assume they know what doxastic means5 6.

This is the real power of the trick: Because you cannot determine if a word is weird without knowing the audience, by following this rule you first have to decide who that audience is. This makes you think about the level of your writing, and what language it is appropriate for you to use and what you should avoid.

Once you’ve done that, the one weird word rule can be seen as a leniency rather than a restriction. It’s not that you’re only allowed one word your audience doesn’t know, it’s that it’s OK to use one word your audience doesn’t know. As long as you explain it well, a single article is about the right amount of text to get someone comfortable with a new word, and it’s fine to try to expand people’s vocabulary where it would be useful to do so, but if you try to do too many new words too fast your audience will quickly get lost, and your point will not come across well.

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The Inner Sense of Gender

I had a conversation with a probably-trans friend last night which they1 found helpful, so I thought it might be worth sharing my thoughts on the subject with a broader audience, as it’s a perspective that I don’t think is heard from often, and may be helpful as a point of reference for people who are wondering if they are “trans enough”.

I am cis. I’m reasonably sure of this. I have asked myself whether I was trans, concluded that I was not, and am pretty confident in this conclusion2. You don’t hear much about this sort of experience, because from the outside it looks like a total non-event, so I thought it would be helpful for me to elaborate on what it feels like from the inside.

Ozy Frantz coined a term a while back, Cis by Default3, which makes the point that a lot of cis people just don’t have anything that you might describe as an internally felt sense of gender. I think this is true and is a very useful observation, and for quite some time I thought it was an accurate description of how I felt. Since then, I’ve decided that there are details that it doesn’t quite capture accurately for me that are worth unpacking a bit further.

I think the distinguishing features of cis-vs-transness can be roughly captured by three important questions:

  1. What was your assigned gender at birth?
  2. What would you like your gender to be4?
  3. How much do you care about the above?

Being trans is essentially having very different answers to the first two questions and caring about it a great deal. I think the significance of the caring part is often missed, because the people who talk about this the most (both cis and trans) are often the ones who care about it the most.

This model is a bit simplistic, so some caveats before I go any further:

  • Gender/sex/etc constitute a very large bundle of roughly related parts. e.g. identity and presentation are different, and there are distinct gendered norms. People will rarely have the same answer to these questions for each of those aspects. That’s fine.
  • I encourage very broad interpretations of the questions. Definitely no assumption of binary gender implied. Also it’s perfectly OK for your preference to be to not have a gender at all (i.e. being agender).
  • Answers to these questions may change over time. The relevant period of time can be on an hourly basis for some people (e.g. genderfluidity).
  • “Oh gods I have no idea” is a perfectly legitimate answer to any or all of these.
  • “What would you like your gender to be?” is a slightly loaded phrasing, but I can’t think of a better one, so please let me emphasise here that I very strongly believe that your gender is whatever you choose or believe it to be.

You can think of the experience of this as breaking down into roughly four quadrants which get labelled as follows:

  1. Agree/Care – “Standard” Cis Experience
  2. Agree/Don’t Care – Cis by Default
  3. Disagree/Care – Trans
  4. Disagree/Don’t care – It Depends

I would consider myself to be in the “It Depends” quadrant. Someone in this category could reasonably choose to consider themselves cis or trans, depending on whatever seems important to them. For my part, I’ve chosen to consider myself cis – I don’t think I or other people would find it at all helpful for me to describe myself as trans, so I don’t, but other people in the same quadrant might make a different decision and that’s fine too. You could think of us as “ambiguously cis” (or, for people in this quadrant who have chosen to consider themselves trans, “ambiguously trans”) – there isn’t a particularly clear cut answer as to whether we count as cis or trans, so it mostly comes down to personal choice and social circumstance.

What does being ambiguously cis feel like? I don’t know. It depends. I can tell you what it feels like for me though: It’s not really that I mind being a man, I just wish someone had asked me first5.

If you wanted to simplify the vastly complex internal experience of human gender into a single number6, you might imagine that there is a percentile scale of 0-100 of “How much you would like to transition?” with 0% being “Under no circumstances would I choose my gender to differ from the one I was assigned at birth” and 100% being “Under no circumstances would I choose to live as my assigned gender at birth”, I’d rate myself somewhere in the 5-10% region.

Practically speaking, what this means is that if you dropped me into the Culture and gave me access to cheap and easy body modification technology and a society that was very encouraging of using it, I would absolutely experiment with different gender presentations, would give you pretty good odds that I would swap back and forth, and maybe slightly better than even odds that I would adopt a more feminine body plan as a default.

In the real world where transition is complicated and subject to social censure, it’s not even close to worth it for me, because my preferences here are really very mild. There are some circumstances7 where it reaches the heady heights of “I guess that would be nice”, but it’s really not a big deal for me. As a result I present as fairly generically masculine because it’s extremely easy for me to do so and not worth it for me to not do so.

Given this, I don’t think it’s in any way useful for me to identify as trans, but someone with essentially the same preferences as me who cared a lot more about them probably should think about identifying as trans.

Someone who cares exactly the same amount as me might still reasonably consider themselves trans if they were in different circumstances. I don’t know what those would be – I can’t really think of any plausible circumstances under which I would, but that doesn’t imply anything about what other people should do.

If you are in any way unsure about your position in this quadrant, there is a useful concept that I got from a post by Kelsey Piper a while back. Although I’m not the target audience, the point generalises very well and I still it found very helpful:

I have now talked with multiple bi women who’ve said ‘sometimes when I have a crush on a girl I get really worried I’m a Fake Bi and not really attracted to women and therefore I won’t ever get to kiss her.’

And I know orientation and labels and so on are complicated but I think there should be a rule that if you are sometimes scared you’re not bi which would be bad because it means you can’t kiss girls, you are totally and categorically allowed to kiss the girls

The generalisation is this: If you are worried that you are not (label) and that that would be bad because it would mean that you don’t get to (do the thing that label people get to do), I think there should be a rule that you are totally and categorically allowed to (do the thing).

I suggested “Disagree/Care” as the intrinsic definition of transness, but a useful extrinsic definition of “being trans enough” is if it would be helpful for you to view yourself as trans.

If you find yourself worried about not being trans because if you’re not you wouldn’t be able to do all these things that would make your life better, I think that you are totally and categorically allowed to do the thing that makes your life better. If you feel that life makes much more sense when you view yourself as trans, or you really hope you’re trans because that would mean you get to transition (in whatever sense of “transition” is helpful to you), that is a pretty big hint that you are not in the “It Depends” quadrant and that you are trans enough to count. The trans umbrella is large and it definitely has room for you.

This is essentially a variant on the model I proposed in “On Not Quite Fitting” – Binary identity labels don’t actually describe real categories, they describe complex cost-benefit analyses where each individual must decide whether something is worth it to them or not. I think this model is particularly important in the case of gender because both the benefits and, sadly, the costs are quite high for many potentially trans people.

I am not the person to give you advice on how to navigate that cost-benefit trade-off, as it contains a lot of trans specific experiences I don’t share, but feel free to use me as a reference point if you need convincing that you’re trans enough: If you care about your gender significantly more than I care about mine, it’s probably a subject you would find worth exploring.

Equally, I am definitely not someone you need permission from, but if you would find my permission helpful then you have it: Do the thing that makes your life better. If you’re worried if you count, you do.


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Two types of viewpoint

Epistemic Status: Framing


Let me tell you about two words. The words are “relip” and “thamagar”1. I’ve found that they’re actually very helpful words to have, and there really don’t seem to be any good alternatives for their meaning, so I thought I would share them more broadly.

I’ll define them for you in a moment, but first I want to tell you how they are used.

They’re adjectives, and more or less opposed – something that is more relip is generally less thamagar, and vice versa. It’s entirely possible for something to be neither relip or thamagar, and the same thing can be both relip and thamagar in different ways.

A thamagar viewpoint can’t see the wood for the trees. A relip one can’t see the leaves for the tree. When you work in your area of expertise, your viewpoint is thamagar. When you explain it to someone unfamiliar with it, you try to give them a relip view.

The way you look at the ingroup is usually thamagar, and the way you look at the outgroup is usually relip. Combinatorics is thamagar, category theory is relip. Writing a poem requires you to be thamagar, teaching someone requires you to be relip.

When you view something as intrinsically complex, you are being thamagar in your view, when you view it as intrinsically simple you are being relip.

Property-based tests are relip, example-based tests are thamagar.

A relip viewpoint abstracts, a thamagar viewpoint treats everything as unique.

Telling a joke is thamagar, telling a story is relip.

Importantly, there is no moral component to these words. Both relip and thamagar are good, and everyone adopts viewpoints of each type all the time, even towards a single subject. Some people will have a strong preference for one or the other (I’m very much a relip sort of person), but it is impossible to get anything done without both.

The usage is genuinely more important than the definition, but to attempt a definition:

A view or an approach is relip if it unifies many things together based on a small set of features, abstracting and simplifying them based on common patterns.

A view or an approach is thamagar if it is deeply concerned with its context and connections, focusing heavily on how it fits in and interacts with everything around it.

You could call them “abstracted” and “situated” viewpoints if you liked, though I think that would be a bit too relip of you and I’d prefer to be more thamagar in this instance.

Even when you know a subject very well, it can be very helpful to take a step back and adopt a relip approach to it. Even when you are learning a subject for the first time, it can be helpful to imagine what a thamagar view of it might be like and to think of yourself as moving towards it. Getting yourself stuck in one or the other view is usually less effective than switching between the two.

One useful thing to do when you get stuck (which you should be doing) is to ask yourself whether you’re currently being too thamagar (in which you take a step back and try to abstract the problem, understanding its key features) or too relip (in which case you focus on the actual problem without its broader context and ask if you are trying to solve a harder more general problem than you need to). Often the viewpoint switch will be enough to unlock the problem for you

This is a large part of why I find having these words useful: It allows me to be more explicit about that process. Which, in case you were wondering, is an extremely relip way of going about it.

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How do you nurture your imagination?

Epistemic Status: Reverse engineered from my brain. I’m pretty sure this is how it works in general, but your mileage may vary.


Stephanie Hurlburt asked this question (“How do you nurture your imagination?”) on Twitter. I thought it was a great question and gave a bunch of answers, but I thought it would be worth on expanding further on the point.

What do I mean by nurturing your imagination?

Nurturing your imagination is mostly achieved as the result of two things:

  1. Nurturing yourself, by ensuring that you have the room and the support you need to thrive.
  2. Developing the skill of having ideas that you find interesting.

Most people’s answers seemed to me to be focused on the former. This is all very well, and it’s certainly a thing worth doing in and of itself, but without the latter it probably won’t do anything for your imagination, so I’m going to focus on the latter.

First let me spell out some things that are not included in this. It’s not the skill of having good ideas. That’s practicality. It’s also not the skill of having ideas that other people fine interesting. That’s taste.

Practicality and taste are both fine skills that it is very valuable to develop. I strongly encourage you to do so. I also strongly encourage you to treat them with caution while working on developing your imagination. They combine very well with imagination, and are a great guide to it, but when your senses of practicality and taste tell you that your ideas are not going to work or are going to bore other people, take a step back and say “OK, that’s fine, but lets see what happens anyway shall we?”

If it turns out those senses were right all along, that’s fine. Your goal here is explicitly to do things that you find interesting, so it’s OK if they don’t work out as long as you’ve learned something in the process.

How do you find interesting things?

A necessary precursor to being able to have ideas you find interesting is the ability to find things interesting.

If you do not have this ability, that’s not a lack of imagination, it’s much more likely to be fairly severe depression. No, seriously, it’s a symptom. I would very strongly encourage you to see someone about it if you’re not already, and I’m afraid I don’t have any very good advice for you beyond that.

Assuming that’s not you, pick anything that you find interesting and would like to work on. Some examples of things I personally find interesting:

Most of the advice in this piece comes from application to one or more of these.

One particular skill that is particularly useful here is to notice when you find things interesting, and start actively recording that. I use a mix of Twitter, my notebook blog, and a physical journal for recording things I find interesting.

What are ideas for?

In order to understand how to get better at having ideas, it’s helpful to understand why we want to have ideas at all. This may seem like a weird question to ask, but it’s actually quite an important one because most people are confused about the answer.

There are two big common misconceptions about ideas. The first is that they are the most important thing, and the second is that they are the least important thing. Both of these are badly wrong, but the truth is not so much in the middle as off to one side.

There’s a fantastic essay by Neil Gaiman that I’m going to completely disagree with in the next section called “Where do you get your ideas?“. I recommend reading it, but to quote the relevant bit to this section:

The Ideas aren’t the hard bit. They’re a small component of the whole. Creating believable people who do more or less what you tell them to is much harder. And hardest by far is the process of simply sitting down and putting one word after another to construct whatever it is you’re trying to build: making it interesting, making it new.

This is spot on. An idea on its own does nothing. Execution and actually doing the hard work are the most important thing in any creative endeavour.

Right up until the point where you get stuck, at which point the idea becomes everything. Ideas are the smallest part, but sometimes the smallest part is crucial.

And this, ultimately, is the main point of ideas: Ideas enable you to do the work.

Understanding this is crucial for working on the ability to have interesting ideas, because it points to a crucial feature: You can only work on the ability to have ideas through a process of doing things (an activity that can consist of just sitting down and thinking real hard if you like, but it’s helpful to have something external that pushes back on you. At the very least try to explain it to someone else by writing about it).

Where do ideas come from?

Neil Gaiman’s answer to “Where do you get your ideas?” is “I make them up. Out of my head”.

I would file this under “true but unhelpful”. It’s like answering “Where does bread come from?” with “the oven”. Yes, bread does come from an oven, but the explanation is missing one or two quite important precursor steps and won’t help you much if you want to make your own bread. The interesting fact is not that the bread came from the oven, but how the bread got to the point of being in the oven in the first place.

(I don’t think Neil Gaiman would really disagree with me on this. A lot of what I’m saying in this section is alluded to in his piece too)

Where do ideas come from? They come from the adjacent possible. This is a concept that originally came from biologist Stuart Kauffman and was popularised in the context of ideas by Steven Johnson in his book “Where Good Ideas Come From” (which I haven’t actually read yet, though I’ve ordered a copy while writing this post and have read his “The Genius of the Tinkerer“, an essay adapted from it).

The adjacent possible is pretty much what it sounds like – the set of things that are currently possible when starting from what you already have.

Ideas build on existing knowledge, one step at a time. Einstein may have had an ah ha moment that lead to the theory of special relativity, and certainly his ability to do so was a testament to his intelligence and imagination, but a person in every way physically and intellectually identical to Einstein but born two thousand years earlier could never possibly have hoped to do it, because Einstein had two thousand years worth of ideas to build on and our hypothetical ur-Einstein did not.

The path from ur-Einstein to Einstein never strayed out of the adjacent possible, but each time humanity added to its collective knowledge the adjacent possible grew with it, and two thousand years of small, incremental steps took us from the point where even the paper that “On the Electrodynamics of Moving Bodies” was published on would have been a bold technological revolution, to the point where the concept of special relativity itself was part of the adjacent possible.

You probably won’t manage two thousand years of innovation all on your own, but the set of ideas you can have works much the same way, albeit on a smaller scale.

Your personal adjacent possible consists of roughly three things:

  1. Variations of things you already know (what happens if I do the thing but change this bit?).
  2. Previously untried combinations of things you already know.
  3. Things that you can find out from other people!

The third of course doesn’t really fall under the heading of “imagination”, but I think you’d be surprised how many “highly imaginative” people are just really good at asking the right people the right questions, and in cases where you actually need the ideas rather than are trying to work on the ability to generate them yourself, it’s often by far the best approach.

It’s also a great precursor for the other two. The reason all of this matters is as follows: If ideas come from the adjacent possible, and the adjacent possible accessible to you on your own is nothing but variation and recombination of things you already know, you can only have interesting ideas if you already know interesting things. You can get there the hard way if you want – starting from the basics and working outwards – but the more you learn the larger the scope of your own personal adjacent possible, and the more interesting things it will contain.

Personally I find the following are by far the most reliable ways of expanding the scope of the adjacent possible for me:

  1. Reading interesting books.
  2. Talking to interesting people.

Explaining the interesting books to the interesting people is often particularly effective.

How do you get ideas?

SpaceThe adjacent possible is big. You just won’t believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it’s a long way down the road to the chemist’s, but that’s just peanuts to spacethe adjacent possible.”

Douglas Adams, The HitchHiker’s Guide to the Galaxy (lightly edited)

Ideas come from the adjacent possible, as we just established – you take something you know, you vary it, or you combine it with something else you know, and you’ve got a new idea. Easy, right?

The problem with this is as a strategy for generating interesting ideas is twofold:

  1. There are a lot of potential ideas reachable this way.
  2. Almost all of the them are boring.

It’s important to ensure that your adjacent possible contains interesting things, but regardless of how many interesting things it contains, most things it contains will be tedious garbage. That’s no indictment on you or your knowledge base, that’s just how the numbers pan out.

What you need is a way to navigate your way through the adjacent possible to find those interesting ideas.

How do you do that?

Well, let me start by telling you what doesn’t work: Sitting down and trying to come up with an idea.

Coming up with an idea for the sake of coming up with an idea is hard and pointless, because ideas don’t do anything on their own. Instead, you come up with ideas by starting with something that needs an idea.

As per earlier, ideas are there to get you unstuck, so the way to come up with interesting ideas is to get stuck. Find a problem or a question that you think is interesting and you’re not sure how to solve, and try to solve it. If you succeed, try something harder – either vary the problem to make it harder if you still find it interesting, or try something new.

Ideally though, you won’t succeed. You will get stuck. Now stay there, because this is the point where ideas happen. You have a specific, concrete, problem that you are trying to solve, which vastly narrows down the area of the adjacent possible that you need to consider, and any idea you come up with to solve it will by definition be interesting because it helps you either solve or better understand an interesting problem.

I can heartily recommend this post by math with bad drawings talking to Andrew Wiles about this state if you want to learn more about being stuck, but broadly speaking my recommendations for once you’re in this state are:

  • Think of problems like it that you have solved. Why won’t the solutions you used then work? Can you modify them somehow?
  • Can you reduce it to a previously solved problem?
  • Once you’ve sunk a few hours into it, take a step back. Don’t force yourself to solve the problem now, but let a certain amount of background processing happen. Sleep on it, go for a walk, take a shower, etc.

Where do you find problems?

It’s helpful for this to have a good source of problems you find interesting. A lack of problems to tackle is definitely not something I experience (send help, please), and it will depend a lot on what you find interesting, so I’m maybe not the best person to answer this.

Some people find it useful to have seed problems, such as writing prompts or using exercises from mathematics textbooks. I don’t do this, although honestly I probably should

There are a few things that are reliable generators of problems in general:

  1. The idea of the adjacent possible applies to problems as well as solutions. Vary old problems to get new ones – e.g. can you solve this without the thing you used to solve this previously, can you explain your solution to a four year old, can you explain it in a tweet?
  2. When you’ve figured out a clever new trick or idea, “What can I apply this to?” is itself an interesting problem that is worth spending some time on.

How do you get better at this?

So coming up with interesting ideas is as “simple” as combining the following:

  1. Knowing interesting things to get you started.
  2. Working on hard interesting problems.

The former is “easy” – you just read lots about things you find interesting and talk to lots of people about it. I’m sure you have lots of free time in which to do this (you probably don’t, but unfortunately there’s not much that you can substitute for it other than do the same things but more slowly).

How do you get better at the latter?

Fortunately, there is a fully general system for getting better at things:

Find things that you can already do that are like the things that you can’t do. Analyse what the difference is, and then try variations where you change one thing about them to make them more like the thing you can’t do. Work on those variations until they are no longer hard.

There are absolutely interesting problems you know how to solve, you just have to remember that they’re interesting – it’s very easy to dismiss something you know how to do already as boring because you know how to do it, but once upon a time you learned how to do it, and that’s probably because it was interesting to you. Start there. Make the problems harder until you don’t know how to do them.

If that doesn’t work for you, learn something new. A different area of maths, a new poetic form. Try writing under a pseudonym with a different style from your own.

Whatever you end up trying, making sure it’s something you have fun doing. It’s OK to be frustrated, but you shouldn’t be bored, and it shouldn’t be painful. If you have to force yourself to do it, try something else instead.

After all, the key feature of this is to think of things you find interesting. If you’re not enjoying doing so, why even bother?

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