One trick that feels related is consistently ignoring your first impulse and generating two additional possibilities.
Your remark that "learning is a process of information compression", plus the math example, reminded me of an old post by Qiaochu Yuan written in 2009 on his blog Annoying Precision:
A little after that, I started reading math blogs, which was probably the best thing that happened to my mathematical education all of last year. It started with the master expositors Terence Tao and Tim Gowers. As I read through their archives, I marveled at how they were able to summarize and generalize technical arguments in non-technical but still enlightening ways. Once I learned that there’s more to mathematics than rigor, I realized that what Tao and Gowers do mentally is something like an enormous feat of compression. Rather than memorize the details of the proofs of the important results in their areas, it is both more efficient and ultimately more enlightening to compress an argument into a few important ideas, and provided you understand the subject well enough, you can (in principle) rewrite the entire argument from these big ideas. And the great thing about focusing on these big ideas rather than on the details of certain proofs is that you can apply these ideas to other situations where the details are different but the big ideas are the same.
One potential implication seems to be that if there are things I need to get done and an 80% level of done is acceptable then I can save a lot of time for things I really need to get 100% done.
Introduction
The 80/20 rule, or the Pareto Principle is a “rule” in economics, saying that 80% of the value comes from 20% of the effort. It is weird to call this a rule, when it’s such a fuzzy, ill-defined statement. And it’s easy to come up with counter-examples. But this is an empirical observation about the world, and in my experience it tends to be true.
And I think this is an incredibly valuable idea - far more so than it seems at first glance. This is a key part of my worldview, and how I live my life. And I consider it an important underlying factor in ways I’ve been successful. The key insight is this: there is always a clever hack. The world is not fair. Effort is not distributed as it should be. And this isn’t because people are dumb, or not trying. This is the default state of the world. Allocating your effort efficiently is hard - if it wasn’t, then the Pareto Principle would not hold. And this is the default state of the world for you.
My underlying model here is that we spend most of our lives stuck in bad local optima. We have a set of default actions, standards ways of doing things and solving problems we come across. And these are way better than nothing, but nowhere near optimal. So to get out of a local optima, you need to develop the skill of noticing when you’re in one, being creative to find a better way, and implementing that to move to a better one. In practice, this insight gets stored in my mind as a conviction that there is a clever hack, an efficient solution. I have a strong aesthetic preference against things that feel slow, effortful, or inefficient.
And solving this is not obvious, nor easy! You need to be creative. Sometimes I can’t find anything better, and do even worse than the naive solution. And you’ll never find a truly optimal solution because the world is complex and everything is uncertain - my new toolkit just gets me to other local optima. And it’s possible to feel overwhelmed by this, and dissatisfied with anything short of perfect. But this is something I find it easy to be excited about - there is a core part of me that is always striving. Focused on progress, not on the end point. The world is full of inefficiency and wasted motion, but you can do better.
Note that I’m making a far broader claim than the Principle obviously implies. It just says that there is a lot of value left on the table, which most people miss. I assert that you can find it, with sufficient effort and skill. And this is an empirical claim about the world, not something you can logic your way into. It’s something I feel very convinced of, because it works for me. And my goal in this post is going to be to outline some of the common ways this manifests, what the mindset feels like from the inside, and ways this can go wrong.
This is the key insight underlying a lot of my previous posts - find ways that the default state of the world is wasted motion, and overcome them:
Learning
One very salient case of this for me is learning, especially maths. The key insight is that learning is a process of information compression.
Maths is often taught as a stream of rigorous, formal information. You see a long stream of unmotivated, incomprehensible proofs, and are expected to study these in detail and remember them. But at the end of the day, I do not care about remembering a proof. I care about building intuitions. Concepts, and ideas, and motivation. A big picture framework in my head, from which I can generate the important parts of a course.
80% of every proof is garbage - it’s a series of mindless algebra, and doing the obvious thing. When my goal is to learn, I want to find that 20% that is insightful, the steps that I would struggle to come up with myself
In practice, this manifests as a conviction that everything can be distilled down to key ideas and insights, and an impatience with implementation details. And sometimes the implementation details are important! It’s good to learn them a bit, and be able to generate them. But I find that most of the time, this conviction lets me cut past all the irrelevant crap, and find what actually matters.
Some tips:
The underlying point here is that my goal isn’t to be able to regurgitate proofs, it’s to achieve mastery. And mastery does not feel like having every detail memorised, it feels like getting to the point where I don’t need to have every detail memorised, because I know which details matter, which can be looked up later, and which can be safely forgotten about. And by having this impulse to impatience, and striving towards efficiency, I can get to mastery far faster.
And I’ve found that these skills transfer pretty well to other fields! Not universally - I’d be a pretty awful doctor for example - but I’ve found that all fields that have caught my interest (major selection bias) have underlying concepts and important ideas. That it’s useful to have this sense of impatience, and this desire for efficiency and a big picture view in my mind. That by remembering to prioritise I can learn far better.
I outline my views on all this in more detail in my post on teaching, and I outline my thoughts on learning concepts from conversation here. A further bit of empirical data for this belief is that I think it makes me a substantially better teacher, and get feedback to this effect.
Be results focused
One key source of wasted motion is a failure to be deliberate. And this makes sense! The default state of the world is wasted motion. This means that there is a constant fight against entropy, if you want to be focused and efficient. And keeping your eye on your true goal, is the key first step to finding the right path, out of the many options you have. So the first key skill is to be results-focused - be grounded, and be ever focused on what you’re aiming for.
And you don’t always get to know what you’re true goal is! And being overconfident about this is also a failure mode! But even if you’re confused about your true goals, you should always have something you’re aiming at - even if it’s just to learn more and become less confused.
Cut out the bullshit
And something often worth trying, if you notice barriers between you and your goal, yet can’t see good justifications behind the barriers, is to see what happens if you try skipping past them. This will not always work, and beware downside risk if you try this, but I’ve found it works far more than it has any right to.
One approach where I’ve had a lot of success with this centre on social things:
The underlying lesson here: To break out of the default local optima, you need to do something different. And one path is to notice when your intuitions are holding you back, and to test whether there’s something important there or not. This is the key insight behind problems are for fixing - a key source of the wins are the things that feel impossible, because they often aren’t. It’s incredibly hard to tell which problems are actually impossible to solve, without going into the world and trying things.
This is difficult to balance, and I have a whole post on how this mindset can lead to failure modes like ignoring “irrational” emotions - and I concede that this advice is somewhat contradictory. But I’ve found this is a useful mindset to cultivate, with hesitation. To me, this forms a core component of being a person who Actually Does Things - the ability to look past the feeling of helplessness and impossibility, and be willing to try things.
Go Meta
Another important source of efficiency boosts that people miss is the skill of going meta. These break down into a few categories:
Noticing problems in your life, and being able to solve them
Humans have a major short-term bias, and developing the ability to go meta rarely feels viscerally important in the moment. Yet it’s clearly important in the long-term - small gains add up, and small gains to meta abilities manifest everywhere. So this is a good source of things people miss, that can pay major dividends.
As you can probably tell from the number of links, this is something I make a point of thinking about a lot. And, while it’s possible to go too far, I’ve found that this has paid major dividends for me.
It’s easy to get lost and stop being grounded while getting meta, and it’s important to be aware of this. But I think effort spent developing good meta-skills is invaluable, and should be a major priority - especially when you’re young!
Skills that compound are especially valuable - getting better at growing, identifying problems, reflection. Understanding your bottlenecks, and being able to overcome them.
Implementation
The final, and most important part, is implementation. It’s easy to absorb all of these ideas, and agree that the world is full of inefficiency. But then forget about it, and fail to really take action on this. This breaks down into two parts.
First, when you notice you’re a bit stuck - things are inefficient, things feel like they could be better - do something about it. Your standard approach will not work, you can’t just try harder. You need to be creative. My main tools:
And, if all that worked, and you identified an interesting solution idea, implement it. It’s not enough to just have the creative idea, you need to do something about it. This step feels far less rewarding, but it’s embarrassing how many problems I’ve failed at this step for - other things always feel more important, the solution never feels urgent, it’s not definitely going to work, etc.
This is an excellent time to practice the skill of taking the first step! In practice, I have systems in place where I spend 2 hours every week implementing all the creative ideas I had, so I just need to add ideas to a queue that I’ll go over then.
Health Warning
I think this entire article should come with a pretty big health warning on it - this mindset is extremely limited and doesn’t always work. I find it contributes to me having a pretty poor work ethic - some problems are genuinely hard and don’t have a clever solution, and I find it difficult to do these. And there’s significant costs to optimising things - it consumes meaningful time and energy - and it’s hard to prioritise this well. I find it easy to spend 3 times as long finding an automated solution to a task versus doing it a dumb but boring way - I once spent several hours during an internship learning how to use regular expressions to add a full stop to the end of every paragraph in my comments.
And as I outlined yesterday, this mindset motivates dismissing anything where I can’t see a robust causal mechanism behind it, a highly unconservative and reckless mindset. And sometimes there are important things which are not legible to me - like the importance of keeping promises, honesty, and listening to “irrational” emotions.
In practice, there’s a balance between conservatism and ruthlessly seeking efficiency. I find the latter mindset incredibly valuable, but a bit too natural, and try to find the right balance. But balance is the key word here. There are costs to being too reckless, but also costs to not being reckless enough - sometimes there is a clever hack that you’re missing, sometimes Chesterton’s Fence isn’t doing anything important, and if you don’t realise this you’re missing out. And on the whole, cultivating this mindset has been an overwhelmingly positive thing in my life.
Giving advice on a balanced topic like this is especially hard, due to the Law of Equal but Opposite Advice. This is a spectrum, and the optimal point is hard to point to. Some people need to seek efficiency more, others need to be more conservative and restrained. My guess is that most people don’t seek efficiency enough, but I also definitely know counter-examples to this!
And getting the right balance is hard! You need to always be grounded. Test things, and try new things, but be uncertain and open to being wrong. When people make arguments against you, be prepared to ignore them, but also listen, and see if there’s anything to them. Notice the feeling of reckless overconfidence, and ask whether it’s truly bringing you closer to your goals. Ground yourself in the pursuit of truth.
Conclusion
Overall, these beliefs have built up over time in me as a conviction that there is always a clever hack. And this isn’t always true! But the default state of the world is that I feel helpless. Problems feel impossible, the idea of finding a better way feels overwhelming, and I never manage to take the first step. Having this semi-irrational conviction is what gets me to step past my intuitions, and break out of my local optima.
So, next time you notice something in your life that feels inefficient, and part of yourself thinks “surely there’s a better way”, listen to that part. Take it seriously, ignore the hesitations, and try to be creative. And if you can wholeheartedly search for a clever hack, it just might work.