How to learn

Intro

• How do humans learn and remember things most efficiently?
• How to improve motivation and reduce procrastination?
• How to improve focus in general, and during study sessions?
• How much should I study a thing before I move on to study the next thing?
• What should I study?

I have listed here a bunch of ideas that I've gathered from various sources, along with some of my own ideas, that try to answer these and related questions for myself.

TL;DR

Study frequently in short incremental steps. Frequently try to recall and apply what you've learned, and test yourself. The quicker the feedback, the better. Study what is most relevant to you, but also learn to make anything you study relevant to you. Think 80/20: focus on the most useful or important stuff, and ignore other stuff for now.

Summary: study skills for efficient learning

Below is a summary of the whole article.

• Set goals. The more specific, the better.
  • Bad: "learn statistics". Good: "learn to use linear regression to predict who will win the next F1 race".
  • Subdivide goals into small, achievable tasks. The smaller the better. This prevents procrastination.
    • An efficient way to do this is to just start working towards a (precise) goal. You'll learn along the way what sub-tasks you need to add.
  • Focus mainly on those small tasks, instead of a single, big, fuzzy, scary goal. Keep solving one task after the other.
• Do frequent, short, and consistent study sessions
  • Frequent study sessions leads to the spacing effect, which is an efficient way to learn
  • Use a calendar: schedule short study sessions to help you form a habit
• Take breaks. 25 minutes of studying, then a 5 minute break.
  • Get away from the computer — this helps your brain recharge and enter "diffuse mode", which helps it focus on the big picture
  • Limit information (social media, YouTube, etc.) that you feed to your brain when you're not studying. Allow your brain to ponder about the topic.
• Pragmatism: focus first on a problem, and find the relevant tools that work for it, rather than studying tools in a vacuum
  • You can always return to study the less relevant tools if they become more relevant later
• When studying a topic, first prepare: do an overview of the big picture
  • Skim a book's table of contents, chapter summaries, exercises, etc. Read Wikipedia summaries. Watch videos.
  • Make it relevant. You want to connect the topic as much as possible to the existing neural connections in your brain.
• Constantly try to apply what you've learned
  • Do practice problems and katas.
  • When you write notes, write mainly terminology and questions. They help you recall later.
    • Copying what you read is a waste of time
    • Rereading notes feels good but is not effective for learning
    • Trying to recall and apply what you've learned is much better for learning. Repeated activation of neural connections in your brain strengthens those connections.
  • Feedback is essential. The quicker you know whether you succeeded or failed at a problem, the better.
    • Aim for a roughly 20% failure rate — otherwise the problems you're trying to solve might not be hard enough for you to learn efficiently
  • Relevance is key: always find or create problems that are related to your brain's current connections (experience and goals). Textbooks won't help you with this, since the books don't know you, so you'll need to be active here.
  • Use spaced repetition for best memory consolidation
    • Spaced repetition is achieved as a by-product of frequent (short) study sessions
• When trying to learn, actually try to improve
  • Active learning
  • Deliberately try to improve on a specific thing
  • "Some people have 10 years of experience. Others have 1 year of experience 10 times."
  • Focus on the quality — not the quantity (i.e. length) — of your study sessions
  • "Practice as much as you feel you can accomplish with concentration. [...] It really doesn't matter how long." [source]
• To form a habit, change your identity
  • Have a growth mindset, not a fixed mindset. The more you learn, the more you get to feel the positive feeling of small wins.

How to study something

The following steps are loosely based on SQ3R, which explains a method for reading a textbook.

1. Skim the material to find the important parts

The goal of this step is to prepare yourself and to make the material relevant to you. Start by constructing a mental map of the topic, onto which you can then place detailed knowledge in the next steps. Connect the topic to your current experience and problems for better motivation and neural connections in your brain.

• Use books, courses, and other structured materials to find the important parts
  • Usually someone has already put together a good book or Wikipedia article on the most essential aspects of a topic
  • A good book gives you an efficient route to knowledge. Otherwise you'd need to do a lot of trial and error to learn the essential stuff.
• Try to understand the big picture of the problems, and the main tools to solve those problems
  • Focus on reading tables of contents, headings, lists, chapter summaries, terminology, exercises
  • Read summaries of the topic on Wikipedia, and watch videos
  • Make short notes of the problems and tools (preferably as questions)
• Skim the details of hard/unimportant parts, and things you already know
  • Important parts = the areas that are most relevant to you. This makes the topic connect better with your brain's existing neural connections, improving motivation and retention.
  • Do this aggressively. Don't feel like you have to read every single page of a 1000-page math book. And if a book isn't working for you, unashamedly switch to another book.
  • Remember the 80/20 rule
  • Testing yourself early and often will tell you whether you're skimming too much

2. Carefully study the important parts

The brain encodes information best when it's trying to actively recall and apply:

Contrary to popular belief, your memory doesn't reproduce information, it reconstructs it in a way that reflects your prior knowledge and expectations. Therefore, the key to improving your recall of information is not to increase the exposure you have to your sources. Instead, you need to make a deliberate effort to think more about the material as you're studying it.

An excellent catalyst for thinking about the material is to ask questions of your sources during the process of reading, such as: "How does the evidence support the assertion being made?" Psychologists call this process elaborative interrogation; this has robust effects on your ability to recall information, establish connections between different concepts and make inferences based on what you read. Avoid reading aimlessly. [source]

• Slow down: when studying the important parts, go slow and focus on accuracy. Slow is smooth; smooth is fast.
• Deliberate practice: understanding requires you to actively engage with the material
  • Ask questions. Read critically.
• Note-taking: simply copying what you read is a waste of time
  • Write down terminology and questions instead. It makes you engage with the material.
  • Prepare self-tests: create your own exercises, and write the solution (or a link to the solution) close to the exercise. You can use these later as flash cards.
  • Keep your notes minimal. You can find information on the web easily. Mainly write down easily searchable terminology in your notes.
• Relevance is very important
  • You have to think of problems that are relevant to you, and try to solve them
  • Textbooks won't help you much here, since they don't know you (i.e. your experience, interests and goals). Therefore you'll have to learn to actively create relevant problems and applications.
  • Relevance makes the topic efficiently connect with the current neural structure of your brain

3. Recall and apply: test yourself

This is possibly the most important thing you can do for effective learning.

• Don't simply re-read your notes
  • Re-reading is not effective for learning. Trying to recall is much better for learning.
  • According to research, re-reading notes/solutions makes humans feel good because the text feels familiar, but it tricks you into thinking that the feeling of familiarity equals learning. It doesn't.
• Apply what you've learned. Solve problems.
  • Try solving the questions you wrote down earlier
  • Do katas: small real-world-like exercises
  • Make sure that the problems are relevant, since that makes the topic connect with the existing neural connections in your brain
  • Find additional exercises from books and the web
    • If you use ready-made tests, make sure that they come with solutions
• Feedback is essential
  • The quicker the feedback, the better
  • Failure is desired: it's feedback that leads to learning
  • Failing roughly 20% of the problems is optimal for learning
  • If you can't remember something, or if you give the wrong answer, that's good. It calibrates your understanding of your level of competency and helps you decide what to study next.
• Try many ways of application and recall (without looking at the source material)
  • Define terminology, summarize, write, teach, break into component parts, create
• Use Polya's problem solving approach
  • Understand the problem (e.g. an exercise, or a question that you wrote down)
    • Polya says: "It is foolish to answer a question that you do not understand. The student should consider the principal parts of the problem attentively, repeatedly, and from various sides."
    • Your questions should be well-defined, i.e. they should be answerable with a unique and exact answer. The answer is a function of the question (mathematical functions can have only one output).
    • What is the unknown? What are the data? What is the condition?
  • Come up with a plan to solve the problem
    • Have you solved a similar problem earlier? Can you restate the problem in a more general or special form? Can you solve a(n easier) part of the problem?
  • Execute the plan
    • Check the correctness of each step carefully
  • Look back
    • Check the correctness of the result. Could you have solved the problem differently?

set xrange [1:6]
set yrange [0:10]
set xlabel "Level in Bloom's taxonomy"
set ylabel 'Marginal utility'
set xtics 1
set ytics 1

$data << EOD
1 10
2 5
3 2
4 1
5 0.5
6 0.5
EOD

$data2 << EOD
1 5
2 8
3 10
4 8
5 5
6 2
EOD

plot "$data" with lines title "Knowledge about poisonous berries", "$data2" with lines title "Skills for your profession"

4. Repeat. Use spaced repetition. Look back.

• Consistently recall and apply your knowledge across time for best memory retention
  • Use a schedule to consistently do frequent short study sessions
  • This leads automatically to the spacing effect, which leads to efficient learning
  • "Useful and important ideas recur frequently, so spaced repetition is naturally built into the process of learning aggressively." [source]
• Do exercises and practice problems
  • E.g. the questions and self-tests you wrote down, or ready-made tests, or real-world problems
    • Take you failures from the past and see how you would've solved those in a better way. Do a post-mortem or a retrospective. Weaponize rumination.
  • Aim for a 20% failure rate. If the success rate is better, wait for a longer time until the next repetition.
• Flash cards (e.g. Anki) are a common technique for writing self-tests (and their solutions), but you can also use your blog or notes for self-tests — whatever is the most time-efficient way for you to create self-tests and their solutions
  • You can also use ready-made tests, or use existing problems from your daily life
  • It's most effective if the problems are relevant to your current experience and interests
• What to memorize?
  • Compare how long it would take you to memorize it, versus how long it takes to look it up or derive it
  • Start by memorizing stuff that you need most often, and stuff that is most time-consuming to look up or derive on-demand

About goals

Focused, hard work is the real key to success. Keep your eyes on the goal, and just keep taking the next step towards completing it. If you aren't sure which way to do something, do it both ways and see which works better. — Carmack

Set goals, and split them into small achievable tasks. Then just keep solving one task after the other.

• To find out your interests and goals, learn a little bit about a lot of things (breadth first)
  • Use the 5/25 rule to find your 5 most important goals
• Divide goals into small and clear tasks that you can see yourself completing quite easily
  • This is important, since having big and unclear tasks easily leads to procrastination and analysis paralysis. Keep splitting the tasks until you feel no analysis paralysis.
  • This way you can keep achieving small wins by focusing on completing mundane daily tasks, instead of focusing on big scary goals
  • Focus on the most essential sub-tasks for highest return on investment
    • You often get the highest jump in relative skill level from learning the basic stuff in some field. Studying the more advanced stuff might not be worth your time.
• Once you have a rough goal, just start. Keep creating more sub-tasks as you keep learning about the topic.
  • Efficient learning is about frequent feedback via iteration, instead of big-bang waterfall
  • Analyzing a problem endlessly feels safer than "just doing it". "Just doing it" will lead you to fail often, but that is desired, and leads to learning. Make the tasks small so that the failures are balanced frequently by successes.
  • In the business world this means prototyping and small proof-of-concept projects that let you learn more about an unfamiliar problem and its solutions
• Periodically re-sort the list of goals according to importance
  • Use a prioritized list of goals in a text file, similar to a TODO list
  • Keep an antilibrary: a set of things you want to study. This way you can easily pick the next thing to study.
• Instead of goals, maybe think of preparation for unknown future opportunities
• Instead of goals, maybe think of systems
• Practice self-reflection (e.g. journaling) to understand your current level of competency, your goals, and any hindrances preventing you from working towards your goals. And appreciate what you already know, since life is short and you can't know everything.

Study whatever thing you're most interested in. It's important that daily practice isn't agony, but instead something that you actually like to do.

• But don't let this be an excuse for not pushing yourself. "Serious fun" is about challenging but achievable small tasks, and frequent small wins when you overcome each small task.
  • Honestly reflect (e.g. journal) and think whether you're just trying to avoid putting in effort into a thing (e.g. due to some mental block), or whether the thing genuinely goes against your built-in strengths, values and whole being
• Focus on the problems first, and then find out what tools can be used to solve them, rather than studying tools in a vacuum
• Use the 80/20 rule: focus on the most important 20% problems and tools, to (hopefully) achieve 80% of the knowledge that you're after
  • Keep diminishing returns in mind: aggressively stop studying a thing and move on to the next thing whenever you can reliably solve problems with your existing tools
  • But be honest. Try to understand the level of competency that you need. If you're able to solve all practice problems with a 0% failure rate, ask yourself whether you already have the skills you need, or whether you're using practice problems that are too easy (relative to your desired level of competency).
    • Solving actual (non-practice) problems would of course remove all ambiguity. Try to solve real-world problems to properly calibrate your understanding of your level of competency. Solving real-world problems should also improve motivation, since such a problem is probably more relevant to you than a synthetic practice problem. Relevant problems in turn improve retention.
• Have a realistic sense of your current level of competency
  • This requires self-reflection and self-testing. Apply what you've learned: do practice problems and apply the skills in real life.
  • This helps you figure out how much additional utility you can get out studying a specific subject, and whether studying another subject instead would be more beneficial

About focus

When studying, don't concentrate on the amount of hours, but on the how deliberately you're using that time to improve.

Practice as much as you feel you can accomplish with concentration. [...] It really doesn't matter how long.

[...] across a wide range of experts, including athletes, novelists, and musicians, very few appear to be able to engage in more than four or five hours of high concentration and deliberate practice at a time. [source]

• "Focus is a matter of deciding what things you're not going to do." — Carmack
  • Drop unimportant things. See 20 slots.
  • Learn to be good at knowing when to skim fast, and when to read slowly. See pseudo-skimming.
  • From your own experience and others' experience you will learn what is unimportant to you
• Two ways to improve signal-to-noise ratio: increase signal, or decrease noise
  • Noise-cancelling headphones
  • Website blocker extension (e.g. Leechblock) for distracting websites
  • Good sleep
  • Limit information (social media, YouTube, etc.) that you feed to your brain when you're not studying. Allow your brain to ponder about the topic. If you spam your brain with other information all the time, it drowns out the stuff that you're studying.
  • Lindy effect: read old books that have stood the test of time (and have been trimmed of bad ideas)
  • Accrue knowledge that will be useful for a long time and in many situations, e.g. critical thinking and mathematics
  • Have clear and specific long-term goals

About consistency, habit, identity and procrastination

Learning requires effort, but that doesn't mean you can't enjoy it. Similarly, lifting weights is enjoyable even though it requires effort. Here's a miscellaneous set of ideas that might help with motivation and forming habits.

• Procrastination: whenever you're procrastinating, try the steps here (based on the book The Procrastination Equation)
  • Just start: simply show up. Study every day, however little. This is similar to how showing up at the gym is the most important step. Scheduling your study sessions for specific days and times of day should help.
  • Use Pomodoro, e.g. 25-minute study sessions separated by 5-minute breaks (away from the computer)
    • This helps your brain go back to diffuse mode and to think about the larger context of what you're learning
  • Understand and regulate your emotions: https://cognitiontoday.com/you-procrastinate-because-of-emotions-not-laziness-regulate-them-to-stop-procrastinating/
• Your environment affects your habits. Modify your environment in such a way that it acts as a forcing function towards better habits (e.g. a studying habit).
  • Minimize distractions. Use browser extensions that block distracting websites.
  • Make it as easy as possible to enter studying mode. Create a study corner in a room. Keep a prioritized list of things to study. Have study material easily accessible.
  • "Monasteries were developed to help people concentrate their minds. In a sense, they were giant, beautiful machines to assist us in avoiding procrastination. They started from a usefully pessimistic assumption: we are naturally very easily drawn off course and need all the help we can get to devote ourselves to tasks we are theoretically committed to." [source]
• Consistency and short bursts: no matter what study techniques you use, if you're consistently studying and actually trying to improve (a.k.a. deliberately practicing), then you will see progress
  • Short and frequent study sessions are better than long and infrequent ones, since frequent sessions leverage the spacing effect, which makes learning more efficient
  • Forming a habit is important, since that way you don't need to have long tiring study sessions, but instead can have short bursts of studying. Short study sessions add up.
• Your identity affects your habits
  • Have a growth mindset: you will learn if you put in the effort
  • Beware of having a fixed mindset, and overestimating your current skills
    • [...] teachers who reward students for successful learning by praising them for being "smart" actually promote a fixed identity and less expenditure of study effort ("I don't need to study because I am smart.") [source]
• Interleaving: study one thing, and when you're tired of that, study a different thing. Iterate through the whole set of subjects multiple times.
• Make it your own: rather than studying only theory, always try to find motivating practical examples and context from your own life for what you're studying
• Diet and sleep: wake up early, since waking up too late can make you feel like a zombie for the whole day. Eat healthy, and not too much, and not too late, to prevent brain fog.
• Visualize failing at your goal: humans fear failure more than they enjoy success. Use that to your advantage.
• Keep track of progress: use a time tracker, a calendar, or simply a piece of paper to track your studying per week. This helps with motivation.
• Effort: learning can be temporarily uncomfortable. Similar to the gym: a certain kind of discomfort is temporary and beneficial, and IMO should be actually enjoyable, if you're working on the right goals, and if the goals are divided into small enough sub-tasks (e.g. "lift these weights for this many times today") to prevent analysis paralysis.
  • Pursue failure and accept it as a part of the learning process (rather than as a part of your identity)
• Compound: if you learn 6% more per month, and if knowledge compounds, then after 1 year you will have 2 times the knowledge ($(1 + 0.06)^{12} \approx 2$), and after 3 years you will have almost 10 times the knowledge ($(1 + 0.06)^{(12 * 3)} \approx 8$).