Learning to Learn Why learn about learning?#
Among the human population we observe a wide range in learning capabilities. There are an infinite amount of factors that come into play to explain someones learning effectiveness, but learning is also a skill that can be consciously developed and refined. I'm talking here about learning in a broad sense, which includes learning new skills, acquiring knowledge and building habits. Some may stumble upon valuable learning techniques early in life, but you can also train yourself to become more competent at learning. In this blog post I discuss 3 books that helped me the most to develop my learning potential.
We have ubiquitous Internet access, free access to YouTube and powerful LLMs like ChatGPT. These are tools that allow us to acquire almost any knowledge and learn almost any skill. Therefore, it is more important than ever to become competent at learning. I often imagine learning as something that compounds over time. Every new thing ties in with everything that was learned previously. The potential for new insights and competence grows exponentially (ex). If we improve our capability to learn, it can be viewed as double exponential growth (eex). We will see in the books discussed that there are patterns and similarities between learning techniques, which we can leverage to learn better. Let's dive into the books.
Books#
1. Scott Young - Ultralearning#
Ultralearning is a book written by Scott H. Young. He used his principles to complete all the exams and projects of a 4-year MIT computer science degree in 12 months using just MIT's OpenCourseWare. He also became fluent in Spanish, Portuguese, Mandarin and Korean in 1 year just by travelling and immersing himself in each language. The main principles described in the book are:
Meta-learning: The first step is to gather resources and start learning about how the skill you want to learn can be learned. You also draw on what you've already learned and leverage it for this new skill. This is the compounding quality of learning I talked about in the introduction.
Focus: Now you will focus on exactly what you want to learn. One of the pitfalls is to procrastinate or get distracted with erroneous details. Here it helps to start with thinking about the end goal and work backward to discover what needs to be learned to achieve your goal.
Directness: directness in learning is powerful, but generally different than what you are used to in school. In traditional education you get a broad overview of a topic but you don't get to decide which aspects of a topic you want to do a deep dive on. Some of the ways you can learn directly is to to do a project. Something you're really passionate about. Try to use everything you've learned directly into that project. Another approach is immersion where you fully engage with the skill. Immersion often involves joining communities and interacting with like-minded people.
Drill: Once you've started with learning you can do drills, which involves repetition, devoting time consistently and doing extreme deep dives on your weakest points. This is where many people give up. If you can consistently work on something it's a good signal that you will likely master it over time.
Retrieval: The human mind can be forgetful so it's important to revisit concepts over time and to train yourself to remember. A powerful method for this is spaced repetition as well as consistent engagement with the material.
Feedback: Seek and incorporate feedback to improve your learning process.
Retention: Focus on strategies to maintain what you've learned over time.
Intuition: Develop a sense and conscious knowingness as you learn and apply principles.
Experimentation: Keep exploring to discover exactly what you want to solve, do deep dives on, and how you want to continue your learning journey.
Later in the book Young goes into setting up a plan for your first Ultralearning project and discusses examples of applying these principles.
Your deepest moments of happiness don't come from doing easy things; they come from realizing your potential and overcoming your own limiting beliefs about yourself. — Scott H. Young
The best ultralearners are those who blend the practical reasons for learning a skill with an inspiration that comes from something that excites them. — Scott H. Young
2. Josh Waitzkin - The Art of Learning#
Josh Waitzkin was a young chess prodigy who won his first national championship at the age of 9. His remarkable chess journey was the basis for the book and movie Searching for Bobby Fischer. On top of that he became a martial arts master, earning the title of World Champion in Tai Chi Chuan. In "The Art of Learning" he describes what he has learned about learning and reaching top performance in various fields. He focuses on building intuition and the importance of creating a learning journey that aligns well with you. It is partly an autobiography of Josh Waitzkin's life. Later in the book he describes in detail his journey of becoming a Tai Chi Chuan world champion in Taiwan and how it ties in with everything he had learned up till then. It has some practical techniques, but I think you will learn most by just reading the book and soaking up the full story.
I discovered Josh Waitzkin's work through German poker player and entrepreneur Fedor Holz, who has been incredibly successful using Josh Waitzkin's methods in poker and business.
The key to pursuing excellence is to embrace an organic, long-term learning process, and not to live in a shell of static, safe mediocrity. — Josh Waitzkin
I have found that if we feed the unconscious, it will discover connections between what may appear to be disparate realities. The path to artistic insight in one direction often involves deep study of another — the intuition makes uncanny connections that lead to a crystallization of fragmented notions. — Josh Waitzkin
3. George Pólya - How to Solve It#
How to Solve It was written by Hungarian mathematician George Pólya. It presents a powerful framework for solving almost any problem. The examples in the book are mostly mathematics problems, but the principles can be generalized to almost any field. The core process is:
1. Understand the problem: What are you asked to do? Can you restate the problem in your own words? What is the unknown? What are the data? What is the relationship between the data and the unknown?
2. Devise a plan: Visualize the problem. Introduce suitable notation. Simplify. What strategies do you have at your disposal? Consider starting from the outcome and working backwards.
3. Carry out the plan: Systematically follow your plan. Check and document every step of your process. If you get stuck, consider starting over.
4. Look back: Did you arrive at a reasonable answer? Did you verify every step of your plan? Are there alternative ways to solve the problem? What have you learned? Can you generalize your solution or apply the same solution to a different problem? How can you improve your process for future problems?
A very valuable tool Pólya discusses to work through these steps is heuristic. The most important types of heuristics discussed are:
Analogy: Do you know a similar problem or pattern? Use your own experience.
Decomposition: Break down the problem into small parts. Introduce suitable notation and variables.
Generalization: Identify broad principles. Can your solution be applied to a broader class of problems?
Specialization: Test special cases of your problem. How can you use special cases to get closer to a solution?
Working backwards: Clearly identify the desired outcome and work backwards from there.
Auxiliary elements: Use suitable notation and variables to explore useful constructions and abstractions. Can you construct intermediate problems or hypotheses that can bring you closer to a solution?
Using heuristics is often unintuitive for technical people since it feels less precise and less scientific than constructing a proof. However, using fuzzy patterns and trying special cases aids the mind in finding new connections that allow us to understand the problem. Fully understanding the problem helps us to solve it and fully understand the solution. After that we are in a much better position to construct a rigorous proof if required. The book provides a whole "dictionary of heuristics" where problem solving techniques are discussed. Both Pólya and Waitzkin highlight the importance of subconscious work. This is the act of working earnestly on a problem, leaving it alone for a bit and allowing the solution to present itself to you. Also note that all three books we have discussed highlight the importance of developing intuition. Intuition is a key competence you develop through practice and the true sign of mastery.
Its interesting to note that many legendary scientists like George Pólya emigrated from Hungary to the US in the first half of the 20th century. These group of scientists, which also included John von Neumann, Paul Erdős and Eugene Wigner were so remarkable that they were given the nickname "The Martians". What was so special about scientists of this specific time from this specific region? Perhaps it can be partly attributed to an education system that taught similar methods to what George Pólya describes in How to Solve It?
An interesting note for programmers is that How to Solve It? is a book which Jeremy Howard often mentions and has been a staple of the fastai/Answer.ai community. Jeremy Howard and his students are living proof of the effectiveness of George Pólya's methods discussed in How to Solve It?. fast.ai's SolveIt course builds on George Pólya's principles. You can check out Jeremy Howard's own summary of How to Solve It here.
Solving problems is a practical skill like, let us say, swimming. We acquire any practical skill by imitation and practice. — George Pólya
Intuitive insight and formal proof are two different ways of perceiving the truth, comparable to the perception of a material object through two different senses, sight and touch. — George Pólya
The intelligent problem-solver tries to first of all understand the problem as fully and as clearly as he can. Yet understanding the problem is not enough; het must concentrate upon the problem, he must desire earnestly to obtain its solution. If he cannot summon up real desire for solving the problem he would do better to leave it alone. The open secret of real success is to throw your whole personality into your problem. — George Pólya
Acknowledgements#
Special thanks to Mickey Beurskens for recommending Ultralearning and Jeremy Howard for turning my attention to George Pólya's work. These books have had a huge impact on how I learn and solve problems.
