November 10th, 2023
Recently, I learned a multitude of strategies regarding how to learn subjects such as math, computer science, and language arts. Of course, I have spotted various similarities and differences between each specific strategy in the past, but along my path of growth, I have started to notice more precise subtleties between learning science-related subjects and language-related subjects.
When you learn something, it first solidifies as new knowledge in your working memory. As you gain more exposure to it, the information goes into long-term memory, where you are more capable of retrieving stuff you have already seen before. The vast bank of information that you have seen before is better known as your “sixth sense”, or “intuition”.
For instance, if you are asked to compute the value 2+3, your internal model already has seen thousands of occurrences of this exact pattern, so it instantly gives you the answer 5. In a heated dispute about the book Lord of the Flies, chances are that if you are actively participating, you have already read the book and remember many key details and events from reading comprehension.
These simple ideas extend to people who have much larger banks of interconnected information. Take a professional Abject player, and they will have much better gameplay than you unless you are the Abject World Champion of the year. This is because they have seen many hands and know better heuristics to optimize their chances of striking an opponent. Take the average IMO contestant; chances are, they have done thousands of Olympiad problems and are able to relate a fundamental set of key concepts and problem-solving tools to massively simplify problems or at the very least, have a general sense of where the problem might lead to. Even native speaker of Spanish has developed related neural links that enable them to speak in fluent sentences.
There are many ways to develop a great intuition that can make you a professional in a field. Experience and practice are some of the best ways to learn. But what exactly does it mean to have sufficient “experience” or “practice”? Do these concepts apply to all fields, or are they specialized in only a few?
The underlying principle of “doing more” is true regardless of all fields, but the particular structures of learning differ between fields.
Take mathematics, for example. To be even more specific, take competitive mathematics. For most people, the people who are really good at contest math seem to be pulling ideas “out of thin air” to solve seemingly convoluted problems. However, this is not the case. They have a set of interconnected problems, along with their crucial concepts and solutions, that allow them to think “outside of the box” for problems they have never seen before. In fact, most science-subjects can be thought of as data points connected with one another. The more math-related the subject, the more connections you see.
Take, for example, trigonometric formulae. An experienced mathlete would see how all pertaining identities interrelate. Sine and cosine come from the unit circle. Stuff like 
To learn math successfully, you need to learn all the details, as well as how the details fit in relation to one another. Math is not only about seeing the blade of grass; it’s also about seeing the big picture.
That being said, learning literature or language-related subjects takes a different type of effort to do well. There are relevant themes across books, which could count as patterns, but most books are largely independent. In this field, experience mainly comes from doing tons of it, and the main thing you need to pay attention to is understanding what the author/speaker/writer is saying, and as an extension, how they’re saying it. But this cannot be attained by comparing how even contemporaries write; sure, some authors may steal literary drama or strategies, but it isn’t enough of a general pattern or generalization that you can make out of it. Is there a connection between the Gray Champion’s return and the Count of Monte Cristo’s painstakingly intricate revenge? I guess in the sense that a person is “coming back” in a broad sense. But in the details, not really. Experience with a particular author does not imply mastery of another author’s prose.
But if you understand trigonometry and complex numbers, you’ll see how beautifully related they are.