Devlog Research Notes

How can I (or anyone) Analytically and Consistently Learn?

• My late night chain of thought while driving:

  ... I feel like I need to give myself more of a chance to actually learn, often times I feel rushed into 'learning' something that I don't actually know what I just went through. It's not as if I CAN'T learn, I can do more than most people in harder subjects, but I feel as if these feelings come from not giving myself enough of a chance to learn properly. But how can I really learn? I guess learning is just iteratively exposing myself to a subject I want to get better at until one day I look back and realize I did get better at it. ... This seems inefficient though, surely there's a better way I can generalize a better learning process, I'll try to synthesize a chain of thought and work through it step by step. What do I (or should I) start with when learning? I need to chose a subject to learn, I obviously know what I want to learn so that's out of the way. The next step would be to actually start, when encountering a new subject, I need to approach it from different angles, this can be done by I guess, reading up on the subject from different sources, looking at worked examples of problems related to this subject, covering it's various edge cases and even maybe looking at other closely related topics and trying to form meaningful connections between them. I feel as if having someone else explain things is also useful, be it through a professor, YouTuber or any other medium.
  
  ... What's next? once I've exposed myself enough to the subject and all it's intricacies, what should I do next? How can I learn to use what I now know about a subject, apply it to real life scenarios, create new things with it, discover new things with it and just make use of it in general?
  
  I guess one example of this is that, when learning Integrals, you can learn how to solve many integrals and get really good at solving them, this doesn't mean that, when given a real problem, you would be able to notice or to infer when to actually use an integral to solve the problem. But how does someone learn when to use an integral? ... Actually do I even know when to use an integral in a real problem?... Hmmm... let's see, let's say someone shoots a ball in a 2D plane, I'm given the start and end positions of the ball as well as the function the ball takes in this 2D plane. I'm then asked to find the total area that the ball covered... how would I do this? ... Switching back to integrals for a second, what even is an integral? what is it used for? integrals have two (amongst other) distinct functions, finding the area under a curve, and summation. ... So there's my answer, the integral is used to find the area under a curve, if I'm given the beginning and end positions of the ball as well as the function it draws on the 2D plane, I can find the required area covered by the ball by computing the definite integral of the ball's function from the beginning to the end position. ... Huh, okay so I do know when and how to use integrals, but how did I get to this point, I obviously didn't always know this, so how did I get to know it? I mainly got to this point through excessive repetition of exercises of all kinds, not just solving integrals and reading/immersing myself on/into the subject.
  
  ... So if I extrapolate my chain of thought on this and apply it to learning after having exposed myself enough to a certain subject, I guess the only next steps to take are to just solve various exercises , exercises and problems on the subject of all kinds. I need to try to solve different levels of problems, fail at almost all of them at first, and then learn from my mistakes in a controlled and intentional manner. It's not enough to just fail and lookup the answer, I need to backtrack and figure out WHERE I went wrong, what I was thinking when I took the wrong step, WHY I took the wrong step and formulate steps to correct my mistake. ... Okay, what's next?, is there even anything else? I guess if there were to be something next it would be to just keep being immersed in the subject, it takes enormous amounts of knowledge and experience in a subject to be able and create/discover new things about it.
  
  Okay... cool, I'll do that.
  
  -- Thought of this 2026/02/03 - 11:50 PM --