explain how to learn how to think

[srele96]

What

While trying to learn a problem from real analysis I realized that I don't know much about real analysis. My mind went blank. I thought about why my mind went blank and how can I learn real analysis and had a breakthrough idea. Just continuously and repeatedly read materials over and over. Read below for more.

I made another person download ChatGPT and she used the microphone to record a message. I was surprised at such use because I was so stuck inside my own box of using it that had been working for a long time.

Additionally I didn't know how to make someone curious about chatgpt, so I asked that person to help me figure something out. That person knows astrology. I told that person if my request is out of abilities, to use the chatgpt to seek answers that can't be found on google. That person proceeded to play with GPT for the next 30 minutes or more and got really curious into asking many questions. I found that phenomenon fascinating.

Why

I believe that here lies something of a key importance for me and my learning process. Something transitive to learning other areas such as computer graphics concepts, ideas, and more...

How

There is something that I only understand now, once I started learning calculus and real analysis from mathematics. I did not understand what I was missing when I started learning programming. Roughly two years ago, I did not know why my code was always messy, not good, it was not clean, I could not comprehend the data flow, I could not comprehend what is going where and why, and what is coming from where and why. I did not understand all the intricate details about my work. However, now once I started learning real analysis and mathematics, I think that now I understand why my code had so many problems always, because I did not know how to think. For example, today I was trying to do some real analysis problem, I asked ChatGPT to list me a problem and he gave me a function with notation from R to R, so I suppose that domain and codomain were a set of real numbers, and that was new to me. My mind felt absolutely blank. Then it proceeds to prove that the function is bounded over some set, and then it proceeds to use a limit to the positive infinity, to the negative infinity, a limit on a bounded interval, and then it proceeds to solve another problem in analysis. I forgot what the other one was, I was only thinking about whether it is bounded or not. And the next one uses, I believe, either integration or differentiation, and it talks about convergence. I think it was whether it converges or diverges to certain values. All of that was unfamiliar, and I was thinking, how can I learn, because I don't understand the problem, I don't understand the solution, I don't understand what I don't understand, and the more I tried to read about why and what and trying to understand, the more I don't understand. I was reading more and more, and the explanations did not make any sense. And then it occurred to me, because I am familiar with deliberate practice, and I think that ultimately how mind works and what understanding means is memorization. I simply didn't have any of these concepts memorized. I did not know whether the explanation is talking about some fundamental thing, or about some more complex things that I can understand. And in terms of this explanation for me, I didn't know if the explanation was, for example, yeah, you can just do dynamic programming, you can use an array, you can do it on graphs, and so on. And for example, I can imagine that, but if I tell that to someone else and he doesn't know what is a graph or what is an array, then he needs to understand what is an array. And it is a bigger problem if he doesn't know what is an array, and it's a smaller problem if he doesn't know what is a graph. So, I did not know whether the explanation is fundamental or more complex. And I had an idea that I simply need to pour an intense focus into memorizing this, into turning these things into images. Because images are much easier to memorize than text. And if I can graph, draw, write, and then somehow, just through intense focus of looking, thinking, to memorize this. Because when I say limit to the positive and limit to the negative infinity of a function, I'm thinking of a curve or a straight line, and I'm thinking about a coordinate system, a two-dimensional coordinate system, and I can go on and on about it. However, when it comes to numbers or the definition of such an equation, I do not have it in my mind. So, it is much easier to remember an image than a text. And this made me think, if I really want to understand these things, then one possible way that I can use is just to read. Read a lot. Think about it. Google questions. Dig deep. Go back. Read more. And keep reading and reading and reading. Because I think this will create and store some ideas in my mind. And I think that if you create some sort of memory, that is important. That's basically going to allow me to use these memorized ideas as I'm learning more and more. And as I'm becoming familiar and as I remember and memorize more and more to solving problems through thinking about these topics, and how can I use them like the derivative, integral, slope, blah, blah, blah, and so on. I think that's the direction I should go in. I think that's the direction I should go in. I should definitely stop pressuring myself. Try to stop pressuring myself to understand. Because it sometimes or always actually pushes me to try to understand. And I feel like I must understand. And then that feeling just makes me skip. That feeling makes me skip learning, skip reading, and watch a TV show or something. When I could have been reading or studying, just simply reading would help incredibly a lot. So this is a self-note and I believe that is the direction I should go in.