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Training yourself to compulsively/always reflect on abstract ideas

  1. Sep 21, 2013 #1
    I work retail, and spend hours each day folding clothes. I would like to ponder interesting facets of mathematics and logic, but am unable to (or plainly, do not). When I go to bed at night, I'd like to ponder abstract questions, yet do not.

    Basically, I see people (and read of people) who think about interesting questions, paradoxes, etc. in mathematics, and would like to do the same. Of course, everyone finds different things interesting, but I think that maths are inherently interesting (that everyone, or at least that I should be able to find areas to think about), and it disturbs me that I waste hours a day that I could be thinking about abstract concepts, letting my mind think about less interesting things. How can I instill passion so that I begin to think about abstract ideas impulsively?

    I have a burning desire to be able to think creatively of/on my own mathematical questions, etc., and I do just fine questioning less abstract topics/ideas, but either because of lack of experience/knowledge in/of math (I am a Senior in high school), or my mind only being able to think about less abstract ideas at a deep level, I have yet to do this well. There are people my age who think in a way I desire (at least they project it) in that they think creatively about maths, but I guess I would be too embarrassed to ask someone in person such a question, because it is vague, and almost paradoxically straightforward (just think about these things), yet at the same time, impossible to answer.
    The step I have taken to stimulate my mathematical creativity is reading and understanding proofs. I am reading Spivak's Calculus, inspired by the rave posts on the forum, and am greatly enjoying it. Pondering the notion of a limit, etc. is interesting, but I do not ponder the ideas in the text compulsively/passionately all day long. Is this just a problem I need to reconcile on my own (the disconnect between what I would like to think about, and what I do think about)? Any ideas, ranging from branches of mathematics or Physics that one can ponder, to open-ended interesting questions to think about (some place to get me started) etc. would be greatly appreciated.
  2. jcsd
  3. Sep 21, 2013 #2
    Pondering mathematics sans pen and paper is incredibly tough in my opinion...
  4. Sep 21, 2013 #3
    Read 'For The Love of Physics' by Walter Lewin. Then you'll have a lot of physical ideas to reflect on, because he explains many ideas (especially in cosmology/astrophysics) that are still unknown/unsolved. As you progress in your education, studying physics and math, you'll be able to progress from pondering the abstract concepts to pondering the mechanics and mathematics behind them.
    PS: "Fear of Physics" (I forget by who) is also a really good one, gives a great outline of the concepts present in many areas of physics without needing to know all the mathematics behind it.
  5. Sep 21, 2013 #4
    Thank you both. I will begin by checking out 'For the Love of Physics' (makes me regret not being able to fit in Lewin's ed.x course this quarter. I signed up for it, but do not have time to take it along with the other classes I am taking). So would most agree that is all has to do with education-level, it is not thought that happens naturally or can be forced upon oneself?
  6. Sep 21, 2013 #5
    You probably won't become the next Feynman if you haven't spent your entire adolescence compulsively pondering stuff. On the other hand, not many people will.
  7. Sep 21, 2013 #6
    Gauss invented new mathematical formulae when he was 6. So, uh. Yeah.
    Lewin's book and his edX course are pretty different, though he references his course plenty in the first couple of chapters of his book. I don't think it's related to education level; you can ponder philosophical or moral ideas without having an education in it. For Physics, some ideas require mathematics before understanding them. With the books I mentioned, you can ponder the concepts without having been exposed to much of the math. Like, in Lewin's book, he talks a LOT about the evolution of cosmology and his area of study. At the end, he presents the existence of some mysteries that are still present today.

    So yeah. Check it out!
  8. Sep 22, 2013 #7
    Thank you both. But I do not know when I implied anything about being the next brilliant mathematician/physicist (Feynman, Gauss...). I merely would like to create/see my own patterns etc. and do not do so naturally, and was wondering ways to compel myself to do so. The book and insight was helpful, so thanks again.
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