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Thread: Thinking in Images

  1. #1 Thinking in Images 
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    It's been said that mathematicians understand things in terms of mental images. This is to say that when mathematicians read about concepts, they analogize those concepts into mental pictures, which are then mentally combined and manipulated to make deductions. My questions are as follows:

    (1) How do YOU understand math? If it's through visual images, explain in detail what you mean by this because I find it fascinating.
    (2) How ELSE could somebody understand math if not through mental image manipulation?

    Does anybody have any resources about learning how to think like the above?


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  3. #2  
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    Quote Originally Posted by gwsinger View Post
    It's been said that mathematicians understand things in terms of mental images. This is to say that when mathematicians read about concepts, they analogize those concepts into mental pictures, which are then mentally combined and manipulated to make deductions. My questions are as follows:

    (1) How do YOU understand math? If it's through visual images, explain in detail what you mean by this because I find it fascinating.
    (2) How ELSE could somebody understand math if not through mental image manipulation?
    Does anybody have any resources about learning how to think like the above?
    You need to read up on P.A.M Dirac - his training in technical drawing led him to use geometric solutions to solve equations


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  4. #3  
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    Quote Originally Posted by gwsinger View Post
    It's been said that mathematicians understand things in terms of mental images. This is to say that when mathematicians read about concepts, they analogize those concepts into mental pictures, which are then mentally combined and manipulated to make deductions. My questions are as follows:

    (1) How do YOU understand math? If it's through visual images, explain in detail what you mean by this because I find it fascinating.
    (2) How ELSE could somebody understand math if not through mental image manipulation?

    Does anybody have any resources about learning how to think like the above?
    Get a math program like Mathcad that will plot the curves for you. I also purchased a book: "CRC Handbook of Mathematical Curves and Surfaces", David H. von Seggern, a number of years ago and found it to be quite useful. Even produced some different curves of my own using Mathcad: "closed hyperboloids". Challenges the mind and produces different views.
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  5. #4  
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    Quote Originally Posted by gwsinger View Post
    It's been said that mathematicians understand things in terms of mental images. This is to say that when mathematicians read about concepts, they analogize those concepts into mental pictures, which are then mentally combined and manipulated to make deductions. My questions are as follows:

    (1) How do YOU understand math? If it's through visual images, explain in detail what you mean by this because I find it fascinating.
    (2) How ELSE could somebody understand math if not through mental image manipulation?

    Does anybody have any resources about learning how to think like the above?


    I think what you're trying to say is that when mathematicians understand things in terms of mental images, they're aiming to mathematically map "reality" so to speak, in order for their mental images as mathematical concepts to be as relevant as possible to the real world.

    I think there have been a number of arguments already about what stream of natural science is the most relevant as a mental image, mathematics or physics.

    Is this what you're trying to work out, the ideology between physics and mathematics?
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