Persistence and Swindling...
You know what...doing there a certain sense in which mathematics 'swindles' you. What I mean is that what goes on in a proof usually has no bearing at all to any kind of 'intuitive picture' that you would imagine.
(For example a proof on linear transformations on vector spaces, one could imagine lines being drawn to represent vectors and the linear transform a movement of those lines).
Really, some proofs are so abstract that it is almost like magic when the result pops right onto your lap. That is why I think, I'm so slow at understanding results, I tend to 'draw' a picture in my mind, when actually the more economical-and fruitful-is to consider the abstract point of view.
Come to think of it, this is why notation is invented in maths-to give precision and abstractness to reasoning, allowing one to single out the implications that really matter.
I swear I'll never look at reflections in the same way again.
(For example a proof on linear transformations on vector spaces, one could imagine lines being drawn to represent vectors and the linear transform a movement of those lines).
Really, some proofs are so abstract that it is almost like magic when the result pops right onto your lap. That is why I think, I'm so slow at understanding results, I tend to 'draw' a picture in my mind, when actually the more economical-and fruitful-is to consider the abstract point of view.
Come to think of it, this is why notation is invented in maths-to give precision and abstractness to reasoning, allowing one to single out the implications that really matter.
I swear I'll never look at reflections in the same way again.
This entry was posted
on Monday, July 25, 2005 at 11:49 PM.
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