feb22b - MIT OpenCourseWare http/ocw.mit.edu 6.055J 2.038J...

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MIT OpenCourseWare http://ocw.mit.edu 6.055J / 2.038J The Art of Approximation in Science and Engineering Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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Chapter 5 Proportional reasoning Symmetry wrings out excess, irrelevant complexity, and proportional reasoning in one im- plementation of that philosophy. If an object moves with no forces on it (or if you walk steadily), then moving for twice as long means doubling the distance traveled. Having two changing quantities contributes complexity. However, the ratio distance/time, also known as the speed, is independent of the time. It is therefore simpler than distance or time. This conclusion is perhaps the simplest example of proportional reasoning, where the propor- tional statement is distance time . Using symmetry has mitigated complexity. Here the symmetry operation is ‘change for how long the object move (or how long you walk)’. This operation should not change con-
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feb22b - MIT OpenCourseWare http/ocw.mit.edu 6.055J 2.038J...

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