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apr02b - 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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6.055 / Art of approximation 54 Whereas using dimensions reveals that the problem is simpler: to find the function h such that kT 2 = h () . m Here h () means a function of no variables. Why no variables? Because the right side con- tains all the other quantities on which kT 2 / m could depend. However, dimensional analysis says that the variables appear only through the combination kT 2 / m , which is already on the left side. So no variables remain to be put on the right side; hence h is a function of zero variables. The only function of zero variables is a constant, so kT 2 / m = C . This pattern illustrates a famous quote from the statistician and physicist Harold Jeffreys [ 6 , p. 82]: A good table of functions of one variable may require a page; that of a function of two variables a volume; that of a function of three variables a bookcase; and that of a function of four variables a library. Use dimensions; avoid tables as big as a library! 7.4 Hydrogen atom Hydrogen is the simplest atom, and studying hydrogen is the simplest way to understand the atomic theory . Feynman has explained the importance of the atomic theory in his famous lectures on physics [ 7 , p. 1-2]: If, in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generations of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis (or the atomic fact , or whatever you wish to call it) that all things are made of atoms
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