[math-fun] How we "do mathematics"
It's often said that among the sciences, supporting mathematics is a great bargain because unlike other sciences it does not depend on using advanced and expensive equipment. This is true. of course, but I claim mathematics is nevertheless technology dependent on a a quite marvelous invention called a pencil (or perhaps a pen, or whatever Euclid and Pythagoras used). Try to imagine how one could do mathematics if there were no such devices. Their usefulness is as a means of storage. If we couldn't write things down we'd have to keep everything in our heads at the same time which is hard. Example. An extra credit problem in my high school algebra book went something like this. Two racers run around a circular track at constant rates. If they run in opposite directions (one clockwise, the other counter clockwise) they meet every minute. If they run in the same direction they meet every hour. Find the ratio of their speeds. If you don't already know the problem maybe some of you can do it in your heads but if you can't, save the paper you used and see how many symbols you wrote down? How many pictures you drew?
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David Gale