Questions About MathDate: 07/31/99 at 14:13:51 From: kiki nwasokwa Subject: Random questions Why was the Cartesian plane invented/developed/discovered? Is the development of the more abstract, or "theoretical," branches of math just for fun? Are they merely an exercise in the application (so to speak) of human logic? What is chaos theory? Why is Einstein's equation e = mc^2? Why not e = mc^3? This still yields a large amount energy from a small amount of mass. Date: 08/01/99 at 15:39:31 From: Doctor Ian Subject: Re: Random questions Hi Kiki, > Why was the Cartesian plane invented/developed/discovered? One story that many people have heard is that Rene Descartes was lying in bed one morning, watching a fly crawl around on the ceiling, when he realized that he could describe the path of the fly by assigning it coordinates relative to orthogonal axes. Is the story true? Descartes definitely invented analytic geometry, and he certainly did a lot of his work lying in bed. However, according to _Men of Mathematics_ by E. T. Bell, Descartes said that the idea was one of many that came to him in the second of three dreams that he had on November 10, 1619, although he apparently never told anyone just what the dream was about. I suppose the moral is, if you ever have a really great idea, write down how you came up with it immediately and send it to the Smithsonian Institute, so people won't have to wonder about it later on. >Is the development of the more abstract, or "theoretical," branches >of math just for fun? Are they merely an exercise in the application >(so to speak) of human logic? It depends on whom you ask. If you ask the mathematicians, the answer is 'yes'. If you ask the people who fund the mathematicians, hoping that even the more abstract fields will turn out to be useful for something, the answer is 'no'. >What is chaos theory? Biologist Arthur Winfree used to tell his students: "The basic idea of Western science is that you don't have to take into account the falling of a leaf on some planet in another galaxy when you're trying to account for the motion of a billiard ball on a pool table on earth. Very small influences can be neglected. There's a convergence in the way things work, and arbitrarily small influences don't blow up to have arbitrarily large effects." Chaos theory is the study of situations in which this assumption turns out not to be true. >Why is Einstein's equation e = mc^2? Why not e = mc^3? This still >yields a large amount energy from a small amount of mass. Take a look at the cartoons by S. Harris on this page from Juergen Giesen's "Around Physics and Astronomy": http://www.jgiesen.de/Divers/Humor/Humor.html Seriously, though, if you look at the units in the equation, you will see that energy = mass * (distance/time)^2 = mass * (distance/time^2) * distance = force * distance which is one of the definitions of 'energy'. If you added an extra 'c' in there, you'd end up with something other than 'energy' on the right side of the equation. Remember, c isn't a dimensionless number like pi, it's a speed. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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