by Elucubrator » Sat May 10, 2003 1:38 am
Mathematics may be elegant or clumsy depending on how it is performed. Just as painting cannot be said to be elegant in itself, but only that painting that has been executed by an elegant hand. I would even venture to call Mathematics an art more than a science. It is used by it's devotees to describe the landscape; Van Gogh with the same purpose in mind used oil on canvass; Herodotus too had done the same with words on parchment, and no art is in some aspect entirely free from mathematics. Paintings obey laws of perception, symphonies those of harmony, the style of Herodotus and of any other ancient writer is today meticulously studied by philologists trapped in dusty libraries, coughing ink, and crunching numbers.<br /><br /><br />I am fascinated by it. It is as moving as any other form of art can be once one learns to appreciate it. It is all a language of it's own, and one that I have not practised enough. I wasn't good enough to read Einstein's theory of relativity without really working on my calculus first, and well, now that I remember, I think first I had to understand Maxwell's electromagnetic wave theories. I loved that class, I wrote a really great electromagnetic wave theory paper, which today I am utterly incapable of following. That's how high my skill in math once rose, and subsequently fell. When I read Einstein's Relativity, I remember the difficulty. My roommate and I would talk about how our brains were going to crack trying to figure it out, and suddenly, just like that, one day I saw it. I'm getting chills now typing this, and it's funny because I no longer remember what the hell I saw, it was a glimpse of something beautiful, but the vision was fleeting and soon lost. I just remember that sense of wonder when I had looked upon the face of some mystery, now lost again behind a veil of darkness. <br /><br /> Sometimes I still wonder whether Einstein was really right? It explained everything, it made sense to me, but there was also a day that Ptolemy had explained everything, and for hundreds of years people navigated according the system of epicycles upon epicycles expounded in his Almagest and accurately predicted the motions of the planets or the wandering stars as they called them, against the backdrop of the sphere of the fixed stars. <br /><br /> Copernicus came later with a theory that turned Ptolemy inside out. No longer was the Earth considered the centre of the ko/smoj, but was now described as another one of the wanderers floating through the vast sea of space, on elliptical orbits round the sun. <br /><br /> For a time men fought about which of these two models was the true representation of the heavens, both of the systems described the observations and predicted events and the positions of the planets perfectly, how could we tell? Ptolemy had the weight of tradition behind him, but with time the balance began to tip in favour of Copernicus and Ptolemy was forgotten. What was the reason for this? <br /><br /> Some say that Copernicus's system was more elegant in that it was simpler; it did not require manifold epicycles positioned at different angles and turning at different rates to describe the retrograde motion of Mars, and hence was an easier system to work with. And I might agree today that simplicity in mathematics is elegance, but back then when I was reading the astronomers I did not. Maybe I've always been pretty complicated myself and the intricacy of all the epicycles in the machinery of the ko/smoj as Ptolemy had described it appealed more to me than the munditia simplex of Copernicus. Maybe I was arrogant and egocentric and demanded that the Universe remain geocentric and fashioned after my own image, and so for about a year while the rest of my companions were circling the sun for me it continued to rise and set, and no one could prove that the world was not the way I preferred to see it, until the day when we began to read the Principia Mathematica.<br /><br /> Newton destroyed the Ptolemaic model with such elegance, and with such beautiful skill using accepted geometrical proofs and assigning planetary bodies to points, orbits to lines, time to area, so that when the geometry worked, the physical description of the ko/smoj Newton had described emerged upon a solid foundation, because the Universe itself was the geometry. He has since then become my favourite, though there are so many others whom I have not read, and I confess that I look forward more now to re-reading Kepler than Newton.<br /><br /> But still, how do we know that Newtons description is right? Everything is hanging together by the tiny thread of Euclid's 5th Postulate, which may not hold if space is curved. There are so many wonders in the world, and I feel that life is best when one is contemplating them, whether the answers come,....or not.<br /><br /><br />valete bene,<br /><br />Seba
<br /><br />Unlike those of you who are fully immersed in the elegance of higher mathematics, I am still delighting in the "challenge" part. Sometimes it feels like Mount Everest; clean cut, clear and starkly beautiful against a bright blue sky, but oh! so very difficult to climb! <br /><br />Which is, of course, just another way of telling people not to wait to post in the Academy until they completely understand the intricacies (or the simplicities!) of Euclid. <br /><br />Keesa
