Hey Molly,
That's a great analogy to the nebulae. Living in New York it's easy to forget that there is a system to the cosmos and that the stars exist in communities just like we do, communities that are more tangible than a series of seemingly unrelated points. One of the most vivid memories I have of visiting Colorado is looking up into the night sky and actually seeing the Milky Way, before then I thought it was just a theoretical possibility not something that could ever be seen with the naked eye.
It's funny how as our picture of the night sky becomes more expansive and all-encompassing, it becomes prettier. It is when the individual stars give way to the nebulae that you begin to see the true colors of the universe in their resounding beauty. As our questions give way to answers, we add more pixels to our greater picture of understanding. And math is the means by which we can add those pixels.
What is most amazing to me about math is that it works. Though I still can't grasp this effectiveness, here is an interesting article that I had to read for a class once about the effectiveness of math to explain the natural world. (The Unreasonable Effectiveness of Mathematics in the Natural Sciences by Eugene Wigner: http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html
The paper begins with this pretty amazing quote by Bertrand Russell
Mathematics, rightly viewed, possesses not only truth, but supreme
beauty, a beauty cold and austere, like that of sculpture, without appeal
to any part of our weaker nature, without the gorgeous trappings of
painting or music, yet sublimely pure, and capable of a stern perfection
such as only the greatest art can show. The true spirit of delight, the
exaltation, the sense of being more than Man, which is the touchstone of
the highest excellence, is to be found in mathematics as surely as in
poetry.
I only recently became fascinated with math and unfortunately I gave it no import during high school so my practical knowledge is limited. As nerdy as it may sound I'm planning on picking out a math textbook and slowly working my way through. Does anyone find a particular type of math actually fun? My friend left behind a Calculus book that I started leafing through but I think I might find geometry more interesting.
Is anyone here of the expertise that they could explain the different mathematical paths and their correspondence to the real world? For my part, if people are interested, I can explain as best I can the theoretical workings of fractals and chaos theory, a truly beautiful area of math that is visible in every tree, but really all of nature.
I look forward to a challenging discussion!
Hello Robin, if you are still around.
I enjoyed reading graph theory, esp. the proof relating to the 7 bridges of Konigsberg. It's neat the way you develop concepts, prove some things, and then use that as a basis for further proofs. One good proof leading to another. I enjoyed for a while solving problems of change with differential equations. Mostly, I liked any concepts that gave me power to apprehend the world. Survey it all to get the basic ideas. I personally lean toward math in solving "real world" problems. Often you don't need to go real deep to get the important stuff, although I do think one should develop some expertise in one or more areas. Others will prescribe a more ordered course of studies, where x and y are the building stones for subject z, and that's all true. But if you aren't studying things that really interest you I question the efficacy of relying too much on that approach. On the other hand, sometimes if you are given a tool, it's use may only become apparent to you sometime in the future.
While in a library I saw a man come in to the check out desk and inquire something. He had a manner of walking, speaking, perusing a book, that was most unusual, gracious, old European gentlemanly, kindly - I remember thinking- this is somebody really special. I attended a lecture given by this guy- Wigner- that evening. I don't recall the lecture, although I suppose it was on philosophical aspects of quantum mechanics, but I remember the man. Gee.
