I'm sure you knew I'd post after that one, so here goes =)
I now remember why I've always disliked math... or at least all the math that I've been subjected to. As a tool, it's great, and definitely gets results... but taken on its own, it's just a series of nebulous rules and tricks we use to compare or transform one value to another value. It doesn't approach an underlying rational truth at all, but instead builds and builds on an arbitrary pile of artificial logic that grows further and further abstracted from rational thought. For all the talk about how it approaches fundamental understanding of the universe, it seems to me that it's actually the furthest thing from an intelligible reality we have... and when people get too entangled in it, they tend to grow distant and separate from the world around them.
;_;
Though to be honest, I don't understand the "fundamental truths of the universe" people, either. That's missing the point. The "nebulous rules and tricks" is more correct, though the problem with the mathematics we teach in the lower levels of school is that we're seeing everything through a single nonadjustable prism. The allure of higher mathematics is, in essence, that we can become masters of our own universes and take long flights of imagination to arbitrary realities. It's like if a physicist could really experience a place with different laws, which he bent to his whim; as though a linguist could put a tribe in a certain situation and watch the language emerge; as though an architect could imagine a house and then, just as suddenly, begin to walk through it.
Mathematics is built from certain observations about the world around us, which we took as examples. We then extended those examples to create new concepts, which had the fortune to correspond to physical reality as well. We did not find the rational numbers, or the irrationals. We built them--so of course it's somewhat arbitrary. What you are looking at is a masterpiece painting, which has been in the making for 6,000 years or more. In some places, mistakes have been retouched messily; in others, the hue of the paint may seem a little bit off. That's all right--we have millenia in spades to continue our work.
The trouble is that you are staring at a single brushstroke, and saying "why?" It's much like taking a single word in a novel--one with no particular significance or context, really--and saying "why this word? Why here?" You know the page number, and perhaps the title of the chapter: "addition," or "non-desarguesian planes," but you cannot hope to analyze the work without any sort of context. It's futile. The imagination of the painters is closed to you.
I suppose it's because of this sort of thing that people don't understand students of mathematics, and our tendency to withdraw from "the real world." Much as the author must take a situation or story well-understood and transform it into a new reality, distant from our own but still familiar in some way, the mathematician performs a similar service. The only trouble is that many people have a good deal of difficulty understanding the roots of the original tale, so that our detachment from reality seems far more pronounced. It's a bit like cubism, I guess.
Eh. If you don't like the direction that particular painting is going, pick a different one =) There's many beautiful pieces of art in the world.
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Topic: Things that made you sad today thread. (Read 9496461 times)