Things that made me unhappy today:
Someone dissed mah physics, and by proxy Steven Hawking, Carl Sagan, Albert Einstein, Issaic Newton (he was a Physicist too <.<), and all the other ghosts of Physics past, present, and future. May they have mercy on your mortal quarks.
Oh god... you're one of
those people, aren't you. It's like there's something
terminally wrong with most physics people that makes them shout "MATHEMATICS IS EASY AND STUPID" from the rooftops at any available opportunity. Seriously, what is with those people (possibly/likely not you, upon greater reflection)? I just don't get it. I may generally dislike physics and anything related to it, but I don't pretend that it's easy. It's generally not rigorous (at all, though the theories of Kepler, Gauss, Riemann, and Newton are well-developed) and most of the mathematical tools built up for it are extremely boring and inelegant, but part of that is just the way physics is (i.e. not mathematics) and the other part is personal opinion.
I mean, let's think about this. Physics is useful because it hones our internal intuitions. There's a good reason why Liebniz's product rule was incorrect, whereas Newton's was right--Newton had a better sense of such quantities and areas and so on as a physics person than did Liebniz. Physics is good <3 What I don't understand is why physicists seem to look at mathematics as nothing but a tool, which they bend, manipulate, and abuse for their pleasure (... Feynman integral, anyone?) to match their measurements and then proceed to denigrate those noble souls who come sweeping up after and say "Yes, your screwy computations work. Can I get back to my fruitless attack on Hilbert's problems now?"
People disbelieved Einstein's theories because they were
too mathematical. What the HELL. I've read the popularization of his work and didn't understand it at all, but I seem to remember there being almost nothing but a fairly basic (but still ugly) coordinate transformation in there, as far as things mathematical go. Come on, people. You can't get afraid of a couple square roots and summations.
Don't even get me started on the various unification theories/string theory/the attempts to shove string theory off as something belonging to mathematicians, because it doesn't pass muster as anything but a special case.
As my favorite professor says:
Physicists are the most optimistic people in the world. They are never right. They are always wrong--but they are not trying to be right! They are just trying to be less wrong than before.
...
</rantventrant>
On a tangentially related note, busy work has always bothered me. Some people "learn" by reasonless repetition, but then that's only memorizing (and not necessarily integrating) the information. Without critical, theoretical thinking, you've lost sight of the purpose of scientific tools like math, and of reason itself.
That's the thing, however: sometimes you need to do "busy work" to train your intuitions. You have to get a basic sense of the rules--what can and cannot be done--and that is only effected by inculcation. I've never been able to get myself immersed in a system without a lot of boring and dry work to make the definitions natural and fluid.
The other problem is that "trivial" is relative. In the case of my metric differential geometry work, "trivial" means "I've learned that I only really need to do one of three things: 1. think about angles 2. take an inner product or 3. take a derivative." This must be learned, however, and it is generally learned by reading and writing a lot of proofs--which is, in many ways, busy work once you're learned the first few tiers of tricks.
Then, if you figure out a problem yourself, you'll sure-fire have to use that method over and over and over again... there's something I call the "turn the blocks around" type of proof (I know, it doesn't really mean anything. It's mostly a mental image more than anything else) and it applies to analysis, abstract algebra, set theory, theory of uniformities, manipulations of filters, and so on. It's a trick, and once you've learned it/discovered it, you'll have to apply it over and over and over again. Maybe you'll have to be a bit clever in its application, but once you've found it the first time it's never gone and the further uses are just repetition of what is already known to get fountains of easy results.
Well, anyway. Enough of that... I'd probably better get back to work.
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Topic: [MILK] There were 12 eggs here what did you do with them? (Happy thread?!) (Read 15876773 times)