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Zack_M_Davis comments on Open Thread: November 2009 - Less Wrong
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So, I'm having one of those I-don't-want-to-go-to-school moments again. I'm in my first year at a university, and, as often happens, I feel like it's not worth my time.
As far as math goes, I feel like I could learn all the facts my classes teach on Wikipedia in a tenth of the time--though procedural knowledge is another matter, of course. I have had the occasional fun chat with a professor, but the lecture was never it.
As far as other subjects go, I think forces conspired to make me not succeed. I had a single non-math class, though it was twice the length of a normal class and officially two classes. It was about ancient Greece and Rome, and we had to read things like Works and Days and the Iliad. Afterwards, we were supposed to write a paper about depictions of society in the two works or something. I never wrote the paper, and I dropped the class.
Is school worth it for the learning? How about for the little piece of paper I get at the end?
Take it from me (as a dropout-cum-autodidact in a world where personal identity is not ontologically fundamental, I'm fractionally one of your future selves), that procedural knowledge is really, really important. It's just too easy to fall into the trap of "Oh, I'm a smart person who reads books and Wikipedia; I'm fine just the way I am." Maybe you can do better than most college grads, simply by virtue of being smart and continuing to read things, but life (unlike many schools) is not graded on a curve. There are so many levels above you, that you're in mortal danger of missing out on entirely if you think you can get it all from Wikipedia, if you ever let yourself believe that you're safe at your current level. If you think school isn't worth your time, that's great, quit. But know that you don't have to be just another dropout who likes to read; you can quit and hold yourself to a higher standard.
You want to learn math? Here's what I do. Get textbooks. Get out a piece of paper, and divide it into two columns. Read or skim the textbooks. Take notes; feel free to copy down large passages verbatim (I have a special form of quotation marks for verbatim quotes). If a statement seems confusing, maybe try to work it out yourself. Work exercises. If you get curious about something, make up your own problem and try to work it out yourself. Four-hundred ninety-three pieces of paper later, I can say with confidence that my past self knew nothing about math. I didn't know what I was missing, could not have known in advance what it would feel like, to not just accept as a brute fact a linear transformation is invertible iff its determinant is nonzero, but to start to see these as manifestations of the same thing. (Because---obviously---since the determinant is the product of the eigenvalues, it serves as a measure of how the transformation distorts area; if the determinant is zero, it means you've lost a dimension in the mapping, so you can't reverse it. But it wouldn't have been "obvious" if I had only read the Wikipedia article.)
Forces don't conspire; they're not that smart.
It's amazing how rarely people -- including textbook authors -- actually bother to point this out. (Admittedly, it's only true over an algebraically closed field such as the complex numbers.) Were you by any chance using Axler?
While I certainly agree with the main point of your comment, I nevertheless think that this particular comparison illustrates mainly that the mathematical Wikipedia articles still have a way to go. (Indeed, the property of determinants mentioned above is buried in the middle of the "Further Properties" section of the article, whereas I think it ought to be prominently mentioned in the introduction; in Axler it's the definition of the determinant [in the complex case]!)
Mostly Bretscher, but checking out Axler's vicious anti-deteminant screed the other month certainly influenced my comment.
I up voted this but I just wanted to follow this tangent.
This isn't true in all worlds where personal identity is not ontologically fundamental. It is a reasonable thing to say if certain versions of the psychological continuity theory are true. But, those theories don't exhaust the set of theories in which personal identity isn't ontologically fundamental. For example, if personal identity supervenes on human animal identity than you are not one of Warrigal's future selves, even fractionally.