I doubt I will read a book more difficult than this this year, and any attempt to summarize it is going to resemble a third-grade book report more than an evaluation of the ideas contained therein. But I have to try anyway, so.
EVERYTHING AND MORE is a discussion of how mathematicians have talked about and used the concept of infinity, leading up to the work of Georg Cantor, a Russian-German mathematician whose ideas on infinite sets were controversial back then but paved the way for almost all modern discussion on the subject. The book lays out the genesis of his ideas through a lot of proofs and definitions, along with commentary on the mathematicians involved, starting with the Greeks (whose stance on infinity was "Don't go there," basically).
I would love to be able to explain Cantor's theory, but the math is frankly beyond me. Here's a very chopped-down, simplified-to-the-point-of-nonsense summary: Imagine you hear two kids arguing about the amount of imaginary money they have. One says "I have $10!" and the other says "Well, I have $20," all the way up until one says "Well, I have infinity dollars" and gets the response "Well, I have two infinity dollars." Then there is hitting and/or crying. Cantor's work deals with how you can mathematically express and manipulate infinite sets -- including adding or comparing them -- without, obviously, being able to assign them a numeric quantity.
I'm glad I made time for this in my Summer of DFW but I'm sure not all those who enjoy the writer should seek this out. The recognizable Wallace style spills through in conjunctions and footnotes, particularly the habit of marking more arcane/ less necessary digressions as IYI (if you're interested) and passing on unexplained jokes from his beloved professor Dr. Goris, but the only character in here is Cantor, and this isn't a biography by any means. This is straight math almost all the way through.
I will break here and admit that I was not a very good math student. I got pretty good grades in it, but it never came easily to me, and I would get enormously frustrated and give up frequently. I survived calculus only through the help of patient friends and a really great math teacher. I ought to send him a copy of this book, though he has probably already read it.
Given that my math education stopped around multivariable calc, and that the most math I do now is in Excel formulas, I was surprised to be able to follow along all right until about the last 50 pages of the book. At that point a lot of the footnotes start to make comments like "Printing the proof of this point would take another hundred pages, and would probably be over the heads of most of you, so just take it on faith." I remember one paragraph that began with "So now that we've proven X" and I thought to myself, No you didn't! I plodded through, but I didn't enjoy that aspect of it.
Those who will not be daunted will probably consider where this fits into the DFW oeuvre. Wallace mentions that he came to write this book through an interest in technical writing, which I assume is related to the background research he was doing into the IRS for THE PALE KING. In an alternate existence he might have become a really good math teacher with a book or two in a drawer.
3 comments:
Oh man, I own this and was hoping I'd be able to grasp it, but as a poor math student now I fear it'll be beyond me too. Regardless, I need it in my DFW collection and maybe, some day.
You were always better at math than you gave yourself credit for, and my guess is you still are.
Which reminds me of one of my favorite experiments (no, not one of those): You take some children, and divide them into three groups. You give all three groups the first half of some sort of assessment: multiple choice SAT-like questions, spatial reasoning tasks, whatever.
The first group, you don't say anything to. They're your control.
The second group, you praise for how smart they are.
The third group, you praise for how hard they tried.
Then you give them the second half of the assessment.
The first group, your control, shows no discernible improvement, or possibly a very minor one, just from the experience of doing the first half.
The second group does significantly worse on the second assessment than they did in the first assessment, and the third group does significantly better.
The interpretation is that the second group, knowing that they are supposed to be smart, panics when they encounter adversity. The third group, knowing that success comes from perseverance, is unfazed by any difficult questions they encounter, and placidly works on them until they get an answer.
The implication? We need to do a better job teaching our children that struggle, rather than a sign of weakness or stupidity, is a good thing: if you never have any difficulty with a material, you're not going to learn much from it. Furthermore, just because something is hard the first time you try it doesn't mean that you're doomed and will never master it. We can't control how intelligent we are, but we can certainly control how much effort we put into a task.
Since I read this study, I for one have been very careful not to praise any children's talents, only their efforts (not that I encounter that many children).
Elizabeth, I like the findings behind that study. One of the barriers to implementation, however (and this would be a hell of an experiment to design) is that it is much easier to quantify success than effort. A student can be working hard on something but seem not to be, or vice versa.
To which I guess the authors would say that it doesn't matter how much effort is being put in, only that your praise emphasizes the effort that's there, whatever it is.
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