I have a deep aversion of the "puzzle" concept. Delving into a problem is a very taxing process for me, and I just refuse to do it for the gratification of solving something that people actually expected me to solve fairly quickly. My brain can only internalize so many concepts in one day (like, maybe 2), and I can't waste this resource just so I can feel good about solving a small little problem.
Thus, when I read a recent blog post about how a theorist and two mathematicians spent their time after meeting randomly on a bus tour, I felt as if I was reading about an entirely outlandish experience, and I couldn't stop thinking "Why the heck... I can't believe they actually did this..."
Of course, I reminded myself that many people seem to love puzzles. An old friend used to say that "the brain doesn't rest, it atrophies." My adviser's office is the nightmare of any claustrophobic person: it is overflowing with small physical puzzles. I often fidget with them when I'm talking to Erik. The fact that I usually "solve" these problems by 5 minutes of random hand movement only confirms that I should never think about such things :)
My brain applies the same self-defense strategies when it comes to olympiad problems, which is why you don't see too many olympiad problems on this blog. When I originally read the Dwarves problem, I said "DP" (dynamic programming) and stopped. Only the next day, when 3 IOI guys claimed they really couldn't solve it, did I persuade myself to think about it...
Tuesday, August 12, 2008
Puzzles
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10 comments:
I agree! (I am a theorist myself.) I think this is the case for many people who do math for a living -- they can't stand to invest time in a problem for trivial reasons! Some biologist friends of mine like sudoku puzzles, but I can't bear to do them in my spare time!
I find the 'muscle' analogy more convincing than the 'limited resource' one.
While on the bus (or after too many beers for that matter) you can discuss about (1) the weather and related topics, (2) about puzzles, or (3) about a hard problem. The third option is most likely unfeasible. In my opinion both (1) and (2) are quite appropriate and I have a hard time believing that you are 'consuming' your brain doing puzzles.
Now, if you are in an environment were you could do serious work but instead you solve puzzles then, yes, you are wasting time.
PS: I dislike sudoku too, even on the bus.
I've heard an opinion, that it's impossible to be good at science and at playing chess (or any other game) at the same time.
OTOH, this clearly shows that you are so narrow-minded with this concept of "serious work", that you entirely miss such an important aspect of our culture as solving puzzles. Pitiful. ;-)
I've heard an opinion, that it's impossible to be good at science and at playing chess (or any other game) at the same time.
Indeed, Einstein told some (really good) chess player once that he's "wasting" his brain. Being very good at chess and being very good in research both require huge amounts of uninterrupted concentration. The context switch overhead is simply too big.
But... puzzles that take a few minutes? How can they possibly "consume" your brain?
I enjoy puzzles, but I am typically not all that good at them. For whatever reason, I seem to lack the knack for thinking outside the box enough to solve most puzzles before I become bored. I certainly don't mind other people enjoying them, and I'm happy to tag along on puzzle hunts, but it isn't my deep satisfaction. Given some free time, I'm usually reading a novel (or catching up on a few papers).
On the other hand, I do love hearing about a problem that is new to me and still open. Even the flimsiest of motivations is usually enough to keep my interest. I don't have a great explanation for why this should be so. After all, unless the problem is in my area or I have some insight into it, it should be roughly as useful to me as a puzzle.
Puzzles are often about finding an elegant solution to a problem that either seems impossibly hard, or just plain impossible. Training yourself to find the elegant solution to such problems could help in research; only recently was there a blog post about much time being spent on complicated solutions to a particular problem, only to find out later that a very simple solution existed.
If you know the profile of my work, you know it's a lot about giving simple solutions to problems that people found impossible. So by my own example I can argue that training yourself on puzzles is not always correlated with finding simple solutions in research :)
Hmmm ... regarding puzzles, I am not that good at the ones that seem to be in vogue in certain circles (such as MS or Google interviews) in general, and I attribute some of my difficulties in CS theory to this. I seem to be unable to consistently think nonlinearly, if that makes any sense. If a problem requires nonlinear (out of the box) reasoning, I might not come up with such reasoning as fast as some other people. I remember asking a study partner in grad school who did better than I did in the theory classes, while spending less time studying the material than I did, what he attributed his success to. He said it was because he solved a lot of puzzles. Puzzles helped him to formulate solutions, and made it less likely that he'd get stuck.
I did solve puzzles when I was younger, but it was not part of an organized approach to cultivating mathematical maturity, or anything like that. It was just something to pass the time after finishing homework, on a rainy day, when there was no one to play with, etc. But I might just as easily have done something like read a (nonmathematical) book, draw a map, play a musical instrument, or play solitaire. I didn't have parents with mathematical backgrounds, or access to people who knew anything about the field of CS (what it was in the 1960s and 1970s, or what it might become), so there was no one to guide or motivate me to do more puzzle solving than was necessary to hold my interest (and I'd venture to say that I enjoyed reading books and playing music as much as solving puzzles). Unlike others I've read about whose parents either recognized, or knew other people who recognized that their child had a talent that could be developed through something like math olympiad training, math camps, etc., they were happy to let me do whatever I wanted to do after I finished my homework, as long as I got good grades.
To make a long story short, I had some trouble in classes at MIT and UCLA that required this sort of nonlinear, puzzle-solving approach. Sipser's class was one example; another was graph algorithms at UCLA taught by Parker. It bothered me quite a bit that I put out a lot of effort to try to do well, but often came up short of my expectations.
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