<p>
[quote]
uniformly very smart people
[/quote]
</p>
<p>As opposed to pointwise very smart people?</p>
<p>Good point.
Uniformly very smart follows directly from pointwise smart. Case by case techers are obviously very smart. Thus the domain is point wise smart. The domain is also obviously compact(CalTech is finite). Since pointwise smarts on compact domains are uniformly smart, our proof is complete. </p>
<p>I think Ben is insulting our intelligence, why else would he state a result that follows trivially instead of the underlying cause.</p>
<p>LOL oh my god I need to get the heck out of the Caltech forum :D</p>
<ol>
<li>Strictly limit working hours. Maybe the above advice is too abstract for you. I have a simple heuristic which fits into it but doesn't require thinking of yourself as two people.</li>
</ol>
<p>Remember the person I described at the start of #17? A specific problem that inefficient people often have is that they think the trick to success and efficiency is to limit resting time, whereas the real secret is to limit working time. Strictly.</p>
<p>Make it illegal for yourself to work or think about work during a certain substantial chunk of each day. After you've spent some time adjusting to Tech, make a permanent rule that any work you get done has to get done, say, between the hours of 10 am and 8 pm daily (adjust based on your personal time preferences). Since you will treasure your scarce working time, you won't waste it.</p>
<p>If you feel like you should always be working or trying to, there is nothing to be gained from working harder or better. No matter what you do, you'll always be working. On the other hand, if the cost of inefficiency is failure, (or at least breaking a personal rule about your time off each day), you will be less likely to waste it.</p>
<p>This advice is NOT the same as saying that you should do a typical Techer thing: wake up at noon and think about how you have a set due tomorrow. Surf the web and lazily go to a few classes, thinking about how you should really be getting started. Look at a few problems and think about how you should start on them. Finally start in earnest at 11 P.M. and work until 6 A.M. to get the set done. </p>
<p>You might say, "Gee, this guy took noon to 11 off and then worked for seven solid hours. Great!"</p>
<p>No. Rest only works if it's guilt-free. If you are "resting" by procrastinating and thinking about how you should start the work, you will get neither the benefits of rest nor the benefits of work. This is the point of deciding in advance when your rest and work will take place. Then the rest will be guilt-free and actually useful; the work will have to be efficient if it is to get done in its allotted time.</p>
<p>A few disclaimers. Obviously, all rules must be bent every now and then in unusual circumstances. That doesn't mean they're not generally good rules. Also, some of the most successful students at Tech sometimes or always do almost the exact opposite of what I am proposing. Different strokes for different folks, but I thought I'd share something that has worked quite well for me.</p>
<p>
[quote]
Since pointwise smarts on compact domains are uniformly smart
[/quote]
</p>
<p>That's not true. For example, consider x^n on [0,1].</p>
<p>Maybe you're thinking of "continuous functions on compact domains are uniformly continuous"?</p>
<p>(Of course, functions are not equivalent to smarts. This can easily be demonstrated by the existence of smart non-functional people.)</p>
<p>Personally, I would've gone with the "functional non-smart people" example...</p>
<p>And Ben, I plan on trying out this "strictly limiting working hours" thing, so thanks for the advice (thinking of myself as two people, while perhaps analytically useful, was just too disturbing).</p>
<p>neapol1s' example is arguably more easily demonstrated in some places.</p>
<p>What's so disturbing about thinking of yourself as two people? Personally I think it's pretty cool to equate "I" and "We." But then again, I tend to talk to myself... (There's the Teacher Me and the Student Me. The Teacher Me knows all and encourages the Student Me, who sits confused.)</p>
<p>yes, most of us who can cash in here on how perfectly reasonable the notion of management is don't lend it all that much credibility.</p>
<p>(this special breed of lending just for credence and pieces of paper and certain inexplicable tangs and mystic appearances puzzles me. just imagine a world where we had all these things back.)</p>
<p>I do have to say, this thread...and the people in this thread are about a big a help as any to see if one will fit into Cal Tech. For the record, I think all you people are kooks. :)</p>
<p>I think you're all crazy too.</p>
<p>
[quote]
Spend time with my wonderful girlfriend (sometimes by flying to MIT in the middle of the term, yum).
[/quote]
</p>
<p>YUM? Come on now, Ben.... :o</p>
<p>Not advice, but a fun fact.</p>
<p>British Parliament proceedings are meant to be held in private, even though they are televised. So, if a member desires to have a secret session, he points to the public gallery and calls out "I spy strangers!", whereupon the members vote that "strangers do withdraw."</p>
<ol>
<li>Talk to a professor at least once a month your freshman year (don't be a mute frosh). </li>
</ol>
<p>There are few things about Caltech that make me angry, but the failure of many students to meaningfully engage with a significant number of faculty members is one of those things. Do not fall into this trap.</p>
<p>Caltech has a truly world-class faculty. Fewer than half of students will ever have an opportunity to interact with a group of this caliber again. Don't waste the present opportunity. </p>
<p>First, some professors actively encourage getting to know them. Nate Lewis takes his Chem 1 students to the Ath (faculty club) for lunch once a week — all you have to do is raise your hand and you get to go one week. The Master of Student Houses invites people to option dinners to meet faculty. If you take these opportunities alone, you'll end up getting to know a significant number of professors.</p>
<p>You can also just drop in during office hours. If there's not something wrong, you should have many of questions and avenues for further thinking opening up as you learn stuff in your classes. (Why is this? Is anything else known about that? Isn't there an easier way to do this?) There's no reason not to talk about them with your professors. Go to office hours and say hi.</p>
<p>Except being within a few feet of a faculty member isn't enough. You have to actually speak. Don't be shy. The most common reason I've heard for not speaking around profs and other "important people" is that people are afraid of saying something stupid and making a bad impression. First, note that it's pretty hard to actually do this. Second, being inert is certainly among the worst impressions you can make.</p>
<p>Still, getting past shyness is hard for people who are naturally not so outgoing. Here's an idea. Work your way up. Start by talking to a grad student TA. They are essentially your age and probably shyer than you are. Do this enough that it doesn't take effort anymore. Then, go to the office of hours of the friendliest-seeming professor you have. Having talked about the same type of stuff with graduate students will make you more comfortable and more confident in your ability to intelligently interact in this context.</p>
<p>It's always a little bit stressful to interact so closely with these great minds, but if you're not going to do it, transfer to Berkeley or something and save your parents some dollars. The things you gain by doing what I suggest are tremendous. You'll get tons of good guidance from people who actually know what they're talking about (in case you were turned off by high school guidance counselors). Also, the faculty are incredibly well-connected people. The number of jobs you will be offered and luminaries you'll get to hang out with if you just know some professors will probably surprise you.</p>
<p>Small caution — don't be obnoxious. Respect professors' time, etc. But if you're not talking to at least one faculty member at least once a month for an appreciable amount of time, you're erring on the low side and not the high side.</p>
<p>"I've seen people turn down $80 dinners at the faculty club (to which they were invited as guests) because they were too busy."</p>
<p>By the way, if I may add my own advice, that's usually not a great move, even leaving aside the excellent food. :-) I've had more interesting conversations with professors over meals than probably at any other time. This dovetails nicely with Ben's #19.</p>
<p>"Maybe you're thinking of "continuous functions on compact domains are uniformly continuous"?" </p>
<p>Exactly. Ben implied that the function mapping techers to smarts is uniformly continuous.</p>
<p>As for your counterexample, I don't believe it. Remember, our domain is CalTech.</p>
<p>
</p>
<p>True, true, true....I've always (don't take this "always" literally) dreamed to be in a school where a guy has to mathematically prove to a girl that he loves her...</p>
<p>And I'm being dead serious</p>
<p>This will never happen.</p>
<ol>
<li>Welcome to the big leagues. No crying.</li>
</ol>
<p>At least now and then, you'll feel like the work you're trying to do is way too challenging for you and that you might not be able to do it at all. At this point, some of you will think some or all of these thoughts:</p>
<p>[ul]
[<em>]I'm too dumb for this.
[</em>]I'm going to drop this class.
[<em>]I'm going to switch majors.
[</em>]I'm going to settle for a low grade.
[li]I should never have come here.[/li][/ul]</p>
<p>It seems implausible to even write it (at the moment), but I've heard these things enough times that I know for sure people actually do think them. Sometimes I think these things myself.</p>
<p>My main piece of advice is blunt, short, and later qualified a little bit. Avoid this pansy nonsense.</p>
<p>You got in because you were judged to be good at what you do by the most demanding standard in college admissions in America today. Chances are high that if you stretch, you can beat the problems, sets, and courses. But since this isn't amateur hour, there is no time set aside for feeling bad about how hard you are working. </p>
<p>Keep in mind that you are getting the most rigorous professional training offered to future scientists, and act that way. Self-pity is no wiser in your situation than if you were a pilot doing your first solo flight or a surgical resident wielding the scalpel. ("Oh no! So many veins and arteries! I think I'll just stop, this is too overwhelming.") What I mean is that, among other things, self-pity will make you bad at what you are trying to do. </p>
<p>In particular, you will be incompetent if you spend more time thinking about what the problem reflects about you and your abilities than you spend thinking about how you can dispose of the problem. A big difference I observe between people who methodically own their classes and people who methodically get owned by them is that the former people always focus on the problems at hand (attack mode) and the latter people focus on themselves (whimper mode). Introspection can be dangerous, as the great philosopher Bertrand Russell noted by analogy in a slightly different context:
[quote]
There were once upon a time two sausage machines, exquisitely constructed for the purpose of turning pig into the most delicious sausages. One of these retained his zest for pig and produced sausages innumerable, the other said: "What is pig to me? My own works are far more interesting and wonderful than any pig." He refused pig and set to work to study his inside. When bereft of its natural food, his inside ceased to function, and the more he studied it, the more empty and foolish it seemed to him to be. All the exquisite apparatus by which the delicious transformation had hitherto been made stood still, and he was at a loss to guess what it was capable of doing.
[ ... ]
The mind is a strange machine which can combine the materials offered to it in the most astonishing ways, but without materials from the external world it is powerless, and unlike the sausage machine it must seize its materials for itself...
[/quote]
</p>
<p>In any case, I should say that I'm not giving philosophical advice about how to live life, but pragmatic advice about how not to get your a** kicked. It may, in fact, be the case that you are not good enough to get the work done. Then, no matter how focused your work is, you will never succeed. However, a more frequent situation is that you are good enough, but self-pity or other mental weakness prevents you from fighting long enough to win. In this case, my advice will save you. </p>
<p>I soften my advice a little by saying this. When working, you should always be in attack mode. But in calmer times, when you reflect and have no pressing task, consider whether you are suited to what you have chosen to do. If, despite your focused attacks on the problems you have to solve, you don't solve them all that well, consider doing something else. But as a pragmatic matter, keep this steering device unavailable when you are fighting it out with a particular problem.</p>
<p>If you can grit your teeth and be a man about it (excuse the sexism), there are rewards. I end with this email exchange from earlier today between myself and a professor, about graduate school:</p>
<p>
[quote]
Me: Thanks for the advice. I will apply to the schools you have suggested. I was going to put Chicago on the original list, but I heard they were kind of rough on the first-years. Surely can't hurt to apply, in any case.</p>
<p>Professor: Relative to the Freshman core, U Chicago is a warm bath. With bubbles.
[/quote]
</p>
<p><em>giggles at change in word choice</em></p>
<p>...i mean, thanks.</p>