<p>asdjkl – I changed my mind. Your willingness to listen suggests that you are not cocky beyond hope in the way that I am. :-D.</p>
<p>I think it’s great that you spend your free time trying to figure things that interest you out in math and science. My only piece of advice is keep that spirit and take Paul Graham’s advice – treat high school as a day job that you do well. (Let’s not kid ourselves, you’re smart enough to pull straight A’s in history and lit, why not do it so that you don’t have to think about that stuff and worry about its impact?)</p>
<p>It’s also good your passion will show through in your writing and recommendations. Just tamp down your contempt for high school when you write the application (it’s okay if there’s a little, but too much is a turn-off).</p>
<p>If you can honestly say in your application that when you come to Caltech you know you will have to give it your all (and mean it!), and if you can say that you’re looking forward to it, then I think your application has a chance.</p>
<p>Best of luck, and come back with any questions. The people here will be glad to help.</p>