Frankly, a major thing that Caltech admissions looked for is a very strong interest in engineering and science. It's gotta be in your bones, or you ain't going to thrive there. With their limited resources (it's small) it's just not pragmatic to accept those with a more casual interest. And really, why would you want to go there if you weren't? After all, 9 out of 10 classes were 90% math, math, more math, and math.
