In order to discover something truly new, one of your fundamental assumptions has to change.
This is an idea that I stole from a Ted Talk. I mean, I kind of stole it from a Ted Talk. It's not uncommon knowledge, but its implications are pretty profound. This idea represents a barrier: the barrier between what you know and what you don't. As a student, this is a barrier which I encounter often. In fact, I claim that my full time job is to take a hammer to this barrier every day of the week. However, students aren't the only people who run into this wall. Have you ever put together a puzzle? There comes a time in the piecing together of any puzzle when you feel like you've been given a bad box-- the puzzle-maker is out to get you, so he gave you a thousand ridiculously similar pieces that just don't fit together the way they should. In the end, you're almost always wrong, and the feelings of frustration, hopelessness, and betrayal (because the puzzle-maker was supposed to be on your side) that you encountered at your lowest moment now contribute to the sense of accomplishment you feel when you've put together the picture that probably shouldn't have been broken up into a thousand tiny pieces to begin with. That's what I want to talk about-- the dichotomy between despair and excitement and the way the former magnifies the latter once the barrier has been overcome.A topic of conversation that often comes up when I'm talking with my fellow science or math majors is the luxury which other students take for granted that is not needing to find a specific answer all the time. Writing papers sucks. It does. But when I sit down with a blank Word Document in front of me, at least I know that in six hours I'll have about ten, sparkling pages that I can fork over to my professor, even if it's the worst paper I've ever written. With science and math, you don't have that assurance. There was an evening when Jacob and I sat down and spent hours struggling with a problem to which we never found the answer. I filled three pages with algebraic manipulations for that one question, but eventually, we just had to move on. There's something horribly depressing about sinking hours of time and energy into a problem which you never solve. But I can guarantee that there was a physics student, we'll call him Jimjam Flimflam, sitting somewhere on the campus of William and Mary that same night who, after pulling out the majority of his hair while his roommate slept soundly in his warm, comfortable bed, landed on a solution that made sense-- and I'm sure it was glorious. I bet Jimjam Flimflam gently set his books aside, stood up from his chair, ripped off his shirt, and quietly danced around the room punching the air and yelling silently in celebration, careful not to wake his snoring roommate.
Do you know why he solved the problem and Jacob and I didn't? He found a crack in the barrier, and he exploited it, smacking it with his hammer as it spider-webbed across the whole surface, until finally, he broke through. That crack is the knowledge you have. That hammer is your textbook and your notes. And the other side of that barrier is a deeper level of understanding. The thicker the wall, the greater your frustration, but the greater your frustration, the more magnificent your victory. Some people go out and look for the thickest barrier they can find and start chipping away at it. Some people start chiseling away without realizing just how deep they'll have to go. Some people turn around at the first obstacle they encounter. It's my job as a student and as a scientist to learn to see the barrier as a chance to accomplish something. It's my job to embrace the challenge of a problem that I haven't solved. One day, it will be my job to embrace the challenge of a problem that no one has solved.
However, embracing the challenge does not mean overcoming the obstacle. There are humans who have spent their entire existence on problems that they never see solved, just like there are students who spend their entire evening on problems that they never see solved. But that's okay. There can be joy in the struggle. I've never won a race, but I loved running track. I've never finished writing a book, but I've had a great time writing chapter one. I've never beaten Arjun in Melee, but I enjoy playing him. You get the idea.
Here's my advice to you: learn to appreciate the puzzle. Have fun taking every likely candidate for the gap in your sky and twisting it every way possible before putting it back on the table. Smile at the ridiculousness of the notion that the puzzle-maker is pitting himself against you (but don't completely discount the idea). Laugh at the simplicity of the solution when you find it. Breaking down the barrier isn't about scribbling down the correct numbers on the page-- it's about the understanding you gained from finding them, and that's something you can't get from an answer key.