Active vs. Passive Problem Solving

Adar Kahiri
July 31, 2020

If you were relatively smart as a kid or teenager, chances are a lot of the early math you were exposed to in school came pretty easily to you. As a result, you were able to solve most problems almost without thinking. For me (someone with a somewhat above average ability to solve puzzles), this manifested in being able to solve most problems after a few seconds or minutes by basically just staring at them until something clicked in my head and I 'got it'.

As I started getting into more serious mathematics, this became a pretty major roadblock in my ability to problem solve. Most of the problems I now had to solve were no longer trivial enough that I could just stare at them until the answer came to me. I now had to actively experiment and spend a lot of time in order to even make progress.

To add to the problem, each time I unfruitfully thought about a problem for a few minutes, my brain would 'check out' and look desperately for something to be distracted by. This obviously doesn't help solve problems–quite the contrary. But old habits die hard, and this is still a major roadblock for me, one that significantly impedes by ability to solve problems, and subsequently, to learn math and other problem-solving-heavy subjects. Unfortunately, I don't think there's an easy way to fix this besides just solving a lot of hard problems and reducing your exposure to attention-atrophying inventions like social media. Both easier said than done, but until we're able to reliably manipulate our brain chemistry they're all we've got.

Notes:
* Often when solving problems, key realizations will still 'hit you', but it's commonly after tens of minutes or hours of thinking, playing around with various conditions, thinking about edge cases, etc. Those realizations are the result of "inspired guesses".

* The internet and other aspects of modern life also certainly contribute to my distraction.