Problems arise not just in sciences but also in everyday life. As a result, learning how to deal with them is of vital importance. There are two classes of strategies for problem solving: algorithms and heuristics. Algorithms are procedures that guarantee the correct solution if properly applied. Heuristics are convenient procedures that do not necessarily yield the desired answer every single time. At first sight, algorithms seem much more preferable. However, their restrictiveness is their disadvantage. Algorithms tend to be specialized methods restricted to a single group of problems. Heuristics, on the other hand, may be applied to a variety of situations. In addition, due to their highly technical nature, algorithms may not be available to everyone.
Here is an example of a problem I recently solved. We had to use a physics simulation to guide a electrically charged particle towards the goal without colliding with any of the obstacles. The practice and first two levels of this ‘game’ are not that difficult. In fact, I believe that one does not need to be a high school student to solve the practice level problem. Nevertheless, Level 3 is truly challenging: the particle has to be directed towards the goal while avoiding up to two long barriers in the process. Here I used some heuristics my AP Psychology textbook suggested. Unfortunately, yet naturally, not all trials yielded the desired outcomes but established the foundation for my discovered solution. I tried changing the mass of the particle and directing it out of the area. (Switching the particle’s charge is another alternative. However, this will probably not make any difference.) After all, the game does not forbid the user to do these things but allows them to modify these settings. I also tried to break the problem down. I tested ways in which I can guide the ‘hockey’ away from one barrier an on a path to avoid another. This works delightfully well. The ‘hockey’ moved in a path resembling Archimedes spiral and went into the goal.
I believe this solution is beautiful for two reasons. First, it accidentally gives me a glimpse into how particle accelerators (such as the Large Hadron Collider) work. Second, it is exact. Even the slightest deviation of the positions of guiding electrically charged particles amends the path of the ‘hockey’ and usually it will miss the goal.
It took me about an hour to solve Level 3. A possible reason for this is my lack of in-depth understanding of electromagnetism. My friend, Peter, discovered that there is a single arrangement of guiding particles that works for all levels. When I asked to see his marvelous solution, however, he said he never wrote it down. His dislike of physics is probably the reason why. 😦