Albert Einstein once said: “The formulation of the problem is often more essential than its solution ... "
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Former Apple CEO Steve Jobs said, "When you start looking at a problem and it seems really simple, you don’t really understand the complexity of the problem. Then you get into the problem, and you see that it’s really complicated, and you come up with all these convoluted solutions. That’s sort of the middle, and that’s where most people stop… But the really great person will keep on going and find the key, the underlying principle of the problem — and come up with an elegant, really beautiful solution that works."
Solving problems, whether in physics or other disciplines, can be learned. Rafis Abazov on the TopUniversities website promotes the IDEAL methodology for his students: Identify, Define, Examine, Act and Look.
1. Identify the problem - identify the nature of the problem by visualizing the physical situation, and translating the written information in the problem into mathematical variables. Draw a diagram showing the objects, and their motions or interactions. For example, an interaction can be two objects connected by a rope.
2. Define the main elements of the problem - on the diagram, label all the known and unknown information. This allows you to translate between verbal, visual, and mathematical modes and their concrete manifestations of words, pictures, and equations. Be sure to include each item's associated units, this will help you identify what is being solved for.
3. Examine possible solutions - once the physical situation has been visualized and diagrammed, and the numerical information has been extracted from the problem statement, students can either use their background knowledge of physics and physics formulae or else they can seek out that information in class notes, instructional packets, textbooks or online resources.
It sometimes helps to work backward by saying, "I want the answer to Z, but if I knew Y, I could find Z, and if I knew X ... and so forth until you get back to something you are given in the original problem statement.
4. Act on resolving the problem - this often includes working through previous problems that are similar, and observing the solution process. Then, the known information is substituted into the identified formulae to solve for the unknown quantity. Always solve symbolically first before putting in the actual quantities. This allows you to make sure your answer makes sense in the physical world.
5. Look for lessons to be learned - by evaluating the solution process, you can formulate the lessons you've learned so that the next problem-solving project will be more effective.
A Solution in a Dream
Sometimes, other hands are at work in the solving of problems. Take chemist August Kekule's solution to the structure of the benzene molecule, and hence the structure of all aromatic compounds. After long struggling with the problem, Kekule took a nap. He dreamed of a snake that was swallowing its own tail, and he awoke with the realization that the shape of the benzene molecule was a ring.