Problem solving

- [Narrator] What's the best route to your new job? How do you decide who to marry? How do you satisfy your growling stomach? Each of these questions represents a problem that we sometimes face. You may not even realize it, but you are an excellent problem solver. Just a few seconds ago, you figured out how to start this video, and that may not feel like a huge accomplishment compared to, say, coming up with the theory of relativity, but every time you engage in an action or thought pattern to move from your current state toward a goal state, you're solving a problem. Problems can be generally broken down into two categories; well-defined problems and ill-defined problems. Well-defined problems have a clear starting and ending point, such as how to make it bright in a room that's currently dark. You know exactly what you're starting with and exactly how you wanna end up. Ill-defined problems, on the other hand, have a more ambiguous starting and or ending point, such as how to live a happy life. It's something you can still try to solve, but you may not know exactly what the outcome will look like. Because you face such a variety of problems each day from the simple to the complex, your brain has several different ways of solving problems. One method of solving problems is trial and error. This means that you just take random guesses until something finally works. For example, imagine you're trying to log in to an email account you haven't accessed in a while. You know that the password is eight numbers long, but you don't remember what it is. If you're using the trial and error method of problem-solving, then you would just try any random combination of letters and numbers until something works. As you can probably tell, that approach would take forever. And with trial and error, you're not necessarily keeping track of what you've already done, so you could get lucky and hit on the right password early, or it could take a very, very long time. A more methodical approach would be to use the algorithm strategy. An algorithm is a logical, step-by-step procedure of trying solutions until you hit on the right one. So if we're still trying to get into our email account, we might start with one, two, three, four, five, six, seven, eight, and if that doesn't work, we'll change one number at a time. Two, two, three, four, five, six, seven, eight, then three, two, three, four, five, six, seven, eight, and so on. This could still take a really long time, but you are guaranteed to find the right solution eventually. Usually though, we don't have time to try every possible solution, so a more common method of solving problems is to use some sort of heuristic. A heuristic is a mental shortcut that allows us to find a solution more quickly than the other two methods we've talked about so far. For example, you probably made a password out of familiar number combinations, so you might try something that includes your birthday or something else that stands out in your mind. This drastically reduces the number of solutions we need to try because it eliminates any unlikely ones right off the bat. Heuristics don't guarantee a correct solution, but they do simplify complex problems and reduce the total number of solutions that we'll try in order to get to a more manageable number. Since heuristics are so common, let's talk about a few different ones that work for different types of problems. One type of heuristic is means-end analysis. This heuristic means that we analyze the main problem and break it down into smaller problems. Then we attack the biggest subproblem in order to reduce the most difference between our current state and the goal state. If you're planning a trip to another country then, the biggest problem might be the distance between you and that country, so your first step would be to book a plane ticket. And that creates another group of subproblems, which you solve one at a time, usually starting with the biggest one. A second heuristic is working backwards. Now, with means-end analysis, we were trying to work from our current state toward our goal state. With working backwards however, you start with your goal state and use it to suggest connections back to your current state. This strategy is commonly used in mathematical proofs. Another example of it is if you've ever done a maze and started at the end and worked your way backwards toward the beginning. Let's try to solve another problem. What if I gave you these six matches and asked you to use them to draw four equilateral triangles? Go ahead, give it a try. If you had trouble solving that problem, you're not alone. Most people get stuck on thinking about this problem in a two-dimensional way. This act of getting stuck is called fixation. The answer, though, requires you to think about the problem in three dimensions. You need to create a triangle pyramid with the six matches in order to form four equilateral triangles. If you did solve that problem, try to think about how the solution came to you. You probably didn't do a series of step-by-step arrangements of matches, and the heuristics we've talked about don't quite work. What probably happened is something called insight, which is that sudden aha moment when the solution just pops into your head. Insight is tricky, it's hard to predict, and harder to encourage, particularly when you're fixated on seeing a problem from the same ineffective perspective. If you do get stuck on a problem, you can let it incubate, or just sit in your mind while you're not really thinking about it. Often, insight comes after a period of incubation. It's like when you're trying to think of the name of that actor in a movie you saw, but it only comes to you later that night after you thought you stopped thinking about it.