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It should be to no one’s surprise that humans are of the most intelligent creatures alive. But what warrants this “intelligence”? Arguably humans are the best problem solvers, and this is accredited to our large and extremely developed prefrontal cortex. Figure 1, shows the prefrontal cortex, in blue, of several mammals. The prefrontal cortex holds a major role in the organization of behavior, specifically the top and front portions as well as the right hemisphere structures. What exactly does this mean? The increased capacity for organizing behavior as well as the ability to think forward about the future and how one action will affect those prior, other functions of the prefrontal cortex; allows humans to solve difficult problems other species would be vexed by.
What exactly is problem solving? Problem solving can be categorized as having these three characteristics: goal directedness, sub goal decomposition, and operator application. Goal directedness is an actions clear organization towards a goal. Sub goal decomposition is breaking the original, large goal into multiple smaller sub goals. Operator application is applying operators to these sub goals; an operator is an action that will help go from one sub goal to another. Essentially operators are the methods we use to solve problems and proceed from one goal to the next.
If operators are so essential to problem solving shouldn’t we know where they come from? Naturally some are taught to us, the dreaded quadratic formula from algebra 2 being one. Some operators we discover ourselves, an example of this would be like having a question you have no idea how to formally or “correctly” solve but through some playing around you work out the right answer. Others we learn from observing another person or even an animal preforming a task of similar structure. Analogies are used to take the operator from one task and apply it to another. This is how observed operators of a task can be used later with a different similar task.
There are several heuristics of problem solving. Analogies are the first, which I touched on, in the previous paragraph. Hill-climbing also known as difference reduction method, is the second one I’ll speak on. This method consists of problem solvers using operators that change the state of the problem to another such to reduce the total difference between the current state and the goal. Means-end analysis is another, this consist of making up multiple sub-goals such that the current means of operation will fit the end or goal of the new sub goals.
So how will one know which of the heuristics or methods is best to use for any given problem? This is the true glory of the prefrontal cortex; there is a level of intuitive knowledge about how to go about solving a problem that every human has. This knowledge comes from past experiences that we don’t consciously recall but are rather guidelines processed by prefrontal cortex. Often times problem solvers must utilize a combination of these heuristics. In the Tower of Hanoi problem the participant must move from a starting set to a final set in the least amount of steps without placing a larger ring on a smaller one. So the two heuristics that must be used together are means-end analysis and hill-climbing. Hill-climbing or difference-reduction method must be used to acquire the minimal steps until completion. While means-end analysis must be used to set up sub goals to go about moving the disks without placing a larger disk on to a smaller. The benefit of combining the two methods is that by applying hill-climbing to the sub-goals you set with means-end analysis you don’t run into false summits and you complete each sub-goal in a minimal amount of moves.
While it is beneficial to use these heuristics together it is also necessary, because each has a distinct downfall. Analogies are great for explaining how to complete a task using another task that someone is already comfortable with. For example, writing a scientific article is like writing any other essay. The trouble with analogies are they are often used too broadly, yes writing a science paper is preformed the same as writing a paper in an English lit class, but the minor details of what should be expected within the writing are not specified in the analogy. Hill-climbing is also tricky. Users of this heuristic are often so concerned with reaching their goal in the shortest time possible they often do not realize they have set themselves up for disaster. Hill-climbing goes hand in hand with backup avoidance where the problem solver is focused on going forward so much that they refuse to move backward in order to progress further forward. The combination of these two factors often result in “false summits” where problem solvers reach a point where they can progress no further towards their goal without first going backwards leaving the user stuck where they are. A perfect example is that from Cognitive Psychology and Its Implications by John R. Anderson, which quotes Köhler (1927) where he “described how a chicken will move directly toward desired food and will not go around a fence that is blocking it.”(Anderson, 1980). Means-end analysis also has a huge downfall. Problem solvers who utilize this often run into a problem with creating too many sub goals. Overwhelming them resulting in them not being able to complete all of these sub goals in order to reach their final goal.
The trouble of problem solving is that the general methods used create new problems in the process. Humans’ highly developed prefrontal cortex works in many ways to help us process situations and overcome the pitfalls of problem solving heuristics. This solidifies humans’ slate as the top problem solving species.
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