February 18, 2012
I really like the story about Archimedes realizing that he could calculate volume by using water displacement. The philosopher/mathematician’s royal relation wanted to know whether a commissioned crown had the density of gold. Archimedes realized one could find the volume of any object by measuring water level before and after the object is submerged in water, and noting the displacement. It was interesting to me that this was compared to the behavior of monkeys reaching for bananas. It seems to me that the “strokes of genius” all share the common trait of being straightforward ideas that solve the problem with a small number of steps, but from a direction that had not been considered previously. This makes me wonder if these insights are limited to “simple” ideas, and if there is a limit to the complexity of an idea that is the result of one spark of inspiration.
I also found it interesting that the common brainstorming technique of recording as many different ideas as possible supported Brown’s 1981 study that claimed “output interference can explain inhibition of retrieval from semantic memory. As we’ve mentioned in class, engineers often latch onto the first solution that makes itself visible. I wonder if perhaps these students have a harder time bypassing the blocks your mind imposes after it has generated an acceptable solution to a problem. I think that engineers and left-brained people (myself included) can really benefit from brainstorming activities that attempt to pull more items from semantic memory.
Creating a system that would take specific problem space and help users work past cognitive blocks would be an interesting final project for this class. For example, if the prompt was to create the a method that tried to determine whether an x, y coordinate existed within a two dimensional shape, the system could ask the user to build a function that solved the problem by determining whether the point was within the shape, then write a second function that decides whether the point is outside the geometric shape. By trying different solutions, you could arrive at a more logical or more efficient algorithm. In the example above, it turns out it’s actually much simpler to prove the point is outside the shape then it is to prove it is inside.