"Problem Solving Has No Absolutes"

Solving a problem that hasn’t been solved before, requires a change in perspective and connecting something known with something unknown. One idea is to view the problem without preconceived bias, which, as we all know is nearly impossible unless you have no experience in the world whatsoever. The term “functional fixedness” is an inability to see an object in different ways or to see its different possible uses. Children do this naturally, but as we mature, we tend to lose this ability. One way that mathematicians use to help solve problems is to give each piece of the problem a name. That name helps us to connect the pieces together and see how they interact. A+B=C is just an abstract way to connect things.

Let’s take a coin for example. We all know that coin has two sides and we’ve given them names. One side we call heads and the other tails. How we arrived at these is immaterial. If we are asked to predict if a coin lands on one side or the other, you may say that there is only one answer to the problem. It's 50-50. If you say this, you would be correct in one sense called the Bayesian view. But a different person might look at this coin and say, that coin can only land on one of two positions, either heads or tails, so there is either a 0% chance or a 100% chance and that will become clear once the coin is seen. This would be the view of the frequentist or the empiricist. I now have three possible answers to a question that appeared at first to be closed but as you can see, asking the right question has a lot to do with the direction that we pursue.

Ask the right question. Some people say that there is an imbalance of women CEOs in this country but what does one have to do to become a CEO? Basically, you have to give up your life for your company, spend 60 to 80 hours a week there and devote your life to it. So instead of asking why there aren’t more women CEOs one might ask why men are insane enough to give up their lives in order to attain this position and we might question their set of values.

We could take glass of water and define it by the volume of water inside of the glass, or I could define it by the empty volume within the glass. Is it ¼ full, ¾ empty? That depends on which problem you are trying to solve. One view looks at positive space and the other looks at negative space. We could say that the negative space is the space of solutions that don’t work, for example, but if we were to map out all of those solutions that don’t work, there’s a good chance that they will point us to a solution that will work now that we’ve eliminated the others. Solutions that don’t work can be useful.

Perspective is the way that we look at things. A glass is a circle from the top and a rectangle from the side. Problems tend to have many sides and they all must be examined. One side is open, the other is closed. A relationship is how these interconnected things work together. The glass constrains the water so that it doesn’t run all over the table. Without the table, the glass would fall to the floor. When we put these together, we are said to have a system.

Problems will always be there and many of them, we’ve seen before in one sense or another. Insight comes when we choose to view the old problem through new eyes and apply what we know to what we don’t yet know.