Improving your Problem Solving
Suppose you had to produce different sounds ending in "ab". Your conscious reasoning could go through the alphabet and produce the sounds bab, cab, dab, fab, gab, hab, jab, etc. To me, that doesn't FEEL very creative. However, if you define creativity as producing something new, your answers fit the definition of creative. So that is one source of creativity -- methodically combining known pieces into new combinations.
Another source of creativity is error or randomness. Once I had to write original melodies for an experiment. If I just thought up melodies, they didn't seem original. So instead, I wrote some notes nearly at random. The outcome was not pleasing to the ear, but it was original. (I then modified the sequences of notes so that they sounded better.) So random error is another source of creativity.
The Inferential System is a third source of creativity. Your Inferential System doesn't try to be creative. It just constructs a conclusion consistent with its input. When there are several solutions to a problem, your Inferential System will tend to produce the most common familiar solution. In other words, your Inferential System would prefer not to be creative. For example, if you ask someone how to get to New York, their first answer probably will probably be something very uncreative, like flying.
But suppose there is no uncreative solution to a problem. Your Inferential System will still try to construct a conclusion consistent with its input. When it succeeds, the answer is creative. Thus, the saying 'Necessity is the mother of invention' applies to the Inferential System. Unlike the creativity produced by random error, the creative answers from the insight are also useful -- they were produced to be consistent with the to-be-accomplished goal.
In real life, you usually do not need the "random-error" creativity. What you need are solutions to your problems. You don't care if the solutions are creative, but when you can't find a noncreative solution, you need a creative solution. So you need the creativity of your Inferential System. Catering to your Inferential System is how you add creativity to your life.
Catering to Your Inferential System
Sometimes you have been taught how to solve a problem and you can recall and use that method, so no insight is needed. If you cannot recall how to solve the problem, you can continue trying to recall how to solve the problem. But to be good at problem solving, you have to also be able to use your Inferential System to produce insights.
However, if you do not know about your Inferential System, you will not cater to the special needs of your Inferential System. You will cater to the needs of conscious thinking. Your Inferential System might still be able to solve the problem, but it will not be as effective as if you had catered to it.
First, when you don't find a solution, you will not see any benefit of your working on the problem. You will think that time has been wasted. In fact, I think one of the great skills of problem solving is simply being able to work on a problem. I teach math to grade-schoolers. A poor problem solver will just give up when the problem can't be solved consciously. Essentially, they try to remember how to solve the problem, and when they don't, they are done. Skilled problem solvers find things to keep working on the problem. In fact, there is an element of "play" to working on a problem. I become interested in something about the problem that is not obviously related to solving the problem, and I investigate that. I meant really be off topic, but more likely I am learning something, and this something, whatever it is, might help me solve the problem.
You also will not see any value in resting (incubation) -- that too is just wasting time. In fact, if you are tired and want to rest, your Inferential System probably needs a rest and cannot effectively work on the problem.
Many people find themselves staring off into space while they are trying to solve a problem. This is not resting; this is not a failure to stay on task. Instead, the feeling is of intense effort. What is happening is that your Inferential System is working hard on the problem. Your brain is filled with thoughts and activity, it's just that none of those thoughts or activities are conscious. If you thought you had to solve the problem consciously, you would see staring off into space as a waste of time.
If you are using conscious techniques to solve a problem, it probably doesn't matter whether you are frustrated or not. If you are using your unconscious, the frustration will interfere. Good problem solvers learn how to deal with frustration, including leaving the problem for a while (incubation). More generally, I think that if you want to maximize the probability that your Inferential System will solve the problem, you need to find a quiet space in your mind, and you can't be directing things consciously. Instead, you wait for an answer.
Think of it this way. You, consciousness, are the boss. Your employee, the Inferential System, is a brilliant but possibly erratic problem solver. You might worry that is not working on the problem. You might worry that it is not using time effectively. You might worry that it is not making progress. But if you are hoping it will solve the problem, you have to let it do what it wants. It thinks something is interesting? You have to let it work on that. It is deep in thought? You have to let it think. It doesn't want to work on the problem? It is probably a waste of time to work on the problem.
What you cannot do is tell your Inferential System how it should work on the problem, because you (your consciousness) don't know. Especially, you cannot expect your Inferential System to solve a problem the same way your consciousness does. Instead, you cater to the apparent needs and desires of your Inferential System.
"Brainstorming" is a technique -- or really a collection of techniques -- designed to help a group of people produce creative and effective solutions and ideas. You can also use it by yourself. I think it works great.
Brainstorming is divided into two stages. In the first stage, people suggest whatever ideas or solutions they can think of. People are supposed to say whatever comes to mind, no matter how silly or stupid the idea might seem. In fact, ideally people are not even evaluating their idea, they are just saying it. To encourage the expression of ideas, one of the most important rules of brainstorming is that there is absolutely no criticism of ideas in this first stage. Thus, there is no conscious inhibition of ideas -- hopefully people are saying every idea as soon as it becomes conscious. Thus, brainstorming creates a direct interface between peoples' Inferential Systems.
These ideas are immediately written down. As will be discussed in the chapter on the Zeigarnik store, when something is written down, people don't have to remember it. If you are trying to remember your idea so you don't forget it, you are using up the resources of your Inferential System on that idea. Then your Inferential System will be less likely to think of other good ideas. So you write down the idea, then you can forget about it and devote your whole Inferential System to new ideas.
Normally, when an idea produced from the Inferential System becomes conscious, people think about it before saying anything. They might modify their idea so that it is better, or they might decide not to mention their idea -- if you are in a group of people trying to think of an idea to solve a problem, you are not going to mention your idea unless you think it is a practical solution to the problem.
Brainstorming breaks this inhibition. So in brainstorming, people end up saying ideas that they otherwise would have rejected as unsuitable. But what is the value in this? What is the value in saying an idea that doesn't solve the problem?
Well, perhaps nothing. But the Inferential System doesn't output thoughts at random. Instead, when your Inferential System produces an idea, there is some reason for its output. Usually, it is a good reason. So, your idea, even though it is impractical and you can't see how to make it work, might be the start of a good idea. If you tell it to everyone else, the idea goes into their Inferential Systems, and they might be able to make it work.
To give a trivial example, suppose the task is to think of a word with 6 i's in it. If we are brainstorming, I will say the first word that comes to mind. Perhaps I say 'Mississippi.' Then you might suggest 'individual'. If we weren't brainstorming, neither one of us would say either of these answers, because they are obviously wrong. In fact, Mississippi isn't useful, but 'individual' has the useful idea of starting with 'i'.
Your suggestion of "individual" might help me think of 'indivisible', which isn't correct but has 4 i's. I say that, then you think of 'indivisibling'. That's not correct, but adding an ending is a good idea, and I might then think of an ending that does work: 'indivisibility'. If either you or I had just said answers we thought were correct, we would not have found the correct answer. Working together, we solved the problem.
Of course, there is a time and place for criticism and evaluation. That time and place is the second stage of brainstorming, where each idea is reconsidered, developed, and evaluated.
Using the Principles of Brainstorming
I suspect that once you understand the principles of brainstorming, that you won't follow the rules of brainstorming in a formal way. Instead, you will follow the principles of brainstorming but short-cut the exact steps. That's fine. But least once, you should probably follow all the rules of brainstorming.
For example, when you have an idea, when someone has an idea, you should not automatically reject it because it doesn't work. Instead, you can think about it maybe being just part of a useful idea. I frequently find that when I give ideas this consideration, they become useful to me. And of course, it is not only other people's ideas you should examine, it's also your own.
The third point was catering to your Inferential System if you want to find creative solutions to problems. Several activities during problem solving -- working on the problem but not solving it, exploring what interests you, staring off into space, resting, unstructured mulling -- make sense once you realize that insights are produced by the unconscious Inferential System.
A fourth point was to realize that ideas from the Inferential System might be useful parts of a solution even if they are not the solution itself.
These discoveries of course were creative. The final discovery wasn't produced by random error or consciousness' formulaic creativity. Instead, these great discoveries usually occurred in a sudden moment of insight. In other words, mathematical and scientific contributions are usually produced by creativity from the Inferential System. So the Inferential System is an important and powerful source of creativity.
Prior to the insight, there is sometimes a second stage called incubation. During incubation, you are not making any active efforts to solve the problem. You might be walking, resting, or whatever. If you are in a hurry to solve the problem, your conscious mind might think this is the wasting time stage.
But incubation might be important for your Inferential System. First of all, your Inferential System might be tired and need a rest. After rest, your Inferential System can make a fresh start on the problem.
The incubation stage also allows you to mull over the problem in an unstructured way. A good incubation activity doesn't have much conscious thought. Traditional activities for incubation including lying in bed, riding a bus, taking a walk, or taking a bath. Without any conscious control, your Inferential System can think about the problem without interference. You will be consciously aware that your Inferential System is thinking about the problem, though if you don't pay attention you might not remember it doing so.