Creating Genius, Part II

Last time, I commented on Richard Hamming's talk to Bell Labs in 1986 entitled "You and Your Research." Let's continue.

He has some interesting things to say about creativity--that mysterious source of new ideas. He gives some advice that will seem familiar to any mathematician:

If you are deeply immersed and committed to a topic, day after day after day, your subconscious has nothing to do but work on your problem. And so you wake up one morning, or on some afternoon, and there's the answer. For those who don't get committed to their current problem, the subconscious goofs off on other things and doesn't produce the big result. So the way to manage yourself is that when you have a real important problem you don't let anything else get the center of your attention - you keep your thoughts on the problem. Keep your subconscious starved so it has to work on your problem, so you can sleep peacefully and get the answer in the morning, free.

This seems to be a common phenomenon. For me personally, I've had this experience many times when programming or doing research intensively. When it happens, there is a real sense of breakthrough--of understanding something you didn't before. Not every time is it sustained--sometimes my subconscious gives me the wrong answer. But more often it's correct, and mysterious about how it got there.

Seeding creativity is important. "You can't always know exactly where to be, but you can keep active in places where something might happen." Hamming means looking out for the important problems.

If you do not work on an important problem, it's unlikely you'll do important work. It's perfectly obvious. Great scientists have thought through, in a careful way, a number of important problems in their field, and they keep an eye on wondering how to attack them.

Part of the seeding comes from having an open door, Hamming says, both as metaphor and literally. Tolerating distractions is the price of staying in the conversation.

Taking the big view is also important.

You should do your job in such a fashion that others can build on top of it, so they will indeed say, "Yes, I've stood on so and so's shoulders and I saw further.'' The essence of science is cumulative. By changing a problem slightly you can often do great work rather than merely good work. Instead of attacking isolated problems, I made the resolution that I would never again solve an isolated problem except as characteristic of a class.

Now if you are much of a mathematician you know that the effort to generalize often means that the solution is simple. Often by stopping and saying, "This is the problem he wants but this is characteristic of so and so. Yes, I can attack the whole class with a far superior method than the particular one because I was earlier embedded in needless detail.'' The business of abstraction frequently makes things simple.

This resonates with me, and that is probably a sign of my own peculiar weakness. I don't like complicated details, doubly so when they seem irrelevant to the problem at hand. My poor brain is always looking for the simplest way to do something. Sometimes that's a good idea, and sometimes not. Remember that generalization is a type of inductive reasoning. Some characteristics of such modes of thinking are that:

• It is creative--there is no general procedure for producing general procedures
• There is no guarantee of success. It takes persistence to get anywhere in this trial and error process.
  
• It requires a knowledge of the analytical tools necessary to check to see if your solution is correct. If you don't know right from wrong, you won't get far.
  

For many types of problems, this means adopting or creating a philosophy that makes sense--one that can incorporate the peculiar nature of the data and processes you're working with. For example, Darwin's Big Idea was that there had to be something in the reproductive process that acted like genes. He didn't know about genes, and it gave him fits because the evidence wasn't there (Mendel's work wasn't well known until later). But he arrived at the right philosophy. Leucippus and others figured out a good general way of thinking about matter as atomic.

Think about your curriculum. Think about the big problems you deal with in your job. How often do you go back and think about the big picture--the most general way of thinking about these issues? In the curriculum, we typically immerse students in detail and fail to emphasize philosophical underpinnings (in my experience). As an example, a liberal arts curriculum is typically a list of stuff. Writing, quantitative skills, etc. are assembled in registrar's lists with the assumption that some whole comes from the parts. What is this gestalt? Is it to enable students to have a grounding in the big problems of our time? To give a personal answer to the meaning of life? To have the technical means to begin to think generally (inductively)? To prepare them for a major or for the job market? Or just to fulfill accreditation requirements? The big WHY of gen ed easily gets swamped in details and lost. Even if we pay lip service to a mission statement, it's very difficult to actually integrate that philosophy into course work and classroom activities to instantiate it.

Alter the problem. Instead of asking how much Stanislav learned, ask how much do we think Stanislav learned. The first problem is probably impossible to answer; the second is trivial. And yet, the second is the more important question. When Stanislav goes out into the big wide world, his supervisor, teacher, or mentor will form an opinion about Stanislav's capabilities and act on that opinion, not some standardized test score, however accurate it is advertised to be.

Hamming concludes with an Apollonian "know thyself."

If you really want to be a first-class scientist you need to know yourself, your weaknesses, your strengths, and your bad faults, like my egotism. How can you convert a fault to an asset? How can you convert a situation where you haven't got enough manpower to move into a direction when that's exactly what you need to do? I say again that I have seen, as I studied the history, the successful scientist changed the viewpoint and what was a defect became an asset.

The idea that defects and limited resources produces creative solutions was mentioned in the first part of the article. Perhaps these limitations spawn conditions to generalize and ask WHY, simplifying and redirecting us to the philosophical underpinnings of the problems to be solved.

AAC&U's LEAP Initiative and Thinking Skills

If you haven't seen it yet, it's worth looking at the AAC&U's long-awaited LEAP recommendations for the liberal arts. (The link is a pdf to the executive summary). There's a lot there, but will just comment on the thinking skills part, shown below.

Later on in the summary, they cite some statistics about what employers wish for in graduates:

Notice anything about the two lists? The thinking skills are permuted somewhat, but they're still there. I'm interested particularly in creative and analytical thinking. In the guidelines these are combined. In the survey data, they are separated. They really should be separated in the guidelines too, because they're vastly different modes of thought. Both of the lists could use some editing. Ideally, the first two of the AAC&U's recommended list would be:

• Analytical thinking
• Creative thinking

I'm not sure what 'inquiry' is supposed to mean or how it's supposed to be taught, so let's toss that one. Much worse is the insidious 'critical thinking' skill that many institutions have in their set of goals. Granted, it sounds good--who doesn't want their graduates to be able to think critically. But what, exactly does it mean? It's far to fuzzy to be useful. I hope to convince you of this by contrasting it to analytical and creative thinking as a working dichotomy that can cover all our cognitive bases. Here are my working definitions for the purposes of curriculum development and assessment:

Analytical Thinking includes knowing facts and how they relate to each other. It includes definitions and languages and rules about how they work. For example, one can imagine a field of knowledge as a semantic field over which manipulations are performed explicitly. To the extent this is true, it is an exercise in analytical thinking. Analytical thinking is algorithmic: information retrieval and manipulation. It derives from deductive reasoning: consequences follow from given rules. In math, finding the derivative of a function is an exercise in analytical thinking. Identifying a piece of music as classical is analytical. Deriving the name of an organic molecule is analytical. Determining what a computer program does is analytical. Note that the rules can become very complex, and so there's no limit to the difficulty of analytical reasoning.

Creative Thinking is inductive or random. It looks for patterns and formulates them. It compresses complexities into simplicities, or does the opposite. It does this in the context of a body of analytical knowledge. Solving a known problem using known methods is not creative--it's analytical. Finding a new way to solve the same problem is creative.

In summary, analytical thinking is knowing facts and applying rules. Creative thinking is creating new facts and new rules. Without a background in some body of analytical thought, it's not possible to be productively creative. This models wonderfully well the way we teach and construct curricula.

Consider. First we seek to teach students the language of our discipline, and facts about the objects they encounter. We teach them theories about these, and show them how to apply theories. This is the analytical stage of learning. Some students may do very well with this. If they have a good memory and are good at following rules, they'll be good analytical thinkers.

Then, in many disciplines there's a shift. It's subtle, but devastating to some students, particularly if they haven't been warned, or if the instructors aren't aware. We begin to expect students to apply theories to new situations, or to create their own objects and theories. We're surprised when what we see initially looks random. Student try to mimic our process, but process takes them only so far--there's something else required: the magic of the human brain in generalizing, applying inductive reasoning, and the flash of insight or just sheer audacity of thought that distinguishes the best thinkers.

Some students have this naturally--this ability to insert randomness in a controlled way to create useful novelty. Others will flail around producing garbage. It's essential that they have some mastery of the analytical rules and knowledge of the discipline, or they can't edit themselves. They don't know right from wrong, good from bad if they don't have the analytical skills.

We as instructors can prepare students for this, if we are ourselves aware of this divide. For me, it came in a class called Introduction to Analysis, where I was expected to come up with math proofs on my own for the first time. My instructor was intuitive enough to know this was a hard class, and helped us enjoy the process, difficult as it was for most. But she didn't really understand, I think, why it was difficult. It was the transition from analytical to creative thought. I know this now, and preach it to my students. I even mark problems in the homework as creative or analytical. It's an extremely useful idea for organizing courses and curricula, in my experience. We assess it too, in a gentle way that doesn't require lots of tedious bureaucracy.

So there you have it. Critical thinking, in my opinion, is some confusion of analytical and creative processes, and is not a useful dimension for a general classification of cognition. It might be a great thing to focus on in an art or performance class, as a specific skill to be developed, but not as a first tier red-letter (i.e. rubric) goal.