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Developing intuition

Many of the most difficult problems have been and are not susceptible to a primarily intellectual approach. Intuition aids us in dealing with these problems as a sort of poor relation to intellect. We recognize the need for inspiration and creativity, but treat these as magical gifts and not as a talent that can be developed or neglected.

The creative arts are further along at developing intuitive talent than academia and the worlds of science and technology. Intuition is at the core of the creative arts, but it is equally central to any creative endeavor. In the creative arts, intuition is often holds center stage. There are disciplined approaches to developing and extending it. Method Acting is one example.

How do we recognize and develop intuitive talent? When I entered the University of Illinois at Urbana as a freshman I took a test for the Math Honors Program. The test consisted of three problems one of which one needed to solve to pass the test. A straightforward solution to the problems required a course in mathematics one level beyond what one had taken in high school. I only got as far as analytic geometry at my small Catholic high school and so a straight forward solution to the problems required a knowledge of calculus. Of course you did not need to reinvent the calculus, but you did need to invent some aspect of the ideas that led to the creation of the calculus. A thorough understanding of the mathematics one had studied was not enough to pass the test. One had to come up with a creative approach to the problem.

This is one approach to testing for intuitive talent. Can one extend what one has learned to solve problems that do not have a straightforward solution? When I taught a course in logical design at UCLA I included a question that most students missed even though it was a `who is buried in Grant's tomb?' type of question. One can construct logical circuits like those described in Section 5.3 with multiple levels of logic. The outputs of lower levels are inputs to higher levels as shown in Table 5.2. If one has a truth table for such a circuit one can construct the minimal two level solution, i. e. the one that has the fewest logical operators: AND and OR. The problem started with the diagram of a logical circuit. There were three parts to the problem. First construct the truth table for the circuit. Second construct the the minimal two level circuit that implements the truth table. Third note that the circuit you constructed has more logical elements than the original circuit. Explain how it can be the minimal two level solution. The answer was that the original circuit had three levels.

Why did so many students miss this obvious answer? I think it is because they are not taught to make connections. They are taught to apply methods. If you are exploring possible connections than the phrase `minimal two level circuit' suggests that a three level circuit gives you more options to try and might be better than a two level solution. Intuition is always making connections and seeing possibilities. Invariably most of these connections and possibilities are meaningless, nonsense or false. But that is how intuition must work. If it is constrained by what makes sense logically than it cannot do its job. Intellect and other functions are needed to evaluate the work of intuition, but they must not limit the scope of its functioning. Often that is precisely what we are taught in formal education.

After all intuition can be extremely distracting. Instead of focusing minds on the material at hand it leads off in all directions. We need the discipline of focus, but we equally need the discipline of intuitive rambling. We need to give space for and encouragement to both. Formal education almost universally discourages intuitive wandering. No doubt one of the effects of Ritalin widely prescribed to children for `Attention Deficit Disorder' is to weaken intuition.

There are three components to developing intuition. First is providing the personal material in terms of learning and life experience that intuition uses. Next is exercising the intuitive muscle by using intuition. This should involve both random rambling and focused problem solving. The problems must always be ones for which one knows no canned intellectual approach. It is a challenge to create such problems. One cannot give a standardized test for intuition because one can always educate for the test. Finally there is the need to develop the archetypal images that intuition relies on. The best of Fairy Tales is one way to do this for small children.

Astrology, the I Ching and Tarot are examples of ancient methods of developing intuition. They focus on archetypal images. They describe the seeds of transformation that exist in a current state. They are are immersed in superstition. No attempt has been made to integrate them with scientific understanding or to create similar new forms that are compatible with contemporary science. This is particularly difficult because archetypal material have a numinous chthonic aspect.

How can we develop intuition, let it lead the way and yet hold it back from leaping into the abyss. For intuition to become more universal it must become more developed and differentiated. We must know when and how to use it and we must know with some, albeit imperfect, reliability when it leads us too far afield from what is practically possible.

The one sided culture I am so critical of has provided one important tool for this. The computer allows us to create artificial universes to play with ideas and refine our intuition. I can learn complex technical material best if I can program it and play with the program. A mass of equations without the opportunity to make them alive in a computer is virtually meaningless to me. It is not that I am unable to understand them, but the mode that I can understand them has to involve an element of playfulness and has to be tolerant of many silly errors which I continuously make. Although a computer is completely intolerant of mistakes, it allows as many tries as you are willing to make to get it right.

Intuition is not as quick as intellect but it is deeper. Intellect can easily grasp things as a series of complex operations. This is impossible for intuition. Intuition must know how the operations relate to each other and to a host of similar operations that are already understood. This takes time and it takes playing with ideas. For complex systems this is impossible without a computer to handle the details. Of course there is no intuitive only or intellectual only learning. All learning involves sequences of steps, playing with ideas and relating new ideas to old ones. The difference is one of emphasis.

The computer combined with communication technology is a powerful aid to intuition in another way. It can create learning and dialog networks of people concerned about a particular issue. The misnamed newsgroups on Internet serve this purpose. Although they do contain some news the vast majority of traffic involves networks of people exchanging ideas and learning from each other material that is far from new. For me this was an effective way to learn the language and some of the technical content of quantum mechanics. It helped me to extend my ideas and put them in a context that others could more easily understand.

Technology can change the value of human talents. Gauss had an advantage over his colleagues in being a skilled calculator. That was an important asset for a mathematician in his time, but is of little use today. No matter how good a calculator you are you can buy a better one for a few dollars.

Computer technology allows us to automate many of the simpler intellectual skills such as calculation. Inevitably this lowers the value of those skills while opening new possibilities to those with different skills. We are just beginning to understand what can be done and still view this opportunity too narrowly. We want to automate mathematical proofs so we try to create completely automated theorem provers. We want to automate chess so we make a computer program that can beat a grand master. Technology is far from being able to replace the human mind. The enormous calculating power of modern computers is sufficient to defeat the best of human chess players with the brute force methods that such chess programs use. That is not the way to make the best chess player. To do that combine the special skills of the computer with the subtle skills of the human. Let the human use a computer program to aid play just as you let a student use a calculator during a physics exam. The best computer aided chess player will almost certainly not be the same person as the best unaided chess player.

Finding the worlds best computer aided chess player may not be important to cultural development, but effectively using the computer to amplify human mental skills is. This is starting to happen with intuitive graphical user interfaces, programs to do mathematical analysis as well as computation and tools for scientific visualization. However we must recognize how primitive our understanding is. People with powerful intuition that have played a major role in science like Einstein and Jung are usually in Jung's terminology thinking types. Their greatest strength is their powerful intuition, but it is only through the dominance of intellect that they are able to digest the fruits of that intuition to a form that can be appreciated by our intellectually dominated culture. To get beyond this stage is no small task. We have regressed in the institutional structures to develop intuition since the middle ages. It is not possible for anyone to say what a world with intuition and intellect in more equal roles would be like other than it will be markedly different and far richer than the world we know.


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