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The Problem (If a-b=0, and 0-0 = 0, then 0-1 = 9)

"We have know for several hundred years that mathematics is a problem subject in school. A small minority of students, certainly no more than one-fifth, seem to have no difficulty with mathematics and learn it easily. The rest never really learn it. It is possible, of course, to drill a very much larger percentage to pass mathematics tests. The Japanese do this through heavy emphasis on the subject. But that does not mean that Japanese children learn mathematics. They learn to pass the tests and then immediately forget mathematics. Ten years later, by the time they are in their late twenties, Japanese do just as poorly on mathematics tests as do westerners. In every generation there is a mathematics teacher of genius who somehow can make even the untalented learn, or at least learn a good deal better. But nobody has ever been able, then, to replicate what this one person does. The need is acutely felt, but we do not understand the problem (The Problem is, If a-b=0, and 0-0 = 0, then 0-1 = 9). Is it a lack of native ability? Is it that we are using the wrong methods? Are there psychological and emotional problems? No one knows the answer. And without understanding the problem, we have not been able to find any solution. (Here is The Problem, If a-b=0, and 0-0 = 0, then 0-1 = 9).

We may even understand a process and still not have the knowledge to do the job. The preceding chapter told of the clear and understood incongruity in the paper making: to find a process that is less wasteful and less uneconomical than the existing one. For a century, able people have worked on the problem. We know exactly what is needed: polymerization of the lignin molecule. It should be easy - we have polymerized many molecules that are similar. But we lack the knowledge to do it, despite a hundred years of assiduous work by well-trained people. One can only say, "Let's try something else."

The solution must fit the way people do the work and want to do it. Amateur photographers had no psychological investment in the complicated technology of the early photographic process. All they wanted was to get a decent photograph, as easily as possible. They were receptive, therefore, to a process that took the labor and skill out of taking pictures. Similarly, eye surgeons were interested only in an elegant, logical, bloodless process. An enzyme that gave this to them therefore satisfied their expectations and values.

But here is an example of an innovation based on clear and substantial process need that apparently does not quite fit, and therefore has not been readily accepted."

Peter F. Drucker
Innovation and Entrepreneurship (p.74)
©1985