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Today & Tomorrow

Philip Wik

Problem Solving

I’ve had many titles over the years: programmer, systems analyst, team leader, consultant, and systems integrator. But my job has basically remained the same. I’m a problem solver. Although the technology changes, my approach to problem solving hasn’t changed, and I go back hundreds of years for my inspiration. I’m indebted to René Descartes (1596-1650), who is generally regarded as one of the most important Western philosopher of the past few centuries. I’ve annotated Descartes’ principles from his Discourse on Method in italics.

The first was never to accept anything for true which I did not clearly know to be such; that is to say, carefully to avoid precipitancy and prejudice, and to comprise nothing more in my judgment than what was presented to my mind so clearly and distinctly as to exclude all ground of doubt. Clear your mind of presuppositions. Approach the subject with tough-minded, skeptical neutrality. Resist jumping to conclusions.

The second, to divide each of the difficulties under examination into as many parts as possible, and as might be necessary for its adequate solution. To break down into its smallest components is to analyze. Keep turning the problem around looking for different ways to atomize the problem. Ask yourself: where is the problem; and where isn't the problem?

The third, to conduct my thoughts in such order that, by commencing with objects the simplest and easiest to know, I might ascend by little and little, and, as it were, step by step, to the knowledge of the more complex; assigning in thought a certain order even to those objects which in their own nature do not stand in a relation of antecedence and sequence. Often we are stumped on solving the problem because we fail to take this step. Pin down what we do know and then build from that from the simplest to the most complex. Look for analogues between what we do know and what we don’t know.

And the last, in every case to make enumerations so complete, and reviews so general that I might be assured that nothing was omitted. All of the conditions exist for everything to remain as it is. So, to change the "what is" to "what should be", work first of all on addressing the predicating conditions and the solution will often reveal itself. Be meticulously detail oriented, but also look at the big picture. Sometimes, putting the problem into deep freeze for a while will bring a solution. Allow for your intuition to work. Walk or jog a few miles. Many Nobel Prize winners got their insights, it has been said, in bed, bath, or bus. Talk over the problem with your colleagues. Use different ways of expressing the problem, with schematics, computer models, mathematics, or whatever else is available. At the same time, constrain your analysis with Ockam’s Razor. The Franciscan monk William of Ockam (1285-1349) gave us the principle that “plurality should not be posited without necessity”. This principle, sometimes known as the principle of parsimony, states that we shouldn’t make any more assumptions then the minimum needed. It helps us shave off concepts or constructs that complicates or confuses the explanation. However, like the verification principle (only that which can be verified is true), this is only a presupposition. Thus, sometimes, the more complex approach or explanation is more valid. A recurring problem indicates a lack of thinking. Finally, theory must be congruent to application. The argument that it works in theory but fails in practice is fallacious. A good theory will always work in practice.

“The long chains of simple and easy reasonings by means of which geometers are accustomed to reach the conclusions of their most difficult demonstrations, had led me to imagine that all things, to the knowledge of which man is competent, are mutually connected in the same way, and that there is nothing so far removed from us as to be beyond our reach, or so hidden that we cannot discover it, provided only we abstain from accepting the false for the true, and always preserve in our thoughts the order necessary for the deduction of one truth from another.” Descartes’ claim is impressive but valid, as I think this approach works in resolving most technical problems.