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Puzzling Mysteries

Edwin N. Lightfoot, University of Wisconsin--Madison, 1415 Engineering Drive, Madison, WI 53706

Suggestions are made for simplifying solution of the poorly posed problems normally encountered by engineers and applied scientists. They are confined to the difficult and critically important early stages of all creative processes, and here the primary concern must be minimizing the extent of parameter space to be investigated. Almost always the original problem is too complex to obtain a complete solution: it is what we may call a mystery. We must then replace the mystery by a puzzle: simpler problem that we are able to solve. Moreover both the selection of the puzzle and its solution is general heuristic, and it will necessarily ignore some potentially useful regions of parameter space. True optimization is by definition impossible.

The first step in this replacement requires something like the flash of genius needed for patentability, and it depends heavily upon the personality and background of the investigator. Here we can only provide hopefully instructive examples.

However, once this first decision is made we suggest a systematic stepwise reduction in parameter space, starting with orders of magnitude.

Examples will be provided, primarily in the areas of biologically oriented separations processes and physiological modeling.