Problem Solving - the pathway to the impossible

Problem Solving – the pathway to the impossible

Life is problem solving. From work to school to religion; in love in pleasure, in strife, we are always solving something. Some problems are simple, some tricky, some poorly defined, some complex. Many are impossible.

We have not set about to discuss school math problems. In a sense, these are the simplest of all because much of the toolkit needed for solving them have been presented in the course. These problems are those with the greatest clarity, a unique solution, and for them there is always a final resolution. You get it or you don’t.

We have an array of problem solving methods, from logic to emotion, from instinct to intuition, from random to programmed, and more. These methods are applied individually or in combination, often generating intrinsic conflicts, resulting is partials solutions, no solution, personal solutions, new problems, new situation, and impossible situations. Results can be satisfying or frustrating, victory or defeat, pleasure or dismay, resolution or resignation, life or death.

One part of the problem solving process contains the seeds of problem solving defeat. That part is with the mind itself, and how it attacks problems. It organizes data and priorities. It complies to internal and external constraints. Solutions must be feasible. It is limited by knowledge and experience. It is both constrained and guided by faith and beliefs. Moreover, the mind must recognize a solution when it arrives.

When a solution is offered or found its acceptance may depend on a panoply of external factors. The cost of implementation is most often the prime factor in business. The compliance is often the prime factor in the law. The prime factors, for example, in others are agreement with scripture in religion, the coherence and adherence to theory in science, the tests of significance in data analysis, the believability in all cases, and the rigor in mathematics. Every discipline has its own prime factors.

All of these distill down to the fundamental goal of correctness. So, finding a solution is but a step toward finding the correct solution. Concomitant with the correct solution is the presence of multiple correct solutions. And this is in part accounted by the multiple problem solving methods. These play a major role in selecting one of them. Usually an optimization criterion is at play. Perhaps cheapest, most reliable, simplest?

Compounded with this straightforward language comes the very definition of correct. This depends on the world in which the problem exists, e.g. automotive ignition switches, deciding on whom to marry, and how to fight a battle. Application of the inappropriate criteria can lead to tactically or strategically impossible consequences.

Indeed, because of the wide variability of problem approaches, multiple logics, multiple solutions, no solutions, criteria for acceptance and correctness, we are led to the doorstep of impossibility, our ultimate concern.

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