Two Orientations to Problems

 One might say that there are two orientations toward looking at problems. The orientation that I am most familiar with is sometimes referred to as a "merge and kill" approach: to break down a problem into individual parts, find commonalities between the parts, isolate the causes, and then conquer the problem (as it were) with a kind of neat solution. Generally, part of what made algebra so appealing to me is that it often symbolically and metaphorically embodies this aspect of eliminating redundant terms and then seeking to find the simplest expression for the remainder. Having taken enough algebra courses in high school, I can personally attest to the beauty of reduction, and it's this approach that might also explain the way people might approach everyday problems. "Simplify" becomes the catch-all phrase for such an approach, and I believe that my early enjoyment of the logical positivists was also a testament to this simplifying tendency.
   There is another approach to looking at problems that I am only beginning to understand at my current age. Rather than seeing problems as isolated "weak links" in a chain of otherwise very strong members, "problems" are often entry points into flipping a worldview or a habitual way of seeing completely upside down. That is, problems become symptoms of an emerging totality, and they can even become signs of exploration and expansion. If I try to solve problems only through the first process of simplification and elimination, my world-view overall remains fairly intact, because I managed to isolate the hardest part and smooth over the other parts that are affected by the problem. But in the second orientation, problems unravel the status quo by showing quirks or kinks, revealing new possibilities that would not have otherwise been known were it not for the awakening affects of the problem itself. While the first approach might favor the demonizing of problems, the second approach might begin to see problems as opportunities to change the way we think of things, and even to make surprising new connections.
   It's useful to see that in both cases, "problems" are framed as such by minds. Even knowing or realizing that a problem is "a problem" because of a human tendency to label such, is a good way to extend its possibilities and find new inroads. But I think that in the second case, there is more wiggle room for problems to actually promote passionate, seeking and adventurous approaches to experiences. In understanding problems as hinting at overall mysteries, one opens to a life of love and intrigue rather than one of "divide and conquer".