Trying to express an area of specialization is surprisingly difficult. But, these exercises in perspective-stretching are important to realize the limits to both your knowledge and the knowledge at the frontier of research. When intently focused on the smallest of details about the implementation of an out-of-kilter algorithm, it’s easy to forget that, while it’s hard to figure out how to implement a stochastic constraint solver in Haskell, there are broader problems.
See, the power of perspective enables us to critically restructure the problems we inherit. The question of how to implement a stochastic constraint solver may not be as important as why we’ve structured the problem in such a way as to require the constraint to be solved.
I’ve talk about this kind of thing in “real life” with many people, and with problems hardly as quantitative. Regardless of the question, we have inherited frameworks that try and help us structure how we arrive at answers. Often, these frameworks worked for someone somewhere. But, no two people are alike, and, while mathematicians love generalization and abstraction, sometimes asking a question in a radically different way can totally change the issues that we must resolve before answering our questions.
So, yes there’s a “canonical” model for certain situations. And it’s possible that someone cleverer than you has implemented a solution technique that’s better than one you could ever hope to devise. But, when you’re dealing with corner cases and trouble spots, it’s important to try and consider how much of your problem is due to the structures you’ve inherited. Maybe you, like Hamilton, should just take a walk to get some perspective, and come back to an area statement that can both provide clarity to your current structures and perspective on those you might need to build.
imported from: yetanothergeographer