Problems are beautiful, and they are among the most interesting things you can come across. You should consider each problem you are faced with as if it was a rare and thoughtful gift (failures are like this too, as Karl Jaspers noted: failures are small ciphers sent to you from God). Often we are annoyed when faced with problems and we see them as things to solve and then forget, but I think that it is much more important to collect them and understand what different kinds of problems there are. And the categories just continue to amaze me. When creating a taxonomy for problems, I believe you reveal a lot about yourself as a person. The best interview question I have ever been faced with was the question “How many different kinds of problems are there?” — The answer is almost certainly going to reveal a bunch about what is going on in your wetware. A couple of different possible answers help show this:
- Solveable and unsolveable. This is a pretty lame answer, admittedly, but it has a certain kind of basic charm. If this is how you think of your problems, you are either a math nerd or simply very, very pragmatic.
- Interesting and uninteresting. I like this much better. If we think about problems as interesting or uninteresting we at least acknowledge their inherent value. Problem is I think the second category is empty. So you may be wrong.
- Deductive, inductive or abductive. Old semiotic and peircean view of problems. This shows that you have an understanding of problems that flow from the structure of the problem, rather than the substance of them.
- Legal, economic, mathematical, et cetera. Subject matter problems. This shows that you think of problems as domain dependent. That something is a problem is decided in the larger language game of the domain where the discourse is playing out.
- Infinite or finite. Some problems are ever evolving and they are not essentially to be solved, they are more continuous games that need to be addressed all the time, and then evolve and change. Some problems have solutions that actually make them go away and disappear. This mirrors, of course, closely the categories infinite and finite games. Shows that you think about problems as games, or at least as ways of engaging the world: we live through our problems. They make us real.
- Mine and somebody elses. Old Douglas Adam’s joke. Somethings in his lovely novels are obscured by Somebody Else’s Problem-fields that make them, effectively, invisible. This shows that you think of problems as owned or things for which you should be accountable. Very responsible, but also somewhat limited.
- Natural and artificial. Some problems are made, others are found. The made problems are problems of human making, and often can be solved by fixing who does what. Found problems are much harder and also likely to remain constant over different teams. A made problem may very well be the consequence of a found problem, by the way. This way of thinking about problems is the natural scientist.
- Networked problems and stand-alone problems. Some problems occur because of the way a network of different factors interact. Some simply exist by their own. I find that those that make this distinction sometimes think that networked problems are intractable, whereas what can be handled on its own is solvable, or at least that networked problems require concerted action (collective action) to solve.
- Primary and secondary problems. Some problems are effects and some are causes. Solving for the problems that are not the root problems only fixes so much. Responses along these line realize the ever-present risk of post hoc ergo propter hoc in building models of reality.
- Out of context problems and context problems. This last category really interests me. OCPs was a term launched by sci-fi writer Iain M Banks, in his novel Excession. OCPs are problems that you hardly even recognize as problems because they are so way outside of the context you operate in. As opposed to context problems that are problems, you see as problems, recognize and have ways of solving. OCPs are NOT black swans as the wikipedia entry argues, however. They are something much more interesting, something that challenges your entire context and world-view and THUS a problem.
Wittgenstein famously noted that a philosophical problem has the form “I don’t know my way”. I think re-phrasing problems in that way, finding representations for them, models and analogies is extremely interesting too. What are your favorite categories of problems? (I have not even mentioned things like Fermi-problems, np-complete et cetera, so there is much still to be done here. I have started a category on my blog for problems, and will keep an eye open for more of them as we proceed.