Four Kinds of Problems

Tales from engineering.

As an engineer, I often see the world in terms of problems and solutions. There are many methodologies for analysis and problem solving, but it always helps to understand the kind of problem you are dealing with. The problem of identifying problems has a solution. At least, for the class of problems I am accustomed to dealing with, this solution works for me. What is unusual about it is that it divides the world into four. Most of the time I’m dividing the world into three or five and then adding dimensions, so the unusual number here gives me pause. Nevertheless, let’s get into it.

Puzzles
The first type of problem is a puzzle. Whether this is a puzzle is represented in a two, three or four dimensional model doesn’t quite matter. A two dimensional puzzle, like a jigsaw or a crossword suffice to explain. The first thing is to recognize that you are in a solvable domain. That is to say, you personally recognize what kind of problem it is and you have a good idea what the correct solution will look like. The entire difficulty of the problem is that there are missing pieces and they need to be put into place. For example, you have put together a tax return and the IRS says you owe $1507. It’s not a problem at all if you have the $1507 and a way to get it to the IRS. Or perhaps your car doesn’t work because you ran it into a telephone pole. Now you need a new bumper, fender, headlight, tire and wheel alignment. Five pieces. Not necessarily easy pieces, but once acquired and put into place, the problem goes away. Notice that I don’t concern myself with why I owe the Feds or how I wrecked the car. That’s done in the past and unfortunately four dimensional problems don’t allow you to crank time backwards. You have a problem, the solution is found in readily identifiable pieces. This is the easiest kind of problem to solve.

Mysteries
A mystery is a puzzle with unidentifiable pieces. Your job is therefore to investigate several aspects of what is broken and use your imagination and intuition to come up with some shapes of missing pieces. The end result is generally something you understand but something is going wrong and you can’t quite explain why. You bought the flowers, you’re wearing a nice suit and you have your Dad’s permission to use the Dodge, but still your date’s father is scowling behind her. You have no idea what it’s going to take. You thought you had all of the ingredients, but it still doesn’t taste right. There are all 9 players on the diamond but you’re still losing the game. With a mystery you say things like “What are we not seeing here?” or “Let’s imagine this whole thing from scratch.” What generally happens with mysteries is that you find the missing pieces in places you never thought to look - you had no idea so many different domains were involved. You are surprised that it’s not just the uniform, the supply lines and the weapons that win battles, but morale and the ability to treat the wounded. Who thought the healing arts would help win a war? That takes imagination. As soon as the aha moment comes, now you have mere puzzles to solve.

Rabbit Holes
The rabbit hole is the most frustrating of all problems because it defies you at every step. Why? Because a rabbit hole consists of mysteries that, once solved, generate not only puzzles, but more mysteries. More often than not, the best way to approach a rabbit hole is to acknowledge that perfect is often the enemy of good. You don’t necessarily want to find out how deep the rabbit hole goes and open up yet another can of worms. That is to say, you just scaffold where you are at an undetermined elevation above the very bottom and allow what’s beneath that floor to remain a mystery. Even doing that generates a new set of problems. Global warming is the perfect example. What if the oceans and forests interact in such a way that will regulate global climate in ways we don’t yet understand? Nobody has enough money to fund that study and we cannot reliably predict the behavior of China and India 50 years in the future. Sometimes it’s best to just buy an electric car and shut up about the entire planet. Of course that invites skepticism, cynicism, disputation and a temptation to force inadequate measures with Leviathan force. Don’t just stand there, do something! Clearly this is worse than a mystery. But it gets worse.

Black Holes
A black hole is a rabbit hole you do not recognize that you are in. It is like me drinking Red Bull so that I have energy to do my hardball circuit training having never been tested for diabetes. It is the pregnant smoker in 1947. It is like the joke about the time traveler who is sick of all of the paintings by Adolf Hitler and decides to travel back in time to make sure he young Hitler never gets into art school. It is the global warming activist who ignores microbial pathogens. It is Nick Leeson running arbitrage for Barings Bank. It is every confident strategy for the future based on the solutions of the past.

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You and I are in a black hole right now. The entire world is. Nothing that doesn’t sound like a conspiracy theory or a wild ass guess is going to get us out of it. Maybe it’s a random habit some grandmother in Kyoto has. Maybe somewhere on the edge of discovery where people are speculating wildly about the unknown and possibly unknowable is a concrete puzzle piece. We have no idea where to put it. In that course, maybe it is put aside and sits plain as day, a solution without a problem to call home. By definition we simply cannot know. So is it really a problem, or perhaps is it the eternal problem of human existence?

If it’s the eternal problem and we always have it, it might not be a problem at all. That would make it convenient for me to say there are only three kinds of problems and thus resolve my meta dilemma. But in fact I think the aim of wisdom is the exact reverse, that is to acknowledge that the black hole is always there. This requires humility of the sort those defiers of good lack in their search for perfection. Wisdom is not about perfection, or at least it seems to me that it might only be about the smallest perfections. The perfect cup of tea. The perfect meter of a rhymed couplet. The perfect outline of a lover’s silhouette in the morning sun.

The matter of solving problems serves a variety of impetuses, some of which have a great deal to do with one’s worldview. We’ve all heard of solutions in search of a problem. Let’s talk about that another day. In the meantime, I’m enjoying the slight imperfection of jasmine tea that is a few degrees cooler than my preference. It’s going to be a good day.