Intractable Problems

May 31, 2020

There’s a saying that stipulates you only need one correct argument to be right. If you need more it probably means you either are wrong or need to think harder.

This mind frame goes against many debating styles, especially against the rule of three, which I’ve come to despise. It’s a laudable defense of conciseness.

However, like most sayings, it is not always true.

Jordan Greenhall describes two problem types: complicated and complex. Complicated problems are bounded and ultimately tractable, complex problems are infinite and intractable.

In complex problems, you cannot expect to have a winning argument because there is none. You will ultimately hit a roadblock that will impede you to formulate a definitive defense. As such, complex problems beget the most heated debates: issues of cultural relativism, morality, the law, politics, globalization, human rights — The fact people have died defending some opinions on these topics hints at their complex nature. No one dies to question the nature of an electron’s spin.

On the other hand, you should look for one single argument to defend your opinion on a complicated issue. Since complicated problems can be completely known, there is a set of absolute truths about them. You can argue that gravity pushes objects apart and therefore we should all be tied to the ground with ropes, but this is easily refutable; Only one argument is needed to negate it.

Complicated problems are personally humbling because I’m an engineer and, counter to what you might think, engineering is a complicated topic, not a complex one. A 747 might look like a complex machine, but it really is not. Put enough time and resources, everything can be known about a plane, no matter its scale.

Of course, the world is messy and humans often operate in a state of incomplete information. Bound by time constraints, we cannot always know everything about complicated systems, and this results in wrong decision making about problems that have one single correct solution.

As an engineer, aim at complete knowledge before aiming at complete convincing.

Addendum: The counterfactual also applies and is better known: you only need one correct argument to invalidate a point. It’s one principle of the sciences, where hypotheses are tested against experiments and one single result can prove a theory wrong.

Addendum 2: I will dedicate more time on how to tackle complex problems in future posts. In the meantime, suffice to say you should aim at managing, not solving, complex outcomes.

Addendum 3: Effectively, artificial constraints (like Q earning reports) turn complicated problems into complex ones. It is fun to think about the cost-benefit calculation of this effect.

Addendum 4: As an engineer, aim at solving the problem at hand with the information you can get, but the last sentence was too fun not to write.

Hi there 👋, I’m Gerard, Software Engineer and aspirant polymath. I write this blog, build Factorial, and publish the best I read on Twitter.