Four kinds of problems


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jacobjacob

I think there are four natural kinds of problems, and learning to identify them helped me see clearly what’s bad with philosophy, good with start-ups, and many things in-between.

Consider these examples:

  1. Make it so that bank transfers to Africa do not take weeks and require visiting physical offices, in order to make it easier for immigrants to send money back home to their poor families.
  2. Prove that the external world exists and you’re not being fooled by an evil demon, in order to use that epistemic foundation to derive a theory of how the world works.
  3. Develop a synthetic biology safety protocol, in order to ensure your lab does not accidentally leak a dangerous pathogen.
  4. Build a spaceship that travels faster than the speed of light, in order to harvest resources from outside our light cone.

These examples all consist in problems that are encountered as part of work on larger projects. We can classify them by asking how we should respond when they arise, as follows:

1. is a problem to be solved. In this particular example, it turns out global remittances are several times larger than the combined foreign aid budgets of the Western world. Building a service avoiding the huge fees charged by e.g. Western Union is a very promising way of helping the global poor.

2. is a problem to be gotten over. You probably won’t find a solution of the kind philosophers usually demand. But, evidently, you don’t have to in order to make meaningful epistemic progress, such as deriving General Relativity or inventing vaccines.

3. is a crucial consideration -- a problem so important that it might force you to drop the entire project that spawned it, in order to just focus on solving this particular problem. Upon discovering that there is a non-trivial risk of tens of millions of people dying in a natural or engineered pandemic within our lifetimes, and then realising how woefully underprepared our health care systems are for this, publishing yet another paper suddenly appears less important.

4. is a defeating problem. Solving it is impossible. If a solution forms a crucial part of a project, then the problem is going to bring that project with it into the grave. If whatever we want to spend our time doing, if it requires resources from outside our light cone, we should give it up.

With this categorisation in mind, we can understand some good and bad ways of thinking about problems.

For example, I found that learning the difference between a defeating problem and a problem-to-be-solved was what was required to adopt a “hacker mindset”. Consider the remittances problem above. If someone had posed it as something to do after they graduate, they might have expected replies like:

“Sending money? Surely that’s what banks do! You can’t just... build a bank?”

“What if you get hacked? Software infrastructure for sending money has to be crazy reliable!”

“Well, if you’re going to build a startup to help to global poor, you’d have to move to Senegal.”

Now of course, neither of these things violate the laws of physics. They might violate a few social norms. They might be scary. They might seem like the kind of problem an ordinary person would not be allowed to try to solve. However, if you really wanted to, you could do these things. And some less conformist people who did just that have now become billionaires or, well, moved to Senegal (c.f. PayPal, Stripe, Monzo and Wave).

As Hannibal said when his generals cautioned him that it was impossible to cross the Alps by elephant: "I shall either find a way or make one."

This is what’s good about startup thinking. Philosophy, however, has a big problem which goes the other way: mistaking problems-to-be-solved for defeating problems.

For example, a frequentist philosopher might object to Bayesianism saying something like “Probabilities can’t represent the degrees of belief of agents, because in order to prove all the important theorems you have to assume the agents are logically omniscient. But that’s an unreasonable constraint. For one thing, it requires you to have an infinite number of beliefs!” (this objection is made here, for example). And this might convince people to drop the Bayesian framework.

However, the problem here is that it has not been formally proven that the important theorems of Bayesianism ineliminably require logical omniscience in order to work. Rather, that is often assumed, because people find it hard to do things formally otherwise.

As it turns out, though, the problem is solvable. Philosophers did not find this out, however, as they get paid to argue and so love making objections. The proper response to that might just be “shut up and do the impossible”. (A funny and anecdotal example of this is the student who solved an unsolved problem in maths because he thought it was an exam question.)

Finally, we can be more systematic in classifying several of these misconceptions. I’d be happy to take more suggestions in the comments.