Easy Solutions to Hard Problems?

I’ve been trudging along knee-deep in tree manipulation algorithms recently, all in Haskell. I admit, calling them “algorithms” makes me sound much smarter than I really am… what I actually worked on was converting one type of tree into another type of tree (functionA) and then back again (functionB), such that I would get back the original tree — all in a purely functional, stateless, recursive way. My brain hurt a lot. I hit roadblock after roadblock; still, I managed to go through each hurdle by sheer effort (I never studied computer science in school).

See, I have a habit of solving typical Haskell coding problems in a very iterative fashion. Here are the steps I usually follow:

  1. Research the problem domain (Wikipedia, StackOverflow, etc.)
  2. Take lots of loose notes on paper (if drawing is required), or on the computer (using emacs’ Org-mode).
  3. Write temporary prototype functions to get the job done.
  4. Test said function with GHCi.
  5. Repeat Steps 1 through 4 until I am satisfied with the implementation.

The steps usually work after one or two iterations. But for hard problems, I would end up going through many more (failed) iterations. Over and over again, hundreds of lines of Haskell would get written, tested, then ultimately abandoned because their flawed design would dawn on me halfway through Step 3. Then I would get burned out, and spend the rest of the day away from the computer screen, doing something completely different. But on the following day, I would cook up a solution from scratch in an hour.

It’s such a strange feeling. You try really hard for hours, days, weeks even, failing again and again. Then, after a brief break, you just figure it out, with less mental effort than all the effort you put in previously.

What can explain this phenomenon? The biggest factor is obviously the learning process itself — that is, it takes lots of failures to familiarize yourself intimately with the problem at hand. But the way in which the solution comes to me only after a deliberate pause, a complete separation from the problem domain, fascinates me. I call it the “Pause Effect” (PE), because I’m too lazy to dig up the right psychological term for this that probably exists already.

So, here’s my new guideline for solving really hard problems:

  1. Try to solve problem in a “brute-force” manner. Don’t stop until you burn out. I call this the “Feynman Step”, after a quote from the televised “Take the World from Another Point of View” (1973) interview, where, toward the end, he describes a good conversation partner — someone who has gone as far as he could go in his field of study. Every time I’m in this step, I think of how animated Feynman gets in his interview, and it fires me up again.
  2. Rest one or two days, then come back to it. This is the “PE Step”.

The best part is when you ultimately find the solution — it feels incredible. You get this almost intoxicating feeling of empowerment in yourself and in your own abilities.