Some Types of Tricky Problems

There are various classifications of problems, often subject to their academic field of interest. An interesting way to look at these types is based on our knowledge.

  • The problem we can make sense of, manipulate and solve
  • A situation where we know that we will never be able to know more
  • An area where we don’t have knowledge but can gain it
  • A situation where the knowledge we have is incomplete in critical ways
  • A problem where we know a lot but the solution is about human values

These areas cover a broad terrain of analysis so it’s hard to take them all out for a walk together, it is even hard to give them good standard names but I try.

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What we know is like LEGO, 
what we'll never be sure of is heads on a coin flip,
what we might is a random walk,
what we think we know, but maybe not, a sandpile quake,
what we know but can't decide is wicked...

It is quite fashionable to think about computing and how it can take over and rationalise the world, have answers for almost anything. But things are not so easy, and from the point of view of the human race, the problems we are coming up against seem to be moving more and more toward the most tricky class of problems.

What can AI do with a blend of many probabilities? It can try to maximise, but how can we be sure that it has a correct model? That it has taken the best route? What if this territory is simply unknown: how can we know ahead of time that a certain path will lead to a better outcome? How do you handle dramatic rare events, like crashes, asteroids and earthquakes?

I translate these 5 types of knowledge to the following areas of study, loosely.

  • Engineering
  • Probability, Statistics
  • Scientific Exploration
  • Long tails, self-organised criticality, etc..
  • Wicked problems

Some of these problems we can address with the tools we have today, some pose really special challenges to a blind quantified approach one might follow.

The Paradox of The Court

Protagoras takes on Euathlus as a student of law under the understanding that his first win in court will be the fee to cover the teaching. But Euathlus decides not to be a lawyer and not to pay, and is taken to court by Protagoras.

Protagoras: “Should you lose the trial, I will get my money, and should you win you owe me the money as we agreed!”

Euathlus: “Should I win the trial, the court has found our contract invalid so I won’t pay. Should I lose the trial, I won’t have won a trial so by our initial agreement I should not pay.”

https://en.wikipedia.org/wiki/Paradox_of_the_Court