Problem Calculus: Introduction

The concept of problems is too general and open-ended to be measured.  A fence may represent a problem for a criminal but it's the solution to the homeowner.  But if the homeowner has a dog then the fence might also be the solution to the criminal to defend against the dog.
 
When something can be a problem and a solution depending on your perspective or even a problem and a solution regardless of perspective, then you've got to narrow down what you mean by 'problem' to make any headway into describing the difficulty of any given problem.

For problem calculus, we're going to focus on concepts that are difficult for people to form an intuition about.  Ideas that are hard to navigate in a mental landscape.  It will be interesting to see if the framework will be applicable for machine learning algorithms as well as people.

One thing to keep in mind is that we will be able to measure some problems and form intuitions both that they are difficult and why they are difficult, but we may not be able to determine which problem is more difficult. 

Different problems may be difficult for different reasons.  And for that matter, different solutions to the same problem may be difficult for different reasons.  In this instance the best we can attempt is to determine how to make a given problem more simple or more complex.  For example, we can't tell which is harder, brain surgery or rocket science, but we can tell that they are hard AND we can tell that if you had to play tag while also doing  brain surgery it would be harder than doing brain surgery without playing tag.