Different Kinds of Difficulty

Introduction

Difficulty is a difficult thing to pin down. I had to expend a good bit of effort to write this piece, counter to my usual method of writing ad hoc. I’ve settled on a tripartite construction of difficulty: effort, time, and familiarity. Effort is what I think the colloquial usage of difficulty is reduced to. Effort is a measure of expended, concentrated energy—e.g. through thinking hard, or lifting something heavy. Time is mostly self-explanatory. There is also familiarity. Familiarity reduces the amount of time and effort needed to do something; it can be viewed as another axis of difficulty itself. Familiarity allows you to build heuristics which have the potential for substantial reductions in time and effort necessitated to do something.

Effort

Things that don’t take effort are simple. Things that take the most effort are hard.

Difficult things that don’t take much effort are tedious.

As mentioned, I posit this is the facet of difficulty most often incorrectly referred to as the whole. Things can be difficult without taking much effort. For example, consider walking 5km (~3mi). For most people, walking this distance at a slow clip wouldn’t take much effort, but it would take a lot of time. In a similar vein, I’m sure most people could multiply two 10 digit numbers by hand on paper without expending too much thought, but it would take some careful bookkeeping and time to work through this problem.

Time

Things that don’t take time are fast. Things that take a lot of time are tedious.

Difficult things that don’t take much time are also fast.

The reason for separating time and effort, which some people may regard as inextricable, is the existence of myriad tasks which don’t take much thought or energy in any way yet demand a large time commitment. A simple example of this would be to sit in a room for one hour. There is no effort involved, as sitting in a room doesn’t cost anything, but you still have to spend an hour which must be measured somehow.

Familiarity

Things that are unfamiliar are called as such. Things that are familiar are also called as such.

Difficult things that don’t benefit from familiarity are aleatoric—i.e., beget by chance. These are things where practice practically doesn’t help, e.g. guessing a computer generated integer from one to ten.

Familiarity is usually built through practice, and can be supplemented by way of advices and tips from relative experts.

Pertinence

With these definitions, let us move into why they are useful. I argue that the usage of “difficulty” to cover all above facets is inappropriate and is unnecessarily lossy. Consider calculus; I think it is a common opinion to think of calculus as difficult, but I would classify it as tedious, as it necessitates a lot of memorization but not much thought.

Building off the prior post about memorization and memoization, we can see that the former is best advanced through spending time, and the latter more through expending effort. Tools such as spaced repetition already exist as a means to almost automatically memorize facts, whereas no such shortcuts exist for memoization—one can only practice. As we can see, practice has the added benefit of tending to make things more familiar—i.e., less difficult.