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Two Types of Systems

Last updated October 24th, 2021.

What makes a problem simple to solve? What makes a problem complex?

Here's one framework for thinking about this question.

I'd like to start by looking up the definitions of three words - condition, problem and solution:

A problem is an inquiry starting from given conditions to investigate or demonstrate a fact, result, or law.
A condition is a state of affairs that must exist or be brought about before something else is possible or permitted.
A solution is a means of solving a problem or dealing with a difficult situation.

In short, difficult situations send us searching for solutions to problems, and problems arise from conditions.

While problems and solutions are interesting in their own rights, for the sake of this discussion, I'd like to focus on conditions.

Let's start by dividing conditions into two categories - immutable and mutable.

Immutable conditions are most commonly present in systems of the physical or logical world. While our understanding of problems rooted in immutable conditions may improve over time, the problems themselves never change. In the large, our understanding of problems rooted in immutable conditions might be described as monotonic - that is, understanding is gained, but never lost. While some individuals or organizations certainly seem to get worse at solving these specific problems, as a society, we only get better. This is especially true if you adopt a more permissive definition of 'we' that includes our written record, rather than whatever local maximum has captured our attention in a given moment.

Mutable conditions tend to be defined by people, both groups and individuals. Consider, for example, conditions described by rule or regulation or custom. Problems rooted in mutable conditions are more difficult to solve than those arising from immutable conditions for at least two reasons. One, when mutable conditions change, those changes must be interpreted and accounted for in the solutions to problems rooted in mutable conditions. Second, problems rooted in mutable conditions can never be rigorously analyzed, only interpreted. The reason for this is subtle: change must be communicated, and - damn you, time - change is not totally ordered. Therefore, problems rooted in mutable conditions are doomed to be constrained by many different (and potentially conflicting) conditions at the same time.

In short: Immutable conditions are; mutable conditions are defined.

What can we learn from this? Two takeaways stand out. One: If you are attempting to solve problems that arise from immutable conditions, then you should probably try to minimize the number of mutable conditions that you introduce in the process. Two: While working within mutable conditions, when given the choice, strive to minimize the frequency with which conditions change.