Absolute and relative simplicity

Wed, Oct 13, 2021 ❝Whether or not you are allowed to rephrase the question itself.❞

Contents

In post “Questioning the scope of simplicity” we pondered whether question is relevant when considering if something is “simple”. In it we pointed out that given a complicated question, e.g. a question that is overly-broad, we cannot expected to give the simplest answer possible. The answer can only be as simple as the question it is stated to answer, and if you can rephrase the question to be more specific, then your answer may become simpler.

Relative simplicity

Given a question (or problem), you can give a simplest answer that is to-the-letter of the question that is posed. The answer is simplest – even if you may be able to express it more elegantly – for the question that is asked, because it is tied to it.

Conversely, a suboptimal question, or – to put it in more practical terms – a suboptimal problem statement, will restrict the simplicity of the solution.

The answer or solution is simple relative to the question being posed.

The question puts an upper bound on the quality of the answer.

Absolute simplicity

Now, consider the following practical scenario, which you may have experienced plenty of times yourself. You have formulated your answer, or solution, if you will. And in doing so, you discover that things should be simpler, that you are able to express it better/simpler. But in doing so, you have to deviate from the question as it was originally posed.

Next you will be evaluating what the question really is, that you are trying to solve. The insight you got from formulating the answer, hinted at or gave nuance to details of the question that were not considered before.

The answer can be “absolutely simplest” if you have also re-evaluated the question itself. Made the question as specific as possible, such that it no longer restrict the quality of the answer.

Property ‘specific’

We previously defined three properties for an answer. There is really only one property for the question: specific. The more specific the question is (expressed), the better the chance to find a suitable simple answer.

As the question defines the problem domain, there cannot be a different level of abstraction. It is similarly impossible for it to be “too general” or “too variable”. It is the question that is supposed to be answered. The question “just” needs to be specific, i.e. expressing exactly what you want to know.

Concluding

This is rather obvious. We simply state that there is a dependence of an answer on its underlying question. We have made it explicit here, such that you are aware of this as you think about the answer.