This afternoon, I suddenly started thinking about how some people automatically believe an argument if its narrative sounds complicated and sophisticated. Others do the opposite: they worship simplicity and assume that whatever is simplest must be the most correct. (Neither of them is me, by the way š¤„)
Then I started wondering: what does simple actually mean? What is complexity? Is a more complex explanation more true?
I also don’t know whether there is any measure of complexity that the entire human population would agree on. But intuitively, I feel that an answer or explanation becomes more complex when it involves many variables and the interactions between them at once, to the point where we need to spend more cognitive resources processing it.
If simplicity is the opposite of complexity, then a simple model might be a model that discards variables considered irrelevant to answering a particular question. Such a model might even be intuitively understandable to the person asking the question.
But I still don’t quite get it. So I tried a thought experiment.
Two Models
Imagine there are two models. Model A and Model B are trying to answer the same question.
Model A explains:
āThe tendency for X increases as variable Y increases.ā
Meanwhile, Model B explains:
āThe tendency for X emerges from 24 psychological factors caused by 50 social factors, consisting of 30 economic and political factors, 20 cultural factors influenced by several ecological parameters such as climate affecting temperature, biodiversity affecting noise from insects and birds in the environment, air pollution, noise pollution, and visual pollution from surrounding human activity.ā
Model B sounds much cooler. š
To me, B is clearly the more complex explanation. But its complexity doesn’t tell us whether the model is true or not.
Model B has something like an aesthetic of explanation. It sounds scientific because it contains many variables, many causal relationships, and many details. From there, I can easily make the following leap:
But this thought experiment creates another problem for my assumption: that a complex explanation might be harder to understand intuitively.
A model can be structurally complex yet written so elegantly that it is easy to understand. Conversely, a model that is actually simple can be explained in isekai language until the reader feels like they are reading a spellbook for summoning a demon king.
So, āhard to understandā is not a reliable indicator of a model’s complexity.
And yes, at this point I am judging my own explanation of Model B to be elegant. š
Are All Those Variables Necessary?
Model B looks more complex.
But now the question becomes:
Are all 24 psychological factors actually necessary?
What if 17 of them have no replicable effect?
What if some of them don’t have a consistent definition?
What if 5 of the factors are actually consequences of Y rather than independent causes?
What if some of the variables merely make the model look more complete without improving its ability to explain or predict anything?
Conversely, what if the very simple Model A actually predicts the data more accurately?
And what if Model A is indeed too simple, causing it to fail when conditions change, while Model B can predict phenomena that Model A cannot explain?
At this point, I started to realise that the question of complexity cannot really be separated from the question of what a model is for.
A model does not have to include everything that might influence a phenomenon, because it is built to answer a particular question. Therefore, variables that are not necessary for that question might actually be better left out.
But leaving variables out can also become a problem if those variables turn out to be important for explaining the phenomenon or cause the model’s predictions to fail when the context changes.