“This is not a pipe.” The Treachery of Images by René Magritte
Coined by philosopher Alfred Korzybski. “The map is not the territory” is a reminder that it is impossible to perfectly model a system (see: Systems), nor it is desirable. Instead of including everything in our model, it’s more useful to include things that will serve our current line of inquiry.
Even if we wanted to model everything, we couldn’t. Gödel’s Incompleteness Theorems say that every non-trivial (interesting) formal system is either incomplete or inconsistent. Extended, this means it’s impossible to know everything about a system that’s worth knowing things about. We must come to accept uncertainty.
Indeed, science is revealing uncertainty at the fundamental levels of physics.
A perfect model of a system would be the system itself. According to Ashby’s Law of Requisite Variety, a perfect regulator must have at least as many distinguishable states as the phenomenon it is intended to regulate. In other words, to build a perfectly accurate model of a system, the model needs to be at least as complex as the system itself. Likely, it will be more complex.
Because of Bounded Rationality, humans are only able to integrate a small amount of information into their Decision-making anyway. Humans have evolved and invented Heuristics in order to filter and compress information so it takes up less space in their memories.
What is more valuable than making detailed models is making models that are useful. Useful models include the a decent amount of relevant information so we can make a decision better than without the model. You can consider a time vs. complexity payoff.
$$ benefit\ of\ modeling = \frac{decision\text{-}making\ improvement} {time\ to\ build\ model} $$
A common problem when making useful models is knowing when to stop. Adding too much has a double penalty of both increasing mental capacity required for reasoning while making it harder to find the useful bits.
TODO: Expand on techniques that help you decide when to stop
If you made a perfect map of France it would be the size of France; it would be France. That would be useless. — Simon Wardley (paraphrased)
Making a perfect investment decision would require modelling at least the entire galaxy.
Making a perfect software model of a cat would require making a cat, down to the subatomic particles.
Making a useful model of a cat would depend on the context of what you’re trying to achieve. It’s possible to make a very useful model of a cat if you’re trying to predict cat health.
Making model of a system that is too complicated, or modelling parts of a system that aren’t relevant to your current inquiry is useless and often a waste of time.