Beware of spherical cows
By: M. J. Mrezar
Tags: Mental Models, Understanding, Maps, Thinking, Biases And Fallacies

Image from Ylanite Koppens at pexels.com

The complexity of the world is astounding. The sheer amount of forces at play is far beyond our intellectual capabilities. That’s why to make sense of the world we are bound to simplify.

To begin to understand is to create a simplified model of the reality in our mind. During this process we are like the cartographers that translate the data gathered by the explorers into a map of the territory. We are subduing the terra incognita into its functional representation. But a map is by definition always an approximation of the world. A map with a 1-to-1 scale with perfect details would need to be as large as the territory itself. That’s why we need to simplify: both in map-making and in our mental models.

Simplification is a tricky thing though. Reducing the complexity into a simplified model might lead to detracting from the reality into a realm of abstraction. It might lead us to assuming a spherical cow. In an old joke, a dairy farm was struggling with a low milk production. Looking for help, its managers contacted a local university to seek the wisdom of the academia. In the course of the next two weeks, a team of scientists carried out experiments and collected data at the farm. Unfortunately, the biologists, chemists and other experts failed to improve the output. But a theoretical physicist found a solution: ‘’Assume a spherical cow!’’, he began his presentation.

The story is an illustration of the perils of oversimplification. Reduction of a complex biological system to a mathematical construct eases the calculations and removes many factors otherwise needing consideration. But getting rid of too much and neglecting the complexity renders our findings useless.

Well-constructed maps are nonetheless valuable inventions. We rely on them to navigate the waters of the world — literally and figuratively. Even if imperfect and devoid of some details, a good map of a city we want to visit will still do wonders. Without it, we are bound to wander blindly, hoping we somehow stumble onto our destination. But a good map will guide us from point A to point B in a most efficient manner, even if it is not a perfect reflection of the city.

So to make sense of the world, we must balance between the highest achievable approximation and the imperative of simplicity. How many corners can we cut and still arrive at our destination? How much of the complexity can we give up to be able to fit our map into the back pocket of our jeans?

A perfect correspondence of the map to the territory by definition gives us a map the size of the actual territory.

A perfect simplicity gives us a spherical cow: an abstract construct without practical application.

A perfect correspondence and perfect brevity is an unobtanium: a pipe dream.

But there is, a guiding principle that we can use to calibrate our mental models. It starts with asking ourselves why are we constructing this model in the first place? Do we need it for its own sake or rather to use it as a map to make sense of the world and get to where we want to be?

In the end, all maps and mental model are tools. And each tool’s purpose is its practical application: the quality of how is helps us solve our problems.

The purpose of each model is to bridge a gap between the reality and our accurate understanding of it. Correspondence divided by the usability is the golden formula.

A map has at least two features: it corresponds to reality in some way, and it allows us to locate ourselves and our destination on it. And that’s a good place to start: figuring out where we are and where we want to be — or what we already know and what we want to learn. Then it’s about adding layers of complexity that matters. It’s about focusing on the outcome while forgetting the topology of all that is redundant. Prioritizing that without which our map would be useless.

A mental model is a system of beliefs about a particular aspect of the world. Each belief is a gamble, let’s play our hand wisely. Let’s consider all that is known and place our bet accordingly. And always be willing to update our models with each new relevant and reliable piece of information. Let’s not cling to any of our models and always be willing to give them up, as they are just that — models. They are not parts of us and its okay to reconsider or replace them altogether.

This piece of advice is also a model — hopefully more of a useful tool than a spherical cow. Use it, if it has practical value. Forget it, if it doesn’t.