How is your journey towards understanding Farnam Street’s latticework of mental models going? Is it proving useful? Changing your view of the world? If the answer is that it’s going well that’s good. There’s just one tiny hitch.
All models are wrong.
Yep. It’s the truth. However, there is another part to that statement:
All models are wrong; some are useful.
Those words come from the British statistician, George Box. In a groundbreaking 1976 paper, Box revealed the fallacy of our desire to categorize and organize the world. We create models (a term with many applications), once to confuse them for reality.
Box also stated:
Remember that all models are wrong; the practical question is how wrong do they have to be to not be useful.
What Exactly Is A Model?
First, we should understand precisely what a model is.
The dictionary definition states a model is ‘a representation, generally in miniature, to show the construction or appearance of something’ or ‘a simplified description, especially a mathematical one, of a system or process, to assist calculations and predictions.’
For our purposes here, we are better served by the second definition. A model is a simplification which fosters understanding.
Think of an architectural model. These are typically a small scale model of a building, made before it’s built. Its purpose is to show what the building will look like and to help people working on the project to develop a clear picture of the overall feel. In the iconic scene from Zoolander, Derek (played by Ben Stiller) looks at the architectural model of his propsed ‘school for kids who can’t read good’ and shouts “What is this? A center for ants??”
That scene illustrates the wrong way to understand models: Too literally.
Why We Use Models- And Why They Work
At Farnam Street, we believe in using models for the purpose of building a massive, but finite amount of fundamental, invariant knowledge about how the world really works. Applying this knowledge is the key to making good decisions and avoiding stupidity.
“Scientists generally agree that no theory is 100 percent correct. Thus, the real test of knowledge is not truth, but utility. Science gives us power. The more useful that power, the better the science.”
— Yuval Noah Harari
Time-tested models allow us to understand how things work in the real world. And understanding how things work prepares us to make better decisions without expending too much mental energy in the process.
Instead of relying on fickle and specialized facts, we can learn versatile concepts. The mental models we cover are intended to be widely applicable.
It’s crucial for us to understand as many mental models as possible. As the adage goes, a little knowledge can be dangerous and creates more problems than total ignorance. No single model is universally applicable – we find exceptions for nearly everything. Even hardcore physics has not been totally solved.
“The basic trouble, you see, is that people think that “right” and “wrong” are absolute; that everything that isn’t perfectly and completely right is totally and equally wrong.”
— Isaac Asimov
Take a look at almost any comment section on the internet and you are guaranteed to find at least one pedant raging about a minor perceived inaccuracy, throwing out the good with the bad. While ignorance and misinformation are certainly not laudable, neither is an obsession with perfection.
Like heuristics, models work as a consequence of the fact they are usually helpful in most situations, not because they are always helpful in a small number of situations.
Models can assist us in making predictions and forecasting the future. Forecasts are never guaranteed, yet they provide us with a degree of preparedness and comprehension of the future. For example, a weather forecast which claims it will rain today may get that wrong. Still, it’s correct often enough to enable us to plan appropriately and bring an umbrella.
Mental Models and Minimum Viable Products
Think of mental models as minimum viable products.
Sure, all of them can be improved. But the only way that can happen is if we try them out, educate ourselves and collectively refine them.
We can apply one of our mental models, Occam’s razor, to this. Occam’s razor states that the simplest solution is usually correct. In the same way, our simplest mental models tend to be the most useful. This is because there is minimal room for errors and misapplication.
“The world doesn’t have the luxury of waiting for complete answers before it takes action.”
— Daniel Gilbert
Your kitchen knives are not as sharp as they could be. Does that matter as long as they still cut vegetables? Your bed is not as comfortable as it could be. Does that matter if you can still get a good night’s sleep in it? Your internet is not as fast as it could be. Does that matter as long as you can load this article? Arguably not. Our world runs on the functional, not the perfect. This is what a mental model is – a functional tool. A tool which maybe could be a bit sharper or easier to use, but still does the job.
The statistician David Hand made the following statement in 2014;
In general, when building statistical models, we must not forget that the aim is to understand something about the real world. Or predict, choose an action, make a decision, summarize evidence, and so on, but always about the real world, not an abstract mathematical world: our models are not the reality.
For example, in 1960, Georg Rasch said the following:
When you construct a model you leave out all the details which you, with the knowledge at your disposal, consider inessential…. Models should not be true, but it is important that they are applicable, and whether they are applicable for any given purpose must, of course, be investigated. This also means that a model is never accepted finally, only on trial.
Imagine a world where physics like precision is prized over usefulness.
We would lack medical care because a medicine or procedure can never be perfect. In a world like this, we would possess little scientific knowledge, because research can never be 100% accurate. We would have no art because a work can never be completed. We would have no technology because there are always little flaws which can be ironed out.
“A model is a simplification or approximation of reality and hence will not reflect all of reality … While a model can never be “truth,” a model might be ranked from very useful, to useful, to somewhat useful to, finally, essentially useless.”
— Ken Burnham and David Anderson
In short, we would have nothing. Everything around us is imperfect and uncertain. Some things are more imperfect than others, but issues are always there. Over time, incremental improvements happen through unending experimentation and research.
The Map is Not the Territory
As we know, the map is not the territory. A map can be seen as a symbol or index of a place, not an icon.
When we look at a map of Paris, we know it is a representation of the actual city. There are bound to be flaws; streets which have been renamed, demolished buildings, perhaps a new Metro line. Even so, the map will help us find our way. It is far more useful to have a map showing the way from Notre Dame to Gare du Nord (a tool) than to know how many meters they are apart (a piece of trivia.)
Someone who has spent a lot of time studying a map will be able to use it with greater ease, just like a mental model. Someone who lives in Paris will find the map easier to understand than a tourist, just as someone who uses a mental model in their day to day life will apply it better than a novice. As long as there are no major errors, we can consider the map useful, even if it is by no means a reflection of reality. Gregory Bateson writes in Steps to an Ecology of Mind that the purpose of a map is not to be true, but to have a structure which represents truth within the current context.
“A map is not the territory it represents, but, if correct, it has a similar structure to the territory, which accounts for its usefulness.”
— Alfred Korzybski
Physical maps generally become more accurate as time passes. Not long ago, they often included countries which didn’t exist, omitted some which did, portrayed the world as flat or fudged distances. Nowadays, our maps have come a long way.
The same goes for mental models – they are always evolving, being revised – never really achieving perfection. Certainly, over time, the best models are revised only slightly, but we must never consider our knowledge “set”.
Another factor to consider in using models is to take into account what they’re used for.
Many mental models (e.g. entropy, critical mass and activation energy) are based upon scientific and mathematical concepts. A person who works in those areas will obviously need a deeper understanding of it than someone who want to learn to think better when making investment decisions. They will need a different map and a more detailed one showing elements which the rest of us have no need for.
“A model which took account of all the variation of reality would be of no more use than a map at the scale of one to one.”
— Joan Robinson
In Partial Enchantments of the Quixote, Jorge Luis Borges provides an even more interesting analysis of the confusion between models and reality:
Let us imagine that a portion of the soil of England has been leveled off perfectly and that on it a cartographer traces a map of England. The job is perfect; there is no detail of the soil of England, no matter how minute that is not registered on the map; everything has there its correspondence. This map, in such a case, should contain a map of the map, which should contain a map of the map of the map, and so on to infinity.Why does it disturb us that the map be included in the map and the thousand and one nights in the book of the Thousand and One Nights? Why does it disturb us that Don Quixote be a reader of the Quixote and Hamlet a spectator of Hamlet? I believe I have found the reason: these inversions suggest that if the characters of a fictional work can be readers or spectators, we, its readers or spectators, can be fictions.
How Do We Know If A Model Is Useful?
This is a tricky question to answer. When looking at any model, it is helpful to ask some of the following questions:
- How long has this model been around? As a general rule, mental models which have been around for a long time (such as Occam’s razor) will have been subjected to a great deal of scrutiny. Time is an excellent curator, trimming away inefficient ideas. A mental model which is new may not be particularly refined or versatile. Many of our mental models originate from Ancient Greece and Rome, meaning they have to be functional to have survived this long.
- Is it a representation of reality? In other words, does it reflect the real world? Or is it based on abstractions?
- Does this model apply to multiple areas? The more elastic a model is, the more valuable it is to learn about. (Of course, be careful not to apply the model where it doesn’t belong. Mind Feynman: “You must not fool yourself, and you’re the easiest person to fool.”)
- How did this model originate? Many mental models arise from scientific or mathematical concepts. The more fundamental the domain, the more likely the model is to be true and lasting.
- Is it based on first principles? A first principle is a foundational concept which cannot be deduced from any other concept and must be known.
- Does it require infinite regress? Infinite regress refers to something which is justified by principles, which themselves require justification by other principles. A model based on infinite regress is likely to required extensive knowledge of a particular topic, and have minimal real-world application.
When using any mental model, we must avoid becoming too rigid. There are exceptions to all of them, and situations in which they are not applicable.
Think of the latticework as a toolkit. That’s why it pays to do the work up front to put so many of them in your toolbox at a deep, deep level. If you only have one or two, you’re likely to attempt to use them in places that don’t make sense. If you’ve absorbed them only lightly, you will not be able to use them when the time is at hand.
If on the other hand, you have a toolbox full of them and they’re sunk in deep, you’re more likely to pull out the best ones for the job exactly when they are needed.
Too many people are caught up wasting time on physics-like precision in areas of practical life that do not have such precision available. A better approach is to ask “Is it useful?” and, if yes, “To what extent?”
Mental models are a way of thinking about the world that prepares us to make good decisions in the first place.