We would lack medical care because a medicine or procedure can never be perfect. 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. 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.
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.
Physical maps generally become more accurate as time passes. Nowadays, our maps have come a long way. The same goes for mental models — they are always evolving, being revised — never really achieving perfection. Many mental models e. 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. In his essay 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?
If the goal of a model is to make a relationship or system clearer, added complexity defeats that purpose although it might make the model more accurate. On a high level, the map-territory relation also describes the relationship between an object and a representation of the object. Models are abstractions. Like maps, or miniature architectural models, or schematics, they cannot capture every detail of the object or system they are based on, if only because they do not exist in the real world and do not function in the same way.
Statistician J. Michael Steele has been critical of the adage see this personal essay. Steele goes on to state:. Steele argues that statistical models are often not up to an adequate fitness measure, and many models developed by statisticians are not sufficient for their intended use cases. He calls on statisticians to spend time learning how data in a given data set were generated and commit to developing realistic statistical models using machine learning and data-adaptive estimation techniques over more traditional parametric models.
This article has responses from statisticians Michael Lavine and Christopher Tong , as well as a response to the responses from the original author. The two refuting statisticians point to examples where models are known to be wrong but are often employed because they are useful, and fit for a given problem.
The response letters are definitely worth a read if you are interested. This represents an active area of debate in the fields of statistics and data science. Despite the limitations of models, many models can be very useful. Therefore, it could also be applied this idea that we will never be able to develop a numerical tool that perfectly describes the reality in all cases.
That may seem obvious or trivial but I think it is very interesting and important to bear in mind, even when you spend months developing a numerical tool completely immersed in your code. Since we are working with computers, it is relatively easy to reach impressive accuracy when doing simple operations and hence, we tend to demand ridiculous errors to our simulations.
Institutions had developed extremely complicated investment vehicles and relied on arcane algorithms to calculate their investment risks. Uncertainties in the underlying assumptions within these models were overlooked and not fully understood.
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