What does ‘all models are wrong’ mean? Why is there never a true underlying model?


“All models are wrong, but some are useful” is a famous saying in science.

This saying is helpful because that all models can be wrong is not completely obvious to us living in everyday life. This reminds of our blind spots in our perception.

We perceive reality, and what we perceive as “reality” is essentially a simplified reflection of reality, not reality itself. The perceived reality is only a representation/projection of certain properties of reality. Although there are certainly useful representations for characterizing a variety of phenomena happening in reality, representations are not reality (just as a map is not the land and a menu is not the meal).

Our inherent blind spots that can mislead us derive from a fact that we can only represent a representation of reality, not reality itself directly. Representations depend on perspective and conditioning, and models are representations.

In modern science, nature’s laws are usually phrased in mathematics. They can be either exact or approximate, but they must have been observed to hold without exception — if not universally, then at least under some set of conditions. For example, one famous set of models are Newton’s laws, which account, at least to a very good approximation, for the orbits of the earth, moon, and planets, and explain phenomena such as the ocean’s tides. But while Newton’s laws work as a good representation to the scales and speeds of everyday life, they fall apart in very small scales, at very high speeds, or in very strong gravitational fields — they only work well sometimes. Models depend on conditioning.

By specifying the underlying principles/theories into a certain domain, models are often so effective and powerful in explanation and prediction, and give us strong impressions that there are some correct models of reality and that the complex happenings around us could be reduced to simpler true underlying models that do not require conditioning.

However, although the fundamental principles that theories carry may be simple, the behavior of composite objects that we target at describing in practice (for example, a physical system with many particles, objects in chemistry, biology, economy, psychology) can be very complicated. To handle this, a model, as a selective representation, is formulated to provide an adequate explanation of observed phenomena, without accounting for all of the underlying processes (i.e., conditioning-out uninteresting phenomena, whereas the “interestingness” criterion is determined by modelers’ specific perspectives), for example, molecules are sometimes modeled as billiard balls, DNA as a twisting ladder, and Newton’s laws as a few numbers instead of every interacting atom in the object.

Since each theory, either exact or approximate, can describe and explain only certain properties and within a certain range, to fill in the details of concrete situations we face in science and in everyday life, a (subjective/empirical or both) model steps in. This model is neither derived entirely from data nor from theory. Model building is rather an art, as, although it deals with the predictability, it emphasizes elegance, simplicity, and the usefulness of the model, and is only conditional on available information, which is rather arbitrary. Model building is not a mechanical procedure- it heavily relies on the eyes of the modelers and their situation. And there are many situations when there are no theories at all available.

Speaking of theories, there are no model-independent theories. Our brains interpret signals from our sensory organs by making a model of the outside world. These mental concepts are essentially simplified reflections of reality. And these mental images modeled through the lens of our brains are the only reality that we can know, on which our theories are based. Ultimately, we are all human beings trapped in our models.

The saying “all models are wrong” is helpful, not because all models we build in practice are particularly wrong, but because it reminds us of our blind spots in our brains and our simplifications and approximations we make in everyday life and in science, as we ponder and form concepts about our surroundings.

(This can also be found at Quora.com.)