All Models Are Wrong

Despite the virtues of Science, Technology, Engineering, and Mathematics (STEM), these fields have a dark side that we ought to shine more light on.

STEM trains the mind to model the world precisely and mathematically. We are tested and interviewed primarily on our understanding of such models; sometimes, to such an extent that we lose sight of the realities they abstract. The distinction between model and reality is nevertheless critical. Choosing the right mental model in any situation—and understanding that all models are inherently imperfect, just as no map entirely captures the terrain it represents—is a more valuable skill than the ability to wield any particular model effectively.

The universe is not only queerer than we suppose, but queerer than we can suppose.

—J. B. S. Haldane, Possible Worlds

Models are tools, and like all tools, their utility is situational. No single person has the luxury of unimpeded access to universal truth. The best we can do is to leverage whichever models are most likely to help us achieve specific goals.

When someone else applies a different model than one we’ve accepted, and thus reaches different conclusions than our own, it’s easy to suppose that one of us must be wrong. That disagreement can be frustrating. It’s helpful to remember that we rarely really know anything, especially when deciding the best way to solve a problem. The single most important trait distinguishing senior engineers from junior ones may well be the humility that comes from having been wrong many times before.

All models are wrong, but some are useful.

—Attributed to statistician George E. P. Box

Engineers, at least, routinely deal in space-time trade-offs, margins of error, mechanical tolerances, etc., whereas many people naively believe pure mathematics to be some kind of absolute truth rather than, like all forms of study, a mere representation of our intrinsically flawed understanding of a fundamentally unknowable world. Having “proven” something doesn’t mean it’s True with a capital T, only that we can’t see how it could not be true. We are imperfect beings though, and often miss things.

Kant, who was ten times more distant from Aristotle than we are from him, even held that nothing significant had been added to Aristotle’s views in the intervening two millennia.

In the last century, Aristotle’s reputation as a logician has undergone two remarkable reversals. The rise of modern formal logic following the work of Frege and Russell brought with it a recognition of the many serious limitations of Aristotle’s logic; today, very few would try to maintain that it is adequate as a basis for understanding science, mathematics, or even everyday reasoning.

—Stanford Encyclopedia of Philosophy, Aristotle’s Logic

None of this undercuts the usefulness or merit of scientific models. The medical and technological advances of the last few centuries probably would have been impossible without the scientific revolution. When you disagree with someone though—and can’t understand how they could be so boneheaded, especially in the face of so much evidence!—rather than thinking they must be stupid or evil, try to understand their mental model. And have the humility to realize that it may be no less valid than your own.