The Model and its Limits

All models are wrong, but some are useful.

– George Box

So you’ve built yourself a model? Here’s the thing to remember. Even when a model checks out wonderfully with the best measurements available, it’s still incomplete. Models boil big, complicated things down into explanations we can actually understand. Do details get lost in translation? You bet they do.

Here’s an example.

Classical mechanics, the physics of Newton and Leibniz, describe the universe in simple equations, graceful curves, and directly-observable phenomena. A ship sailing at constant speed v will reach its destination s at a time t, where s is the product of v and t. A teacup cools to the temperature of the surrounding room at a rate relative to the temperature difference between them. In both cases, the experimental result checks out with intuition.

Yet as better instruments and experimental techniques granted physicists keener vision into the mysteries of the universe, gaps began to appear. Time bends in funny ways for a ship traveling at some significant fraction of the speed of light. Radiative heat transfer—whether in a teacup, steam engine, or black hole—makes no sense at all.

Semiconductors, GPS, and glow-in-the-dark watch hands all depend on a less-intuitive (but ultimately more useful) model than the one gone before, but relativity and quantum mechanics–those pillars of modern physics–are still only the best speculation available. We’re better at balancing the books on observed behavior than we were a century ago, but someday the standard model too will give way to others.

If you ever start thinking that we’re close to figuring it all out, remember this: every model we propose, from the simplest machine to our latest, greatest guess at “why the universe” is still just a model, with all the extrapolation and conjecture that implies. We’ve formed hypotheses, taken measurements, and for the most part things line up. But the moment we happen across something better, you can bet the theory of gravity will go the way of the flat earth.

But you said you have a model?

If you want that model to be the best it can be, get it out in the open. Challenge it every way you can, then invite your friends to do the same. Let them test, challenge, embrace, or discredit it. Think of Linus’ Law—”given enough eyeballs, all bugs are shallow”—with a spoonful of skepticism for those eyeballs’ own limits. But whatever the project, topic, or goal, the model will never be worse for the feedback of others.

And when it turns out it’s not perfect? Shame, that, but it never is.

If it was, it wouldn’t be a model.