Template:M intro design how the laws of data science lie

When a man throws a ball high in the air and catches it again, he behaves as if he had solved a set of differential equations in predicting the trajectory of the ball. He may neither know nor care what a differential equation is, but this does not affect his skill with the ball. At some subconscious level, something functionally equivalent to the mathematical calculations is going on.

—Richard Dawkins

Really powerful explanatory laws of the sort found in theoretical physics do not state the truth.

—Nancy Cartwright, How the Laws of Physics Lie (1983)

In 1983 philosopher Nancy Cartwright wrote the seemingly scurrilous How the Laws of Physics Lie — not quite the post-modernist tripe it sounds, but rather a serious and literate work of analytical philosophy. Cartwright’s point was that scientific laws are formulated in conditions so rigid, isolated and controlled that, even though they might be perfectly valid within those conditions, they are practically useless “in the real world,” where those conditions have no hope of existing. So the principles of Newton’s mechanics, assuming as they do no inconveniently intervening forces like friction, gravity, inelasticity, might plat the trajectory of an object on a graph, but have no chance of plotting the trajectory of the proverbial crisp packet blowing across St Mark’s Square. You will spend a lot of time with a slide rule and an anemometer; when you look up the packet will be gone.

The same observation animates Gerd Gigerenzer’s faith in heuristics over science: despite Richard Dawkins’ trite conviction to the contrary, a fielder performs no differential equations on the way to catching a flying cricket ball.

We trick ourselves into believing the power of our scientific laws, wilfully blind to the ad hoc variations, adjustments and glosses that our messy world inposes upon them; we put down any apparent disparity to this ineffable collection of intervening forces: we tell ourselves the laws of physics describe an idealised, Platonic model; our messy world is anything but, so we should expect variances from those pure predictions.

Now this is all well and good: we are simply pragmatising scientific laws: recasting them as rules of thumb and generalistic guides to what should happen — they can set outer bounds to our expectations — but will not give us a fine-grained real-time means of navigating the world. We need to rely on our judgment and acquired experience for that: you cannot, as Nassim Taleb says, lecture birds on how to fly.

But the physical world is a complicated system: generally, a very, very complicated system, but insofar as the law of physics are concerned, not complex: we do not, by applying our laws of physics to it, change how it behaves. It is still in a sense linear: it is just our rules are approximations, not specific predictions. So the lie perpetrated by the laws of physics is broadly benign.

We have a sense a similar thing may be true of data science.