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 imposes 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 generalised guides to how the physical world will behave — they set outer bounds to our expectations but will not give us a fine-grained real-time means of navigating the world. For example: the laws of physics tell us no cricket ball will attain escape velocity from a human bat, however well struck; nor will it morph into a bowl of petunias as we try to catch it. But as for the precise trajectory of spacetime it will pass through as I try to catch it — if science could ever yield an approximation of that, it would be far too late to be useful, and really we don’t have anything like enough data to run the calcuations in any case.

So we need to rely on our judgment, the facility for catching we have acquired through a lifetime of experience and practice, none of which involved solving a single differential equation: you cannot, as Nassim Taleb says, lecture birds on how to fly. Science is a convenient post-hoc explanation of what we did, not a guide to what we must do.

But the physical world is a complicated system: generally, a very, very complicated system, but insofar as the law of physics are concerned, not a complex one: we do not, by applying our models of physics to to the world, change how the world 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.

The JC’s sense is a similar thing may be true of data science, only it is less benign. We tell ourselves that data models can predict our behaviour, are unfailingly accurate, that we should yield to the greater power of data analytics. We no longer need “thick” rules of principle to moderate our behaviour, because we have thin rules that can equably adjudicate on any given particular. This is all the more concerning with the advent of neural networks and large learning models that we readily confess we do not understand at all, but it is already there, in our collective obeisance to, for example, the truth of DNA testing, or GPS navigation, or automated self-triage.

So we have DNA tests which will tell us, for example, we are 99.4% Scottish, with a smudge around Scandinavia, 4% Neanderthal, but don’t pick up any African heritage at all— despite the fact that every human on the planet is, ultimately, 100% African by origin (homo sapiens diverged from homo neanderthalensis hundreds of thousands of years before any human departed Africa).