Precision Falls as You Climb the Ladder of the Sciences

Here is an observation anyone can check, and I have not seen it stated as bluntly as it deserves. The more accurate a science is, the less it relies on words. Take the sciences in order and watch the vocabulary degrade.

The Gradient

Physics uses mathematics for nearly everything. Its terms — mass, charge, spin, the Higgs boson — are defined by equations and by the measurements that pin them down. Two physicists cannot disagree about what a Higgs boson is; they can only disagree about whether one has been found.

Chemistry uses less mathematics. A water molecule is still a sharply defined thing, but the field already leans on qualitative rules of thumb about reactivity and structure that physics would not tolerate.

Biology uses less again. "An immune cell" is a real category, but its boundaries are fuzzy, its members are diverse, and much of the field's knowledge is stated in words: this pathway usually does this, under conditions that are hard to specify.

Go up one more level, to the biology of populations, and the term is "a pack of wolves." That is a description, not a definition. How many wolves make a pack? When does one pack become two? The question has no answer because the word was never meant to have one.

Now leave biology. Economics gives you "the market trend." Sociology gives you "religiosity." Political science gives you "democracy" — a word that a dictatorship, a republic, a Swiss canton, and a constitutional monarchy all use about themselves, and that no two theorists define the same way.

Line them up and the pattern is impossible to miss. At the bottom of the ladder the terms are exact and the tools are mathematics, statistics, and simulation. At the top the terms are ordinary words and the tools are more ordinary words. The precision of a field's vocabulary is a direct index of how much it actually knows.

Why It Runs This Way

The usual defence is that the higher sciences study more complex things and complexity forces vagueness. That is true, and it is not a defence. It is a concession with a hopeful gloss on it.

Consider how hard physics itself finds complexity. The three-body problem — three masses under gravity, nothing else — has no general closed-form solution. Three objects, one force, perfectly known laws, and the best we can do is approximate. That is the state of the art in the most exact science humans have.

Now consider what a "market" is: millions of agents, each with a different model of the others, acting under laws nobody has written down. If three bodies under one known law defeat exact description, what chance does that have? The honest answer is that the higher sciences are not vague because their practitioners are lazy. They are vague because the subject is far beyond our capacity to compute, and words are what you use when you cannot compute.

I have written elsewhere about why philosophy in particular pays this price, and about what a better vocabulary for politics might contain. The point here is broader. The gradient is not a fact about philosophy. It runs through every field, and it tells you where to place your confidence.

The Corollary Nobody Wants

If words are a poor tool for describing reality, then stories — which are made of words arranged for effect — are a worse one.

This follows directly, and it is uncomfortable, because it indicts literature, poetry, and cinema as instruments of knowledge. Not as sources of pleasure; that is a separate matter. But when someone tells you they understand a war because they read a novel about it, or a society because they saw a film set in it, they are claiming to have learned about a system at the top of the ladder using the least precise tool available for any rung of it.

A story is a single trajectory through a space we cannot map. Physics would not accept a single trajectory as evidence of a law even for three bodies. We routinely accept it for a country.

What To Do With This

Three things.

First, when you read a claim, look at its vocabulary before its argument. If the key terms are words that could be defined five ways, the claim has already told you how much weight it can bear.

Second, treat the higher sciences as what they are: fields doing their honest best on problems that exceed our tools. Not fraudulent, but not physics, and not entitled to speak with physics' confidence.

Third, notice when a term from the top of the ladder is being used as if it came from the bottom. "Democracy" said with the assurance of "electron" is the most common move in political argument, and it is a category error dressed as a conviction. The word does not know what it means. Neither, for the most part, do we.