"Physics Envy" Is A Meme: In Defense of Mathematical Modeling Across the Sciences
February 25th, 2026
"Precisely constructed models for linguistic structure can play an important role, both negative and positive, in the process of discovery itself. By pushing a precise but inadequate formulation to an unacceptable conclusion, we can often expose the exact source of this inadequacy and, consequently, gain a deeper understanding of the linguistic data. More positively, a formalized theory may automatically provide solutions for many problems other than those for which it was explicitly designed. Obscure and intuition-bound notions can neither lead to absurd conclusions nor provide new and correct ones, and hence they fail to be useful in two important respects. I think that some of those linguists who have questioned the value of precise and technical development of linguistic theory have failed to recognize the productive potential in the method of rigorously stating a proposed theory and applying it strictly to linguistic material with no attempt to avoid unacceptable conclusions by ad hoc adjustments or loose formulation."
—Noam Chomsky
I come from linguistics, which is often grouped among the social and natural sciences and has had a storied history with mathematics in many forms. Semantics takes inspiration from predicate logic and set theory (and more recently linear algebra), syntax takes inspiration from graph theory, variationist sociolinguistics makes use of frequentist statistics, Bayesian phylogenetics from evolutionary biology has been used in the typological analysis of language families, and those are just a few examples out of many, many more. The use of computational analysis for languages has only added more mathematics into linguistics. One good empirical example is the Vesuvius Challenge, where the charred remains of a library in Herculaneum (modern day Ercolano) discovered in the 1700s were only recently partially deciphered with machine learning based optical character recognition. Another would be the use of stylometric analysis in forensics, ransom notes and manifestos being uncovered through the writer's word choices, sentence constructions and spellings, partly what got the Unabomber caught.
I hinted at this in my last essay, where I described a distinction in the social sciences between qualitative and quantitative approaches, and tacitly argued this distinction isn't helpful, so this article will be less descriptive, more argumentative towards the use of mathematical modeling. My argument is as follows: mathematical models nearly always offer a benefit to research, not only in what a model can say but what it can't. For a model to be tested against data, it needs to be made precise, lest loose definitions are twisted to support the data. This idea is universal, not just in the social sciences, but in biology and even some parts of physics. The reason why the Standard Model can be said to be incomplete is because it's precise, not because it isn't.
One argument often posited is that humans are far too complex to model with precise models. I say, that's why we use them. In the natural sciences (including biology), there are many complex phenomena that models cannot fully explain. Hell, even in physics (with the aforementioned Standard Model). Statistics exists precisely to give qualitative analysis error bars, in finding where expectations break and where they hold. Statistics gives precision, where a model is precisely right and where it's precisely wrong, and in what manners it's right and wrong. Statistics does not determine with full certainty a specific and reflective result given descriptive input, rather it is there to find correlations and divergences in data. This exists in medicine (PPV and sensitivity of tests), this exists in linguistics (typological analysis of language features, conservative-innovative split), and in many other sciences. It's the exceptions that make the rule, not the other way around.
And I will give them this: many models in the social sciences are brittle, some even ideologically enforced and so non-descriptive of wide swaths of data. But this is not a justification for the complete cessation of mathematical modeling, rather, it's proof of the good of mathematical models. Without precision, there is no exact methodology for the restating of a hypothesis. One may ask: So, what do I think is the problem? Not mathematics period, but the manner in which it's used. For many scientists, it has become an oracle that returns results and one you can query repeatedly until you get a result you want. Then, of course, they're surprised that the results given differ according to who's asking, unable to see that the oracle at hand is one they are supposed to construct, not one that they're supposed to worship. In less metaphorical speech, it's not merely that they're not predictive, it's that by their own nature, they can be fine-tuned, reconstituted, some assumptions thrown out and others remaining, until they maintain general robustness. By virtue of their precision, by virtue of the fact they mention exactly where they're right and where they're wrong, we can build new models that improve upon the old, and the blueprint is the model itself.
It's a tendency to believe the desire to mathematize traditionally qualitative fields is down to "physics envy", but no matter how individual scientists feel, mathematics is the toolbox by which a sculpture becomes more detailed, where the crooked spots are easily seen and patched. Instead of seeing the problems of mathematical models as proof that they're exercises in futility, we can look at the model itself and see what it justifies and what it doesn't. This does require an understanding of mathematics, of course, but it's something I think everyone should have at least to some level. The advent of the computational sciences has given us a playground to test out our assumptions and see where they fail, so why not keep using them?
I'll end this with yet another quote, this time from economist Irving Fisher:
"The contention often met with that the mathematical formulation of economic problems gives a picture of theoretical exactitude untrue to actual life is absolutely correct. But, to my mind, this is not an objection but a very definite advantage, for it brings out the principles in such sharp relief that it enables us to put our finger definitely on the points where the picture is untrue to real life."
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