The Brute-Force Formula
LLMs Do What Scientific Formulas Do, Only At a Different Scale
A scientific formula squeezes a phenomenon down to a set of parameters and a procedure. So does an LLM. The shape is the same; the scale is not. One fits on a napkin, the other needs billions of weights. It is compression stripped of elegance and driven by brute force.
From Observation to Structure
Say you’re in front of some phenomenon and you want to describe it. You start where anyone starts: you write down what happens, and the data piles up.
For a while the data is all you have. When you need an answer, you look it up. You’ve captured the phenomenon, in a sense, but only as a list, and every question costs you a search through it. The list keeps growing.
Take the planets. Tycho Brahe spent decades recording where each one sat in the sky on every night of the year, page after page of numbers. Want to know where Mars would be next month? You walked to the shelf, pulled the right volume, and read the entry.
Then Kepler inherited the tables and stared at them for years. At some point a structure surfaced inside the data, one that could generate the rest of it. Kepler saw ellipses. Three laws now did the work of thousands of observations: give them a moment in time, get back the position of a planet.
The structure had replaced the tables. Shelves of tables collapsed into a few lines. Same answers, far less to carry.
That collapsed form, a handful of parameters plus an algorithm that regenerates the phenomenon, is what we’ve always called a scientific law. Newton went further and folded Kepler’s three laws into one. Each compression buys the same predictions with less to remember.
The Formula and the LLM
Open up a scientific law and you usually find a mathematical formula inside. The law names a domain (orbits, falling bodies, electric charge) and the formula does the work.
A formula has three parts: a set of parameters, input data, and an algorithm for combining them. Feed it an input, run the algorithm against the parameters and the input, get an answer.
Now ask the same of an LLM. What is it?
The same three parts show up again. The parameters are the weights, billions of them. The input is the prompt. The algorithm is a procedure for combining them. Feed it the prompt, run the algorithm against the weights and the prompt, and an answer comes out.
The shape matches, but the scale is wildly different. A scientific formula might use only a handful of parameters, often fundamental constants of nature. An LLM uses billions, none of them fundamental, all of them tied to one particular training run. The formula is small enough for a human mind to grasp, a tool for thought that tells you something about the phenomenon even without a computer. The LLM isn’t. Its weights and algorithm reveal nothing about the phenomenon directly, and without a computer the compression is effectively out of reach. It is a compression, scaled past elegance and driven by brute force.
Scientific laws also reach past the data they came from. Newton’s law predicted planetary motions nobody had observed yet. Whether LLMs can do the same remains genuinely open: can they generate representations worthy of being called scientific laws?
For centuries science prized explanations elegant enough for a human mind to hold. Kepler, Newton, Maxwell, each compressed a huge amount of reality into something a person could reason about directly.
The LLM isn’t that. Its compression is real, but you can’t get at it without a computer. Billions of parameters and a heavy algorithm stand in for the handful of constants and equations we usually associate with understanding, and it still predicts well. If a representation continues to produce useful predictions, does it matter whether anyone understands it?
Interesting perspective. History shows that brute force, when scaled enough, often beats elegant theories. The real intelligence may not be avoiding brute force, but knowing where to apply it—and turning the patterns it finds into understanding.