Since Newton's time, the scientific method has sought a single equation for a single phenomenon. Even modern symbolic regression, which automatically derives formulas from data, silently inherits this assumption: it looks for one optimal curve. But real systems switch between mechanisms as conditions change, much like an ecosystem shifts its dominant species with climate. The authors of the new work abandoned the quest for the "best" equation and instead asked: how many laws coexist at once?
The answer turned out to be remarkably consistent. Across four very different systems—elastomers, boiling, galaxy rotation, and droplet evaporation—the algorithm identified exactly three independent mechanisms. For rubber, these are the power law of crystallization, the root law of entropic elasticity, and Hooke's linear law; prediction improved by 72% over gradient boosting. For boiling, accounting for monotonic regime changes added 20% accuracy.
The most striking result came from 3269 measurements of 163 galaxies. The system independently recovered three gravitational laws: Newtonian, transitional, and a "constant acceleration floor." The characteristic acceleration a0, at which the Newtonian regime gives way to the flat one, differs by a factor of 2.2 between gas-poor and gas-rich galaxies. This rules out a single modified Newtonian dynamics curve with a significance of p < $10^{-34}$, turning the debate over MOND's universality from a philosophical one into a computational test.
The method opens a new direction: not improving individual equations, but describing their coexistence. Instead of hard boundaries between regimes, a continuous field of weights is constructed, where each law has its own "territory" of influence. This approach applies to turbulence, material fatigue, and stellar evolution, as well as to debates about one versus several laws in biology and climatology. The next step is to test whether the number of mechanisms changes over time, like species succession in an ecosystem.
A candle, which we see as a single flame, is actually governed by four different equations: heat conduction in the wax, diffusion combustion in the blue zone, radiation in the bright part, and convection in the tongue above the flame.