Many scientists dream of finding a unified theory of something, a theory that would encompass others and explain, with a few equations, a large number of observations. Physicists in particular have been looking for fundamental equations. In economics, there is currently a drive among growth theorists to find a unified growth theory, although here the focus is not on a single equation, but rather a model. Indeed, one has to realize that explaining several thousand years of economic growth involves some complexity.
And now the physicists get interested in the topic. Andrey Korotayev and Artemy Malkov actually go beyond a simple one equation model and use some theory, linking surplus output to population growth à la Malthus. Up to 1970, population is hyperbolic, while GDP is quadratic-hyperbolic (in both cases levels, and not growth as the authors assert). They conclude from this that technological progress is expanding because of the larger number of inventors as population grows. That seems a bit simplistic, as one should also bear in mind that there are decreasing returns to inventing, as documented by rather constant long-run growth rates for total factor productivity in modern history despite an increasing share of a growing population dedicated to research and development. But one can get misled when one looks only at few indicators.
And now the physicists get interested in the topic. Andrey Korotayev and Artemy Malkov actually go beyond a simple one equation model and use some theory, linking surplus output to population growth à la Malthus. Up to 1970, population is hyperbolic, while GDP is quadratic-hyperbolic (in both cases levels, and not growth as the authors assert). They conclude from this that technological progress is expanding because of the larger number of inventors as population grows. That seems a bit simplistic, as one should also bear in mind that there are decreasing returns to inventing, as documented by rather constant long-run growth rates for total factor productivity in modern history despite an increasing share of a growing population dedicated to research and development. But one can get misled when one looks only at few indicators.