Still reading Roodman
Calculus ignores randomness
classical calculus ignores randomness. It is great for modeling the fall of apples; not so much for the price of Apple.
The foundations of Calculus treats paths as a collection of infinitely many small steps. To model shocks to this path, say the collapse of a civilization Roodman thinks that stochastic modelling, accounting for randomness in model parameters is the way forward.
Incorporating randomness still leads to the GWP explosion in finite time, so it doesn’t ‘solve’ the original issue.
An even better mathematical description of the past still predicts an impossible future.
One interesting aspect of Roodman’s modelling is that ‘revolutions’ like the industrial and agricultural can be viewed as deviations or bumps on a standard path.
His model does account for the idea that in 1820, the actual GWP vs what the model predicted was in the 90th percentile. It reduces its percentile then as he moves through the 20th century.
It turns out that a superexponential growth process not only fits the past well. It is rooted in conventional economic theory, once that theory is naturally generalized to allow for investment in technology.
Why do good models of the past predict an impossible future?
A deeper take is that infinities are a sign not that a model is flatly wrong but that it loses accuracy outside a certain realm of possible states of the world. Beyond that realm, some factor once neglected no longer can be. Einstein used the fact that the speed of light is the same in all inertial reference frames to crack open classical physics. It turned out that when such great speeds were involved, the old equations become wrong.