On production and abatement time scalesin sustainable development.Can we loosen the sustainability screw?

In this paper we carry out a preliminary exploration of a time scales’ conjecture, whichpostulates that “reasonable” notions of sustainability must include a suitable synchronisationof time scales of both the processes of human development and those of the naturalenvironment. We perform our analysis within a coarse, five variable, model of man-natureinteractions expressed as a system of differential equations where production and humancapital are coupled with both renewable and non-renewable natural resource. We demonstratea phenomenon that we name the “sustainability screw” that describes a spiral like trajectory ofthe three key variables: non-renewable and renewable resources as well as the productioncapital. Under many plausible scenarios, this spiral tends unacceptably fast to an undesirableequilibrium. However, we also show that by adjusting the ratio of “intensity of productioneffort” and “intensity of abatement effort”, parameters of the relative time scales of productionand natural recovery processes can be altered in a manner that produces, arguably, moresustainable tra jectories.....