On the architecture of the rings of Saturn: An “identity” theory of the distribution of gaps within rings

In the physical world the “identity” of something is taken generally as a given; an apple is an apple; this apple is this apple. When dealing with planetary structure and extension into space, however, the problem of the planet’s “identity” in the surrounding cosmos is writ large. What does a planet’s “identity” imply? What functions must it take on? What internal logic holds it together as a functional “being” in the universe? A model of long-wave economic activity and crisis in the United States – “the Political Economy wave” – portrays the quest for social and economic “identity” with three simple curves: a sine curve over 56 years (20,454 days), a damping cosine curve of one-half the period of the sine curve, and the addition of these two in a “Political Economy Wave.” The logic of this wave is a recurring structure which shapes social “identity” over time. This paper compares the main peaks, intersections and troughs of the Political Economy wave for the United States, 1800-to-present, with the structure of the rings of Saturn, one of the most confounding structures known to science. At the present time gaps appear between rings which are unexplained; dynamism within the rings which should disperse the rings does not do so; edges of the rings are not diffuse but well defined; satellites between rings appear to have an impact but this is uncertain. Comparing these gaps with the various “crises” which predictably impact the “self identity,” the self-understanding, of society, this paper explores the possibility that the mathematics of identity may assist in the understanding of astrophysics, and possibly vice versa.