Vigorous forays into the thickets of time and space in pursuit of absolutes.
Erickson endeavors to reestablish and refine an approach to reason â€œthrough a defense of the infinitesimal and the return of the number line.” His work relies on both the senses and intuition, operating on both finite and infinite levels, observable now and, then, conjectured: Of pi, â€œalthough we know that we cannot find it, we know that it must exist.” Infinitesimals are points of location, without area, indivisible, constant, innumerable within a finite expansion, providing continuity. Infinitesimals exist on a different level of reality than finites, requiring the use of irrational numbers to make a unit continuous. Though the infinitesimal is Erickson’s champion, irrational numbers and veritable number systems are his Virgils to explore what operates below the sheath of the finite. Time, too, has continuity, comprised of discrete instances: here, then gone forever, moving without breach and everywhere at the same pace (thus skewering parallel dimensions). The author’s explanation of motion is more mind-bending: â€œMotion is not between the instants, but at the instant. The whole of the change takes place at that unbroken suddenness,” while measurable speed must cross differing numbers of infinitesimals. If dense with dark matter, and occasionally allusive to a fault when introducing mathematical theories, Erickson proceeds logically from finite to actual and potential infinity, to minimum angles and division by zero, the role of the tangent in points and the foibles of sets and the mathematical limit. But in his rupture with relativism, lucidity is critical, and an irksome number of statements are not so much challenging as obliquitous; for instance, â€œspace lies beyond all man can do” doesn’t get us any closer to understanding space as an entity â€œneither material, nor mental.” And when a challenged reader encounters â€œa finite neckless made of intersecting rings of the same size would have a continuous pattern,” one immediately suspects a ruse is at play.
Not for the mathematically faint of heart, but a serious, rarefied attempt to construe reality outside the dominant paradigm.