The germ of annulation — JOI's childhood cycloid

texture · Winter B.S. 1963, Sepulveda CA

• When: Winter B.S. 1963 (scene-099 header), JOI's California boyhood
• What: In the mattress-moving memory that ends the scene, a sheared closet knob rolls on its own circumference around the stationary end of its hex bolt, describing "two perfectly circular motions on two distinct axes, a non-Euclidian figure on a planar surface, i.e., a cycloid on a sphere." The boy JOI — already a collector of prisms, lenses, and a scale-model magneto — recognizes the figure as L'Hôpital's cycloid solution to Bernoulli's Brachistochrone Problem, but rolling around its own circumference, so the parametric trig becomes first-order differential equations. This self-eating, self-returning curve is the conceptual seed of the whole annular idea (a process whose output feeds its own input) that his later optics work will help realize (events 2, 7). The thread's earliest beat: the fusion culture's founding intuition arrives as a child's accident of geometry — and the filmmaker later mythologizes this very memory as Valuable Coupon Has Been Removed (Y.T.M.P.), whose boy, helping dismantle his parents' bed, "intuits the future feasibility of D.T.-cycle lithiumized annular fusion" (n024). See the JOI timeline (the biographical scene); the Filmography & Entertainment thread (the film).