Abstract :
Summary form only given. Discusses the unified field theory of juggling (Horgan, 1990): if B equals the number of balls, H the number of hands, D the time each ball spends in a hand, F the time of flight of each ball, and E the time that each hand is empty, then B/H=(D+F)/(D+E). Highly skilled juggling has been analyzed through methods of nonlinear dynamics. The assumptions guiding this work can be expressed as follows. Let K=D/(D+E). Then assumption 1 is that the scientific problem of timing in juggling is one of partitioning the real number line (of K) into rational and irrational numbers, and assumption 2 is that the mechanism for this partitioning is in the competition between the discrete variables (N and H ) and the continuous variables (D, F, and E ). Results show that the partitioning, or gapless tiling, of the two-dimensional time space is achieved in units of |D-E| and that the temporal variance in juggling is physically interpretable as phase modulation away from the absolute potential minimum defined by the lowest possible phase-locked mode
Keywords :
cognitive systems; dynamics; learning systems; neural nets; nonlinear equations; absolute potential minimum; continuous variables; discrete variables; gapless tiling; irrational numbers; juggling; learned skill; lowest possible phase-locked mode; neurocognition; nonlinear dynamics; partitioning; phase modulation; rational numbers; real number line; time of flight; timing; two-dimensional time space; unified field theory;
