Modelling continuous progress

Abstract

A mathematical model, based on a prior formulation by Eliezer Yudkowsky and Nick Bostrom, was constructed to investigate the differences between discontinuous and continuous progress of AI takeoff, addressing disparities in viewpoint between proponents of both views. The model considers the abruptness of discontinuity and the overall strength of recursive self-improvement (RSI) as variables, capturing the respective assumptions of discontinuous and continuous trajectories. Simulations show that continuous progress leads to earlier acceleration above the exponential trend, a smoother transition to faster growth, and a potential overlap with a “Paul slow” takeoff, where intermediate doubling intervals occur before a rapid collapse in doubling time. Examining varying takeoff speeds reveals that the smoothness of the takeoff curve and the timing of doubling intervals depend on both the continuity and speed of progress. – AI-generated abstract.