Sometimes, it really is discontinuous in the variables that one has chosen to plot. The continuous change is happening along some other variable not plotted. For example, if we plot “achieved AI power” against “supplied computing power in FLOPS”, then at a point where it gains self-improvement capabilities, “AI power” can skyrocket while FLOPS remains constant. The continuous variable not plotted is time.
Sometimes, it really is discontinuous in the variables that one has chosen to plot. The continuous change is happening along some other variable not plotted. For example, if we plot “achieved AI power” against “supplied computing power in FLOPS”, then at a point where it gains self-improvement capabilities, “AI power” can skyrocket while FLOPS remains constant. The continuous variable not plotted is time.
Illustrative analogy: