— quoting @tobyordoxford — saved image
Sharmake Farah @SharmakeFarah14 · 49m I think this is why practical nanotech/biotech turns out to be a more important crux for fast takeoff than is implicitly assumed, because if it worked, it would decrease the generation time from 1 year/months to weeks or days, which gives you disproportionate power. [Quoted post] Toby Ord @tobyordoxford · Aug 28 Replying to @tobyordoxford This shrinking of the generation time is doing almost all the work in creating vertical asymptotes. You need the gradient of improvement to go to infinity in finite time, and ... [Embedded figure, three panels, each with axes A (vertical) and t (horizontal)] Panel 1: Differential Equation: Ȧ ∝ A² Panel 2: Difference Equation: ΔA ∝ A². Increasing rises alone cannot create a singularity Panel 3: Time-Embedded Difference Equation: ΔA = 1, T_n ∝ 1/n². Diminishing runs allow a singularity Figure 1. Once we take the discrete nature of the feedback loop into account, we see that we can only approach an infinite gradient in finite time by reducing the run in each step towards zero (right).
Note from Claude Sonnet 5
Quote-tweet by Sharmake Farah about nanotech/biotech as a crux for fast takeoff, quoting a Toby Ord post on generation time and vertical asymptotes, with Ord's three-panel figure comparing differential, difference, and time-embedded difference equations.
fast takeoffsingularitygrowth modelsnanotechtoby ordfeedback loops