The Sigmoids Won't Save You

"All exponentials eventually become sigmoids" is an annoying AI talking point. If someone presents a graph like this…

….and points out that it seems like AI capabilities could soon reach the level marked "High", then the height of intelligent debate is to point out that actually, the trend could go like this:

…and then it would never reach the level marked "High"!

In slogan form, this is "all exponentials eventually become sigmoids" (a sigmoid is the s-shape of the second graph, which starts exponential but gradually flattens out). It's technically true. No process can keep growing forever; eventually it hits physical or practical limits. For example, total cases during an epidemic is classically sigmoid: