GoKawiil“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:
They start slow - patient zero infects patient one, and so on. They grow exponentially until most people are infected. Then, as almost everyone is infected and they can only mop up the last few holdouts, they slow down again. Finally, after everyone has been infected, the growth rate is zero.
Technological progress in a given field can also be sigmoid. Here’s airspeed record over time:
My understanding is that this represents 3-4 “generations” of different technology (propellers, turbojets, etc). Each technology went through normal iterative improvement, then, when it reached its fundamental limits, got replaced by a better technology. The last technology, ramjets, reached its limit at about 3500 km/h, and there wasn’t the economic/regulatory will to develop anything better, so the record stands.
You can imagine something similar happening with AI at some point. Does that mean people are right, and there’s no need to worry that the graph will ever reach the line marked “high”?
Before we come up with a general answer, let’s look at the Sigmoid Misidentification Hall Of Fame.
Third place goes to UN birthrate projections in countries with declining birthrates. These countries’ birthrates keep going down at a constant rate, and the UN keeps predicting they will flatten out and go down at some lesser rate. On this graph, red is the real data, and each blue line is a different UN attempt from a different year to “extrapolate” the “trend”.
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