Two facts about exponential growth:
- In a finite world, exponential growth can’t keep going forever. Eventually, it must stop. In many cases, the growth curve transitions from exponential to logistic or some other form of sigmoidal.
- In most cases, it’s impossible if determine when an exponential growth curve will stop.
The second point is crucial. Any real-world data that’s a little noisy will not allow fitting of a sigmoidal curve with a reliable inflection point. This is especially the case when the upper limit to growth isn’t known, as is the case for AI performance. We have no idea if most of AI growth is still ahead, or if there isn’t much more to squeeze out of our models.
Our inability to predict if AI performance is going to flatten off anytime soon is the is the subject of a recent post by Scott Alexander on Astral Codex Ten. He illustrates this with several historical examples of people who wrongly predicted the end of exponential growth for e.g. solar power deployment. Alexander reminds us of Lindy’s law, which states that the longer a trend has been going on, the longer it’s likely to persist. This is a special case of the Copernican principle, which states that there’s nothing privileged about the present. This is a useful heuristic, but it also highlights our ignorance.
Another phenomenon for which we don’t know where on the sigmoidal curve we are is economic growth. Economic growth has been going on for a long time now, and substitution and efficiency gains could keep it going for much longer. Obviously, the world economy can’t keep growing forever, but we have no idea if we have 1% of that growth behind us, or 50%, or 99%.
Thinking about growth and its limitations makes me want to read Vaclav Smil’s Growth again. It’s the most comprehensive treatment of growth curves I have come across.
Nehaveigur 