The point of a model is to be validly predictive of something. Fitting your exponential is validly predictive of local behaviour more often than not. Often, insanely so.[1] You can directly use the numerical model to make precise and relevant predictions.
Your exponential doesn’t tell you when the trend stops, but it’s not trying to, for one because it’s incapable of modelling that. That’s ok, because that’s not its job.
Fitting a sigmoid doesn’t do this. The majority of times, the only additional thing the result of a sigmoid fit tells you is how an arbitrarily chosen dampening model fits to the arbitrary noise in your data. There’s nothing you can do with that, because it’s not predictive of anything of value.
This doesn’t mean you shouldn’t care about limiting behaviour, or dampening factors. It just means this particular tool, fitting a numerical model to numerical data, isn’t the right tool for reasoning about it.
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“I answered that the Gods Of Straight Lines are more powerful than the Gods Of The Copybook Headings, so if you try to use common sense on this problem you will fail.” — Is Science Slowing Down?, Slate Star Codex, https://slatestarcodex.com/2018/11/26/is-science-slowing-down-2/
The analogy falls apart at the seams. It’s true Stockfish will beat you in a symmetric game, but let’s say we had an asymmetric game, say with odds.
Someone asks who will win. Someone replies, ‘Stockfish will win because Stockfish is smarter.’ They respond, ‘this doesn’t make the answer seem any clearer; can you explain how Stockfish would win from this position despite these asymmetries?’ And indeed chess is such that engines can win from some positions and not others, and it’s not always obvious a priori which are which. The world is much more complicated than that.
I say this not asking for clarification; I think it’s fairly obvious that a sufficiently smart system wins in the real world. I also think it’s fine to hold on to heuristic uncertainties, like Elizabeth mentions. I do think it’s pretty unhelpful to claim certainty and then balk from giving specifics that actually address the systems as they exhibit in reality.