For example, take something like a fad or trend; they don't have a hard end date like human lifespan, so it should follow Lindy's law.
However, the likelihood, on average across the population, that you observe a trend is going to be higher at the end of a trend lifecycle than at the beginning. This is baked into the definition - more and more people hear about a trend over time, so the largest quantity of observers will be at the end of the lifecycle, when the popularity reaches its peak.
In other words, if you are a random person, finding out about a trend likely means it is near the end rather than the middle.
The law only applies for certain types of processes, and is completely wrong for other types (e.g. a human who has lived 50 years may live 50 more, but one who has lived 100 years will certainly not live 100 more). So the question becomes: what type of process are you looking at? And that turns out to be exactly the question you started with: is there a fundamental limit to this growth curve, or not.
Did you even read the post? It’s an estimate in the context where you have zero information on which to base an accurate estimate. The author’s point is that if you’re making a different estimate you need to actually say what information is informing that.
Human lifespan is obviously not a case where we have zero information, so what is your point in bringing that up?
But often we don't have the information that we wish. Even more often, the information that we have leads us to a story, that severely misleads us. Reminding ourselves of the zero information version of the story, can be an antidote to being mislead that way.
Therefore it is valuable to know how to make the most out of zero information. And if we have information, to think about exactly why it leads to a different conclusion.
"The Lindy effect applies to non-perishable items, like books, those that do not have an "unavoidable expiration date"."
And later in the article you can see the mathematical formulation which says the law holds for things with a Pareto distribution [2]. I'd want to see some sort of good analysis that "the life span of exponential growth curves" is drawn from some Pareto distribution. I don't think it's completely out of the question. But I'm also nowhere near confident enough that it is a true statement to casually apply Lindy's Law to it.
The argument given is the same as the one that I first ran across, not by that name, in https://www.nature.com/articles/363315a0. https://en.wikipedia.org/wiki/Doomsday_argument claims that it was a rediscovery of something that was hypothesized a decade article.
I hadn't tried to give it a name, or thought to apply it outside of that context.
As for the mathematical qualms, I'm a big believer in not letting formal mathematical technicalities get in the way of adopting an effective heuristic. And the heuristic reasoning here is compelling enough that I would like to adopt it.
But that's the entire idea of Bayesian reasoning. Which has proven to be surprisingly effective in a wide range of domains.
I'm all for quantifying my ignorance, and using it as an outside view to help guide my expectations. Read the book Superforecasting to understand how effective forecasters use an outside view to adjust their inside view, to allow them to forecast things more precisely.
So for example, the longer a time bomb ticks, the less likely it is to go off any time soon. (Assuming the timer isn't visible.) :)
We expect fresh processes to terminate quickly and long running processes to last for a while longer.