alt Hacker NewsLindy’s Law is an absolute gem, that I'm keeping.
If we don't understand the fundamental limits to any particular kind of trend, our default assumption should be that it will continue for about as long as it has gone on already.
We can, in fact, easily put a confidence interval on this. With 90% odds we're not in the first 5% of the trend, or the last 5% of the trend. Therefore it will probably go on between 1/19th longer, and 19 times longer. With a median of as long as it has gone on so far.
This is deeply counterintuitive. When we expect something to last a finite time, every year it goes on, brings us a year closer to when it stops. But every year that it goes on properly brings the expectation that it will go on for a year longer still.
We're looking at a trend. We believe that it will be finite. Our intuition for that is that every year spent, is a year closer to the end. But our expectation becomes that every year spent, means that it will last yet another year more!
How can we apply that? A simple way is stocks. How long should we expect a rapidly growing company, to continue growing rapidly?
Replies
While this is very fun as a mathematical exercise, it's completely irrelevant as a real tool for getting a better understanding of unknown processes in the real world.
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.
It's an interesting idea, and it may be something that could be mathematically justified, but I do think this is an abuse of Lindy's Law in the absence of such a justification. Per Wikipedia [1]:
"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.
You can do that but you're laundering ignorance into precise-seeming mathematics. Better to just say "we're probably somewhere in the middle, not at the beginning or end" and leave it at that. Calling a peak is hard.
Closely related is Laplace's Rule of Succession[1], which basically says that (in lieu of other information), the odds of something happening next time go down the more times in a row that it doesn't happen (and vice versa).
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.) :)
This is the exact same heuristic used in CPU scheduling.
We expect fresh processes to terminate quickly and long running processes to last for a while longer.
I feel like Lindy's law doesn't work for things whose observation is partly controlled by the thing itself.
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.