Comment by seanhunter

> I understood it as if you know absolutely nothing about a process, your best guess is that it's half done.

That is the argument that is being made, but that only holds if the process is drawn from an underlying Pareto distribution with epsilon > 1[1].

As a counterexample, I’m jetlagged and disorientated. I go to sleep and wake up. It’s light outside but I don’t know the time. What’s the best guess of the time of day? By the “Lindy law” the best guess is that the process of daytime is halfway done so if I’m half-way through the day, my best guess is it’s noon.

Clearly that’s not the best guess that could be made. The distribution of times I might wake up is heavily skewed towards the morning, so the best guess is going to be some time in the morning. Now you might argue that we don’t know absolutely nothing about the cycle of the day and night and that’s true. But we also don’t know absolutely nothing about any of the examples in TFA either.

The point is, the times of day I might wake up are not drawn from a pareto distribution with the right parameters so the Lindy Law heuristic completely fails. In TFA the author gives no justification for why the remaining lifespan of the exponential growth of AI might be drawn from such a distribution either, so there’s no reason to think the heuristic will be accurate in that case either.

[1] From https://en.wikipedia.org/wiki/Lindy_effect. epsilon = 1 + 1/p where p is the parameter of the conditional expectation E[T-t|T>t] = p t. So only things with p positive but finite exhibit this effect. If p is negative then the best guess is going to be that the lifetime of the thing will end immediately because we’re already past the expected lifetime, and if p is infinite then the thing will never end so all finite guesses about its length are equally bad. So whether half-way is a good heuristic depends entirely on the underlying process and you’d need to demonstrate that the majority of things have positive p for half-way to be the best guess. That’s far from clear.