Why it took so long to do the Fermi calculation right?

The more interesting question is where else do we see something similar occurring?

For example, historically income in retirement was usually discussed in terms of expected value. More recently, we've begun to see discussions about retirement focusing on the probability of running out of money. Are there other areas where people focus on expected outcomes as opposed to the probability of X occurring?

I don't find it surprising that it took this long.

Speaking only for myself, when I encounter a superior technique I almost always fail to go back through my life and re-evaluate everything according the new technique.

Thinking about the research community, I have no reason to expect the same mechanism does not apply. I also note that only recently did the replication crisis, and the discussion about standardizing on better statistical methods, seem to hit saturation.

I feel like I have seen other papers that revisit old results with a new technique, always with some new insight to offer. This causes me to suspect that the same positive-results bias that usually affects publication still affects revisiting old equations.

It would be a good idea to systematically update all point estimates with distributions, but I don't see any reason to expect that this was already happening.

Tangentially related: this seems like the kind of thing that language AI and theorem-provers would be pretty good at - having the machine automatically review the literature and apply the new technique instead of the old technique.

Doesn't this paper boil down to "Some factors in the Drake equation are highly uncertain, and we don't see any aliens, so those probabilities must be small after all?"

Note that the conclusion of the toy model rests not on "we did the 9-dimensional integral and got a very low number" but "we did Monte Carlo sampling and ended up with 21%"--it seems possible that this might not have been doable 30 years ago, but perhaps it was 20 years ago. (Not Monte Carlo sampling at all--that's as old as Fermi--but being able to do this sort of numerical integration sufficiently cheaply.)

Also, the central intuition guiding the alternative approach is that the expectation of a product is the product of the expectation, which is actually true. The thing that's going on here is elaborating on the generator of P(ETI=0) in a way that's different from "well, we just use a binomial with the middle-of-the-pack rate, right?". This sort of hierarchical modeling of parameter uncertainties is still fairly rare, even among professional statisticians today, and so it's not a huge surprise to me that the same is true for people here. [To be clear, the alternative is picking the MLE model and using only in-model uncertainty, which seems to be standard practice from what I've seen. Most of the methods that bake in the model uncertainty are so-called "model free" methods.]

Did anyone make a mistake? Did anyone ever consider the "Fermi paradox" a paradox in need of dissolution? Can you point to anyone making any argument that would be improved by this analysis? This community has generally focused on the "Great Filter" framing of the argument, which puts weight on multiple hypotheses, even if not explicit weight.

All this calculation says is that some people say that life is difficult. Did anyone ever say that they knew with great certainty that life is easy? On the contrary, many people have said that it is the key parameter and looking for traces of life on other planets will shed light on the question. Other people have said that it is important to pay attention to panspermia, because the presence of panspermia allows the possibility that life is difficult and happened only once in the universe, and yet spread to many planets, requiring another filter.

(The only paradox I can imagine is: if we don't see any life, then life isn't out there (perhaps first asserted by Hart 1975), so life is practically impossible, so we're practically impossible; So why do we exist? This paradox is resolved by anthropic update (Carter 1983). The phrase "Fermi paradox" only appears around 1975, but I'm not sure that Hart or anyone else reached this paradoxical conclusion. In fact, lots of people complained that it's not a paradox.)

Perhaps people confuse "expected value" with "the value you can expect to see?" Even people who know the distinction and can articulately explain it?