I am looking for the name of a scientific or statistical principle or term of art that codifies whar I will loosely phrase “if you find one instance when you first look, the odds are there are many.” In other words, it’s vanishingly unlikely that an initial search would find a unique case (species, object, fossil, star, whatever). Finding one easily/immediately implies tgere are more.

Nosing around, I have felt I am close to finding what I am thinking of with things like the Signor-Lippseffect, rregression toward the mean, tge Copernican principle, and so on, but have yet to fibd a clear match.

Seems like an application of Bayesian reasoning, which is basically probabilistic reevaluation of your model based on sampling or new information.

If your prior probability of finding X is 0 or nearly 0 (you believe none exist), and then you find one, you need to revise your model. And the proper way to revise it is not to assume that there’s exactly one and you found it in one try.

Example: If you have a bag with 1000 marbles in it, and you think they’re all black, then the prior probability of pulling a white marble out is very small (< 0.1%). If you then reach into the bag, grab a marble, and it’s white, then the new model suggested by Bayesian theory is not that there was exactly one white marble in the bag, and that you happened to pull it out. It’s much more likely that there were, say, 10, or 50, (or even 1000) in the bag, and you got one of those.

Another way to think about it is if you thought something didn’t exist at all, then looked and saw it immediately, you should suspect that your original reasoning was invalid, not cling to it and assume you found an anomaly.

I think that Asimov’s “never only two” reasoning only applies to things for which the Anthropic Principle applies, and so it’s really “never only one other than ours”. In particular, it’s first applied to universes. We make contact with another universe… which implies that there are probably others as well.

Possibly… IIRC, his context was astronomic objects, like Saturn’s rings. It might have been that Saturn was the only object in the cosmos that had rings, absolutely unique. But once we found other objects with rings, we started seeing them more places and yet more. Now we think they’re pretty common.

The idea that there might be only two ringed planets in the cosmos seems silly… Or at least it did to Asimov.

(Obviously, he wasn’t proposing an actual scientific law. It’s more like jnglmassiv’s observation about cockroaches. There just might be only one cockroach in my apartment. It could happen. But that there might only be two seems drearily unlikely.)

Knowing Asimov, it’s quite likely that he made the same statement two (or more, of course) different places. But the one context that I know of specifically was in The Gods Themselves, where it was indeed universes.

That’s our Isaac! I’m remembering it as an observation on rings in one of his science-fact essays. But it certainly fits The Gods Themselves.

Makes me think a little of Sturgeon’s Law, which he didn’t really mean when he said it, but got stuck with it, and had to run with it.

(Someone else: “Ninety per cent of science fiction is crap.”
Sturgeon: “Ninety per cent of everything is crap.”
:: Sturgeon’s Law: “Ninety per cent of everything is crap.” The change in emphasis changes the meaning quite a bit!)

Why mediocrity? (I learned it as the Cosmological Principle, and have heard it called the Copernican Principle.)

Anyway, I wouldn’t call it “mediocrity” because the universe that we observe is just absolutely pipping wonderful! Top drawer! This is one A+, Spiffing, E-Ticket universe!

I think I read something to the same effect in one of Ian Stewart’s book; From Here To Infinity - i.e. things either exist zero, exactly one or many times.

(he may have been referencing or paraphrasing Asimov).