Posing a question like "if [X] was expected, then how come we haven't found [very specific indicator of X]" does not make a lot of sense right now, neither from a logical point of view nor scientifically.

First of all, the absence of detectable vN probes does not somehow retroactively change the expectation we had for the presence of alien life, because that expectation arose from a statistical perspective on environmental and biological factors. Until invalidated, this is still the default expectation. It may well turn out that expectation was based on faulty assumptions at some point, but the deciding factor will not be the absence of your favorite arbitrary indicator.

It also makes no sense to stop looking based on the argument that we haven't found anything yet. Resolving the Fermi paradox is a higher stakes game than many people realize: Either we're just isolated from discovery for whatever reason (which would be fine as a class of explanations), or there is something fundamentally wrong about the universe.

Based on the information we have right now, ET must be out there. If it turns out he definitely isn't, we'd better find out why, because it's one of the biggest areas in modern science where prediction dramatically mismatches observed reality. We can't afford to just call off the search because we haven't found probes.

I think almost everybody agrees that looking for drones is a worthy endeavor, but it can't be the pivot point of the entire ET discussion for the simple reason that it's one more probability stacked on top of an already unknown probability (= the probability that any civilization will colonize the galaxy with a runaway drone program that can be easily detected). That's a very specific thing.

Depending on where you're coming from, you may assign a big probability to it, but there is by far no consensus. So for now the best we can do is to look at as many possible indicators as we can.

If you enjoy probabilistic arguments, then you'll appreciate why I think that B-vN probes are inevitable.

  P(probes) = 1 - P(no probes)
            = 1 - (1 - P(civ launches one probe))**Nciv

You seem to be under the impression that I wasn't familiar with that argument, even though I explicitly described it as "the probability that any civilization will colonize the galaxy with a runaway drone program that can be easily detected". I don't think there is a person in this thread who doesn't understand the basic assumption.

Your claim of inevitability only applies to an infinite amount of time, so in our universe at this point in time the number can still be (and probably is) zero.

So I'm trying to talk about a more refined model instead, namely one that tries to at least reserve room for factors such as the overall number of active civilizations, and the likelihood that we actually discover a drone.

To start off with, we have no idea what the probability of a single civilization colonizing the galaxy with drones even is, and we're also making a lot of implicit assumptions about the nature of these drones. The argument that "one case is enough" is valid, but still the overall likelihood of that one very specific case may be too low.

There is also the possibility of drones going by undetected. We don't know what the drones' navigation algorithm would look like, but it's at least conceivable that some solar systems might have been left out altogether. Finally, I'm not sure if we could necessarily detect moderate drone activity in the outer solar system at all.

  P(probes) = 1 - P(no probes)
            = 1 - (1 - (P(civ launches one probe)*P(probe reaches Earth)))**Nciv

I don't have time for this but I'd suggest looking into other discussions on this. The Fermi paradox opens an entire monstrous tree of possibilities, but it's not quite as simple as "there are no VN probes therefore there are no aliens."

My two favorites are:

(1) Interstellar travel might just be too damn hard. Going fast enough to get there in a reasonable time seems to require insane physicists' nightmare propulsion systems like antimatter or fusion rockets or artificial black hole drives, while taking too long means cosmic radiation has too much time to cook both organic matter and electronics... or you can't build a power source that will last that long, etc.

(2) The "uniform cooling hypothesis" -- maybe life is common but intelligences able to build (or become) VN probes are so far incredibly rare. Since the entire universe is (according to the leading theory) the same age, such things simply haven't happened yet.

(1) and (2) could work together-- maybe there are pretty advanced aliens everywhere but so far very few are advanced enough to attempt interstellar flight. If the probability of interstellar flight is less than, say, once per galaxy per billion years, then we would not see VN probes.

Neither (1) nor (2) rules out signals at all.

(2) is arguing for some kind of middle ground between "it's just us" and "lots of tech civs"; i.e., that life can get to the point of sending signals way easier than it can get to the point of launching a probe. But in our case the delta's just going to be a couple centuries, so no, that doesn't work for me either.

There's a lot of reasons there. Certain areas are unhabitable, or at least annoying to create a habitat (the arctic tundra, for example). Beings may want to cluster together (cities). There may be no interest in going to one territory over another - why bother spreading to all places, where there's so much out there?

Finally, you could have situations in which a probe or a highly advanced civilization could deliberately not contact a lesser-advanced civilizations. How do we know that we're not the less-advanced civilization? See: https://en.wikipedia.org/wiki/Uncontacted_peoples

(Yes, I'm being glib, but it's not that much of a stretch.)

I don't know. Maybe the vast, sentient ooze of distant moons doesn't understand why anyone would want to explore the universe. Maybe the dissipant entities of gas giants don't use materials commonly found in the rest of space for construction. Maybe the chittering hivemind of habitable worlds reached incredible advancement without developing a concept of individual intelligence, and thus has no understanding of how to make a single self-sufficient AI on a probe. Maybe there are more things in heaven and Earth than are dreamt of in etc.

Sure cells can reproduce but they can't build spaceships.

We ourselves arguably have good reason not to broadcast our presence, reasons which we have come to belatedly but which are now widely known; e.g. the widely-cited belief that 'whenever' two cultures of significantly different technological prowess have interacted, the less-advanced one invariably went extinct / degraded / whatever.

I haven't read it yet but IIRC the Three-Body Problem trilogy proposes a universe in which advanced species stay silent for fear for just such interaction.

I can myself propose a variant idea, which is this: if we conclude from perceived silence/solitude that other species are likely out there but keeping their heads down,

...maybe we should do the same, not knowing what we might invite by broadcasting our presence.

If the first species to encounter this question incorrectly guessed its own probability of being first, and came to the same conclusion, we might actually be surrounded by a saturated sea of advanced species... all playing it unnecessarily safe...

<shrug>

Seriously? We probably shot them down: https://www.youtube.com/watch?v=cZWs8116Q-E

Funny that...

Anyway there's a bunch of these "pilot encounters UFO with description not matching any known aircraft" stories.

http://ufos.about.com/od/bestufocasefiles/p/mantell.htm

How sure are you that you are not (part of) one?

I think the parent was suggesting directed panspermia-- that the Earth's biosphere is itself a B-vN probe in the process of self-replication.

That's one way to do it.

If there are ETs, I really want to know whether they're using DNA with triplet codons that map to the same 20 amino acids.