It impressed Fermi, and many others since. The entire argument, which I posted in shorthand because I am tired of repeating it, goes like this:
(a) We're children of a 3rd-generation star.
(b) If intelligent life is common then we are (among) the most primitive ones; there has been ample time for hyper-advanced technical civilizations to spring up before our advent.
(c) Some of them will be as curious--or more curious--than we.
(d) Some of them will hit upon the idea of launching a modest number (~100) of "Von Neumann robots". These machines, travelling at (say) 0.05 "c", are instructed to pick a star at random, go there, conduct extensive studies, build a copy of themselves, dump their entire memory into the scion, and then both 'parent' and 'child' probes each select another random star and the process continues.
(e) Some stars will lack proper conditions (materials) for constructing a scion, or the parent probe is destroyed. That's why you start with more than one.
(f) This process is guaranteed to result in a geometric explosion of probes, all flitting about and finding stuff out at an ever-increasing rate.
(g) Occasionally, a probe wanders home by random walk. The payoff is that it dumps the memories of itself and all of its ancestors; for a relatively small investment you get a gigantic payoff in terms of data. [Remember, you are a super-tech civilization which has had technology for thousands of years].
(h) There has been ample time--even at 0.05c--for every star in the galaxy to have been visited at least once. Where is "ours"? Actually, if intelligence is common, many races will figure this out [remember, we're dumber than they are, and we figured it out!] and there ought to be a traffic jam of probes buzzing around Sol.
(i) We fail to observe any evidence of even a single probe, much less a swarm.
(j) Therefore some assumption in this chain must be flawed. The key ones are [1] intelligent life is common and widespread; [2] technological means are sufficient to reach at least 0.05 'c'.
(k) Therefore either [1] or [2] or both must be false.
QED.
Fermi, being much smarter than us, simply asked his question; the rest was understood.
--Boris
Incidentally, every assumption in there is an ASSUMPTION. Unproven and, under current conditions, unprovable.
Your conclusion may well be correct, but your argument still stinks.
Is that only supposed to work within our own galaxy, or is it supposed to be intergalactic? I would guess that the distances between galaxies have to be greater than the distance between any two stars within our own galaxy.
Also is there not some third assumption in the picture, i.e. that the robot probes would be able to travel vast distances without suffering damage from debris, dust, and radiation?
[3] intelligent life has no further interest in just another stupid lifeform?
We don't study every ant hill we come across - most are ignored.
[4] intelligent life prefers secrecy and stealth?
(c) Some of them will be as curious--or more curious--than we.
(d) Some of them will hit upon the idea of launching a modest number (~100) of "Von Neumann robots".
There is an underlying premise here that such advanced civilizations are also intent upon disclosing their presence, abilities, and location.
Why would they risk it? Why would they not observe passively, remotely?
What is gained by 'inserting themselves' (or otherwise allowing their presence and/or home location to become known) into environs selected not for low risk, but at random and ultimately encompassing the entire galaxy (if not universe)?
Why would they not endeavor to keep their observation undetected - if indeed observers are sent at all?
Wouldn't they risk potential extermination, either by conflict or by contamination?
(g) Occasionally, a probe wanders home by random walk.
This seems a rather haphazard way to collect information, but without reducing the risks noted. I.e, the risk/reward ratio is worse than if the observers were designed to 'phone home'.
Fermi seems to presume no competitve dangers to exploration. Which could be true, but if true, either implies no competitors or a gamble that any competitor encountered will be a lesser threat. But why take that gamble?