Ah, but this is only true about we, humans rather than earth/solar system.
It cannot be excluded that other sources of radio have been around here in the past :)
It also assumes that outside observers have the same difficulty understanding the make-up and probable evolution of a system as we do. If they were able to observe that Earth would have some properties they were interested in, or would be a likely candidate for such, then they wouldn't need us to announce our presence to guess it.
IMHO the aliens will not be specifically seeking life that is intelligent. Singularities and interstellar traveling alien civilizations share a problem. If one is in essence immortal the only purpose that can endure forever is the pursuit of new knowledge. Even if alien entities are able to learn all there is to know about all the other sciences, biology will be inexhaustible as the novel patterns that can be produced by evolution are effectively infinite. The biosphere of just our planet where the latest estimates are that there are a trillion species if you count all the microorganisms, probably contains more information than all the lifeless planets and stars in the galaxy combined. The aliens will value biodiversity more than we do. And if they arrive they will oppress us "only" to the extent required to counteract our propensity to cause species extinctions (including our suicidal alteration of the planet's climate). I actually would prefer that the Singularity or the aliens arrive sooner rather than later as I have less and less hope of our species getting its act together on its own.
>> biology will be inexhaustible as the novel patterns that can be produced by evolution are effectively infinite
But why do you assume they would be interested in observing the patterns that actually have been produced, instead of running high-precision evolutionary emulators that can generate patterns that could be produced at a much higher rate, and maybe even some automated filters to condense it down to "interesting" stuff? It's still knowledge, and there's no innate value scale for knowledge which says that things that have "actually happened" are more valuable.
In fact, how's that for Fermi paradox? Civilizations that are sufficiently technologically advanced to communicate, much less travel, across the stars, are also sufficiently technologically advanced to simulate the things they are interested about and get answers faster that way.
Basically, the end result of any civilization is creating, maintaining and expanding a simulation of the universe. Which, of course, goes recursive...
Thermodynamics still limits what you can compute and, given the output of a single star, you're still limited in what can be computed.
But I think it's a mistake to try to characterize any civilization by a single motivation. People on Earth do things for many different reasons and I think we should expect the same of alien civilizations even if single motivations tax our imaginations less. The questions is if any of the motivations driving a stellar civilization would be enough to prompt the establishment of colonies. I don't think you can say that the answer will be 'no' reliably for every civilization that might arise and it only takes on to colonize a galaxy in short order (by cosmic standards). Hence sophisticated life is probably very rare.
In a similar vein, a possible Fermi paradox solution would be that civilizations sufficiently technologically advanced to travel between stars are also advanced enough to develop good VR and learn which buttons of their brains to push, so they all end up stuck in virtual worlds, or even wireheaded.
A counterargument to that would go along the the similar lines as to why we don't, and can't, resolve wars by e.g. playing chess (or StarCraft). Even if all nations mutually agreed that the shall will be won bloodlessly by some other kind of competition, the first nation to nuke its enemies would be a winner. In conflict situations, you want to seek as much advantage from the "most real" reality as you can get. So, in your recursion example, you'd travel up the call stack...
You can't just wave a wand called "emulation" to hypothesize whatever speed, precision, or rate of calculation you want. Emulators are physical objects and you'd need to show that it's possible to build an emulator that calculates the same amount of information as the Earth's biosphere, but faster, more precise, etc.
Then, once you have the attributes of that emulator, you'd have to calculate how long it would take that emulator to deliver the same information that can be harvested today on Earth with simple observations. And even if it completed, how would you confirm it is indeed the same information without traveling here to check?
The energy budget would be immense of course, but heat management might be the limiting issue on how fast it can run. It's hard to dump heat into space.
I'm not intending to argue one or another about hypothetical god-like alien civilizations. It's just a pet peeve when programmers make open-ended claims about simulations or emulations without considering physical constraints. We tend to think of electronic computers as powerful, but their information handling capabilities are quite slow and diffuse compared to what biology has produced on Earth so far.
Thinking that pursuit of knowledge is only activity for immortal is naively idealistic.
Elimination of of all life not like me. Or simply eliminate life that might singularity and become a threat. Even if, who's to say one aliens pursuit of knowledge latest experiment dose not require and earth sized amount of raw materials.
Our aggression reflects the zero sum physical resource context of our evolutionary past. Knowledge in contrast grows fastest through cooperation. As power including the power to defend oneself grows with knowledge, knowledge seeking entities will quickly evolve to maximize cooperation. And as many have pointed out, unlike most of our sci fi, it is very unlikely for two alien civilizations to meet where their technology levels are similar - one will be permanently vastly advantaged over the other. Aggression will be pointless - the pecking order will be obvious. As to your last point I am sure lifeless planets will do for any experiments.
My unprovable assumption is that only beings who value knowledge and cooperation highly enough will get to the point of crossing the difficult technological threshold of achieving singularity or space travel. I think the more likely Achilles heel for my scenario is sexual selection - the trap that perpetuates selfish behavior in both sexes even when there is no resource scarcity. Even in this, humans at least are sometimes able to escape the trap by being meta enough to see kindness as strength and beauty. I think the fastest, and most likely first, route to our singularity will start with reverse engineering one human mind, and I will hold onto hope that that mind will hear the call of light, and the truth and beauty feedback loop will be unstoppable. It helps that I also believe that as information increases, morality converges on a process for maximizing the long term preservation of information (where on this planet, human minds are the most information dense and therefore the most valuable things we can preserve). /end sci fi sermon
An anthill-like species can value cooperation among themselves without necessarily valuing knowledge for knowledge's sake - imagine the Hive Queens from Ender's Game, or MorningLightMountain.
