The high value matter/energy or real estate is probably a tiny portion of the total, and is probably far from stars, as stellar environments are too noisy/hot for advanced computation.
Can you expand on this?
See this post.
Extrapolating from current physics to ultimate computational intelligences, the most important constraint is temperature/noise, not energy. A hypothetical optimal SI would consume almost no energy, and it's computational capability would be inversely proportional to it's temperature. So at the limits you have something very small, dense, cold, and dark, approaching a black hole.
Passive shielding appears to be feasible, but said feasibility decreases non-linearly with proximity to stars.
So think of the computational potential of space-time as a function of position in the galaxy. The computational potential varies inversely with temperature. The potential near a star is abysmal. The most valuable real estate is far out in the interstellar medium, potentially on rogue planets or even smaller cold bodies, where passive shielding can help reduce temperatures down to very low levels.
So to an advanced civ, the matter in our solar system is perhaps worthless - the energy cost of pulling the matter far enough away from the star and cooling it is greater than it's computational value.
All computation requires matter/energy.
Computation requires matter to store/represent information, but doesn't require consumption of that matter. Likewise computation also requires energy, but does not require consumption of that energy.
At the limits you have a hypothetical perfect reversible quantum computer, which never erases any bits. Instead, unwanted bits are recycled internally and used for RNG. This requires a perfect balance of erasure with random bit consumption, but that seems possible in theory for general approximate inference algorithms of the types SI is likely to be based on.
that the stars were huge piles of valuable materials that had inconveniently caught fire and needed to be put out.
This is probably incorrect. From the perspective of advanced civs, the stars are huge piles of worthless trash. They are the history of life rather than it's future, the oceans from which advanced post-bio civs emerge.
This idea implies a degree of coordination that does not happen in actual ecologies we have seen. Thus we get trees extravagantly sucking up mineral nutrients and building massive scaffolds to hold their photosynthetic structures over their competition, and weeds that voraciously multiply and compete with each other to take up every bit of sunlight and soil they can that the bigger things can't establish themselves in, rather than a thin scum of microbial mats that efficiently intercepts energy. You are implying a climax community without any other sere...
After a 6+ month hiatus driven by grad school and personal projects, I am finally able to continue my sequence on astrobiology. I was flabbergasted by the positive response my last post got, and despite my status as a biologist with a hobby rather than an astronomer I decided to take a more rigorously mathematical approach to figuring out our biosphere's position in space and time rather than talking in generalizations and impressions.
Post is here: http://thegreatatuin.blogspot.com/2016/03/space-and-time-revisited.html. Seeing as this post is an elaboration on the last one, I am posting a link rather than reproducing the text.
To summarize, I found some actual rigorous observational fits to the star formation rate in the universe over time and projected them into the future. These fits show the Sun as forming after 79% of all stars that will ever exist, and that 90% of all stars that will ever exist already exist. This makes sense in the light of recent work on 'galaxy quenching' - a process by which galaxies more or less completely shut off star formation through a number of processes - indicating that the majority of gas in the universe probably won't form stars if trends that have held for most of the history of the universe continue to hold. It relies heavily on analysis I began in comments on this site a few months ago.
I then lift two distinct metallicity normalizations from a paper that was making the rounds here a while back ("On The History and Future of Cosmic Planet Formation"), in an attempt to deal with the fact that that is a measurement of STAR formation, not terrestrial-planet-with-a-biosphere formation. Depending on which metallicity normalization you use (and how willing you are to take a couple naive assumptions I make in order to slot the math that is too complicated for me to comment on on top of my star formation numbers) the Earth shows up as forming after either 72% or 51% of all terrestrial planets.
These numbers are remarkable in how boring they are. We find ourselves in an utterly typical position in planet-order, even if I am wrong by quite a bit. We are not early. Of interest to many here, explanations of the so called Fermi paradox must go elsewhere, into the genesis of intelligent systems being exceedingly rare or the genesis of intelligent systems not implying interstellar spread.
Now that I seem to have a life again, I will be getting back to my original plan next, talking about our own solar system.