Banned because I've been thinking:
I believe I've found something interesting that those of you who consume large quantities of science fiction will find helpful. I'm sure some of you have wondered as to the probability of the usual "Space-Based 4X Game" (SB4X) Model- namely a group of five or six or ten or some other manageable number of interstellar civilizations existing together in a single galaxy, at approximately the same technological level.
It's easy to arbitrarily set the number or more precisely the rate of civilizations arising- to have a civilization you need to have life, and since we don't know the probability of abiogenesis we can arbitrarily set that rate. This helped me a lot in TCTR, to explain how there came to be two biologically discrete civilizations within 5 light-years of each other: in that universe, intelligent life is ridiculously common, but most civilizations are exterminated by natural disasters before they leave the hunter-gatherer stage. Thus results a galaxy that is constantly being filled and re-filled with millions of primitive cultures and very few space-faring ones (which are exponentially harder to kill off once they get there). This system suits the two-planet (technically, planet-and-moon) scope of TCTR just fine, but it does NOT work for the SB4X model, where civilizations are rare but nearly all survive to a high level of technology in an environment of frequent uninhabited planets.
If we just let probability run willy-nilly, we run into a problem. We know technological growth to be an autocatalyitic process- civilizations at least on Earth spend tens of thousands of years learning to use tools, milennia mastering agriculture, centuries industrializing, decades developing the computer, and potentially years trying to break the lightspeed barrier before very very quickly achieving a form of singularity that launches them to levels of technological prowess we would more commonly associate with gods. This creates one of the solutions to the Fermi paradox, but ruins the SB4X model for the same reason- intelligent life can arise at any time, go through maybe 50,000 years of basically nothing, then quickly become near-omnipotent and probably invisible to us mortals. That 50,000 year span itself is a tiny time period in the history of the universe- the odds of two civilizations arising proximate to one another in both space and time AT ALL are minute, and on the rare occasions it did happen the tiny sliver of time in which one would be exploring space before singularity whisked them from the mortal coil would in all probability fall while the other was still trying to figure out the wheel. They could very easily still interact, with the astronauts either ignoring, conquering, or assimilating the cavemen, but that's TCTR again, not SB4X.
To create a system that satisfies these conditions, we will obviously need to rely somewhat on the concept of deterministic evolution. This idea is a real concept currently under intense debate by biologists: in it, the laws of physics favor only a few forms and structures as optimally efficient, so even radically different creatures in radically different environments will over time come to adopt the same physiology. I used deterministic evolution in its pure form in TCTR, to justify the existence of humans and extremely humanoid aliens in adjacent star systems, but that's not its only form. Deterministic evolution theory may also apply to technological progress- even radically different engineers in radically different cultures will over time come to adopt the same technological devices, and it is also believed to apply to time- it will take about as long for these common forms to arise in different situations. Put them together, and we have a theoretical form good enough for non-fact-breaking science fiction that says all civilizations will develop at about the same speed once they begin.
This concept allows me to create the flawed cyclical model. Taking deterministic evolution to its unrealistic extreme, we can say that on all planets in a galaxy intelligent life will arise at the same time, undergo technological progress in lockstep, and reach space at the same exact point. There they will probably fight with one another, and the losers will either be subsumed into another civilization or destroyed utterly, but at the end of the day whatever ones are left will undergo singularity at the same time. New intelligent life would emerge (all at the same time) on different planets now suitable for it, and it would all start again. This model is flawed for one simple reason- Technological deterministic evolution makes things happen at the "same" time in historical terms, with a margin of error of years or decades, but biological deterministic evolution makes events occur at the "same" time on geological or cosmic scales, with a margin of error in the thousands or hundred-thousands of years. This means that civilizations will not be started at the same time relative to one another. Thus, the Fermi Solution still applies, but this model does serve as a good place to explain some other factors:
Why we can't see the singularity cultures. A universe filled with physically present and astropolitically-active megacivilizations would not be fun for the rest of us to live in, and makes for bad science fiction- every story would end with one big deus ex machina! Instead, I floated the theory that these societies would simply not be comprehensible to us, and care about our affairs as much as we care about the imbroglios of ants. It's possible for them to physically be living "somewhere else", their palaces walled off behind higher dimensions, contracted to points, or ensconced within personal pocket universes: here they would never interact with us at all. It's also possible that they do exist in whole or in part within our mundane reality: in that case their vast, inimitable and utterly indifferent machinations would be indistinguishable from natural phenomena. Either way, they themselves are not an issue. There is one problem that remains- the ruins they left behind before their ascension would remain for a while unless for some odd reason they chose to "take it all with them." But this will be rectified later on.
How the effects of astronomical phenomena- known to be chaotic and differentiated- would not interfere with this neat little progression. This one is simpler, to some extent. Cosmic phenomena such as galaxy formation, star lifespans, and the expansion of the universe itself all happen on ridiculously large time scales, and most importantly to all planets in a large region at once, so the cycles of civilizations are not broken up internally by them.
Now, to address the flaws of the flawed cyclical model, I looked at the HALO universe to create a one-shot cyclical model. Although not the most widely applicable, I for one think it's the most perfect. In this model, the galaxy starts out with a lot of different civilizations at a lot of technological levels. One of them is a bit more ambitious, and starts to expand more than the others, assimilating less-advanced civilizations into itself. Those it cannot consume never bother to try to wipe it out, instead achieving singularity and wiping out any trace of their own presence. The glutton eventually subsumes everyone else into itself- any species that hows any signs of intelligence is a part of this one titanic hegemony (note that this empire need not be "evil"- it could have any number of reasons for expanding as it does, many of them quite altruistic). The leviathan prospers for a while, constrained from expanding further by the difficulties of crossing the intergalactic void, before some epic-level calamity wipes it out of existence. Since all of the species everywhere are a part of it, we end up in a galaxy utterly devoid of sentient species, filled with open niches. Some stay open longer than others, of course, but by the time the very FIRST new crop of sentients (who, by technological determinism will have developed spaceflight at about the same time) have achieved singularity and ceased to be relevant, they will only just be beginning to develop their own tools. This requires a biological-time--scale butter zone in which a species occupies its niche and prevents other sentient species from arising on the planet, but is not yet ready to use tools and progress technologically, and is not easily identifiable as sentient (or cannot be assimilated). The first new crop mentioned above were in their butter zone at the time of the cataclysm. By the time they are around to find them, any ruins left behind by previous singularity cultures will (having had over ten thousand years) be decayed beyond recognizeability as anything artificial.
This model works VERY well for the classic SB4X model. However, the ruins of a leviathan are not actually required to be lying around in the infinite cycle model. Here, we assume that civilizations always come together to form a leviathan at some point in their development, but it doesn't cease to exist. It simply achieves singularity, totally emptying the galaxy (galaxies?!) of all intelligent life not in a butter zone. The next group of butter zone cultures achieve technology shortly (on conventional timescales) afterwards, and eventually they too become a leviathan dead-set on singularity. We must also assume that for a while the leviathan does something special before singularity, however- it must exist for a while in a state where it still assimilates other cultures into itself, but has transcended the need to leave behind physical ruins.