Assumption #1: In the solar neighborhood, there exists about one stellar system for every 300 cubic light-years of space. Stellar systems average about 1.2 stars each.

Assumption #2: There exists one habitable world for every 16 stellar systems, or about one habitable world for every 4800 cubic light-years of space.

Commentary: As I remarked before, these are based on HIPPARCOS data for the solar neighborhood, with some educated guesswork as to how many very dim red dwarfs are not properly accounted for by HIPPARCOS. The Architect of Worlds draft design sequence was used to generate planetary systems for a large sample of the solar neighborhood, which yielded a rough estimate for the prevalence of habitable worlds.

Assumption #3: On any given habitable world, a sentient tool-using civilization will appear about once every 500 million years.

Commentary: Based on the experience of Earth as our one data point (one sentient tool-using civilization – that we know of – since the Earth became habitable back in the Devonian era).

Assumption #4: Left to themselves, sentient tool-using civilizations have a 75% chance of an average lifespan of about 12,400 years, remaining in a pre-industrial status, followed by extinction. They have a 25% chance of an average lifespan of about 12,800 years, attaining industrial status late in that period, followed by extinction. The probability of a sentient tool-using civilization attaining interstellar capability on its own is vanishingly small.

Commentary: This is one of the foundational assumptions of the Human Destiny setting, and a partial solution to the Fermi Paradox. Effectively, I’m arguing for a set of “Great Filters.” Most civilizations never reach an industrial era before falling to some natural disaster. The few that do almost invariably destroy themselves.

Result: Assuming no interstellar-capable civilizations appear, then at any given time there should be about one tool-using civilization for every 40,000 habitable worlds.

Assumption #4: The first culture to attain interstellar capability filled up the galaxy in a short period of time (<< 250,000 years) and gave rise to an era of pan-galactic civilization which lasted several hundred million years. This period is usually called the “era of the Precursors” today.

Assumption #5: The Precursor meta-civilization collapsed in an era of pan-galactic conflict. The winning (or surviving) Precursor faction gave rise to a meta-civilization called the Synarchy, which has carefully limited the growth of all subsequent interstellar-capable cultures. The Synarchy “cultivates” the galaxy by recruiting new interstellar-capable cultures as its proxies.

Assumption #6: Once a civilization has attained interstellar capability under the Synarchy or one of its proxies, its average lifespan after that point is about 250,000 years.

Assumption #7: The Synarchy normally permits one of its proxies, together with its client cultures, to occupy no more than about 25,000 habitable worlds. This allocation is divided between the proxy and its clients, with the expectation that the proxy itself may occupy no more than 5,000 habitable worlds, and each client culture may occupy no more than 1,000 habitable worlds. Within those constraints, a given proxy culture has broad discretion as to how to manage the volume of space under its supervision.

Commentary: More foundational assumptions. The specific numbers have been set to lead to a model which permits many small interstellar societies to exist at the same time in the galaxy. More to the point, aside from the very first “Precursor” civilization, no culture has ever had the opportunity to overrun the galaxy. The Synarchy values variety and acts to prevent such runaway growth.

Results: The policies maintained by any given Synarchy proxy can be characterized by several variables.

• M, the number of habitable worlds considered to be within the proxy’s supervised volume. In a typical case, many or even most of these worlds will be maintained in a “fallow” condition, unoccupied and waiting for the appearance of a naturally evolved tool-using civilization.
• N, the number of client cultures normally maintained by the proxy at any given time (can be any value but is generally <= 20).
• K_P, the number of habitable worlds occupied by the proxy (must be < 5,000).
• K_S, the average number of habitable worlds occupied by client cultures (must be < 1,000).

We observe that if R_E is the rate of extinction of client cultures, then:

To maintain a steady state, the proxy must have a rate of uplift R_U equal to R_E. The rate of uplift is dependent upon M and the proxy’s level of selectivity when choosing candidate cultures to uplift. Some typical values are:

• If the proxy uplifts no candidate cultures, then , , and M can be any value < 5,000.
• If the proxy uplifts all candidate cultures which reach the industrial era, then and .
• If the proxy uplifts all candidate cultures, even at a pre-industrial level, then
• and .
• If the proxy seeks out pre-sentient species for uplift, then R_U is undetermined but possibly as large as , which would imply .

Assumption #8: The volumes of space occupied by a proxy culture or by one of its clients will tend to obey the following guidelines.

• The supervised volume of a proxy culture is likely to be a compact volume of space, such as a sphere with radius roughly equal to . A habitable world which drifts away from that volume will no longer be monitored, and any civilization which arises there will be on its own.
• The volume occupied by a given culture will not be compact, since stellar drift and the requirement to leave certain habitable worlds “fallow” will create gaps and voids. If K is the number of habitable worlds currently occupied by a culture, and A is its age as an interstellar-capable civilization, then as a rough estimate its occupied space will be bounded by a sphere of radius S, where:

• The first term in that estimate is related to the size of the compact volume that might contain the appropriate number of habitable worlds, while the second term is related to the scattering of stellar systems over time due to their different space velocities.
• This last estimate may be reduced if the culture in question practices migration, moving populations back toward the core as their stellar systems drift too far away. Most proxy cultures will engage in this kind of behavior. Otherwise, some of their occupied systems would tend to drift out of the supervised volume over time.

Assumption #9: For at least the last 600 million years, and until quite recently, Sol and Earth have not fallen within the volume of supervision of any Synarchy proxy culture.

Results: Within the past 600 million years, the 25,000 nearest habitable worlds to Sol would have given rise to 30,000 tool-using civilizations. This suggests that without intervention and uplift, the probability for any one tool-using civilization to attain interstellar capability is no greater than about 1 in 60,000.

Combining this with the galactic-history model developed earlier, we find that:

• The Precursor civilization most likely appeared 9.8 billion years ago, and the era of great galactic conflicts was about 9.4 billion years ago.
• Today, depending on the typical lifespan of a proxy culture (probably longer than the quarter-million years of a client civilization), there are likely to be several thousand such proxies in the galaxy at any given time.

Another result is that it would be very unusual for more than one proxy culture to appear independently in the same galactic neighborhood at the same time. However, it may be possible for client civilizations to “graduate” to independent proxy status rather than “ascension” or voluntary extinction. Proxy cultures might be thought of as reproducing by “budding” during periods of stability. Also, when the proxy eventually passes on, it may reproduce by “spawning” some of its last few client civilizations into independent proxy status.