Introduction

The simplest model of a growing galactic empire is a swelling balloon. Starting at the origin planet the spherical colonization wave will grow at the rate of empire expansion.

The much more messy and difficult to figure model of expansion is via Civilization Clusters. But this model more or less precludes the existence of an empire anyway, so it can be ignored by science fiction writers trying to build an empire.

Imagine a planet inhabited by imperialistic little opportunistic aliens, just like us, whose star is in a galaxy totally uninhabited by any other intelligent creatures (or at least uninhabited by creatures who can defend themselves). Once our imperialists discover interstellar travel, they will spread to the surrounding stars in a manner similar to a watermelon hitting the sidewalk. As previously mentioned, their empire will approximate an expanding sphere, with their homeworld at the center.

It is useful to be able to calculate a bit of geography for your interstellar empires. The control radius between the Imperial (or Sector) Capital and the Rim give you the size of your empire. It would be nice to be able to figure out how many stars are inside the empire, especially if you want to ensure that the Imperial Bureaucracy can actually handle it.

Warning, the galactic plane in the neighborhood of Sol is only about 1,000 light-years thick. If the radius is over 500 light-years the equations will calculate give an incorrect result (too many stars).

Given the empire radius in light-years, the number of stars and habitable stars inside the borders is:

Nstars = Rly3 * StarDfactor

NhStars = Rly3 * HStarDfactor

where:

  • Nstars = number of stars
  • NhStars = number of stars with habitable planets
  • StarDfactor = star density factor, use 0.017 or see below
  • HStarDfactor = habitable star density factor, use 0.002 or see below
  • Rly = empire radius in light-years
  • x3 = cube of x, i.e., = x * x * x

Given the number of stars or habitable stars inside the imperial borders, the empire radius is:

Rly = cubeRoot(Nstars * StarRfactor)

Rly = cubeRoot(NhStars * HStarRfactor)

where:

  • Rly = empire radius in light-years
  • Nstars = number of stars
  • NhStars = number of stars with habitable planets
  • StarRfactor = star radius factor, use 59.68 or see below
  • HStarRfactor = habitable star radius factor, use 464.46 or see below

StarDfactor, HStarDfactor, StarRfactor, HStarRfactor: all depend upon the stellar density, that is, how many stars per cubic light year. Currently the best estimate I could find for stellar density in Sol's neighborhood is Erik Gregersen's 4.0×10-3 stars per cubic light year. The density of stars with human habitable planets I calculated by using Tarter and Turnbull's Habcat dataset. Simplistic math on my part gave a value of 5.14×10-4 habitable stars per cubic light year. But keep in mind that the HabCat dataset came out in 2003.

StarRfactor = StellarDensity / ( (4/3) * π )

StarDfactor = 1 / StarRfactor

HStarRfactor = HStellarDensity / ( (4/3) * π )

HStarDfactor = 1 / HStarRfactor

where:

  • StellarDensity = stars per cubic light-year
  • HStellarDensity = habitable stars per cubic light-year

You can find how I derived this equation here.

SourceStellar
Density
StarRfactorStarDfactor
Erik Gregersen4.0×10-3 s/ly359.680.017
HabCat5.14×10-4 s/ly3464.460.002
Globular Cluster2.02×100 s/ly30.1188.461
Omega Centauri
average
3.8×100 s/ly30.06315.917
Omega Centauri
core
8.6×101 s/ly30.003360.236
Omega Centauri
center
1.8×102 s/ly30.001753.982
Galactic Core2.88×100 s/ly30.08312.064
Galactic Center8.5×101 s/ly30.003356.047
WHERE SHOULD I SITE A GALACTIC EMPIRE?

You need an evil galactic empire, or a benevolent  planetary federation, to set your scorching page turner of space opera in. The problem is that, to help your readers suspend their disbelief, you now have to figure out a believable interstellar civilisation. And write it a plausible sounding history. With a way of being founded and of expanding that makes sense. And you can't look that stuff up with Google...

....weeeeell.... actually...

I've spent far too much time reading papers and sitting courses on the search for extraterrestrial intelligences, so I know a surprising fact: Some very very clever brains (they include Stephen Hawking and Carl Sagan) have devoted serious man hours to what a huge galactic civilisation could be like. Not for fiction, but because they think we should be checking the sky in case there really is one somewhere.

That means there's a lot of stuff been written that can help you. Much more than a blog posts worth (I'll have to write a book... hmmm) so here I'll just try and sum up their thoughts on most important aspect, re-mixed for SciFi instead of SETI. And that big important aspect is, of course: Location, location, location.

It’s very much like looking for a house – you need to think about location, access to amenities, commuting, and what won’t break your budget. Admittedly the the plumbing is rather more complicated on an interstellar empire. And the call-out fees are a nightmare if it breaks...

In much the same way that it’s only a truly exceptional house that doesn’t need the ground*, unless your empire builders can wave away fundamental laws of physics** you’ll at least need your location to fill some really basic needs:

  • It will need an energy source. This probably means stars, but other energy sources – like the matter falling into a super massive black hole or the radiation beams of a pulsar, do exist. There is even a scale - the Kardashev scale - for rating any alien empires by how much power they use.
  • It will need planets, or at the very least the kind of heavy elements planets are made out of  as building materials for artificial living structures like ringworlds.
  • It doesn’t have to be friendly to life – your empire builders could have migrated there from a more hospitable part of the universe when they had the technology to handle the difficult conditions – but it needs to be close enough to at least one friendly environment for someone to have made the trip.

Then there are other things that it’s very useful to have, but a lack (or overabundance) of which could be overcome to a greater or lesser extent using technology or good planning:

  • Commuting: You’ll probably want your empire to be small enough to get messages across in a reasonable time. Many authors do this by introducing a Faster Than Lightspeed (FTL) drive - although other methods, such as much longer than human-normal lifespans (via gene engineering or suspended animation), are also thrown about by both authors and scientists. But another way, if you’re not committed to an Earth centred civilisation, is to just set your empire in a part of the universe where the distances between stars are smaller than the five light years that the stars near Earth average (see below). If George Lucas can have a galaxy far, far away then why not you...?
  • Stable environment: In the same way at you wouldn’t buy a house in the part of town where gangs occasionally leave heads in dustbins (although I once rented such a place), you wouldn’t set up a civilisation in a part of the galaxy where there are good odds that radiation from a supernova, neutron star collision, or belch from a supermassive black hole might fry it to a crisp. True, you could overcome this with technology, but let me assure you: No house alarm is truly unbeatable, and I expect that so no technological solution to stellar dangers will be either.
  • Minimum age requirement: This goes hand in hand with the need for a quiet neighbourhood – young areas of the galaxy, like young clusters and star forming nebula, tend to be crowded with troublemakers like unstable blue giant stars, dense molecular clouds, and wandering black holes. Older locales tend to be much quieter, since the dangerous stars tend to have blown up or burnt out eons back. Older locales also have had more time to spawn native life forms who can rebel against (or ally with) your empire.
  • Conditions suitable for life (of some kind) to arise: Not an absolute need - a sterile locale could be colonised from outside. Still, it’s simpler in terms of backstory for a thriving civilisation to grow up near to the planets that spawned them, and that means they need a few things: A stable environment, a ready supply of chemical energy, some form of chemistry complex enough to support things like DNA, and some way of mixing everything together – usually a good solvent like water – are generally regarded as the minimum. You can waive at least some of them, however, if you make your life form exotic : A.I, sentient gas clouds, energy based, or whatever your imagination can conjure.
  • Life forms suitable to reach technological era: NASA and ESA are spending a lot of money looking for evidence of bacterial life on Mars, but it’s unlikely bacteria are going to build stargates or leave their home planet by anything other than accident^* . Hence you need creatures that could invent and use technology. 

Just based on those we can rule out some locations already: The great voids between galaxies would be impossible to build in without importing massive amounts of both matter and energy across billions of light years. Some galaxies have stars that are much further apart than normal, so trips would take longer and they would be scarce of energy and building material too. The same applies to the galactic halo, and intergalactic space. Active galaxies, where massive black holes are sucking down matter and belching back out radiation, are hard places for life to ever arise in or anywhere near.

If you’re not employing FTL engines, or if they’re limited to some practical upper limit, you probably want some improvement on the travel times to the nearest stars to Earth -  so the Milky Way's galactic core is attractive with its close packed solar systems, but the risk of supernova, neutron star collisions, and mega flares from giant black holes make it much less attractive long-term. Something similar applies to young clusters of new formed stars, or active star forming nebula.

But there are good locations to be found - here are a few suggestions:

  • A multiple star system. The Universe abounds with stars and solar systems that are bound in small clusters by gravity, orbiting about each other. The individual stars are usually much less than a light year apart, often only light months or weeks, but there’s usually enough room between them for each star to have a habitable zone and fully developed system of planets. You could invent your own such star system - which is what the writers of the Battlestar Galactica remake did - for example: Four red dwarf stars with seven planets orbiting each star, might plausibly give you twelve habitable worlds (three in the habitable zone of each star) all packed into a light month of space^.  There would also be another sixteen uninhabitable but potentially mineable worlds. True, this is the entry level galactic empire - but it’s limited extent is compensated for with other advantages. In particular, if you want a real locale that is also close to Earth, then the nearest star system to Earth (the three star cluster of Proxima, Alpha, and Beta Centauri) actually fits the bill^^: Small by galactic standards, but still an empire greater than every civilisation of Earth combined.
  • Globular clusters:  These collections of hundreds of thousands of stars have a lot to recommend them – they’re old, so there are few or no dangerous, radiation spitting, potentially explode-ey young stars around. Instead most of the stellar population are red dwarfs, with their tight wound systems of planets, or red giants destined to die relatively quiet deaths. Average distance between stars is down to less than three light months – so even a sub-light speed starship could cross between several star systems over the course of a year. On the downside: Planets orbiting any Sun-like stars would be pulled out of orbit by neighbouring stars, and Globular clusters are generally quite poor in heavy, planet building elements, so only fairly small planets (like Earth) would form around their stars. But these aren't showstoppers: Planets orbiting red dwarf stars would be much more likely to stay with their suns, as these hug their planets much closer, and some of these clusters do have enough planet forming elements. On top of that the age of these stars - 5 billion years at least -  makes it more likely for a technological civilisation to have had time to arise^°. Globular clusters are not without hazards to navigation However: The long dead blue super stars, the absence of which makes the cluster fairly quite, will have left behind things like black holes and pulsars, which will be concentrated in the core. 
  • Open clusters: Open clusters, on the whole, are not great spots for civilisation building - most open clusters are both too young for any worlds to have given rise to complex life, and are filled with big, radiation spitting, supernova prone, blue stars. Older ones, where things have settled down, are rare – the members of open clusters are usually born with enough speed to escape the cluster, so they drift apart in a few tens of millions of years. But some of the biggest have got enough gravity to have stayed together for hundreds of millions, or even billions, of years. Examples are places like the Beehive cluster, which is coming up on 3/4 of a billion years old, and is composed mainly of red dwarfs and sunlike stars. Near the clusters core these are packed within maybe as little as 1/2 a light ear of each other, and while these clusters may not be old enough time for technological life to arise (that took over 4 billion years on Earth), they have had time for a stable ecosystem to form that would support colonists. 
  • Ultra compact dwarf galaxies. These are quite a new discovery, and something of a mystery – tiny galaxies less than 200 light years across, that are as jam packed as the cores of globular clusters. Like globular clusters they’re mainly made of older, redder, stars and many of the same things apply to them, but they have higher levels of planet building heavy elements. 
  • Giant elliptical galaxies: For the big dawgs only – old and stable but up to 6,000,000 light years across, one of these could be home to a titanic empire of trillions of star systems – and is more likely to be so than the Milky Way ever will: The majority of stars in these galaxies are old, stable, and long lived - and there are trillions, so they have a good chance of having spawned a civilisation. But these are vast, vast places that could swallow our galaxy without noticing, so your empire builders better have mastered a powerful means of FTL travel, immortality, or both. 

These are just suggestions, but there are locations out there to fit most plot needs. The question is, simply, what kind of empire does your Imperial Majesty want?

*  Space stations, maybe, would count.

** You could write an empire like that: A civilisation so advanced it can more or less conjure matter and energy out of nothing, lurking in the utter darkness between the galaxies. Sounds like it might have some potential in a very Lovecraftian way, no? But a civilisation that advanced would be capable of almost anything, and so would suffer from the superman effect – it’s almost impossible to write a story for them because it’s impossible to think up a problem or obstacle they couldn’t solve almost instantly. If you don’t believe me I cite every superman film since superman 2 as evidence.

^* There really are plausible ways bacteria might naturally leave their home planet and colonise another by accident, such as riding the debris from a giant asteroid strike, but you’d need to be writing a very esoteric story for that to count as an empire. Some kind of communal bacterial intelligence might work, but you’d have to have your heroes charge into battle against the evil empire by scrubbing every kitchen work surface on the planet with Dettol.

^ For hard SF writers: That means the furthest worlds could be travelled between in five months with a starship that could hit 20% of lightspeed – a speed many researchers believe we could reach with engine designs we could build in the next century. A radio message could make the same journey in one month, giving a slightly better messaging time than existed between the furthest corners of the Roman empire.

^^Two sun like stars (alpha and beta centauri)about the same distance apart as the Sun and Saturn, with a red dwarf star (proxima centauri) orbiting the larger two at a distance of ¼ of a light year. There’s a confirmed planet in the habitable zone of the red dwarf, and a possible detection of one in a very tight orbit around one fo the Sun like stars. Small, undetected planets in the habitable zones of the sun like stars are possible. It’s very plausible to put a human colony around each of the stars, with the occupants able to visit each star system in less than a year with sub light speed engines. A small empire of three solar systems - but still bigger than every empire on Earth combined.

°^ A civilisation taking in a whole such cluster would control hundreds of thousands of systems, but its inhabitents would need to be longer lived than modern humans, or have FTL – these clusters are often over a hundred light years in dimeter despite being so close packed.

GROWTH OF TRANTOR

Abel had a map of Trantor in his study, so designed as to show the application of that force. It was a clear crystalline ovoid in which the Galactic lens was three-dimensionally laid out. Its stars were specks of white diamond dust, its nebulae, patches of light or dark fog, and in its central depths there were the few red specks that had been the Trantorian Republic.

Not "were" but "had been." The Trantorian Republic had been a mere five worlds, five hundred years earlier.

But it was a historical map, and showed the Republic at that stage only when the dial was set at zero. Advance the dial one notch and the pictured Galaxy would be as it was fifty years later and a sheaf of stars would redden about Trantor’s rim.

In ten stages, half a millennium would pass and the crimson would spread like a widening bloodstain until more than half the Galaxy had fallen into the red puddle.

That red was the red of blood in more than a fanciful way. As the Trantorian Republic became the Trantorian Confederation and then the Trantorian Empire, its advance had lain through a tangled forest of gutted men, gutted ships, and gutted worlds. Yet through it all Trantor had become strong and within the red there was peace.

Now Trantor trembled at the brink of a new conversion: from Trantorian Empire to Galactic Empire and then the red would engulf all the stars and there would be universal peace—pax Trantorica.

Abel wanted that. Five hundred years ago, four hundred years ago, even two hundred years ago, he would have opposed Trantor as an unpleasant nest of nasty, materialistic and aggressive people, careless of the rights of others, imperfectly democratic at home though quick to see the minor slaveries of others, and greedy without end. But the time had passed for all that.

He was not for Trantor, but for the all-embracing end that Trantor represented. So the question: How will this help Galactic peace? naturally became: How will this help Trantor?

The trouble was that in this particular instance he could not be certain. To Junz the solution was obviously a straightforward one. Trantor must uphold the I.S.B. and punish Sark.

Possibly this would be a good thing, if something could definitely be proven against Sark. Possibly not, even then. Certainly not, if nothing could be proven. But in any case Trantor could not move rashly. All the Galaxy could see that Trantor stood at the edge of Galactic dominion and there was still a chance that what yet remained of the non-Trantorian planets might unite against that. Trantor could win even such a war, but perhaps not without paying a price that would make victory only a pleasanter name for defeat.

So Trantor must never make an incautious move in this final stage of the game.

From THE CURRENTS OF SPACE by Isaac Asimov (1952)
SHIFTING BORDERS

      The stranger said, “My name is Hober Mallow. I come from a far province.”
     Barr nodded and smiled, “Your tongue convicted you of that long ago. I am Onum Barr of Siwenna — and once Patrician of the Empire.”
     “Then this is Siwenna. I had only old maps to guide me.
     “They would have to be old, indeed, for star-positions to be misplaced.” “My house is poor and my resources few. You may share what I have if your stomach can endure black bread and dried corn.”

     Mallow shook his head, “No, I have eaten, and I can’t stay. All I need are the directions to the center of government.”
     “That is easily enough done, and poor though I am, deprives me of nothing. Do you mean the capital of the planet, or of the Imperial Sector?”
     The younger man’s eyes narrowed, “Aren’t the two identical? Isn’t this Siwenna?”
     The old patrician nodded slowly, “Siwenna, yes. But Siwenna is no longer capital of the Normannic Sector. Your old map has misled you after all. The stars may not change even in centuries, but political boundaries are all too fluid.

     “That’s too bad. In fact, that’s very bad. Is the new capital far off?”
     “It’s on Orsha II. Twenty parsecs off. Your map will direct you. How old is it?”
     “A hundred and fifty years.”
     “That old?” The old man sighed. “History has been crowded since. Do you know any of it?”

From THE BIG AND THE LITTLE by Isaac Asimov (1944)

Rate of Empire Expansion

Once you have decided that your Terran Empire is X number of light years wide or contains Y number of stars, it would help to have a realistic number for the amount of years it will take for the empire to expand to that size. Or from the other side, if you have decided how long the empire has been around, it would help to be able to figure out how many stars and how wide it is. This is a little more difficult.

The SETI scientists are always fretting about the Fermi paradox. As a result, there have been a couple of attempts to model the speed of galactic colonization by a hypothetical alien race. These can be used, keeping in mind that they always assume slower-than-light starships. Such models have inhabited planets colonizing nearby worlds. When the population of the colonies grows large enough, they send out their own colonization missions.

A comprehensive but mathematically intensive model is Burning the Cosmic Commons by Robin Hanson. Another interesting model is Computer Simulation of Cultural Drift: Limitations on Interstellar Colonisation by William Sims Bainbridge. I would like to explain how to use them, but I'm still trying to digest the models myself.

EXPANSION RATE IS TWICE SHIP SPEED

The races of man had spread across the spiral arm and toward the great whorl of the central galaxy.

By the year 970 H. C. (Calendar of the Holy Church), date of the last known Empire Census, there were more than 11,000 inhabited planets in the Empire, plus a known 1,700 more on the frontier—and estimates of at least 3,000 more beyond that whose existence was known but not confirmed. How many human beings there were simply could not be estimated.

Vast fleets of starcruisers whispered through the darkness, the fastest of them journeying a hundred light-years every three hundred days.

—but the Empire spanned a thousand light-years. More.

No matter how great the speeds of the starcruisers were, the distances of the galaxy were greater. At the fastest speed known to man it still took more than ten years to cross from one end of known space to the other. And the distance was growing. For every day that passed, 240 light-days were added to the scope of man's known frontiers.

Man was pushing outward in all directions at once, an ever-continuing explosion. For every ship travelling toward the galactic west, there was another headed for the galactic east; and the rate of man's outward growth was twice as fast as anyone could travel.

At the farthest edges of the Empire was the frontier. Beyond that lay unexplored space. Every man that fled into that wilderness dragged the frontier with him. The frontier followed willingly, and after a while, when that particular piece of itself matured, it became a part of the Empire, and the state of mind known as frontier had moved on. Thus, the Empire grew.

From SPACE SKIMMER by David Gerrold (1972)

Newman & Sagan

Newman & Sagan (Galactic civilizations; population dynamics and interstellar diffusion. Icarus, 46, 293-327) attempted to apply the gas diffusion equation to interstellar migrations.

∂P/∂t = αP (1 - P/Ps) + γΔ2 ∂/∂x (P/Ps ∂P/∂x)

where

  • P = population of a settlement
  • Ps = the carrying capacity of a settlement
  • t = time
  • x = spatial coordinate
  • α = local population growth rate (percentage of current population)
  • γ = emigration rate (percentage of current population)
  • Δ = mean separation of settlements
  • ∂ = partial differential (Yes, I know. Scary Calculus. But don't panic)

The solution to the equation is:

P/Ps = 1 - exp((x - vt) / L)

where

  • L = Δ sqrt(2γ / α) = gradient length scale
  • v = sqrt(αγ / 2) = wave speed

However, when Newman and Sagan analyzed the problem, they came to the belated realization that the local growth rate (α) greatly exceeds the emigration rate (γ) so that L <<Δ. Translated into English, this means that the galactic colonization resembled an explosion more than it did a slow gaseous diffusion. Which means the equation is worthless for this purpose. Back to the drawing board.

Eric M. Jones

Eric M. Jones found a more promising approach. In Discrete calculations of interstellar migration and settlement( Icarus Volume 46, Issue 3 , June 1981, Pages 328-336. Costs $15 for the article) he uses a Monte Carlo simulation (i.e., rules are established then a lot of dice are metaphorically thrown). Jones found the following equation will approximate the Monte Carlo results:

v = Δr/ [(Δ/vs) + (1/α) ln(2α/γ)]

where

  • Δr = average radial distance traveled (i.e., distance as meaured from the center of the empire)
  • Δ = average distance traveled
  • vs = ship speed
  • Δx/vs = average travel time (years)

Jones says one can usually assume that Δr = 0.7Δ and neglect the travel time, resulting in:

v = 0.7αΔ / ln(2α/γ)

Assuming the mean separation between settlements (Δ) is 7.2 light years (2.2 parsecs), local population growth rate (α) is 10-3 per year, and the emigration rate (γ) is 10-4 per year, this means the colonization wave will travel at about 2 x 10-3 light-years per year (5 x 10-4 parsecs per year). This would colonize the entire galaxy in a mere 60 million years.

The emigration rate could become much larger. In the 1840's the great Irish emigration reached a whopping 0.01/year. The population of Ireland at the time was about four million, so the emigration was an incredible 40,000 per year or about one hundred per day.

Using the upper equation, with my figure of 8.3 light years for Δ, and a slower-than-light ship speed of 10% c, I figure an expansion wave speed of 1.93 x 10-3 light-years per year. Unfortunately, upping the speed of the ships has little effect. At 50% c it's 1.97 x 10-3 ly/yr, at 100 c it's still 1.97 x 10-3 ly/yr, at ten times the speed of light it's 1.98 x 10-3 ly/yr, and at one thousand times the speed of light it is still 1.97 x 10-3 ly/yr!

At this speed, it would take about 50,000 years to expand to a 100 light year radius empire, which seems like an overly long time to me.

But maybe not. Mr. Jones is talking about a population growth of 10-3 or 0.1% per year. The United States has a growth rate closer to 0.6%, and some nations are crowding 3.0%. If our empire had a growth rate α of 0.6% and a modest emigration rate γ of 10-4 per year, it could reach 100 light years in radius in about 6900 years. And if it had a draconian γ of 10-2, it could reach that size in a mere 260 years.

Comments

Issac Kuo questions the assumptions contained in Eric M. Jones's model:

One thing I don't like about these models is that they tend to be based around "average" trip distances and speeds. However, the rate of expansion will be determined by the "pioneering" trip distances and speeds.

The sorts of interstellar propulsion I find plausible involve an incredible amount of initial investment and economic buildup, but then the marginal costs for additional colonization missions are small. This suggests that the third generation of colonization missions might as well be long range missions. The second generation of colonies will have saturated the nearby systems so the only direction to expand is into long range missions.

For example, suppose it takes 5000 years to build up from an initial colony into something that can send out missions of their own. In the meantime, the home system could be sending out colonization missions at a rate of one per decade. By the time the first generation of colonies is up for sending out colonization missions, the nearest 50 systems have already been colonized. The first generation then sends colony ships to fill out the nearest 2500 systems.

Assuming no one has yet bothered to try any long range colonization missions, the result is a compact ball of 2500 colonized systems, of which only a thin shell on the outside can expand with short range missions.

It seems to me plausible that at least some of the "core" systems will embark on long range missions. Maybe some of those long range missions will merely just barely outrun the expanding border. That's a rather short-sighted strategy. Other long range missions will daringly punch across the galaxy, starting up seeds which won't run into the "slowpoke" border for dozens of millenia.

The result is an overall frontier of expansion that is defined by sporadic long range "seed dots". They fill out eventually, but it's entirely plausible for the overall rate of expansion to be entirely defined by far reaching long range high speed missions from the home system or early generation systems.

Issac Kuo

Rick Robinson had this to say:

Just glancing though your section there, the key challenge for a lot of purposes is time scale — and oddly, it doesn't have much to do with ship speed; an STL civilization might expand over the long haul nearly as fast as an FTL one.

The key issue - and this comes up in all sorts of contexts — is how long does it take for a planet to go from raw young colony to major world, the kind that could and might send out colonies of its own? This is the basic problem you have to solve for settings in which anyone has a space fleet of their own but Earth.

Let me try to put a few numbers on it.

The threshold for having a space fleet is arguably lower than for colonization, because a planet of 100 million people could probably maintain starships, but probably is not feeling a big population squeeze. To be sure, on some planets the habitable area will be pretty much filled, and even on the more earthlike ones the human presence is getting pervasive, so some impulse to colonize might be developing.

Whether a planet of 10 million people - the equivalent of a single large urban region — could realistically have a diversified enough economy to maintain and operate a fleet of starships seems a bit iffy, unless they are putting a massive effort into it, so massive that it may stunt their other prospects.

The most likely scenario for a world of 10 million people sending out a colony might be that they've decided their current home sux, and they're going to try their shot at another one.

Looking at the other end, how many people for a viable colony. I'd say 10,000 at the low end, with 100,000 seeming a lot more comfortable. That's the population of one semirural county. How many machine shops and such does it have, how much can they specialize for efficiency, and oh yeah, you need raw material, a mining sector and all that.

If you can't make it you have to import it, paying starship freight instead of truck freight, and what have you got for sale? The market for colony-world curios is going to get crowded fast, and if you really do have something to sell, you'll probably need more than a one-county economy to produce it in commercial quantities.

So I would say that you usually have to put 100,000 people onto a colony planet for it to thrive. Colonies with fewer than that can hang on, but if subsidies are cut off they may die off outright, or be stuck in a marginal existence; only lucky ones will overcome it and do okay.

For a colony to really go as a largely self-sufficient post industrial world it had better have on order of a million people — more or less the equivalent of Bakersfield and environs. I am certain that Australia has a Bakersfield, but I do not know what it is. Maybe our Oz contingent can inform us.

But once again, if they can't make it or pay starship freight for it they do without it, and the equivalent of Bakersfield has a tough challenge producing nearly all the needs of post industrial civilization. And for exports it is good to have one sizeable airport that can double as the shuttle port and provide steady employment for a lot of the techs.

Big proviso, so hold your pitchforks. This is predicated on the 23rd century, or 28th or whatever, having about the same productive efficiencies of scale that we are used to. If you have got replicators where you shovel dirt in one end and get a washing machine or air car out the other, things are different. But you still need a wide range of human skills, very hard for small communities to provide, maintain, and keep active.

So maybe my figures could all be squeezed down by an order of magnitude, so that a colony of 10,000 is fairly viable, a colony of 100,000 can maintain a full industrial base, and one of a million people can keep its own starships in service. That helps for story settings, but you wouldn't generally expect worlds like that to be active colonizers.

Finally, and most central to time scale, how fast do colony populations grow, either from immigration or birth rate? I would call a million emigrants from Earth each year a benchmark figure for large scale colonization. That's several thousand people each day, one huge ship or several merely big ones, and it still takes a century of sustained effort to plant 100 colonies, each of a million people.

From the colony's point of view, people are another expensive import, if you have to pay them to come. If they can afford a ticket and house stake they will only go to desirable colonies. If someone is paying to ship people to you, you may want to know why, because colonies could be a good place to dump dissidents, minor troublemakers, and similar riffraff.

On the export side, I'm more dubious of shipping off refugees, because by definition you're dealing with lots of them, and shipping them all off world is horribly expensive. Much more so than just plucking the town crank and town pickpocket off the streets and getting them to volunteer for emigration.

But by and large you expect that mass colonization involves people who weren't doing so great on Earth, because the supply of nut enthusiasts like people on this board who would actually like to colonize is limited, and a million people a year is a lot.

The other side of colonial growth is reproductive growth. Doubling the population each generation is about the historical sustained maximum. That corresponds to 10x per century, so Deseret World might go from 100,000 people to 10 million people in 200 years.

But even doubling per century is a pretty robust population growth rate. That's roughly 1.2x per generation. Unless you're growing 'em in vats, about half the women are having three or four kids, and one way or another the society encourages and accommodates itself to this.

It's no given that post industrial societies will generally have this population growth rate, though colony worlds may not follow the current trend in industrialized societies toward ZPG or even less.

If colony populations do tend to grow, I suspect the driving force is not the Heinleinian trope of ranchers with half a dozen marriageable — and "husband-high" — daughters, but the pervasive shortage of skilled specialists of all sorts. How this is transmitted to social attitudes I'm not sure, and no doubt can vary widely.

A colony with population doubling each century will go from 100,000 people to 10 million people in about 700 years, pushing us into the second half of the millennium.

Looking at it broadly, say that the age of colonization is around 2250-2350. That is a fairly common time frame for interstellar SF with a geocentric setting; (Star) Trek is vaguely in this era, AD2300 of course, and it's implied by some of Heinlein's interstellar stories.

After a century or so colonization from Earth sputters out, because all the low-hanging fruit has been plucked, and it is increasingly costly to reach virgin planets.

Emigration from Earth to the existing colonies can continue after that, but at some point the rate will likely fall. Successful colonies will no longer want people dumped on them, unsuccessful colonies can't absorb them, so emigration falls to the level of people who can pay to go and want to go, or who the colonies are willing to pay for.

So. At some point around 2400, colonization has tapered off and emigration is tapering off. We can guess that there are at least a dozen or so full colony planets - if you can reach any you can probably reach about that many (and you need a good handful for a decent scenario).

The upward limit is about 100 or so true colony worlds, set - regardless of how many worlds are in reach of your FTL - by the postulated size of the colonization wave. A hundred million people, a hundred worlds - an average of about a million immigrants per colony, though the distribution may well be oligarchic by a power law, a handful of colonies getting a large share of total immigrants, growing to populations of up to a few tens of millions, while most have less than a million and kind of struggle along.

Beyond and between the colonies there may be planets never made into self-sustaining colonies, but remaining as outposts, and likely with some permanent populations. If someone pulls the plug on these, though, don't miss the last bus out. Same with space stations and such.

As with the chronology, I think this is a fairly classical scale for a mid-interstellar setting — when there are already established colony worlds, that you can get to by starliner, not just outpost transport or even colonization ship.

There are enough worlds for a diverse interstellar setting, but few enough that people who deal with space, at least, will have some notion of them all as distinct places. (The way "Spain" conveys something to you, or "New Delhi," but "Florianópolis" probably does not.

A few of these colonies already in 2400 have upwards of 10 million people and some potential to colonize themselves, but these were the immigration magnets, so they probably still feel short-handed if anything, not inclined to send lots of people off.

It will take 200 or 300 years for smaller colonies with rapid population growth rates to start pushing up into the 10 million population range, and might have the impulse and capability to colonize. But it might take closer to 500 years for a substantial number of the original colonies to have much motivation to colonize.

The early goers, though, will have filled in the next layer of easy pickings. Here is where your FTL really matters - whether you can light off freely into the vastness to hunt for a suitable planet, or are constrained by a colonization sphere that is starting to grow again.

But broadly speaking, it seems that secondary colonization couldn't be expected in any serious way until sometime well after 2500, and perhaps not in a big way till sometime around 2700-3000.

Rick Robinson

Jason Wright

GALACTIC SETTLEMENT AND THE FERMI PARADOX

A spacefaring species could easily settle the entire Milky Way given billions of years. Yet the fact is that there is no obvious one in our solar system right now. The supposed inconsistency between these statements is the Fermi Paradox, named for the Nobel Prize-winning physicist who supposedly first formulated it. In a trenchant formulation of the Fermi Paradox, American astrophysicist Michael H. Hart called the lack of extraterrestrial beings or artifacts on Earth today “Fact A.” He showed that most objections to his conclusion—that a spacefaring civilization could have crossed the galaxy by now—stem from either a lack of appreciation for the timescales involved (it takes a small extrapolation from present human technology to get interstellar ships, and even slow ships can star-hop across our galaxy in less time than the galaxy’s age) or else the dubious assumption that all members of all extraterrestrial species will avoid colonizing behaviors forever (an example of what I’ve called the monocultural fallacy).

William Newman and Carl Sagan later wrote a major rebuttal to Hart’s work, in which they argued that the timescales to populate the entire galaxy could be quite long. In particular, they noted that the colonization fronts Hart described through the Milky Way might move much more slowly than the speed of the colonization ships if their population growth rates were so low that they only needed to spread to nearby stars very rarely. They also argued that being a long-lived civilization is inconsistent with being a rapidly-expanding one, so any species bent on settling the galaxy would not last long enough to succeed. In other words, they reasoned that the galaxy could be filled with both short-lived rapidly expanding civilizations that don’t get very far and long-lived slowly expanding civilizations that haven’t gotten very far—either way, it’s not surprising that we have not been visited.

Being a long-lived civilization is inconsistent with being a rapidly-expanding one.

In a 2014 paper on the topic, my colleagues and I rebutted many of these claims. In particular, we argued that one should not conflate the population growth in a single settlement with that of all settlements. There is no reason to suppose that population growth, resource depletion, or overcrowding drives the creation of new settlements, or that a small, sustainable settlement would never launch a new settlement ship. One can easily imagine a rapidly expanding network of small sustainable settlements (indeed, the first human migrations across the globe likely looked a lot like this).

Another factor affects Newman and Sagan’s numbers on timescales and colonization-front speeds. Most of the prior work on this topic exploits percolation models, in which ships move about on a static two-dimensional substrate of stars. In these models, a star launching settlement ships can quickly settle all of the nearby stars, limiting the number of stars it can settle. But real stars move in three dimensions, meaning that they can carry their orbiting settlements throughout the galaxy, and that a settlement will always have fresh new stars to settle if it waits long enough.

Jonathan Carroll-Nellenback, at the University of Rochester with Adam Frank, not long ago finished work, with Caleb Scharf and me, on analytic and numerical models for how a realistic settlement front would behave in a real gas of stars, one characteristic of the galactic disk at our distance from the galactic center. The big advances here are a few:

  1. Carroll-Nellenback validated an analytic formalism for settlement expansion fronts with numerical models for a realistic gas of stars.
  2. He accounted for finite settlement lifetimes, the idea that only a small fraction of stars will be settle-able, and explored the limits of very slow and infrequent settlement ships.
  3. He also explored a range of settlement behaviors to see how galactic settlement fronts depend on them.

The idea that not all stars are settle-able is important to keep in mind. Adam Frank calls this the Aurora effect, after the Kim Stanley Robinson novel in which a system is “habitable, but not settle-able.”

The results are pretty neat. When we let the settlements behave independently, Hart’s argument looks pretty good, even when the settlement fronts are slow. Even if all the ships have a very limited range (only able to reach, say, the nearest stars to Earth) and even if they are no faster than our own interstellar ships today (like Voyager 2), we find they can still settle the entire Milky Way in less than its lifetime, supporting Hart’s version of the Fermi Paradox.

Carroll-Nellenback also explores regimes where they have been here, but we just don’t notice because it was so long ago. Frank and Gavin Schmidt explored this possibility in their Silurian Hypothesis paper, and I did something similar in my paper on “prior indigenious technological species” in the solar system. The idea is that “Fact A” only applies to technology that has visited very recently or visited and then stayed permanently. Any technology on Earth or the solar system that is not actively maintained will eventually be destroyed and/or buried, so we can really only explore Earth’s history back in time for something like millions of years, and not very well at that.

The question, in other words, isn’t, “Has the solar system ever been visited?” It’s, “Has it been settled recently?”. Carroll-Nellenback shows that there is actually a pretty big region of parameter space where the solar system is amidst many settled systems but just hasn’t been visited in the last 1 million years.

Of course, there are still lots of other reasons why we might not have been permanently settled by a galactic network of settlements—as we note in the paper:

Hart’s conclusions are also subject to the assumption that the Solar System would be considered settleable by any of the exo-civilizations it has come within range of. The most extravagant contradiction of this assumption is the Zoo Hypothesis (Ball 1973), but we need not invoke such “solipsist” positions (Sagan & Newman 1983) to point out the flaw in Hart’s reasoning here. One can imagine many reasons why the Solar System might not be settleable … including the Aurora effect … or the possibility that they avoid settling the environment near the Earth exactly because it is inhabited with life.

In particular, the assumption that the Earth’s life-sustaining resources make it a particularly good target for extraterrestrial settlement projects could be a naive projection onto exo-civilizations of a particular set of human attitudes that conflate expansion and exploration with conquest of (or at least indifference towards) native populations (Wright & Oman-Reagan 2018). One might just as plausibly posit that any extremely long-lived civilization would appreciate the importance of leaving native life and its near-space environment undisturbed.

Our results are a mixed bag for SETI optimists: Hart’s argument that settlement fronts should cross the whole galaxy—which is at the heart of the Fermi Paradox—is robust, especially because of the movements of stars themselves, which should “mix” the galaxy pretty well, preventing simply connected “empires” of settlements from forming. If Hart is correct that this means we are alone in the galaxy, then this is actually very optimistic for extra-galactic SETI, because it means other galaxies with even a single spacefaring species should rapidly become endemic with them. Indeed, our analysis did not even consider the existence of halo stars, which do not rotate with the galactic disk, or the fact that stars closer to the center take less time to go around—both will make settlement timescales even faster than we calculate.

On the other hand, there are a lot of assumptions in Hart’s arguments that might not hold. In particular, his assertion that if the sun has ever been in range of a settled system then it would have been settled and the settlers would still be here. Perhaps Earth life for some reason keeps the settlements at bay, either because “they” want to keep Earth life pristine or it’s just too resilient and pernicious for an alien settlement to survive. Perhaps Earth is Aurora?

Manifold

MANIFOLD TIME

     Reid Malenfant

     You know me. And you know I'm a space cadet.
     You know I've campaigned for, among other things, private mining expeditions to the asteroids. In fact, in the past I've tried to get you to pay for such things. I've bored you with that often enough already, right?
     So tonight I want to look a little farther out. Tonight I want to tell you why I care so much about this issue that I devoted my life toil.
     The world isn't big enough any more. You don't need me to stand here and tell you that. We could all choke to death, be extinct in a hundred years.
     Or we could be on our way to populating the Galaxy.
     Yes, the Galaxy. Want me to tell you how?
     Turns out it's all a question of economics.
     Let's say we set out to the stars. We might use ion rockets, solar sails, gravity assists. It doesn't matter.
     We'll probably start as we have in the Solar System, with automated probes. Humans may follow. One percent of the helium-3 fusion fuel available from the planet Uranus, for example, would be enough to send a giant interstellar ark, each ark containing a billion people, to every star in the Galaxy. But it may be cheaper for the probes to manufacture humans in situ, using cell synthesis and artificial womb technology.
     The first wave will be slow, no faster than we can afford. It doesn't matter. Not in the long term.
     When the probe reaches a new system, it phones home, and starts to build.
     Here is the heart of the strategy. A target system, we assume, is uninhabited. We can therefore anticipate massive exploitation of the system's resources, without restraint, by the probe. Such resources are useless for any other purpose, and are therefore economically free to us.
     I thought you'd enjoy that line. There's nothing an entrepreneur likes more than the sound of the word free.
     More probes will be built and launched from each of the first wave of target stars. The probes will reach new targets; and again, more probes will be spawned, and fired onward. The volume covered by the probes will grow rapidly, like the expansion of gas into a vacuum.
     Our ships will spread along the spiral arm, along lanes rich with stars, farming the Galaxy for humankind.
     Once started, the process will be self-directing, self-financing. It would take, the double-domes think, ten to a hundred million years for the colonization of the Galaxy to be completed in this manner. But we must invest merely in the cost of the initial generation of probes.
     Thus the cost of colonizing the Galaxy will be less, in real terms, than that of our Apollo program of fifty years ago.
     This vision isn't mine alone. It isn't original. The rocket pioneer Robert Goddard wrote an essay in 1918—ninety-two years ago—called The Ultimate Migration, in which he imagined space arks built from asteroid materials carrying our far-future descendants away from the death of the sun. The engineering detail has changed; the essence of the vision hasn't.
     We can do this. If we succeed, we will live forever.
     The alternative is extinction.
     And, people, when we're gone, we're gone.
     As far as we can see we're alone, in an indifferent universe. We see no sign of intelligence anywhere away from Earth. We may be the first. Perhaps we're the last. It took so long for the Solar System to evolve intelligence it seems unlikely there will be others, ever.
     If we fail, then the failure is for all time. If we die, mind and consciousness and soul die with us: hope and dreams and love, everything that makes us human. There will be nobody even to mourn us.
     To be the first is an awesome responsibility. It's a responsibility we must grasp.
     I am offering you a practical route to an infinite future for humankind, a future of unlimited potential. Someday, you know it, I'll come back to you again for money: seedcorn money, that's all, so we can take a first step—self-financing even in the medium term—beyond the bounds of Earth. But I want you to see why I'll be doing that. Why I must.
     We can do this. We will do this. We're on our own. It's up to us.
     This is just the beginning. Join me.

(ed note: thanks to Ian Mallett for bringing this quote to my attention)

From MANIFOLD TIME by Stephen Baxter (2000)
EXPAND OR DIE

I came from Deneb," she said. “Do you know it?”

“No.”

“Sixteen hundred light years from Earth—a system settled some four centuries after the start of the Third Expansion. It is quite different from the solar system. It is—organized. By the time the first ships reached Deneb, the mechanics of exploitation had become efficient. From preliminary exploration to working ship yards and daughter colonies in less than a century…Deneb’s resources—its planets and asteroids and comets, even the star itself—have been mined to fund fresh colonizing waves, the greater Expansion—and, of course, to support the war with the Ghosts.”

She swept her hand over the sky. “Think of it, tar. The Third Expansion: between here and Sol, across six thousand light years—nothing but mankind, the fruit of a thousand years of world-building. And all of it linked by economics. Older systems like Deneb, their resources spent—even the solar system itself—are supported by a flow of goods and materials inward from the growing periphery of the Expansion. There are trade lanes spanning thousands of light years, lanes that never leave human territory, plied by vast schooners kilometers wide. But now the Ghosts are in our way. And that’s what we’re fighting for!”


Pael said, watching me, “You see, child, as long as the explorers and the mining fleets and the colony ships are pushing outward, as long as the Third Expansion is growing, our economy works. The riches can continue to flow inward, into the mined-out systems, feeding a vast horde of humanity who have become more populous than the stars themselves. But as soon as that growth falters—”

Jeru was silent.

I understood some of this. The Third Expansion had reached all the way to the inner edge of our spiral arm of the galaxy. Now the first colony ships were attempting to make their way across the void to the next arm.

Our arm, the Orion Arm, is really just a shingle, a short arc. But the Sagittarius Arm is one of the galaxy’s dominant features. For example, it contains a huge region of star-birth, one of the largest in the galaxy, immense clouds of gas and dust capable of producing millions of stars each. It was a prize indeed.

But that is where the Silver Ghosts live.

When it appeared that our inexorable expansion was threatening not just their own mysterious projects but their home system, the Ghosts began, for the first time, to resist us.

They had formed a blockade, called by human strategies the Orion Line: a thick sheet of fortress stars, right across the inner edge of the Orion Arm, places the Navy and the colony ships couldn’t follow. It was a devastatingly effective ploy.

This was a war of colonization, of world-building. For a thousand years we had been spreading steadily from star to star, using the resources of one system to explore, terraform and populate the worlds of the next. With too deep a break in that chain of exploitation, the enterprise broke down.

And so the Ghosts had been able to hold up human expansion for fifty years.

Pael said, “We are already choking. There have already been wars, young Case: human fighting human, as the inner systems starve. All the Ghosts have to do is wait for us to destroy ourselves, and free them to continue their own rather more worthy projects.”

Jeru floated down before him. “Academician, listen to me. Growing up at Deneb, I saw the great schooners in the sky, bringing the interstellar riches that kept my people alive. I was intelligent enough to see the logic of history—that we must maintain the Expansion, because there is no choice. And that is why I joined the armed forces, and later the Commission for Historical Truth. For I understood the dreadful truth which the Commission cradles. And that is why we must labor every day to maintain the unity and purpose of mankind. For if we falter we die; as simple as that.”

“Commissary, your creed of mankind’s evolutionary destiny condemns our own kind to become a swarm of children, granted a few moments of loving and breeding and dying, before being cast into futile war.” Pael glanced at me.

“But,” Jeru said, “it is a creed that has bound us together for a thousand years. It is a creed that binds uncounted trillions of human beings across thousands of light years. It is a creed that binds a humanity so diverse it appears to be undergoing speciation…Are you strong enough to defy such a creed now? Come, Academician. None of us chooses to be born in the middle of a war. We must all do our best for each other, for other human beings; what else is there?”

From ON THE ORION LINE by Stephen Baxter (2000)
THE LIGHT CAGE

(ed note: obviously this assumes that faster-than-light starships are impossible)

4.1. Light Cage

McInnes shows that an expanding sphere of colonization cannot expand fast enough to avoid complete societal collapse due to exponential population growth and increasing population density (McInnes, 2002). Furthermore, after such a crash, the society may be so impoverished of resources that it is forever blocked from making a second attempt. If this theory is universally true of all civilizations, then it offers significant insight into the Fermi Paradox. McInnes extends the intuitive notion of a constant expansion rate with a steadily increasing population density to a linear expansion rate which maintains constant population density. However, the expansion velocity must have some maximum speed limit. To generate an upper-bound for this theory, McInnes considers a maximum expansion velocity of 1.0c. Obviously, in a real scenario, the expansion rate would be considerably slower, but that only exacerbates McInnes’ fundamental point which is that once the maximum expansion velocity is reached, population density once again begins to rise. Eventually, total societal collapse is inevitable. The only way to avoid catastrophe is to shift from exponential growth to logistic growth.

Given a specified growth rate and an initial sphere of some specified size, one can calculate the size of the expanded sphere when the increasing expansion rate reaches the 1.0c limit. McInnes calls this sphere the light cage. Assuming 1% annual growth and a starting sphere the size of Earth, he determines that the light cage is at a 300ly (light-years) radius and that the time to reach the light cage is 8000 years. Out of curiosity, we ran the numbers for a more realistic maximum expansion velocity. If we assume a maximum flight speed of 0.1c, a common estimate for fusion-powered starships such as Daedalus (Group, 1978; Matloff, 2005), which yields voyages to nearby stars on the order of decades, and if we assume a regeneration period of a few decades — and therefore comparable to the duration of the voyages themselves — then we estimate a more realistic maximum expansion velocity to be ~.05c. When applied to McInnes’ equations, this velocity reveals a far more realistic cage of a mere 15ly, and an associated saturation time of 7000 years. Interestingly, while a considerably slower expansion rate drastically reduces the cage, it only slightly decreases the time until the cage is hit. This follows naturally from exponential growth. To make matters worse, .05c may be entirely too fast if the stasis period between voyages is longer than the few decades of the previous estimate. If we briefly consider a maximum expansion velocity of .01c, we derive a cage of only 3ly!

Considering that there are only 52 stars within 15ly of Earth (and none within 3ly!), and that only some fairly small subset will support habitation, this does not provide us with very many systems to colonize before we implode in a population density catastrophe. More crucially, 15ly probably lies within the single-voyage horizon, which implies that early waves of colonization may fill the cage all at once as opposed to diffusing radially. In other words, according to light cage theory, interstellar travel hardly provides any population relief at all, right from the beginning.

McInnes is careful to admit that his model is continuous and symmetrical. Admittedly, galactic colonization is loosely like an expanding sphere, but more precisely it is like traversal of a rooted tree (a graph), where the root is the homeworld, vertices are solar systems, and labeled edges connect stars whose distances are below a maximum traversal threshold with the labels indicating interstellar distances (and associated travel times). In addition to the inherently discrete nature of this graph, the natural distribution of stars will impose notable asymmetries on the edge length and per-node degree (branching factor). McInnes admits to the simplicity of his model, but points out that such details should not affect the model’s outcome. We agree, but in practicality, a tree of no more than 52 nodes (probably far fewer), all of which have direct edges to the homeworld, no longer resembles a continuous sphere in even the weakest sense. A Monte Carlo simulation might help illuminate any interesting properties of the discrete model.

Assuming that the continuous model is apropos to the discussion, then we envisage two ways by which the model may not predict actual events. The first is admitted by McInnes, that populations may succeed in converting to logistic growth and therefore avoid the prescribed collapse. Given the calculation of a 15ly cage and the observation that it would saturate in a single emigration wave due to direct homeworld access, any hope of survival would depend on adopting logistic growth prior to interstellar colonization; any later would be too late to avoid disaster. However, Earth appears to be following just such a course, leveling off its population growth in the 21st century, long before undertaking interstellar travel (Haqq-Misra and Baum, 2009). Not only does this bode well for humanity, it suggests that other ETI civilizations can do the same...but such a conclusion weakens McInnes’ theory that the Fermi Paradox is resolved due to a finite expansion before societal collapse. If ETI are once again enabled to continue steady outward expansion, then the original questions underlying the paradox resurface.

The second challenge we would raise in response to McInnes’ model will be explained in section 4.3 when we introduce ITB theory. Briefly, we are unconvinced that interstellar distances don’t impose an insurmountable paucity of interaction events between solar systems such that contagions of societal collapse fail to adequately infect neighbors. Our final thoughts on McInnes’ model reflect on his postanalysis. He proposes the example of a civilization which permits exponential growth at its frontier but enforces logistic growth wherever resource limits are reached, i.e., deeper within the sphere. He shows how such a civilization could achieve phenomenal rates of unbounded expansion, filling the galaxy in a few millions years. While McInnes’ concedes this scenario, he nevertheless questions its validity by citing Landis’ percolation model, namely to doubt that the civilization would expand indefinitely. Considering that in section 3 we demonstrate some weaknesses of the percolation model, we likewise conclude that the proposed scenario stands relatively unchallenged. Should it turn out to be reasonable, then the Fermi Paradox remains, well, paradoxical.


Group, P.D.S., 1978. Project Daedalus : the final report on the BIS starship study. Journal of the British Interplanetary Society.

Haqq-Misra, J., Baum, S.D., 2009. The sustainability solution to the fermi paradox. Journal of the British Interplanetary Society 62, 47–51.

Matloff, G.L., 2005. Deep Space Probes: To the Outer Solar System and Beyond. Praxis Publishing Ltd

McInnes, C., 2002. The light cage limit to interstellar expansion. Journal of the British Interplanetary Society 55, 279–284

MANIFOLD: SPACE

(ed note: this assumes that faster-than-light starships are impossible)


     “Something’s wrong,” Ben whispered.
     “There always is.”
     “I’m serious.” He let his fingers trace out a line across the black sky. “What do you see?”
     With the Sun eclipsed by the shadow of the FGB module, she gazed out at the subtle light. There was that bright planet, andthe dim red disc of rubble surrounding the Chaera black hole, from here just visible as more than a point source of light.
     “There’s a glow around the star itself, covering the orbit of that single planet,” Ben said. “Can you see?” It was a diffuse shine, Madeleine saw, cloudy, ragged-edged. Ben continued. “That’s an oddity in itself. But—”
     Then she got it. “Oh. No zodiacal light.”
     The zodiacal light, in the Solar System, was a faint glow along the plane of the ecliptic. Sometimes it was visible from Earth. It was sunlight, scattered by dust that orbited the Sun in the plane of the planets. Most of the dust was in or near the asteroid belt, created by asteroid collisions. And in the modern Solar System, of course, the zodiacal light was enhanced by the glow of Gaijin colonies.
     “So if there’s no zodiacal light—
     “There are no asteroids here,” Ben said.
     “Nemoto. What happened to the asteroids?”
     “You already know, I think,” virtual Nemoto hissed.
     Ben nodded. “They were mined out. Probably long ago. This place is old, Madeleine.”
     “It’s like a fragment of a GMC—a giant molecular cloud,” Ben said. “Mostly hydrogen, some dust. It’s thick—comparatively. A hundred thousand molecules per cubic centimeter... The Sun was born out of such a cloud, Madeleine.”
     “But the heat of the Sun dispersed the remnants of our cloud... didn’t it? So why hasn’t the same thing happened here?”
     “Or,” virtual Nemoto said sourly, “maybe the question should be: How come the gas cloud got put back around this star?
     They came at the planet with the Sun behind them, so it showed a nearly full disc. It glared, brilliant white, just a solid mass of cloud from pole to pole, blinding and featureless. And it was surrounded by a pearly glow of interstellar hydrogen, like an immense, misshapen outer atmosphere.
     They could see nothing of the surface. Their instruments revealed a world that was indeed like Venus: an atmosphere of carbon dioxide, kilometers thick, scarcely any water.
     There was, of course, no life of any kind.
     Ben was troubled. “There’s no reason for a Venus to form this far from the Sun. This world should be temperate. An Earth.”
     “But,” Nemoto hissed, “think what this world has that Earth doesn’t share.”
     “The gas cloud,” Madeleine said.
     Ben nodded. “All that interstellar hydrogen. Madeleine, we’re so far from the Sun now, and the gas is so thick, that the hydrogen is neutral—not ionized by sunlight.”
     “And so—”
     “And so the planet down there has no defense against the gas; its magnetic field could only keep it out if it was charged. Hydrogen has been raining down from the sky, into the upper air.
     “Once there, it will mix with any oxygen present,” Nemoto said. “Hydrogen plus oxygen gives—”
     “Water,” Madeleine said.
     “Lots of it,” Ben told her. “It must have rained like hell, for a million years. The atmosphere was drained of oxygen, and filled up with water vapor. A greenhouse effect took off—
     “All that from a wisp of gas?”
     “That wisp of gas was a planet killer,” Nemoto whispered.
     “But why would anyone kill a planet?
     “It is the logic of growth,” Nemoto said. “This has all the characteristics of an old system, Meacher. Caught behind a wave of colonization—all its usable resources dug out and exploited...
     Madeleine frowned. “I don’t believe it. It would take a hell of a long time to eat up a star system.”
     “How long do you think?”
     “I don’t know. Millions of years, perhaps.”
     Nemoto grunted. “Listen to me. The growth rate of the human population on Earth, historically, was two percent a year. Doesn’t sound like much, does it? But it’s compound interest, remember. At that rate your population doubles every thirty-five years, an increase by tenfold every century or so. Of course after the twentieth century our growth rates collapsed; we ran out of resources.”
     “Ah,” Ben said. “What if we’d kept on growing?”
     “How many people could Earth hold?” Nemoto whispered. “Ten, twenty billion? Meacher, the whole of the inner Solar System out to Mars could supply only enough water for maybe fifty billion people. It might have taken us a century to reach those numbers. Of course there is much more water in the asteroids and the outer system than in Earth’s oceans, perhaps enough to support ten thousand trillion human beings.”
     “A huge number.”
     “But not infinite—and only six tenfold jumps away from ten billion.”
     “Just six or seven centuries,” Ben said.
     “And then what?” Nemoto whispered. “Suppose we start colonizing, like the Gaijin. Earth is suddenly the center of a growing sphere of colonization whose volume must keep increasing at two percent a year, to keep up with the population growth. And that means that the leading edge, the colonizing wave, has to sweep on faster and faster, eating up worlds and stars and moving on to the next, because of the pressure from behind...
     Ben was doing sums in his head. “That leading edge would have to be moving at light speed within a few centuries, no more.
     “Imagine how it would be,” Nemoto said grimly, “to inhabit a world in the path of such a wave. The exploitation would be rapid, ruthless, merciless, burning up worlds and stars like the front of a forest fire, leaving only ruins and lifelessness. And then, as resources are exhausted throughout the light-speed cage, the crash comes, inevitably. Remember Venus. Remember Polynesia.
     “Polynesia?”
     “The nearest analog in our own history to interstellar colonization,” Ben said. “The Polynesians spread out among their Pacific islands for over a thousand years, across three thousand kilometers. But by about A.D. 1000 their colonization wave front had reached as far as it could go, and they had inhabited every scrap of land. Isolated, each island surrounded by others already full of people, they had nowhere to go.
     “On Easter Island they destroyed the native ecosystem in a few generations, let the soil erode away, cut down the forests. In the end they didn’t even have enough wood to build more canoes. Then they went to war over whatever was left. By the time the Europeans arrived the Polynesians had just about wiped themselves out.”
     “Think about it, Meacher,” Nemoto said. The light-speed cage. Imagine this system fully populated, a long way behind the local colonization wave front, and surrounded by systems just as heavily populated—and armed—as they were. And they were running out of resources. There surely were a lot more space dwellers than planet dwellers, but they’d already used up the asteroids and the comets. So the space dwellers turned on the planet. The inhabitants were choked, drowned, baked.
     “I don’t believe it,” Madeleine said. “Any intelligent society would figure out the dangers long before breeding itself to extinction.”
     “The Polynesians didn’t,” Ben said dryly.

(ed note: The Chaera are the aliens who formerly lived on the murdered Venus-like planet. They currently live in miserable tiny space colonies orbiting a dangerous black hole artifact.)

     “But there remain mysteries,” Ben said. “The Chaera look too primitive to have constructed that artifact. After all, it manipulates a black hole’s gravity well. Perhaps their ancestors built this thing. Or some previous wave of colonists, who passed through this system.”
     “You aren’t thinking it through,” virtual Nemoto whispered. “The Chaera have eyes filled with salty water. They must have evolved on a world with oceans. They can’t have evolved here.”
     “Then,” Madeleine snapped, “why are they here?
     “Because they had no place else to go,” Nemoto said. “They fled here—even modified themselves, perhaps. They huddled around an artifact left by an earlier wave of colonization. They knew that nobody would follow them to such a dangerous, unstable slum area as this.
     “They are refugees.
     “Yes. As, perhaps, we will become in the future.”
     “Refugees from what?
     “From the resource wars,” Nemoto said. “From the hydrogen suffocation of their world. Like Polynesia.
     The core artifact trembled.
     And Nemoto kept talking, talking. “This universe of ours is a place of limits, of cruel equations. The Galaxy must be full of light-speed cages like this, at most a few hundred light-years wide, traps for their exponentially growing populations. And then, after the ripped-up worlds have lain fallow, after recovery through the slow processes of geology and biology, it all begins again, a cycle of slash and burn, slash and burn... This is our future, Meacher: our future and our past. It is after all a peculiar kind of equilibrium: the contact, the ruinous exploitation, the crash, the multiple extinctions—over and over. And it is happening again, to us. The Gaijin are already eating their way through our asteroid belt. Now do you see what I’m fighting against?
     Madeleine remembered the burster, the slaughter of the star lichen fourteen times a second. She remembered Venus and Australia, the evidence of ancient wars even in the Solar System—the relics of a previous, long-burned-out colonization bubble.
     Must it be like this?

(ed note: As it turns out, our solar system is not primordial. Venus used to be a Terra type planet, before a colonization wave swept through and murdered the planet. Millions of years later a second wave from a subsequent civilization swept through. This one killed most life on Terra with an asteroid bombardment. That is the reason Terra has continental plates and plate tectonics.)


     Life, Cassiopeia (the Gaijin alien) said, was emergent everywhere. Planets were the crucible. Life curdled, took hold, evolved, in every nook and cranny it could find in the great nursery that was the Galaxy.
     Characteristically life took hundreds of millions of years to accrue the complexity it needed to start manipulating its environment on a major scale. On Earth, life had stuck at the single-celled stage for billions of years, most of its history. Still, on world after world, complexity emerged, mind dawned, civilizations arose.
     Most of these cultures were self-limiting.
     Some were sedentary. Some—for instance, aquatic creatures, like the Flips—lacked access to metals and fire. Some just destroyed themselves, one way or another, through wars, or accidents, or obscure philosophical crises, or just plain incompetence. The last, Madeleine suspected, might have been mankind’s ultimate fate, left to its own devices.
     Maybe one in a thousand cultures made it through such bottlenecks.
     That fortunate few developed self-sustaining colonies off their home worlds, and—forever immune to the eggs-in-one-basket accidents that could afflict a race bound to a single world—they started spreading. Or else they made machines, robots that could change worlds and rebuild themselves, and sent them off into space, and they started spreading.
     Either way, from one in a thousand habitable worlds, a wave of colonization started to expand.
     There were many different strategies. Sometimes generations of colonists diffused slowly from star to star, like a pollutant spreading into a dense liquid. Sometimes the spread was much faster, like a gas into a vacuum. Sometimes there was a kind of percolation, a lacy, fractal structure of exploitation leaving great unspoiled voids within.
     It was a brutal business. Lesser species—even just a little behind in the race to evolve complexity and power—would simply be overrun, their worlds and stars consumed. And if a colonizing bubble from another species was encountered, there were often ferocious wars.
     “It’s hard to believe that every damn species in the Galaxy behaves so badly,” Madeleine said sourly.
     Malenfant grinned. “Why? This is how we are. And remember, the ones who expand across the stars are self-selecting. They grow, they consume, they aren’t too good at restraining themselves, because that’s the way they are. The ones who aren’t ruthless predatory expansionists stay at home, or get eaten.”
     Anyhow, the details of the expansion didn’t seem to matter. In every case, after some generations of colonization, conflicts built up. Resource depletion within the settled bubble led to pressure on the colonies at the fringe. Or else the colonizers, their technological edge sharpened by the world-building frontier, would turn inward on their rich, sedentary cousins. Either way the cutting-edge colonizers were forced outward, farther and faster.
     Before long, the frontier of colonization was spreading out at near light speed, and the increasingly depleted region within, its inhabitants having nowhere to go, was riven by wars and economic crisis.
     So it would go on, over millennia, perhaps megayears.
     And then came the collapse.
     It happened over and over. None of the bubbles ever grew very large—no more than a few hundred light-years wide—before simply withering away, like a colony of bacteria frying under a sterilizing lamp. And one by one the stars would come out once more, shining cleanly out, as the red and green of technology and life dispersed.
     “The Polynesian syndrome,” Madeleine said gloomily.
     “But,” Malenfant growled, “it shouldn’t always be like this. Sooner or later one of those races has got to win the local wars, beat out its own internal demons, and conquer the Galaxy. But we know that not one has made it, across the billions of years of the Galaxy’s existence. And that is the Fermi paradox.”
     YES, Cassiopeia said. BUT THE GALAXY IS NOT ALWAYS SO HOSPITABLE A PLACE.
     Now a new image was overlaid on the swiveling Galaxy: a spark that flared, a bloom of lurid blue light that originated close to the crowded core. It illuminated the nearby stars for perhaps an eighth of the galactic disc around it. And then, as the Galaxy slowly turned, there was another spark—and another, then another, and another still. Most of these events originated near the Galaxy core: something to do with the crowding of the stars, then. A few sparks, more rare, came from farther out—the disc, or even the dim halo of orbiting stars that surrounded the Galaxy proper.
     Each of these sparks caused devastation among any colonization bubbles nearby: a cessation of expansion, a restoring of starlight.
     Death, on an interstellar scale.
      
     Her attention came to rest, at last, on a pair of stars—small, fierce, angry. These stars were close, separated by no more than a few tens of their diameters. The two stars looped around each other on wild elliptical paths, taking just seconds to complete a revolution—like courting swallows, Madeleine thought—but the orbits changed rapidly, decaying as she watched, evolving into shallower ellipses, neat circles.
     A few wisps of gas circled the two stars. Each star seemed to glow blue, but the gas around them was reddish. Farther out she saw a lacy veil of color, filmy gas that billowed against the crowded background star clouds.
     “Neutron stars,” Malenfant said. “A neutron star binary, in fact. That blue glow is synchrotron radiation, Madeleine. Electrons dragged at enormous speeds by the stars’ powerful magnetic fields...”
     The Gaijin said, PERHAPS FIFTY PERCENT OF ALL THE STARS IN THE GALAXY ARE LOCKED IN BINARY SYSTEMS—SYSTEMS CONTAINING TWO STARS, OR PERHAPS MORE. AND SOME OF THESE STARS ARE GIANTS, DOOMED TO A RAPID EVOLUTION.
     Malenfant grunted. “Supernovae.”
     MOST SUCH EXPLOSIONS SEPARATE THE RESULTANT REMNANT STARS. ONE IN A HUNDRED PAIRS REMAIN BOUND, EVEN AFTER A SUPERNOVA EXPLOSION. THE PAIRED NEUTRON STARS CIRCLE EACH OTHER RAPIDLY. THEY SHED ENERGY BY GRAVITATIONAL RADIATION—RIPPLES IN SPACETIME.
     The two stars were growing closer now, their energy ebbing away. The spinning became more rapid, the stars moving too fast for her to see. When the stars were no more than their own diameter apart, disruption began. Great gouts of shining material were torn from the surface of each star and thrown out into an immense glowing disc that obscured her view.
     At last the stars touched. They imploded in a flash of light.
     A shock wave pulsed through the debris disc, churning and scattering the material, a ferocious fount of energy. But the disc collapsed back on the impact site almost immediately, within seconds, save for a few wisps that dispersed slowly, cooling.
     “Has to form a black hole,” Malenfant muttered. “Two neutron stars... too massive to form anything less. This is a gamma-ray burster. We’ve been observing them all over the sky since the 1960s. We sent up spacecraft to monitor illegal nuclear weapons tests beyond the atmosphere. Instead, we saw these.”
     THERE IS INDEED A BURST OF GAMMA RAYS—VERY HIGH-ENERGY PHOTONS. THEN COMES A PULSE OF HIGH-ENERGY PARTICLES, COSMIC RAYS, HURLED OUT OF THE DISC OF COLLAPSING MATTER, FOLLOWING THE GAMMA RAYS AT A LITTLE LESS THAN LIGHT SPEED.
     THESE EVENTS ARE HIGHLY DESTRUCTIVE.
     A NEARBY PLANET WOULD RECEIVE—IN A FEW SECONDS, MOSTLY IN THE FORM OF GAMMA RAYS—SOME ONE-TENTH ITS ANNUAL ENERGY INPUT FROM ITS SUN. BUT THE GAMMA-RAY SHOWER IS ONLY THE PRECURSOR TO THE COSMIC RAY CASCADES, WHICH CAN LAST MONTHS. BATTERING INTO AN ATMOSPHERE, THE RAYS CREATE A SHOWER OF MUONS—HIGH-ENERGY SUBATOMIC PARTICLES. THE MUONS HAVE A GREAT DEAL OF PENETRATING POWER. EVEN HUNDREDS OF METERS OF WATER OR ROCK WOULD NOT BE A SUFFICIENT SHIELD AGAINST THEM.
     “I saw what these things can do, Madeleine,” Malenfant said. “It would be like a nearby supernova going off. The ozone layer would be screwed by the gamma rays. Protein structures would break down. Acid rain. Disruption of the biosphere—”
     A COLLAPSE IS OFTEN SUFFICIENT TO STERILIZE A REGION PERHAPS A THOUSAND LIGHT-YEARS WIDE. IN OUR OWN GALAXY, WE EXPECT ONE SUCH EVENT EVERY FEW TENS OF THOUSANDS OF YEARS—MOST OF THEM IN THE CROWDED GALAXY CORE.
     Madeleine watched as the Galaxy image was restored, and bursts erupted from the crowded core, over and over.
     Malenfant glared at the dangerous sky. “Cassiopeia, are you telling me that these collapses are the big secret—the cause of the reboot, the galactic extinction?”
     Madeleine shook her head. “How is that possible, if each of them is limited to a thousand light-years? The Galaxy is a hundred times as wide as that. It would be no fun to have one of these things go off in your backyard. But—”
     BUT, Cassiopeia said, SOME OF THESE EVENTS ARE... EXCEPTIONAL.
     They were shown a cascade, image after image, burst after burst.
     Some of the collapses involved particularly massive objects. Some of them were rare collisions involving three, four, even five objects simultaneously. Some of the bursts were damaging because of their orientation, with most of their founting, ferocious energy being delivered, by a chance of fate and collision dynamics, into the disc of the Galaxy, where the stars were crowded. And so on.
     Some of these events were very damaging indeed.
     FROM THE WORST OF THE EVENTS THE EXTINCTION PULSE PROCEEDS AT LIGHT SPEED, SPILLING OVER THE GALAXY AND ALL ITS INHABITANTS, ALL THE WAY TO THE RIM AND EVEN THE HALO CLUSTERS. NO SHIELDING IS POSSIBLE. NO COMPLEX ORGANISM, NO ORGANIZED DATA STORE, CAN SURVIVE. BIOSPHERES OF ALL KINDS ARE DESTROYED...
     So it finishes, Madeleine thought: the evolution and the colonizing and the wars and the groping toward understanding. All of it halted, obliterated in a flash, an accident of cosmological billiards. It was all a matter of chance, of bad luck. But there were enough neutron-star collisions that every few hundred million years there was an event powerful enough, or well-directed enough, to wipe the whole of the Galaxy clean.
     It had happened over and over. And it will happen again, she saw. Again and again, a drumbeat of extinction. That is what the Gaijin have learned.
     “And for us,” Malenfant growled, “it’s back to the f**king pond, every damn time... So much for Fermi’s paradox. Nemoto was right. This is the equilibrium state for life and mind: a Galaxy full of new, young species struggling out from their home worlds, consumed by fear and hatred, burning their way across the nearby stars, stamping over the rubble of their forgotten predecessors.”
     But her mind was racing. “There must be ways to stop this. All we have to do is evade one collapse—and gain the time to put aside the wars and the trashing, and get a little smarter, and learn how to run the Galaxy properly. We don’t have to put up with this sh*t.”
     Malenfant smiled. “Nemoto always did call you a meddler.”
     BUT YOU ARE RIGHT, the Gaijin said. SOME OF US ARE TRYING...

(ed note: a coalition of advanced civilizations has located the next sterilize-the-entire-freaking-galaxy gamma-ray burster and are trying to prevent or at least delay the onset of its burst)

From MANIFOLD: SPACE by Stephen Baxter (2000)

Empires In Collision

WHAT HAPPENED WAS NOT A WAR

(ed note: The Terran Empire is old and decadent, but still very powerful. The alien Roidhunate of Merseia is young and expansive, but not quite as strong. They are both engaged in covert plots and staged border incidents as a cosmic chess game. When one of them finally makes a serious mistake, cosmic Armageddon will ensue. Meanwhile the common folk of both empires walk softly in fear.)

      On Daedalus, the world without a horizon, a Tigery was still an uncommon sight, apt to draw everybody’s attention. Targovi had made an exception of himself. The capital Aurea, its hinterland, communities the length of the Highroad River as far as the Phosphoric Ocean, no few of the settlements scattered elsewhere, had grown used to him. He would put his battered Moonjumper down at the spaceport, exchange japes with guards and officials, try to sell them something, then load his wares into an equally disreputable-looking van and be off. His stock in trade was Imhotepan, a jackdaw museum of the infinite diversity that is every planet’s. Artifacts of his people he had, cutlery, tapestries, perfumes; things strange and delicate, made underwater by the Seafolk; exotic products of nature, skins, mineral gems, land pearls, flavorful wild foods—for the irony was that huge Imhotep had begotten life which Terrans, like Starkadians, could safely take nourishment from, whereas Terra-sized Daedalus had not.
     For a number of years he had thus ranged, dickering, swapping, amusing himself and most whom he encountered, a generally amiable being whom—certain individuals discovered too late—it was exceedingly dangerous to affront. Even when tensions between Merseia and Terra snapped asunder, sporadic combats erupted throughout the marches, and at last Sector Admiral Magnusson took his forces to meet an oncoming armada of the Roidhunate, even then had Targovi plied his trade unhindered.

     Thus he registered shock when he landed in routine fashion a twelvemonth later, and the junior port officer who gave him his admission certificate warned: “You had better stay in touch with us. Interplanetary traffic may be suddenly curtailed. You could find yourself unable to get off Daedalus for an indefinite time.
     “Eyada shkor!” ripped from Targovi. His tendrils grew stiff. A hand dropped to the knife at his side. “What is this?”
     “Possible emergency,” said the human. “Understand, I am trying to be friendly. There ought to be a short grace period. If you then return here immediately, I can probably get you clearance to go home. Otherwise you could be stranded and unable to earn your keep, once your goods were sold and the proceeds spent.”

     “I think your efforts might fail,” he said low. Easing: “However, surely naught untoward will happen. You are kind to advise me, Dosabhai Patel. You wife may find some pleasant trinket in her mail. But what is this extremity you await?”
     “I did not say we are bound to have one,” replied the officer quickly.
     “What could it be, does it come on us?”
     “Too many wild rumors are flying about. Both naval and civil personnel are under orders not to add to them.”

     Targovi’s chair had been designed for a human, but he was sufficiently supple to flow down into it. His eyelids drooped; he bridged his fingertips. “Ah, good friend, you realize I am bound to hear those rumors. Were it not best to arm me with truths whereby I may slay them? I am, of course, a simple, wandering trader, who knows no secrets. Yet I should have had some inkling if, say, a new Merseian attack seemed likely.
     “Not that! Admiral Magnusson gave them a lesson they will remember for a while.” Patel cleared his throat. “Understand, what happened was not a war.”
     Targovi did not overtly resent the patronizing lecture that followed, meant for a half-civilized xeno: “Bloody incidents are all too common. It is inevitable, when two great powers, bitter rivals, share an ill-defined and thinly peopled buffer zone which is, actually, an arena for them. This latest set of clashes began when negotiations over certain spheres of influence broke down and commanders in various locations grew, ah, trigger-happy. True, the Roidhunate did dispatch a task force to ‘restore order.’ Had it succeeded, the Merseians would undoubtedly have occupied the Patrician System, thereby making this entire sector almost indefensible and driving a salient deep into the Empire. We would have had to settle with them on highly disadvantageous terms. As you know, Admiral Magnusson beat them back, and diplomats on both sides are trying to mend things. . . . No, we are in no immediate danger from outside.”

     “From inside, then?” Targovi drawled. “Even we poor, uprooted vaz-Toborko—aye, even the vaz-Siravo beneath their seas—have learned a little about your great Empire. Rebellions and attempted rebellions have grown, regrettably, not infrequent, during the past half century. The present dynasty itself, did it not come to power by—?—
     “The glorious revolution was necessary,” Patel declared. “Emperor Hans restored order and purged corruption.”
     “Ah, but his sons—
     Patel’s fist struck the desktop. “Very well, you insolent barbarian! Daedalus, this whole system, the Empire itself were in grave peril last year. Admiral Magnusson rectified the situation, but it should never have arisen. The Imperial forces in these parts should have been far stronger. As matters stood, under a less brilliant commander, they would almost certainly have been smashed.” He moistened his lips. “No question of disloyalty. No lèse majesté. But there is a widespread feeling on Daedalus, especially among Navy personnel, that Emperor Gerhart and his Policy Board have — not been well advised — that some of the counsel they heeded may actually have been treasonable in intent — that drastic reform has again become overdue. The Admiral has sent carefully reasoned recommendations to Terra. Meanwhile, dissatisfaction leads to restlessness. He may have to impose martial law, or—Enough. These matters are not for subjects like you and me to decide.” Nonetheless eagerness lighted his features and shrilled in his voice. “You have had your warning, Targovi. Be off, but stay in touch; attend to your business and nothing else; and you will probably be all right.”

From THE GAME OF EMPIRE by Poul Anderson (1985)

Single Empire

A single empire can have all sorts of relatively quiet drama: trying to incorporate irate planetary natives, independent-minded star sectors attempting to secede, ambitious tratorous governors trying to carve out a pocket empire, the empire declining and falling, barbarians waiting in their interstellar long-boats at the rim of the empire, etc.

Two Empires

Neutral Zone

For truly cosmic-scale excitement it is hard to beat a second empire at war with the first empire over the same real estate.

Starting with two empires: assuming that they have a rough technological parity the two spheres will expand until the borders make contact. Then it will resemble two soap bubbles stuck together, with a flat "neutral zone" populated by spies, smugglers, covert battlefleets intent on causing border incidents, and planets named "Casablanca". The technical term is Buffer Zone.

In Star Trek this is called a "Neutral Zone". In the episode Balance of Terror, the Romulans violate the neutral zone in order to destroy the series of Federation outposts who monitor the zone.

In the real world such an area is called "No Man's Land" or a "Demilitarized Zone" (DMZ), depending upon whether or not there is ongoing active warfare. No Man's Land is typically located between two hostile armies or battlefleets during a battle, a very unhealthy area to enter. A Demilitarized Zone is typically located between the current national borders separating two hostile nations who are not currently at war. A military incursion into a DMZ is considered an act of war.

A related concept is a Border Zone. These are less about preventing invasion by enemy battle-fleets and more about a nation controlling traffic across the zone. Traffic to be controlled can include:

  • Evil people who want to penetrate a protected wildlife area in order to ravage it of valuable minerals or other resources
  • Illegal immigrants
  • Illegal emigrants (example: East Germany using the Berlin Wall's "death strip" to prevent its citizens from escaping the oppressive regime into the freedom of West Berlin)
  • Smugglers
  • Spies

In reality, the "neutral zone" will be the less like a plane and more like the intersection of the two spheres. It will be like a lop-sided lens shape. The equation for calculating the volume of the neutral zone can be found here

ROMULAN NEUTRAL ZONE

      "WE WERE EXCITED,"said the captain of the Federation vessel USS Carrizal during the postmission debriefing following its return from the Trianguli stars, a little more than a hundred years ago. "It was the first hit we'd had in nine months of scouring that sector. A hominid culture, obviously highly developed, a large population, it was everything we had hoped for. Better yet, the same people were on two worlds … an Earth-Moon configuration. Mike Maliani, our astrogator, suggested Romus and Remus as nicknames for the planets until we found out their real names from the people who lived there. After the twin brothers in an ancient Italian myth." On the debriefing tape, Captain Dini smiles rather ruefully. "I was never a specialist in the classics: I wish I were. Mike's misspelling of 'Romulus' is going to haunt me to the grave. But at that point I thought he knew what he was talking about."

     A pause. "Anyway, we were really excited. You know how few spacefaring species there are: the standing orders are to closely examine any we find. But we weren't so excited that we went in without the proper protocols. We gave them everything we had: the classic first-contact series—atomic ratios, binary counting, pictures. You name it. There was never any answer, even though we're sure they knew we were there. They had an outer cordon of defense satellites that noticed us, and after the messages from the satellites were received on the planets, the message traffic on the bigger planet increased by about a thousand percent. But there was nothing we could do with it by way of translation—after that first message there was silence, and everything that came later was encoded—some kind of closed-satchel code, very sophisticated, and no way to break it in anything short of a decade, without a supercomp or the code key."

     There is a long silence on the tape as Captain Dini shakes his head and looks puzzled. "We never came any closer to their planet than two orbits out," he says, "right beyond the fifth planet in the system. We never came near them. We just observed, and took readings, and went away quietly. I'll never understand what happened."

     What happened was the First Romulan War, as the Federation later called it. What it looked like, from the Federation side, was a long, bloody conflict started without provocation by the Romulans. From the other side it wore a different aspect.

     The appearance of Carrizal caused such a panic as the Rihannsu (Romulans) had never known since they became Rihannsu. In terms of a Rihanha's lifetime, it was thirty generations and more since the Settlement, and the actual records of the appearance of aliens on Vulcan, all those many years ago, were not so much lost as largely ignored. People knew through the history they were taught in the academies what had happened on Vulcan in the old days … and the history had bent and changed, what with telling and retelling, and neglecting to go back to the original source material. Not that that would have helped much. The source material itself had been altered in the Journey, but very few—scholars and historians—knew this, or cared. What the Rihannsu knew about this incursion into their space was that it closely matched the pattern followed by the Etoshans so long ago: quiet observation coupled with or followed by proffers of peaceful contact. They were not going to be had that way again.

(ed note: The Etoshans were the dreaded Pirates of Orion. When the Rihannsu still lived on planet Vulcan, the Etoshans made the exact same first contact overtures as did the the Carrizal. The Etoshans used the contact to learn all they could about the people of Vulcan. Then they kidnapped some Vulcan leaders and held them for ransom. The Vulcans refused to pay, and the Vulcan-Etoshan insterstellar war started.)

     Ch'Rihan and ch'Havran had, over sixteen hundred years, become superbly industrialized. The Rihannsu have always had a way with machines: and this, coupled with their great concern for taking care of the worlds they found after such Journey and suffering, produced two planets that were technologically most advanced at manufacture, without looking that way. Few factories were visible from the atmosphere, let alone from space. Aesthetics required that they be either pleasant to look at, or completely concealed. Many factories were underground. Release of waste products into the ambient environment, even waste so seemingly innocuous as steam or hot water, was forbidden by Praetorial indict, and a capital crime. A starship passing through, even one looking carefully, as Carrizal did, would see two pastoral-looking worlds, unspoiled, quiet. One would hardly suspect the frenetic manufacture that was to start after Carrizal's departure.

     There was frantic action elsewhere as well. In the Praetorate and the Senate some heads rolled, and the survivors scrambled to start working on the defense of the planet—or to otherwise take advantage of the situation. The defense satellites had not been approached closely enough by the invading ship to trigger their weaponry. Cannily, it had stayed out of range. There was no way to tell if the Two Worlds could be defended against the ship that had appeared there, no telling what kind of weaponry it had. But from their experience in air combat (almost every nation of each planet had its own air force, which they used liberally for both friendly and unfriendly skirmishes), the Rihannsu military specialists knew that even a heavily armed ship should not be able to do much against overwhelming numbers.

     They got busy, digging frantically through ancient computer memories and printouts and film and metal media for the forgotten space technology they needed. Had the Ships been spared, even one of them—had their data been preserved in one place rather than scattered all over two worlds—the Federation's boundaries might be much different now. But even what remained was useful, and the Rihannsu were frightened. It is unwise to frighten a Rihanha. Within a year after Carrizal's visit, ch'Rihan's numerous nations had built, among them, some three thousand spacecraft armed with particle-beam weapons and the beginnings of defensive shields. Ch'Havran had built four thousand. They were crude little craft, and their cylindrical shapes recalled those of the Ships, though there was no need for them to spin for gravity: artificial gravity had been mastered a century or so earlier.

     It was three more years before the next ship came. The unlucky Balboa came in broadcasting messages of peace and friendship, and was blown to bits by the massed particle beams of a squadron of fifty. After that the Rihannsu grew a little bolder, and went hunting: a task force caught Stone Mountain, to which Balboa had sent a distress call, and captured her by carefully using high-powered lasers to explosively decompress the crew compartments. They towed Stone Mountain home, took her apart, and shortly thereafter added warp drive to their little cruisers.

     The Federation considers the War to have begun with the destruction of Balboa. In the twenty-five years of warfare that followed, no less than forty-six Federation task forces of ever-increasing size and firepower went into Rihannsu space to deal with the aggression against them, and even with vastly superior firepower, most of them suffered heavy damage if not annihilation. "I can't understand it," says one fleet Admiral in a debriefing. "Their ships are junk. We should be able to shoot them down like clay pigeons." But the huge numbers of the Rihannsu craft made them impossible to profitably engage; even "smart" photon torpedoes could target only one vessel at a time. When there were twelve more climbing up your tail, the situation became impossible. Starfleet kept trying with bigger and better weapons—until two things happened at once: there was a change of administration, and the Vulcans joined the Federation.

     The only indication of what the Rihannsu looked like had come from a very few burned and decompressed bodies picked up in space. When Vulcan was discovered, and after negotiation entered the Federation, their High Council was pointedly asked whether it knew anything about these people. The Vulcans, all logic—and selective truth—told the Federation that they were not sure who these people were. There had indeed been some attempts to colonize other worlds, they admitted, but those ships had been out of touch with Vulcan for some seventeen hundred years. The first Vulcan Ambassador, a grimly handsome gentleman who had just been posted to Earth, made this statement to the Admirals of Starfleet in such a way that they immediately found it politic to drop the subject. But through the ambassador, the Vulcan High Council gave the Federation a piece of good advice. "Make peace with them," Sarek told the Admirals, "and close the door. Stop fighting. You will probably never beat them. But you can stop your ships being destroyed."

(ed note: the Romulans were descendants of the hot-headed dissidents who left Vulcan 1,700 years ago in sublight starships, unwilling to adopt the new Vulcan way of removing emotions. The Vulcans knew this, but was not about to tell the Federation High Council that these warriors had anything to do with Vulcans. )

     The advice went down hard, and Starfleet tried to do it their own way for several years more. But finally, as Vulcan's increasing displeasure became plainer, Fleet acquiesced. The War ended with the Treaty of Alpha Trianguli, probably the first treaty in Federation history to have been negotiated entirely by data upload. No representatives of the two sides ever met. The Rihannsu had no interest in letting their enemies find out any more about them than could be revealed by autopsy. They might be back someday.

     The treaty established what came to be called the Romulan Neutral Zone, an egg-shaped area of space about ninety lightyears long and forty wide, with 128 Trianguli at its center. The Zone itself was the "shell" of the egg, a buffer area all the way around, one lightyear thick, marked and guarded by defense/ monitoring satellites of both sides. Everything inside the Zone was considered "the Romulan Star Empire," even though there was as yet no such thing. The Federation was not exactly hurt by this treaty: as far as they were concerned, there were no strategically promising planets in the area. Perhaps they were not looking hard enough. Later some Federation officials would kick themselves when finding out about Rhei'llhne, a planet just barely inside the Neutral Zone in Rihannsu space, and almost richer in dilithium than Direidi.

     So the war ended, and as far as the Federation was concerned, for fifty years nothing came out of the Zone, not a signal, not a ship. Perhaps, some thought, the people in there had gotten sick of fighting. Wiser heads, or those who thought they knew what stock the "Romulans" had sprung from, suspected otherwise.

     The Rihannsu had stopped fighting indeed, but as for being tired of it, this was unlikely. There was a matter of honor, mnhei'sahe, still to be resolved. So much of the Two Worlds' economies were poured into starship weapons research that they still have not recovered entirely from the austerity it caused the contributing nations. They rebuilt the defense satellite system to hundreds of times its former strength, and trained some of the best star pilots ever seen in any species anywhere.

     They also decided not to make the mistake their forefathers had made with the Etoshans. The Rihannsu scientists spent literally years translating the complete contents of the reference computers of the Federation ships they had so far managed to capture. They realized from what they found that they were one small pair of planets caught between two Empires (Federation and Klingon), and that to survive, they were going to have to have an Empire themselves.

     So began the "expansionist" period of Rihannsu history, in which they tackled planetary colonization with the same ferocious desperation they had used to build a fleet out of nothing. They needed better ships to do this, of course. They wound up reconstructing numerous large people-carriers along the Ship model, though, of course, with warp drive these craft did not need generation capability. Twenty planets were settled in eighteen years, and population-increase technology was used of the sort that had made ch'Rihan and ch'Havran themselves so rapidly viable. Not all the settlements were successful, nor are they now: Hellguard was one glaring example.

From THE ROMULAN WAY by Diane Duane and Peter Morwood (1987)
KURAMESU DRIFT

Kuramesu Drift: A modestly-sized modular drift-habitat located in the Omane (First Expanses) System, at the Solar-Diageri (Omane IV) trailing libration point.

Kuramesu Drift is an independent drift, unaffiliated with any of the polities or law providers of Omane Actual, the freesoil world with which it shares a system. Rather, Kuramesu Drift is chartered to the Microstatic Commission, providing a data haven and negotiation space for the Worlds’ many micronations and small freeholds to play politics out from under the eyes of their much larger cousins. Omane, one link outside the Empire’s border, protected from intimidation by other polities by its position in an isolated loop route only accessible by passing through an Imperial border world – Ionai (First Expanses) – and yet only 13 links from the Conclave Drift by optimal routing, is essentially perfect for these purposes.

Naturally, Kuramesu Drift has a very high density of spies per capita. In fact, gentle reader, you may find it easiest to assume that everyone not an actual delegate or you, yourself, is a spy for someone.

The drift is, however, well worth visiting for reasons other than espionage. The lifestyles of even minor notables ensure that Kuramesu Drift is blessed with excellent shopping districts, banking facilities, and cultural events, including a spintronic symphony orchestra, tholin baths, and microgravity ballet, and the Commission offsets the running costs of the Drift by renting out their facilities to a variety of conferences (especially those seeing an advantage in a location near, but not within, the Empire) and conventions when they are not otherwise in use.

Meanwhile, the Agent’s Rest offers one of the finest polyspecific selections of liquors and other hedonics to be found in the central Worlds. Just don’t ask for a double – everyone’s heard that one already.

– Leyness’s Worlds: Guide to the Ecumene

Engulfing Each Other

In his paper Long-term consequences of observing an expanding cosmological civilization S. Jay Olson explores the consequences of colliding empires. One of the assumptions is the growing spheres are domains of expanding civilizations belonging to distinct species who do not wish to share resources; i.e., they are selfish bastards just like us. This results in the formation of hard boundaries between the spheres; i.e., "national" borders which can only be crossed at the expense of sparking interstellar wars and all manner of unpleasantness.

The boundary that forms between two expanding civilizations is a hyperboloid. The exact form depends upon empire expansion speed, separation distance between empires, and starting time of each empire's colonization expansion.

In the diagrams below, Empire Alfa's origin world is located at coordinates -C,0,0 and Empire Bravo's origin world is at coordinates +C,0,0. The distance between the two is 2C. Empire Alfa starts their colonial expansion at time t1 while Empire Bravo starts at time t0. t1 is earlier than t0, meaning that Empire Alfa starts first. It is assumed that Empire Alfa's expanding domain has not yet engulfed Empire Bravo's origin world at time t0, meaning Bravo gets a chance to expand instead of starting out enslaved by Alfa.

The paper assumes that both civilizations will have the same expansion speed, which is as fast as physically possible. Both empires will frantically research how to accelerate their expansion speed until both run up against the theoretical maximum.

At time t1 Empire Alfa starts their colonial expansion. Later at time t0 Empire Bravo starts their expansion (at point C), while Alfa has expanded to a sphere with a radius of 2A (the blue circle). r1(t0) is a fancy way of saying "radius of empire 1 at time zero."

Both spheres will expand, and collide at a point halfway between the edge of the blue circle and point C; that is halfway between boundary of Alfa's sphere at time t0 closest to Bravo's origin world, and the location of Bravo's origin world itself (orange hyperboloid).

When Alfa's sphere has expanded to the violet circle and Bravo's sphere has expanded to the yellow circle, the border between will be the orange hyperboloid.

Mathematically, the hyperboloid will have its foci at -C,0,0 and +C,0,0 (the coordinates of the two empire's origin planets). The semi-major axis will be A (half the radius of Alfa's sphere when Bravo starts expanding). The border will be the x > 0 sheet of the hyperboid.

The "canonical form" of the border hyperboid is:

B2 ≡ C2 - A2
(x2 / A2) - (y2 / B2) - (z2 / B2) = 1

The volumes of two empires can be calculated by hideously complicated equations (2) and (3) found in the paper. No, I'm not going to try and transcribe them here.


The main focus of the paper is what happens when the inhabitants of Origin Planet Bravo become panicked when they observe Origin Planet Alfa start their colonization program. Bravo will instantly start their own colonization drive.

The trouble is, the speed of light means that when Bravo sees Alfa's starting expansion, Bravo is seeing what happened in the past. If Alfa is ten-thousand light-years away from Bravo, it means that when Bravo sees Alfa's start, Alfa actually started ten-thousand years ago. Which is a heck of a head-start.

What this boils down to is that time t0 will occur X years after t1, where X equals the distance between the two empires in light-years.

t0 = t1 + (2 * C)

where t0 and t1 are in years, and C is in light-years.

In FIG 2, the separation distance 2C is an absolutely enormous three billion light years. Graphs (a), (b), (c), and (d) are for expansion speeds of 0.3, 0.6, 0.9, and 0.99 the speed of light respectively. The faster the expansion speed, the smaller the size of Empire Bravo (blue area)


If Origin Planet Bravo observes two empires start their expansion, Bravo is in big trouble.

The graphs in FIG5 shows what happens if Empires Alfa and Charlie are the same distance from Bravo (3 billion light-years, angular separation of 90°), and both start their expansion simultaneously.

At expansion speeds of 0.3 and 0.6 of the speed of light (a and b), Empire Bravo is squeezed (blue area). At the critical expansion speed of 0.75765 of the speed of light (c) Empire Bravo will become "trapped", it will become englobed by Alfa and Charlie with further expansion being impossible. At higher expansion speeds such as 0.9 (d) the size of Bravo's blue area grows smaller.

AGGRESSIVELY EXPANDING CIVILIZATIONS

Ever since I became an environmentalist, the potential destruction wrought by aggressively expanding civilizations has been haunting my thoughts. Not just here and now, where it’s easy to see, but in the future.

In October 2006, I wrote this in my online diary:

A long time ago on this diary, I mentioned my friend Bruce Smith’s nightmare scenario. In the quest for ever faster growth, corporations evolve toward ever faster exploitation of natural resources. The Earth is not enough. So, ultimately, they send out self-replicating von Neumann probes that eat up solar systems as they go, turning the planets into more probes. Different brands of probes will compete among each other, evolving toward ever faster expansion. Eventually, the winners will form a wave expanding outwards at nearly the speed of light—demolishing everything behind them, leaving only wreckage.

The scary part is that even if we don’t let this happen, some other civilization might.

The last point is the key one. Even if something is unlikely, in a sufficiently large universe it will happen, as long as it’s possible. And then it will perpetuate itself, as long as it’s evolutionarily fit. Our universe seems pretty darn big. So, even if a given strategy is hard to find, if it’s a winning strategy it will get played somewhere.

So, even in this nightmare scenario of "spheres of von Neumann probes expanding at near lightspeed", we don’t need to worry about a bleak future for the universe as a whole—any more than we need to worry that viruses will completely kill off all higher life forms. Some fraction of civilizations will probably develop defenses in time to repel the onslaught of these expanding spheres.

It’s not something I stay awake worrying about, but it’s a depressingly plausible possibility. As you can see, I was trying to reassure myself that everything would be okay, or at least acceptable, in the long run.

Even earlier, S. Jay Olson and I wrote a paper together on the limitations in accurately measuring distances caused by quantum gravity. If you try to measure a distance too accurately, you’ll need to concentrate so much energy in such a small space that you’ll create a black hole!

That was in 2002. Later I lost touch with him. But now I’m happy to discover that he’s doing interesting work on quantum gravity and quantum information processing! He is now at Boise State University in Idaho, his home state.

But here’s the cool part: he’s also studying aggressively expanding civilizations.

Expanding bubbles

What will happen if some civilizations start aggressively expanding through the Universe at a reasonable fraction of the speed of light? We don’t have to assume most of them do. Indeed, there can’t be too many, or they’d already be here! More precisely, the density of such civilizations must be low at the present time. The number of them could be infinite, since space is apparently infinite. But none have reached us. We may eventually become such a civilization, but we’re not one yet.

Each such civilization will form a growing ‘bubble’: an expanding sphere of influence. And occasionally, these bubbles will collide!

Here are some pictures from a simulation he did:

As he notes, the math of these bubbles has already been studied by researchers interested in inflationary cosmology, like Alan Guth. These folks have considered the possibility that in the very early Universe, most of space was filled with a ‘false vacuum’: a state of matter that resembles the actual vacuum, but has higher energy density.

A false vacuum could turn into the true vacuum, liberating energy in the form of particle-antiparticle pairs. However, it might not do this instantly! It might be ‘metastable’, like ball number 1 in this picture:

It might need a nudge to ‘roll over the hill’ (metaphorically) and down into the lower-energy state corresponding to the true vacuum, shown as ball number 3. Or, thanks to quantum mechanics, it might ‘tunnel’ through this hill.

The balls and the hill are just an analogy. What I mean is that the false vacuum might need to go through a stage of having even higher energy density before it could turn into the true vacuum. Random fluctuations, either quantum-mechanical or thermal, could make this happen. Such a random fluctuation could happen in one location, forming a ‘bubble’ of true vacuum that—under certain conditions—would rapidly expand.

It’s actually not very different from bubbles of steam forming in superheated water!

But here’s the really interesting Jay Olson noted in his first paper on this subject. Research on bubbles in the inflationary cosmology could actually be relevant to aggressively expanding civilizations!

Why? Just as a bubble of expanding true vacuum has different pressure than the false vacuum surrounding it, the same might be true for an aggressively expanding civilization. If they are serious about expanding rapidly, they may convert a lot of matter into radiation to power their expansion. And while energy is conserved in this process, the pressure of radiation in space is a lot bigger than the pressure of matter, which is almost zero.

General relativity says that energy density slows the expansion of the Universe. But also—and this is probably less well-known among nonphysicists—it says that pressure has a similar effect. Also, as the Universe expands, the energy density and pressure of radiation drops at a different rate than the energy density of matter.

So, the expansion of the Universe itself, on a very large scale, could be affected by aggressively expanding civilizations!

The fun part is that Jay Olson actually studies this in a quantitative way, making some guesses about the numbers involved. Of course there’s a huge amount of uncertainty in all matters concerning aggressively expanding high-tech civilizations, so he actually considers a wide range of possible numbers. But if we assume a civilization turns a large fraction of matter into radiation, the effects could be significant!

The effect of the extra pressure due to radiation would be to temporarily slow the expansion of the Universe. But the expansion would not be stopped. The radiation will gradually thin out. So eventually, dark energy—which has negative pressure, and does not thin out as the Universe expands—will win. Then the Universe will expand exponentially, as it is already beginning to do now.

(Here I am ignoring speculative theories where dark energy has properties that change dramatically over time.)

Jay Olson’s work

Here are his papers on this subject. The abstracts sketch his results, but you have to look at the papers to see how nice they are. He’s thought quite carefully about these things.

• S. Jay Olson, Homogeneous cosmology with aggressively expanding civilizations, Classical and Quantum Gravity 32 (2015) 215025.

Abstract. In the context of a homogeneous universe, we note that the appearance of aggressively expanding advanced life is geometrically similar to the process of nucleation and bubble growth in a first-order cosmological phase transition. We exploit this similarity to describe the dynamics of life saturating the universe on a cosmic scale, adapting the phase transition model to incorporate probability distributions of expansion and resource consumption strategies. Through a series of numerical solutions spanning several orders of magnitude in the input assumption parameters, the resulting cosmological model is used to address basic questions related to the intergalactic spreading of life, dealing with issues such as timescales, observability, competition between strategies, and first-mover advantage. Finally, we examine physical effects on the universe itself, such as reheating and the backreaction on the evolution of the scale factor, if such life is able to control and convert a significant fraction of the available pressureless matter into radiation. We conclude that the existence of life, if certain advanced technologies are practical, could have a significant influence on the future large-scale evolution of the universe.

• S. Jay Olson, Estimates for the number of visible galaxy-spanning civilizations and the cosmological expansion of life.

Abstract. If advanced civilizations appear in the universe with a desire to expand, the entire universe can become saturated with life on a short timescale, even if such expanders appear but rarely. Our presence in an untouched Milky Way thus constrains the appearance rate of galaxy-spanning Kardashev type III (K3) civilizations, if it is assumed that some fraction of K3 civilizations will continue their expansion at intergalactic distances. We use this constraint to estimate the appearance rate of K3 civilizations for 81 cosmological scenarios by specifying the extent to which humanity could be a statistical outlier. We find that in nearly all plausible scenarios, the distance to the nearest visible K3 is cosmological. In searches where the observable range is limited, we also find that the most likely detections tend to be expanding civilizations who have entered the observable range from farther away. An observation of K3 clusters is thus more likely than isolated K3 galaxies.

• S. Jay Olson, On the visible size and geometry of aggressively expanding civilizations at cosmological distances.

Abstract. If a subset of advanced civilizations in the universe choose to rapidly expand into unoccupied space, these civilizations would have the opportunity to grow to a cosmological scale over the course of billions of years. If such life also makes observable changes to the galaxies they inhabit, then it is possible that vast domains of life-saturated galaxies could be visible from the Earth. Here, we describe the shape and angular size of these domains as viewed from the Earth, and calculate median visible sizes for a variety of scenarios. We also calculate the total fraction of the sky that should be covered by at least one domain. In each of the 27 scenarios we examine, the median angular size of the nearest domain is within an order of magnitude of a percent of the whole celestial sphere. Observing such a domain would likely require an analysis of galaxies on the order of a giga-lightyear from the Earth.

Here are the main assumptions in his first paper:

1. At early times (relative to the appearance of life), the universe is described by the standard cosmology – a benchmark Friedmann-Robertson-Walker (FRW) solution.

2. The limits of technology will allow for self-reproducing spacecraft, sustained relativistic travel over cosmological distances, and an efficient process to convert baryonic matter into radiation.

3. Control of resources in the universe will tend to be dominated by civilizations that adopt a strategy of aggressive expansion (defined as a frontier which expands at a large fraction of the speed of the individual spacecraft involved), rather than those expanding diffusively due to the conventional pressures of population dynamics.

4. The appearance of aggressively expanding life in the universe is a spatially random event and occurs at some specified, model-dependent rate.

5. Aggressive expanders will tend to expand in all directions unless constrained by the presence of other civilizations, will attempt to gain control of as much matter as is locally available for their use, and once established in a region of space, will consume mass as an energy source (converting it to radiation) at some specified, model-dependent rate.

Three Or More Empires

Adding even more empires makes for a more interesting situation, but the complexity goes up by something like the square of the number of empires.

Obviously the following analysis could also apply to sectors within a single empire.

The following analysis assumes that empires are evenly spaced apart in the galaxy and have equal radius. Which is highly unlikely to be true, but close enough for a first approximation. Meaning you can plot out evenly spaced empires to examine their mutual gross geography, then later randomly move them by hand to make something more believable.

Flat Geometry

The easiest way to simplify the analysis of galactic empire geography for your science fiction novel is to cheat and make the empires have a diameter of about one thousand light-years, e.g., the average thickness of the galactic disk. This means the empires all lie in a plane, so you can draw a two-dimensional map and not have to worry about three-dimensional overlapping. Assuming all the empires have the same diameter the empires will arranged like hexagons on a hex-grid (assume even spacing, remember?). For what it is worth the latest estimate of the distance between Sol and the galactic plane is 20.8 +/- 0.3 pc (i.e., about 69 light years above the galactic plane). So Sol is close enough for government work to being exactly on the galactic plane.

Looking at the diagram, one can see that Empire Charlie can attack Empire Sol, Empire Bravo, and Empire Delta without trespassing on any other empire. But Empire Charlie cannot attack Empire Echo without sending their battlefleet through either Empire Sol or Empire Delta.

The diagram uses spheres for simplicity, but those concave triangle regions are going to be gobbled up by empires as well. Divide each triangle region into thirds, with slice of the pie going to the nearest empire. In other words the spheres will become vertical hexagonal prisms

Instead of making each empire's diameter the same you can assume that the origin stars of each empire are on average equally spaced, so the centers of the empires will be in a hexagonal array but the diameter of each empire may vary. The galactic disk is only 1K light-years thick, but each empire can spread horizontally until it runs into the current extent of each of the six neighbor empires at the border.

Empire Center Coordinates
(Flat Geometry)
(Empire Diameter 1,000 LY)
(Cluster Diameter 3,000 LY)
(Cluster Height 1,000 LY)
EmpireCenter Coords
(x,y,z)
Empire Sol(0, 0, 0)
Empire Albert(500, 870, 0)
Empire Bravo(1000, 0, 0)
Empire Charlie(500, -870, 0)
Empire Denver(-500, -870, 0)
Empire Echo(-1000, 0, 0)
Empire Foxtrot(-500, 870, 0)

3D Geometry

The more complicated way is to use as a first approximation something based on the close-packing of equal spheres. This is usually used for stacking oranges or cannon-balls, but it works for interstellar empires as well. This allows one to have empires arranged three-dimensionally without making you pull your hair out by the roots.

This assume even spacing, remember?

The following analysis uses what is known as hexagonal close-packed (HCP), do not use face-centered cubic.


The secret is to harness the awesome power of the Cuboctahedron.

Of all the quasiregular polyhedrons this is the only one where the center-to-vertex radius equals its edge length. In other words, in the diagram to the right, every single line is the same length.

It is sort of a three-dimensional equivalent to a hexagon. Hexagon grids make great two-dimensional flat maps. So cuboctahedron grids make great three-dimensional space-filling maps. You place your galactic empires on the vertexes, and use the line to figure the distance from empire to empire. By the same token square grids make lousy 2D flat maps (see link above), and cube grids make similarly lousy 3D maps.

Buckminster Fuller admired this polyhedron, naming it a "Vector Equilibrium" (which I am telling you because you may encounter the term if you do any research on the topic). The name is because if the edges are considered to be vectors, the outward force of the center vectors is exactly balanced by the confining force of the surface vectors. The polyhedron is in equilibrium. But I digress.

One-Layer Empire Map

So at each vertex of the cuboctahedron you place an empire-sphere with a diameter of one edge-length to approximate the geometry of the empires.

This is called a "one-layer" map, because it has the center sphere surrounded by one layer of additional spheres.


Empire Center Coords
(3D Geometry)
(One Layer around core)
Multiply center coords by
chosen empire diameter
EmpireCenter
(x,y,z)
Top Level
[1] Empire Albert0.0, 0.59, 0.81
[2] Empire Bravo0.51, -0.29, 0.81
[3] Empire Charlie-0.51, -0.29, 0.81
Middle Level
[0] Empire Sol0.0, 0.0, 0.0
[4] Empire Denver0.5, 0.87, 0.0
[5] Empire Echo1.0, 0.0, 0.0
[6] Empire Foxtrot0.5, -0.87, 0.0
[7] Empire Golf-0.5, -0.87, 0.0
[8] Empire Hotel-1.0 ,0.0, 0.0
[9] Empire India-0.5, 0.87, 0.0
Bottom Level
[10] Empire Juliette0.51, 0.29, -0.81
[11] Empire Kilo0.0, -0.59, -0.81
[12] Empire Lima-0.51, 0.29, -0.81

To use the Empire Center Coords (3D Geometry) table: choose the desired DIAMETER (not radius), and multiply each coordinate by the diameter. For instance, if you chose an empire diameter of 200 light-years, Empire Charlie would be at coordinates -102, -58, 162.

Empire names are just letters in the NATO Phonetic Alphabet, as place holders. Replace them with your own really cool names that you've invented. In the same way empire numbers (e.g., 4 for Empire Denver) are arbitrary.

Here is a quick example. The above diagram shows the empire of Sol, and the twelve alien empires in the layer that surround it. All of them are one empire-diameter away, and the border between each alien empire and the Solarian Empire is one-half an empire-diameter away. The entire cluster fits inside a sphere with a diameter of three empire-diameters, and a radius of one and one-half empire diameters.

Meanwhile, this simplistic map also shows for each alien empire its closest four other neighbor alien empires. For instance, the five empires closest to the Vorpal Bunnies are: Sol, Berserkers, Space Vikings, Death Robots, and Gray Goo. These are empires that the Vorpal Bunnies might ally with or be at war with.


As mentioned above, you can use this to define the relationship of sectors within a single empire, as well as for relationships between full empires.

Just for fun, a science fiction author can name sectors according to a colorful motif. For example, in Brian Aldiss' collection Starswarm, the sectors are named after colors (vermillion, azure, violet, etc.), though one was named Sector Diamond. That did catch my fancy. So if you have 13 sectors, a gem stone motif would name them something like Sector Aquamarine, Diamond, Emerald, Opal, Ruby, Sapphire, Spinel, Topaz, Amethyst, Citrine, Peridot, Zircon, and Trystine.

In Asimov's novels, sectors are named for the brightest star contained. So Sol is in the "Sirius Sector".

Michael Andre-Driussi decided to take matters into his own hands. Using the Internet Stellar Database, he has compiled a gazetteer of the first thirteen sectors:

SectorBrightest Star#G#F#K
[0] SolSirius1008
[1] AlbertMegrez81328
[2] BravoZubenelgenubi 22332
[3] CharlieRegulus18419
[4] DenverOkab19424
[5] EchoSabik15815
[6] FoxtrotAlsephina12710
[7] Golfq Puppis1498
[8] HotelMenkalinan10420
[9] IndiaTéng Shé jiǔ15622
[10] JulietteAl Na'ir11819
[11] KiloDelta Hydri14627
[12] LimaSheratan131028

Sector is from my table, Brightest Star is the brightest star in the sector (so sector Charlie would be the "Regulus Sector"), and #G, #F, #K is the number of stars of spectral class G, F, and K respectively (i.e., the spectral classes most like our sun and presumably have the highest chance of hosting human-habitable stars). One can also see that Sector Zubenelgenubi is the richest in class G stars (our sun's spectral class). Nice work Michael!

Please note that the Internet Stellar Database is slightly obsolete, it lacks star data from the RECONS, DENSE, CTIOPI, and EXTENDED HIPPARCOS star catalogs. The brightest star values are probably good, but the number of stars in each spectral class may be inaccurate.

AstroSynthesis

I'm toying with AstroSynthesis to try and visualize a set of interstellar empires in a cuboctahedral array.

You can download the AstroSynthesis file here and the readme file here. Warning: you need to purchase the AstroSynthesis software to display the map, it is Windows only, the file is a work in progress and contains mistakes, and the blasted thing is 3.5 megabytes.


If you just want to play around with my empires, load my file into Astrosynthesis and go nuts.

If you want instructions on how I made the file (in case you want to customize it with a different set of stars or different empires or something), read on:

I started with the star dataset compiled by the Evil Dr. Ganymede. I combined RECONS, DENSE, CTIOPI, and EXTENDED HIPPARCOS 22 to 100 light-years. This gives a sphere full of stars with a radius of 100 light-years and a diameter of 200 light-years. Be sure you use the datasets marked "Astrosynthesis XYZ" NOT the ones marked Galactic XYZ.

Since the cluster is three empire-diameters in diameter, this means each empire has a diameter of 200 / 3 = 66.6 light-years and a radius of 33.3 light-years.

Go to my handy-dandy Empire Center Coord Table and multiply each of the coordinates by diameter 66.6. For instance, Empire Albert on the table has coords of 0.0, 0.59, 0.81. Multiply them by 66.6 to get map coords of 0, 39, 54.

I imported Dr. Ganymede's star dataset into AstroSynthesis. Next I went to the menu Sector | Sector Properties and opened the Sector Properties window. On the Sector Setup tab I checked Spherical Sector and set the Sector Radius (R) to 100 light years. On the Grid tab I checked Sphere Grid. Then I clicked the OK button.

The next task is to create "markers" for each of the empires using the map coords just calculated. These would define the centers of each empire. Click the Place New System button and set the type to Marker, and follow the instruction manual.

Then I had to figure out how to draw some lines connecting stars, but limit them to being within a given empire. If you are not interested in the details of AstroSynthesis, just skip over the rest of this.

I selected the marker for Empire Albert, which is at the center of that empire. I opened up the Advanced Search window. In the query I entered within 33.3 where 33.3 is the radius of each empire. Click the Search button and a bunch of stars appear. Click the Select All button then the Close button.

All the stars inside Empire Albert are now selected.

The important step is go to menu Actions | Mass Edit | Political Affiliation and set it to "Empire Albert". This allow you in the future to use the Advance Search to select all the stars in a given empire. You can search on political="Empire Albert" to select all empire stars. When selecting for purpose of making routes, do search on root only, political="Empire Albert" because you only need to make routes on root objects.

This next step is not stricly needed, but I use it. You see, by default, routes are not shown on the screen if the screen viewpoint is farther away from a route than 20 light-years. Since the map is 200 light-years diameter, if the viewpoint is far enough so see the entire map, all the routes are invisible. To avoid this unhappy state of affairs, click the menu Actions | Mass Edit | Label Display Distance. In the dialog, I change both numbers to 500 and click OK. While you are at it, you might want to do Actions | Mass Edit | Display Style to set the star and label color to the color you assigned to that empire

Now click the Create Proximity Routes button. A dialog appears. Check the Selected Systems Only radio button. Make the max route length 67 (empire diameter), just to be sure. Set the max routes per system, I use 2 for a sparse map and 3 for a busy map but you can experiment.

THIS IS IMPORTANT!! In Route Type, enter some unique name, e.g., "Albert Route". IF YOU FAIL TO DO THIS, THE ONLY WAY TO DELETE THE ROUTES FOR A GIVEN EMPIRE IS MANUALLY ONE-BY-ONE!!

Set the route color to the empire color. Select line style and line width. Click OK and patiently wait while it adds all the routes.

This would be a good time to save your work. Now go and do the next empire.

In the example above you can see the white routes belonging to Empire Sol and the red routes belonging to Empire Albert. Pollux is a star in-between the empires that is in one of the little voids, see below.

The cute little gridded spheres are AstroSynthesis sub-sectors. Each has the same location and radius as the empire. The utility is that you can temporarily hide each sub sector and all the stars inside, to unclutter the map in order to focus on a section of interest. For fun you can have them display the sphere grid.

I also added markers for "Zenith", "Spinward", "Trailing", etc. for orientation. But you don't have to do this.

AstroSynthesis uses a non-standard attribution for the x, y, and z axes: Dr. Ganymede's star data has already been adjusted to take care of this. Read his notes on Conversion from Galactic XYZ to Astrosynthesis XYZ for details.

Placing the markers for this map, keep in mind that the radius of the entire cluster is 100 light-years. Change this if your cluster has a different radius. Make sure you make the Display Distance of each marker 500 or so, to ensure they will always be visible.

ORIENTATION MARKERS
(100 light-year radius cluster)
Label TextAstroSynthesis
Coords
Description
ZENITH0, 0, 100Towards galactic north
NADIR0, 0, -100Towards galactic south
SPINWARD0, 100, 0Towards the direction of galactic spin, aka "turnward", "down-spin" or "deosil"
TRAILING0, -100, 0opposite the direction of galactic spin, aka "anti-spinward", "up-spin" or "widdershins"
COREWARD100, 0, 0Towards the galactic center, aka "hubward"
RIMWARD-100, 0, 0Directly away from the galactic center

The maps below were created in a slightly more complicated manner. The trouble with the method above is that there are quite a few stars that are outside of all the empire spheres. So I wrote a Python program that went through the entire list of stars, and assigned each star to the closest empire center. The empires are no longer spherical, but at least all the stars are included.

The 100 light-year radius sphere contained 2842 stars (counting all stars in binaries and trinaries) with roughly 100 to 200 stars in each of the 13 empires.

I made the stars that are near equidistant from two closest empire centers to be assigned to "Neutral Zone". These will be the hot-spots of intra-Empire hostilities. By experimentation I got good results with my current star data by defining "near equidistant" as "within ±20% of equidistant."

I manually found the sun-like star closest to each empire center, and assign that as the homeworld of each empire.

Once I have all the bugs worked out, I want to try it with a 55 empire map.

The maps below look like a tangles mess, but are surprisingly clear when they are rotated in 3D within AstroSynthesis. I tried making a video but the results were very disappointing.

Avoid the Void

As with the 2D flat map, the little voids between spheres will also be gobbled up by various empires. If you inflate each empire sphere so it gets its fair share of all the adjacent voids, the sphere will turn into an odd geometric polyhedron called a Rhombic dodecahedron. I didn't mention this at first because you are probably unfamiliar with the shape and they are confusing. But everybody has seen a ball.

Yes, my quick-n-dirty AstroSynthesis technique sadly omits these voids. I figured out a rube-goldberg method to include the voids, but it needs a bit of polish for people who are not comfortable with writing Python programs and AstroSythesis plug-ins.

Rhombic dodecahedron can be stacked with zero voids between them, just like cubes. But they are better than cubes since a given cube's neighbors are at variable distances from the empire center. Since Rhombics are duals of Cuboctahedrons, they too are equidistant from all their neighbors. Which is vital for an empire map.

A rhombic dodecahedron just small enough to contain an empire sphere (that is, the empire sphere is an inscribed sphere within the rhombic dodecahedron where the sphere is tangent to each face of the RD) with have an enclosed volume that is about 1.36 times the volume of the empire sphere. Which makes sense since you are adding the volume of the little voids to the empire. You need to know this since the volume tells you how many stars are inside.

The volume of a rhombic dodecahedron enclosing an empire sphere of a given empire radius is:

RDvol = 1.36 * (4/3) * π * EmpireRadius3

RDvol ≅ 5.6967544 * EmpireRadius3

where:

RDvol = volume of rhombic dodecahedron, in cubic light-years or whatever
EmpireRadius = radius of the empire sphere, in light-years or whatever.
π = pi = 3.14159265...

The same rhombic dodecahedron with have an edge length which is about 1.2247 times the length of the empire sphere radius. You may or may not need to know this, but it may come in handy if you were carving a physical model or something.


I am now going to show my math of how I derived those multiplication factors. If you could care less, skip ahead to the next section.

EmpireVolume = (4/3) * π * EmpireRadius3 (basic formula for volume of a sphere)

where:

EmpireRadius = radius of the empire sphere, in light-years or whatever.
EmpireVolume = volume of empire sphere, in cubic light-years or whatever
π = pi = 3.14159265...

EmpireRadius = (√6 / 3) * RDedge (formula for radius of inscribed sphere in rhombic dodecahedron, where the sphere is the empire sphere)

RDedge = EmpireRadius / (√6 / 3) (use algebra to solve for RDedge)

RDedge ≅ EmpireRadius / 0.8165

RDedge ≅ EmpireRadius * 1.2247 (multiplying by reciprocal is same as dividing)


RDvol = ((16 * √3) / 9) * RDedge3

RDvol = ((16 * √3) / 9) * (EmpireRadius / (√6 / 3))3

RDvol ≅ ((16 * √3) / 9) * (EmpireRadius * 1.2247)3

RDvol ≅ 3.0792 * (EmpireRadius * 1.2247)3

Two-Layer Empire Map

Now to do an in-depth analysis, you need more than the 12 empires in the first layer surrounding Sol, the Sol-shell empires. You should also know the 12 empires surrounding each Sol-shell empire, not just five of them.

To do this you'll need to add a second layer of empires around the original single-layer map.

So if you have just one sphere (Sol Empire) and surround it with a layer of other spheres in the form of a cuboctahedron, you have what Buckminster Full calls a "one-frequency" layer. The number of spheres in a layer is (10*F2) + 2 where F is frequency. So the one-frequency Sol-shell layer has (10*12)+2 = 12 spheres. Add the center sphere and you'll see the basic map has 13 spheres.

Add a layer to that and you'll have a two-frequency layer. (10*22)+2 = 42 spheres. Add the original 13 spheres and you'll see the expanded map has 55 spheres.

With this expanded map, you will have the 12 neighbors of each of the Sol-shell layer empires. Sadly you will only have five neighbors of the outer-layer empires but you have to stop somewhere. The next outer layer will need 92 more spheres, that way lies madness. 55 empires is more than enough to keep you busy.


I used Blender 3d to whip up a couple of charts of 55 in a cuboctahedral array, for your empire plotting convenience. Make notes using your favorite paint program. Alternatively, download the PDF versions and print them on your printer (they are sized to be 8 inches wide) and make notes using a pencil. Go nuts plotting the locations of rival empires in three dimensions.

About thirty years ago I tried to draw such a chart manually on triangular graph paper but the result was not usable. Blender made it a snap. Especially making the twisted version so you could see all the empires, that would have taken me months to do with pen and paper.

This effort comes under the heading of "create custom artwork for diagrams and illustrations of difficult concepts", which I promised to do and have been doing.

Empire Center Coords

(3D Geometry)

(Two Layers around core)

Multiply center coords by chosen empire diameter

Level One
(Top Level)
EmpireCenter
(x,y, z=1.64)
13 Mike0.00,1.14,1.64
14 Nov0.50,0.29,1.64
15 Oscar-0.50,0.29,1.64
20 Tango1.00,-0.57,1.64
21 Uniform0.00,-0.57,1.64
25 Yankee-1.00,-0.57,1.64
Level Two
(Upper Mid Level)
EmpireCenter
(x,y, z=0.81)
1 Albert0.00,0.59,0.81
2 Bravo0.50,-0.29,0.81
3 Charlie-0.50,-0.29,0.81
16 Papa0.50,1.45,0.81
17 Quebec1.00,0.57,0.81
18 Romeo-1.00,0.57,0.81
19 Sierra-0.50,1.45,0.81
22 Victor1.50,-0.29,0.81
23 Whiskey1.00,-1.14,0.81
24 X-Ray0.00,-1.14,0.81
26 Zulu-1.00,-1.14,0.81
27 Alpha-1.50,-0.29,0.81
Level Three
(Middle Level)
EmpireCenter
(x,y, z=0.00)
0 Sol0.00,0.00,0.00
4 Denver0.50,0.87,0.00
5 Echo1.00,0.00,0.00
6 Foxtrot0.50,-0.87,0.00
7 Golf-0.50,-0.87,0.00
8 Hotel-1.00,0.00,0.00
9 India-0.50,0.87,0.00
28 Gamma1.00,1.71,0.00
29 Delta1.50,0.87,0.00
30 Epsilon0.00,1.71,0.00
33 Theta2.00,0.00,0.00
34 Iota1.50,-0.87,0.00
37 Mu1.00,-1.71,0.00
38 Nu0.00,-1.71,0.00
40 Omicron-1.00,-1.71,0.00
41 Pi-1.50,-0.87,0.00
44 Tau-2.00,0.00,0.00
45 Upsilon-1.50,0.87,0.00
47 Chi-1.00,1.71,0.00
Level Four
(Lower Mid Level)
EmpireCenter
(x,y, z=-0.81)
10 Juliette0.50,0.29,-0.81
11 Kilo0.00,-0.57,-0.81
12 Lima-0.50,0.29,-0.81
31 Zeta1.00,1.14,-0.81
32 Eta0.00,1.14,-0.81
35 Kappa1.50,0.29,-0.81
36 Lambda1.00,-0.57,-0.81
39 Xi0.50,-1.45,-0.81
42 Rho-0.50,1.45,-0.81
43 Sigma-1.00,-0.57,-0.81
46 Phi-1.50,0.29,-0.81
48 Psi-1.00,1.14,-0.81
Level Five
(Bottom Level)
EmpireCenter
(x,y, z=-1.64)
49 Omega1.00,0.57,-1.64
50 Aleph0.50,-0.29,-1.64
51 Beth0.00,0.57,-1.64
52 Gimmel0.00,-1.44,-1.64
53 Daleth-0.50,-0.29,-1.64
54 Zayin-1.00,0.57,-1.64

To use the Empire Center Coords (3D Geometry) table: choose the desired DIAMETER (not radius), and multiply each coordinate by the diameter. For instance, if you chose an empire diameter of 100 light-years, Empire Charlie would be at coordinates -51, -29, 81.

If you felt the need to continue the gemstone motif, I made a quick list. The ones after #11 are all in alphabetical order, feel free to scramble them up.

RocketCat's Map

RocketCat was making some notes about the galactic empires existing several centuries in the future, using the two-layer map. He says the empires are as described by some descendant of his named "GalactiCat". All my questions about where he got this information were met with his best "that's for me to know and you to find out" facial expression. Oh well, he always did have sort of a laissez-faire attitude towards causality.


Each empire is approximately 65 light-years in diameter (20 parsecs), 32 light-years in radius (10 parsecs). The entire cluster of 55 empires has a diameter of approximately 325 light-years (100 parsecs). As per my standard directions are: plus X points Coreward, minus X points Rimward, plus y points Spinward and minus y points Trailing. I regret to say that I screwed up: plus Z is Zenith while minus Z is Nadir, the exact opposite of what it should be. Oh well, I'll fix it when I get the time.

Details on Layer One
(empires 0 to 12)
Empire
Sphere
Center coords
(x,y,z in l-y)
Sector
Name
Empire
Culture
Throne
Star
0 Empire Sol0.00,0.00,0.00Sirus
aka Dog Star
(Diamond)
Human-
Cetacean
Alliance
Sol
1 Empire Albert-57.70,5.54,41.08Iota Ursae Majoris
aka Talitha
(Aquamarine)
Receptor
Culture
BD+46°139
(HIP 41484)
2 Empire Bravo-53.79,-33.25,-17.60Beta Eridani
aka Cursa
(Opal)
Noise
Culture
BD-06°1339
(Gliese 221)
3 Empire Charlie-62.59,44.01,-24.78Beta Persei
aka Algol
(Emerald)
Transmitter
Culture
12 Persei
(HIP 12623)
4 Empire Denver-4.90,-29.60,49.20Delta Leonis
aka Zosma
(Sapphire)
Evolver
Culture
83 Leonis
(Wolf 394)
5 Empire Echo-30.32,-22.82,21.19Delta Velorum
aka Alsephina
(Ruby)
Solar-
Phoenix
Culture
CPD-42°2834
(Gliese 319.1)
6 Empire Foxtrot-6.00,-39.00,-52.00Kappa Phoenicis
(Garnet)
Memory
Culture
Iota Horologii
7 Empire Golf0.92,35.20,-52.20Sigma Pegasi
(Topaz)
Sun
Parasites
HIP 115445
(BD-11°6064)
8 Empire Hotel3.26,62.92,-0.65Alpha Cephei
aka Alderamin
(Amethyst)
Tunneler
Culture
BD+45°3371
(Gliese 816.1)
9 Empire India2.43,25.70,55.00AlcorMizar
(Citrine)
Mirage
Culture
BD+42°2508
(HR 5423)
10 Empire Juliette23.00,-12.00,27.00Iota Centauri
(Onyx)
Amorphoid
Culture
CD-44°9181
(Gliese 540.3)
11 Empire Kilo52.90,-2.82,-46.50Eta Indi
(Zircon)
Tensegrity
Culture
HD 199288
(Gliese 812.1)
12 Empire Lima65.90,41.50,16.20Delta Herculis
aka Sarin
(Agate)
Camouflage
Culture
BD+4°3589
(Gliese 702.2)
  • EMPIRE SPHERE: empire sphere label
  • CENTER COORDS: the coordinates of the center of the empire sphere. X, Y, and Z co-ords in light-years
  • SECTOR NAME: flashy name for the empire sphere, named after the brightest star in the sphere. So Empire Sol is in the Sirius Sector or Sector Diamond
  • EMPIRE CULTURE: code name of the alien civilization ruling the sphere
  • THRONE STAR: star hosting the capital planet of the empire. In most cases this is also the home planet that gave birth to the alien race, the cultural origin planet

Empire Culture and Technology Notes

For lack of a better algorithm, I am using the same idea that Piers Anthony used when world-building for his Cluster series. He created his alien species by starting with a unique central organizing principle for each species, and applied it to all facets of their existence. This determined their standard method of solving problems, techniques of debate, method they used to move their bodies across the landscape, sexual organs, and everything else.

Human beings are a "thrust" culture. They solve problems by analysis, that is, cutting away like a scalpel or woodcutting tool. They debate by "getting to the point". They move by thrusting one leg forward in sequence. Their sexual organs thrust in and out.

Meanwhile the Polarians are a "rolling" culture. They solve problems by circling around it and examining it from all sides. They debate by moving around in circles. They move by balancing their bodies atop an organic sphere and roll along. Their sexual organs are used to spin spherical germ cells between the participants. And so on.

Occasionally he would use the same principle for two difference alien species, and use it to highlight how similar they were underneath even though superficially they looked different.

Yes, this is a simplistic and silly way to create an alien culture, but at least it provides good initial brain-storming ideas as a springboard.

  1. Human-Cetacean Alliance: basically the Terran Empire. By that time cetaceans were recognized as being intelligent, abet weird. The cetaceans forgave humans, eventually, after some eye-watering restitutions were paid.

  2. Receptor Culture: past masters of the art of energy harvesting. True, the energy sources are low-grade, but waste-not-want-not. They also have a limited ability to harvest the energy from incoming hostile weapons fire. Inspired by Star Trek: The Animated Series episode Beyond the Farthest Star (see image to the right)

  3. Noise Culture: their combat, tactics, and psychology is based on jamming sensors. Basically sending noise, interference, and false information to an opponents sensors to drown out the signal. Radar jamming, misinformation, disinformation, that sort of thing.

  4. Transmitter Culture: the entire culture is based around matter transmission. Requires transmitter and receiver (including need to transport receiver via sublight starship). Transmitter recreates what is transmitted, including people (also means original is stays at home and transmitter is also a duplicator. With all that implies).

  5. Evolver Culture: their combat, tactics, and psychology is based on using genetic algorithms to evolve a solution. Which they are constantly doing all the time.

  6. Solar-Phoenix Culture: they are the past masters of the art of nuclear fusion. They can fuse any element lighter than Iron-56. Including proton-proton fusion which is real hard to do short of using an entire star. Which means they can use almost half the periodic table as fuel.

  7. Memory Culture: their culture is based around storage of information. For instance, their warships have memory banks containing detail blueprints. This means that if the ship is damaged, they can recreate the damaged sections perfectly (given energy for the nano-forges and a supply of feedstock). They can practically recreate the ship's armor as fast as enemy weapons fire can blast it away. Buildings and equipment can last for millions of years, or until the power runs out, whichever comes first. Inspiration was from Captain Scarlet and the Mysterons, with the latter's power to "reverse matter". Also inspiration from the computers of Diaspar (see quote) in Arthur C. Clarke's The City and the Stars.

  8. Sun Parasites: this is less of a culture and more like a disease. Sentient patterns of magnetism and plasma which infect stars. They use the star's energy for food and reproduction, which does not do the star any good. They spread from star to star using microscopic "seeds" attached to astronomically sized magnetic sails. If you make them angry, they can control the star they are infesting enough to make it spit accurately at planets a series of geomagnetic storms powerful enough to make the Carrington Event look like a wet firecracker. Inspired by the Photino Birds from Stephen Baxter's Xeelee Sequence and Out Of The Sun by Arthur C. Clarke (see quote).

  9. Tunneler Culture: their technology is based around utilization of Einstein–Rosen bridges. They have wormholes small enough to teleport atoms to large enough to transport entire moons. Used for transport, sensors, data transmission, and computation. This also means that some of their machines are composed of components that are physically distant from each other; but exchanging data, fuel, feedstocks, etc through wormholes. Rumor is that some of the aliens can do that with their bodies. Inspired by The Light of Other Days by Stephen Baxter and Arthur C. Clarke.

  10. Mirage Culture: their combat, tactics, and psychology is based on fooling sensors by refracting electromagnetic radiaion. Generally takes the form of displacing the location of an image by gravitational lensing. Star fleets attacking Mirage Culture ships often feel like they are fighting inside a house of mirrors. They are similar to the Mirror Culture but are more focused on bending light from ambient sources, i.e., they are more concerned with defeating passive sensors instead of active ones.

  11. Amorphoid Culture: their weapons and technology are inspired by the Protean Weapons of Larry Todd's The Warbots. Weapon complex looks like a puddle of mercury, but can be formed into hundreds of different weapon systems. Weapon circuits are composed of magnetic and gravitic domains, which could not be altered by any amount of twisting and contorting.

  12. Tensegrity Culture: their philosophy and technology is based around tensegrity. While compression members (like steel girders) have a maximum size, tension members (like cables) can theoretically be of any length. Tensegrity combines compression and tension members for the creation of structures that are infinitely scaleable. The same goes for their philosophy and negotiation style: a combination of push and pull.

  13. Camouflage Culture: they are so good at camouflage that their genetically engineered worker creatures and equipment can become indistinguishable from asteroid and other natural celestial bodies. By which I mean you could grind one into atoms and it would still look like asteroid dust. Turn your back on it, however, and the asteroid can morph back into the original creature. Inspired by "existing implicate order" from The Ring of Charon by Roger MacBride Allen.

  14. The Grid:

  15. Argus Culture: culture is based on the theory that you can never have too many sensors. Ships and installations bristle with sensors and scanners for as many frequencies as is practical, looking in all directions. Sophisticated analytical algorithms ensure that units do not drown in oceans of data. You cannot sneak past an Argus ship, they will spot you.

  16. Field Culture:

  17. Mirror Culture: their combat, tactics, and psychology is based on manipulating the vectors of enemy sensors or scanners. They are similar to the Mirage Culture but are more focused on bending light from enemy scanners instead of from ambient sources, i.e., they are more concerned with defeating active sensors instead of passive ones. They also are fond of replacing an image of their spacecraft with an image which is a reflection of their opponent. They do that with debates and negotionations as well.

  18. Wind Culture: their combat, tactics, and psychology is based on manipulating objects with swarms of particulates or gaseous clouds instead of by solid tools. It is the difference between being knocked down by a hurricane as opposed to being hit with a club. Their warships are more like artificial nebulae composed of billions of microscopic units rather than a single metal spacecraft.

  19. Cloak Culture: their combat, tactics, and psychology is based on invisibility via reducing their emissions and absorbing or deflecting opponents scanning beams. There ain't no stealth in space, but they do their best.

  20. Thanatos Culture: no, not "Thanos" but related I suppose. Basically a death-cult civilization in space. Their interaction with other species is hard to distinguish from Beserkers or Morn Cyborgs; but they are religious-nut-job organic beings, not a left-over robot doomsday weapon. Inspired by the Necromonger Empire from the The Chronicles of Riddick.

  21. Nova Makers aka "Sun Slayers": just what it says on the label. The culture has the technology to create nova bombs. Apparently strangelets are involved. They were spotted in 1968 by Arthur C. Clarke.

  22. Hive Robots:

  23. Heisenberg Culture: their combat, tactics, and psychology is based on Heisenberg's uncertainty principle and the observer effect.

  24. Causality Culture: the culture is based around sophisticated knowledge of cause and effect. They can optimize for the minimum necessary change to create the maximum desired response. Some of their systems resemble byzantine Rube Goldberg machines but they get the job done using the minimum energy.

  25. Crystal Culture: they use crystal-based technology for everything, especially for data storage, weapons and power sources. Because you should never let a good trope go to waste. Their biochemistry is based on crystals as well.

  26. Probability Culture: their combat, tactics, and psychology is based on calculating probabilities and probability amplitudes. You don't have to tell them the odds because they already know them to nineteen decimal places.

  27. Entropy Culture: their combat, tactics, and psychology is based on decreasing or increasing the rate that entropy accumulates in a given system or situation. Generally they try to slow the entropy increase for themselves while speeding it up for their opponents.

  28. Speed Culture:

  29. Cyborg Culture:

  30. Energy Culture: their technology utilizes components made of electromagnetic fields where others would use matter. Directed energy weapons instead of kinetic energy weapons, force fields instead of armor plate. More or less the opposite of the Mass Culture

  31. Mass Culture: their technology utilizes components made of matter where others would use electromagnetic fields. Warships use armor made of muon-iron instead of defensive force fields, kinetic energy weapons instead of laser beams, technologies utilizing degenerate matter and neutronium, etc. They are more or less the opposite of the Energy Culture.

  32. Bubble-Cloud Culture:

  33. Composite Creatures: a colonial siphonophorae, similar to a Portuguese man o' war. That is, while it looks like a single creature it is actually a composite of different types of organisms glued together. Inspired by the "Godspeakers" from The Dragon Never Sleeps by Glen Cook. They look like a group-grope involving giant hydras and starfish atop a heap of exposed intestines.

  34. Warp Culture:

  35. Seeder Culture: Directed Panspermia Я Us. They terraform (or "seederform") worlds to make them garden worlds for their species. Along with this the worlds are seeded with microorganisms and nanotechnology to jump-start the evolution of their type of life.

  36. Seetee Culture: ships and artifacts are composed of equal parts matter and antimatter. Inspired by Seetee Ship by Jack Williamson

  37. Mutator Culture:

  38. Precognition Culture:

  39. Marine Neuron-net: inspiration: Starswarm by Jerry Pournelle, the alien neuron-net super-intelligent plant-like creatures dwelling in the bottom of the planet’s countless shallow lakes and oceans. Secondary inspiration was from The Skeptic alien species from the game Cosmic Encounters.

  40. Euphoron Culture:

  41. Living Computer-chip:

  42. Sculptured Laser Culture:

  43. Orbital Brains:

  44. Wave Lattice Culture:

  45. Aikido Culture: much like the Japanese martial art, the culture's philosophy, psychology, and military arts are based on bending with and redirection the energy of an attack. This does tend to make the culture more defensive than offensive. A member of the Aikido culture surrounded by attackers would calmly walk out of the center of the melee, while the attackers would discover they had grabbed each other. This holds true with a legal debate, hand-to-hand combat, or a starship battle.

  46. Robot-core Culture:

  47. Fog Culture:

  48. Patterns of Chaos: Inspire by Patterns of Chaos by Colin Kapp and Agent of Chaos by Norman Spinrad

  49. Aura Stars:

  50. Standing-wave Culture: the culture's psychology and technology is based on the concept of standing waves. In some respects they both move and are stationary simultaneously.

  51. Plateau-eye Region:

  52. Star-web Region:

  53. Bent-space Region:

  54. Desolid Culture:

  55. Hyperaging Culture: these creatures evolved on the surface of a neutron star. Ordinary aliens (like humans) are composed of atoms bound by the electromagnetic force. The hyperagers on the other hand have bodies composed of atomic nuclei bound by the strong force. Nuclear reactions are about one million times faster than chemical reactions, so the hyperagers move and live that much faster than humans. A hyperagers 76 hyper-year life space seems like only 40 minutes to a human. This also means the hyperager's rate of technological advance is a million times faster. And you thought "Wink of an Eye" was dangerous. Inspired by the cheela of Dragon's Egg by Robert L. Forward.


Wandering Cultures

Some galactopolitical powers have no fixed address, being more like nomads. They sort of wander through the various empires, wreaking havok along the way.

  • Tempath Justice Fleet: an impressively huge star fleet crewed by a species cursed with the power of telempathy. Meaning that if any stellar empire commits a savage act of oppression or genocide, the Justice Fleet will psionically hear the screams of the victims across the galactic spiral arms. And the fleet will come for you. There is a long trail of burnt-off planets marking the tombs of empires that found out the hard way that the Tempath's idea of justice is "an eye for an eye."

  • Lungfish: mutated von Neumann probes. Originally meant as a scalable way to explore the galaxy, they have mutated into paperclip maximizers. There are many types, and different types are also at war with each other. Some have become beserkers. Inspired by Lungfish by David Brin.

  • The Plunder Fleet: planet looters who strike from some hidden homeworld whose location is being sought after by stellar empires that are sick and tired of being given the "Space Viking" treatment.

  • The Ravage Horde: larger swarm of planet looters who have no home planet. Instead, they have mobile space habitats that travel in tandem with the looter fleet, nomad-style.

  • Cybervirus: The best description is like a cross between an AI and a rapidly mutating computer virus. It doesn't matter what type of computer or operating system a stellar empire uses. As long as it is Turing Complete the Cybervirus will adapt and find a way in. The model here is The Blight from John Varley's A Fire Upon The Deep

  • Living Nebula: intelligent organisms in the form of a living Bok Globule. They like to travel to stars and engulf them for a couple of centuries to suck up solar energy. Pretty much as described in Fred Hoyle's The Black Cloud.

  • Electromagnetic Daemons: malevolent organisms composed of patterns of electromagnetic radiation instead of matter

  • Stellar Vultures: galactic scavengers who harvest the larger technological resources of dead civilizations

  • Stellar Reducers: galactic decomposers and detritivores. Pretty much like Stellar Vultures, except they harvest the stuff the Vultures leave behind as too low grade to be worth it. Since detritivores subsist on waste products, they might be present in civilizations that are not dead yet.

  • Morn Cyborgs: pretty much like Fred Saberhagen's Beserkers. Except these are cyborgs instead of robots, which doesn't really make much difference. Both want to destroy all life in the universe, and become a poetic metaphor for Death.

  • The Forgotten Empire: basically Forerunners. Their ancient ruins often contain incredibly valuable (and incredibly dangerous) paleotechnology.

  • Monolith Culture: basically the star gods from 2001: A Space Odyssey. They have long ago departed for the fourth dimension or something, but their monoliths are lying around everywhere. They are tools designed to foster the birth of new intelligent species. Otherwise they are inert and indestructable.

Interactions

Three or more empires can interact in quite a few interesting ways, depending upon the relative strengths of the empires involved.

WEB AND STARSHIP DESIGNERS NOTES

(ed note: Web And Starship by Greg Costikyan is a table-top wargame of conflict between interstellar empires. He does have some other interesting things to say about multi-empire interactions.)

      There are two things I tried to do in Web And Starship. One is fairly evident: to design a viable three-player game. Three-player games are inherently unstable: they tend to devolve into two-player alliances against a third. It is possible to design a game with this element built in — one strong versus two weaker players — but that makes the three-player game merely a variant on two-player ones. The goal is to produce a game which can support shifting alliances and preserve some element of multi-player diplomacy. The only truly successful game I know of which does this is Conquistador, which succeeds by pitting the players more against the game system than against one another. In Web And Starship, I decided to tackle the problem head on.

     The economic game/war game dichotomy is an important element of my strategy; the idea is that wars will be interspersed with breathing periods, during which time players may back off from alliance commitments and rebuild. Another attempt to break the two-player alliance lock is the nature of the player’s positions; Terra is midway between the other two players and, initially, practically defenseless. Either player can, with some ingenuity, knock the Terrans out in the first few turns of the game — unless, that is, the other player comes to Terra’s aid, a virtual given. Too, the channelized nature of the board means conflict among all three players is likely; Terra and the Gwynhyfarr are in conflict virtually from the beginning, the Gwynhyfarr and Pereen will clash in the 70 Ophiuchi/41 Arae area, and the Terrans and Pereen in the 61 Cygni/Sigma Draconis area. Every player has a reason to fight every other — so, one hopes, a breakdown into a permanent two-on-one alliance will rarely occur.


     Another goal was to depict two incompatible systems of warfare. An analogy to Renaissance naval warfare may be useful here; warfare in the Mediterranean was dominated by the galley. that in the Atlantic by the sailing ship. Gunnery was considerably more primitive than in later eras. primarily because gunports had not been invented, but also because bronze cannon were hideously expensive and iron cannon had a nasty tendency to explode. Consequently, sailing ships. with their relatively small manpower component, were unable to do much damage to galleys. Galleys were crammed with men — who could do little faced with a sheer wall of wood. A sailing vessel could not reasonably hope to attack a galley, nor vice versa.

     The situation in Web And Starship is similar; the Gwynhyfarr are masters of space, able to strike where they will, but without the ability to transport large numbers of troops quickly. FTL navies are all very fine, but in the final analysis, it’s the poor bloody infantry who gets the job done, as always. The Pereen can mass troops at a moment’s notice — but have very limited ability to send them anyplace. The result is a series of strategic and tactical problems that require some ingenuity to solve.


     Finally, Web And Starship was the next in series of games which I privately call the “Earth's Future" series. The goal of the series is not, as with a fiction series, to put the same characters through different adventures, but instead to examine a spectrum of possible futures, given interstellar travel.

     The first game of the series was Trailblazer, published by Metagaming and hence now out of print; it was a simulation of free-market micro-economics — and assumed that nothing much was out there, that humanity would have the stars to itself.

     The assumption of Web And Starship is that we’ll be faced with powerful competitors, but, despite our weakness, will be able to develop fast enough to deal with them.

     I plan several future games, but the next two will be Terra Uber Alles, which, as one might guess, will pit a small but vigorous Earth against a nasty but decadent alien empire;

     and The Treaty of Io, which will be a diplomatic game in which a pitifully weak Earth tries to survive by playing several alien races off against one another.

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