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
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)
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)

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

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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