Once more we MATHS! I mean, sort of. Broadly.
The Boom; Where It Happens
This post is brought to you by the number nine hundred million. Or point nine billion, if you prefer. The Romulan headcount for Picard's proposed evacuation fleet, before F8 went all T2.
That number got itself stuck in my head, and I never really dislodged it. Where did it come from? Was it just the projected total of people the fleet would be able to carry? Or had the Federation been allotted that number, as part of a larger logistical undertaken being organised by the Romulans themselves? What were the implications to the relief effort (as opposed to Picard's ego) in cancelling these people's Fed Air flights two years before boarding? And just how many people lived in the Romulan system anyway?
The answers to these questions do not, as yet, exist, and that will only change when someone decides to make them up. The wait for new lies to be told aren't going to stop me wondering how all this hangs together, though. Like all good statisticians, my first instinct when I come across a value I can't quite figure out is to build a model to try and figure out what's going on under reality's hood. The regular reader will be fully aware that it doesn't really make much difference how loosely the word "reality" can be applied in that process. Something need not be real to be believable, after all, as I go on about at length in the first IDFC book. It's always perfectly coherent (if not necessarily a strong use of one's finite time on this earth) to think about how fiction hangs together, and anyone insisting otherwise should be handed milk and cookies and ask to go quietly sit in the corner.
What does cause a problem, though, is the lack of fictional facts around the catastrophe. We have no sense of how the Romulan government responded to the threat, or even for that matter what the Romulan government looked like after Shinzon assassinated the entire Senate a decade or so before the supernova. The disposition of the Romulan fleet is also a complete unknown (though later I hypothesise it was probably quite active on the other side of Romulan space), as is whether any other races were willing to help out with the evacuation.
Where we might get somewhere in applying logic here is in considering the size, shape and population distribution of the Star Empire/Free State, and the effect a supernova might have on same. We'll start with stellar density. We are told here that the average density of stars in our area of the galaxy is 0.004 stars per cubic light year. A supernova with a blast radius of r light years would therefore be expected to encompass S star systems, where:
But what does a "blast radius" mean for a supernova? The actual explosion itself would likely engulf only part of a star system. Stars are colossal objects with even more colossal energy output, but the inverse square law digs in pretty quick, and shockwaves are tricky things to maintain in the absence of, you know, anything at all. In stellar terms, you don't have to be very far out from, uh, space zero, before the chance you're hit by a tumbling chunk of ex-sun becomes trivially small. You might even find structures within the outer system itself surviving, though the sudden shifts in gravitational fields are likely to cause some issues.
That's not the big headache, though. The real thumping in the temples comes about from the colossal doses of radiation a supernova flings into the void. Your house might survive on Romulan's Pluto-equivalent, but your internal organs won't. This paper suggests that even a supernova occurring within 10 parsecs (32.6 light years) of Earth would irradiate the planet to the point of causing a mass extinction event. We might hypothesise that future tech might be able to alleviate this problem somewhat, but even the most reliable shields seem to fail from time to time. I don't think real estate will go for much when a single flicker in the power supply will get you cooked to charcoal before you can say "Tea, Earl Grey, superheated vapour".
If we assign, somewhat arbitrarily (and get used to that approach, is my advice) assign 30 light years as being the radius at which even a warp-capable species can't hold back the radioactive flooding of a supernova, we can get a sense of how catastrophic the coming devastation is going to be: a sphere sixty light-years across is going to capture approximately 450 stars.
Some of this still lies ahead of the Romulan Free State at the time of "Remembrance". Radiation waves cannot travel faster than light – they are light - so twelve years after the explosion, the galaxy's largest microwave would be “merely” cooking an approximate 29 stars. That doesn't necessarily translate into 29 systems, either. We need to take binary and ternary (or "trinary", as Starfleet refers to them) systems into account. This requires additional guesswork to consider, but hey; we’ve come this far, yes? The overall proportion of multiple-star systems appears to be a source of disagreement in astronomical orbits, but some estimates suggest only around 15% of stars aren’t sharing their system without at least one neighbour. If we assume every other system is binary (not true, but potentially not too far from the truth either), the 29 stars referenced above represent around 16 stellar systems (there are 18 systems within 12 light years of Earth).
That still seems pretty appallingly bad, though. An average of four systems lost every three years, with the rate of destruction increasing every year. And just in terms of apocalypse by volume, things were only going to get worse.
Sphere Of Bad Influence
The ultimate scale of this ultimate disaster is hard to fathom. Bad enough the Romulans were about to lose the central planet in their empire; their culture’s only shared reference point since pointing aft sensors at Vulcan some two millennia earlier. Bad enough Remus would be destroyed alongside, costing the central worlds their primary sources of both the dilithium and the deal-dealers they needed to keep the outlying territories in line, right at the point that was going to become more difficult than ever. That’s already a triple catastrophe – the obliteration of the planets themselves, and the creation of a power vacuum which would require who could know how much green blood to fill. But on top of all of that, the number of systems rendered uninhabitable by the time the supernova ran its course could easily be in excess of four hundred.
The sphere scooped out of the Star Empire would be stupefyingly colossal, then. But then, that must surely be true of the size of Romulan holdings in general. As horrifying as the phrase “four hundred systems stripped of life” must have been to everyone who heard it, there’s work to be done in figuring out what proportion of Romulan civilisation was under threat. To touch on a topic which may be familiar for those like me who dabble in the realms of mathematics, how much bigger is one incomprehensibly vast number than another incomprehensibly vast number? And how do we show that?
We might start by considering how much interstellar space the Senate had available to expand into. To no-one’s surprise, a major part of the necessary noodling will involve the Neutral Zone. We know from the chart that opens this post that the ol’ November Zulu stymied the Romulans in at least two directions along the plane illustrated in the chart that opens this post (taken from “Balance Of Terror”, as if you didn’t already know). From now on, we shall refer to the direction from bottom to top on that chart as “galactic North”, and the direction from right to left as “galactic West". We know further from one of Geoffrey Mandel's maps in Star Trek Star Charts (now at least broadly canonised in both Picard S3 and, more prominently, the recent Star Trek: Section 31 film) that what we’re calling galactic North points toward the centre of the Milky Way, and that the chart above displays a plane more or less parallel to that of the galactic plane as a whole.
The first question we’ll tackle is just how close the Neutral Zone comes to Romulus. This is already what mathematicians call “non-trivial” (rough translation: “One pot of coffee ain't gonna get it done”). The complications here are probably clear enough. There’s no discernible scale to the chart. All we can tell is that each sixth of a square is approximately equal in length to 5000 somethings. Or maybe the 5000 figure is for the whole length of the legend, i.e. two and two-third squares. There's no way to tell, and to make things worse, we're looking at a chart precisely one dimension short of what's needed to get to grips with galactic real estate.
There are still conclusions to be drawn, though, or at least wild speculation you can't stop me engaging in. We know from a map briefly seen in "Disengage" on the the SS Eleos XII that the supernova blast radius had reached about halfway to the Neutral Zone to Romulus' west by 2401. That puts the Romulan's border some 28 light years distant in that direction, and maybe 26 light years at its closest point, assuming the Neutral Zone in the figure is drawn on the same "vertical" plane as Romulus.
In comparison, the Mandel map puts the minimum planar distance between Romulus and Neutral Zone as being just seven light years. Both measurements can be correct, of course - the Mandel map centering of the Sol system in its plane makes it pretty likely its using Earth as the centre of the vertical axis as well.
Assuming both these measurements are accurate, then, we can assume Romulus lies above Sol in the galactic plane, and the Neutral Zone passes close to or fully underneath the former. The simplest border we could consider would be planar, but the curve of the Neutral Zone to the north-west of the "Balance Of Terror" chart suggests a sphere, or a partial sphere, as being more plausible.
We'll therefore assume a sphere 26 light-years in radius, centered on Romulus, with the lower western quadrant (the one facing Earth) forming the border to their side of the Neutral Zone.
The Hemming-Inining
One advantage of considering a partial sphere for the border is that it plausibly doubles as an indication of how far the Romulans had spread from their adopted home system by the time they encountered Starfleet. This implies an extremely conservative rate of expansion, but perhaps that shouldn't surprise us. A gradual build seems entirely consistent with what we know of Romulan society. Paranoid isolationists presumably would need to move slowly outward, so as to maintain full control over every aspect of the settlers' lives. New frontiers mean new ideas, after all, and totalitarianism gets tricky at long distance.
Perhaps there's something to be said about resisting a headlong charge into the stars (certainly the Vulcans thought so). Ultimately, though, the end result was that everything the Romulans built prior to the mid 22nd century - and likely much afterward - lay within the supernova 'splodezone.
As a result, the ability of the Romulan state (whichever form it was in by the time it became clear what was coming) to evacuate the entire sphere of devastation would depend almost entirely on the status of their comparatively recent settlements of the last two centuries. We know almost nothing about these worlds, of course - hell, you can barely count the times we've seen Romulus on two hands - but we can again turn to the shape of the Neutral Zone to gain (or at least feign) some insight.
What's initially strange about the Neutral Zone border we see in the Mandel chart/Section 31 graphic is how close that border comes to Romulus in the west and north, but how far it allows expansion to the south east. Why are they hemmed in so tightly to the north west, when every one of the four founding members of the Federation lie to the south west?
The most plausible scenario I can think of is that, pre-contact with the Romulans, human expansion in the Beta Quadrant was mainly happening to Sol's galactic north. The Mandel chart has Suliban and Nausicaa as not too far from Earth to the east, which may well have dissuaded serious attempts at expansion in that direction even before considering the comparatively distant but extremely active western Klingon border. As a result, the war was likely initially fought mostly to Sol's north, and Romulus' west, and not too far in relative terms from the latter, due to their slow expansion compared to humanity's.
After hostilities broke out, though, it would have been clear to both sides that attacks south of the initial front would be strategically advantageous - for Starfleet because they could get ships there faster, and for the Romulans because humanity, fearing attacks by Klingon raiders, Nausicaan pirates, and Suliban time-bastards, had spent less time colonising in that area.
As a result of this, a new interstellar front open up to first Romulus' south, and then its south-east. And that front just kept widening, as each power worked to prevent the other from flanking them, The result was a sudden supercharged land-grab on both sides, along a front which galloped south east, roughly perpendicular to the straight line between the combatants' home systems, until the war came so close to the Klingon border both sides realised they were about to have bigger problems.
I imagine there are some pretty dark tales to be told about those days of headlong map-staining, on both sides of the front. I'm sure the Vulcans at least were appalled, and given how Starfleet can let its morals get murky whenever they're in a fight for their lives, it's not hard to imagine they might have had a point [1]. I also imagine that it was inevitable that, sooner or later, one side was going to overextend itself in trying to maintain so recently expanded a front. We know from "The Defector" that this turned out to be the Romulans, at Cheron. From the charts, that's a system almost exactly thirty light years on the galactic plane from Sol, and a little under fifty light years from Romulus on that same plane (Cheron's elevation not being something we can determine). Presumably some combination of the Romulan fleet being further from home, them starting with a smaller sphere of influence (based on comparative distances to the original front line of the war), and the proximity of Andoria to Cheron, all contributed to the loss.
Whatever the reason for their "humiliating" defeat, though, "The Defector" implies the result was Romulus agreeing to a treaty which both brought peace, and defined the Neutral Zone's shape. We could assume that shape is one which at least roughly approximates that of the front lines during the war, though with those lines either forming the Federation border, or even allowing the Federation a little extra space, as the victors - this is evidenced by Cheron being some fifteen planar light-years from the Neutral Zone, despite presumably previously having been close to or on the front line of the war. It's possible Earth and her allies might have been able to push the south-eastern border even further east - the Romulan hold on the local systems was presumably tenuous even before fleet losses at Cheron, but it's not like the Earth/UFP holdings out there were much more developed, and there's presumably only so far the Romulans could have been pushed before the treaty itself was in danger, and war broke out once again.
All of which would explain the strange shape to the Empire - it's initial sphere of influence is forever delineated by the western and northern Neutral Zone border, but it encompasses entire sectors of space to the east and south east, which the Romulans likely returned to trying to fill up as quickly as possible after the war, in order to ensure they never faced an existential threat so close to the homeworld again.
Which I guess might have worked in theory.
Return Of The Math
So what does all this supposition get us? It implies two distinct phases to Romulan expansion. The first was centuries or even millennia long, and hugely hyper-cautious, as the totalitarian regime took pains to ensure absolute control over every new colony and installation. The second was far faster, after the Empire learned that even a far younger culture could prove a significant threat to them if they enjoyed far greater territory to buffer their central powerhouses, and to draw people and materiel from.
There will have been consequences to this sudden increase in the pace of expansion. In particular, it's not at all implausible that the Senate would find their attempts to maintain their totalitarian approach over such vast distances would fail. We know there were two extended periods in which the Romulans seemed to absent themselves entirely from activity near their western border. "Matters more urgent caused our absence", as the Romulan Captain puts it in "The Neutral Zone". It is possible those urgent matters, on both occasions, represented not (or not wholly) external concerns, but the need to re-repress insurgent tendencies in the Eastern Empire. Indeed, that half of Romulan territory probably oscillated repeatedly between comparative freedom and brutal crackdowns, as Romulus alternated between focussing on stifling internal descent, and dealing with the humans/Federation/Dominion to their west. Indeed, that last war, which occurred on a scale never before seen along the Alpha/Beta Quadrant border, likely provided another opportunity for widespread Eastern unrest, particularly given the assassination of the entire Romulan Senate as part of a failed coup just four years later. Little wonder we see the Empire replaced by the Free State by the time of Picard - the comparatively new and liberal-minded Eastern holdings were already slipping from Romulus' grasp even before they became the new centre of sustainable Romulan power.
All of which is fun supposition. I think it's even plausible, insofar as I can't see any other specific scenario which would be more likely, even if the sheer chain of assumptions here is so long it's likely there's some deviation from it at some point (though again, it's all made up anyway, so Romulan shoulder-pad shrug).
What it doesn't do, though, is get to where my mind really wants to take me, which is the possible population density of Romulan civilisation, and how that would have been affected by the supernova.
The good news on this front is that models of how an interstellar civilisation might expand do exist. Carl Sagan, for one, thought about this quite a bit, though that was a while ago, and there might be some opportunity for bringing it a little more up to date.
The bad news is that Sagan's model isn't based in the find of stochastic processes I cut my teeth on during my PhD, but on differential equations, which I find gross and disturbing.
Fortunately, I know just the person to help me interpret that paper, and build the necessary model, taking the assumptions discussed in this post regarding expansion rates and available space into account. Give us a few months, and we'll see what we can cook up.
For now, though, I'm going to draw a line under all this line-drawing. Hopefully all this noodling has been diverting, if not in any way useful; that's about all one can hope for for any of the posts around this place anyway. Next month we'll be back to our primary purposes, with an essay on the first ever episode of Lower Decks: "Second Contact".
To be continued...
[1] That said, I do enjoy the irony of Earth's zone of influence expanding further in four years than the Vulcans had previously allowed in over a century, in response to a war with what later proved to be a dissident Vulcan faction.
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