Fridge logic: Ender's Game

Okay, so we've got hyper-intelligent children. We've got antigravity and instantaneous FTL communication and (if only in the first three pages of the book) direct neural interfaces. We've got bug-eyed, telepathic space aliens with hive minds, and a nasty breed of wasp that stings without waiting to be insulted first. We've got a Fantasy Game which cannot quite decide whether it is HAL or merely Eliza.

And we accept all that because science fiction is all about disbelief properly suspended. We accept that interstellar war works exactly like Napoleonic-era land warfare, except that it's in 3D. One side's army meets another side's army at a designated time and place in empty space, and then they have a battle, and one of the armies win. Each battle can be planned and fought and won in a single sitting, 10 to 15 hours tops (this appears to imply that battles take place on a spatial scale much, much smaller than the distance between IPL and Eros, which takes three months to traverse in the fastest available craft). We even accept that Special Relativity seems to apply only halfway, because time dilation does occur but everybody shares the same time coordinate, or the ansible would make no sense.

I don't complain about any of this. Really. It's okay.

But I've been wondering about the Battle School and how it hangs together on its own premises.

See, the point is to take gifted children and train them for military command from an early age. You want to identify and stimulate those children who turn out to excel at leadership. They'll get the most demanding subsequent education and have golden career paths ahead of them. Those who don't excel quite that much will nevertheless end up commanding something. "None has retired from a position of lower rank than chief executive officer on an interplanetary vessel".

However: Not many of the Battle School students seem to get much, or any, hands-on command experience. Commanders do, of course. Toon leaders, perhaps. The subtext seems to be that before Ender, toon leaders are mostly for passing on the commander's executive decisions. But the majority of students are common soldiers, whose responsibility is limited to keeping formation and shooting straight. That's supposed to prepare anybody for command? Are two thirds of the children the I.F. spends fortunes launching into orbit doomed to never get a chance anyway? Or is the system set up such that almost everyone get a turn at commanding before they graduate? (Mick implies as much: "All the guys from my launch have their own teams now. Not me.")

So I sat down to do the numbers on the Battle School, in its pre-Ender steady state.

We have some hard input data. An army comprises a commander and 40 kids, 4 of which will be toon leaders. We don't know how many armies there are, but that's OK; everything will scale with the number of armies. Students enter the school at age 6. They are promoted into an actual army after they turn 8. The earliest possible graduation is at 12 years, but I cannot find a definite source for the typical graduation age. Let's put it at 13 years; that leaves three years for pre-Command before entering Command School at 16. Now if we can estimate the average time a commander is in command before he graduates, we can compute the percentage of students who get to be commanders at some point in their course.

Major Anderson tells us that "Usually they go [commander] at 11". That leaves one or two years of command before graduation, which is consistent with other data. For example, fresh commanders do not have battles for the first three months; they would need to be in the rotation for battles for an appreciable multiple of that time, or comparative rankings of armies and soldiers would be meaningless. Battle is usually every two weeks. When we first meet Bonzo Madrid, we hear that "Salamander Army is just beginning to emerge from indecent obscurity. We have won twelve of our last twenty games", which presumably means 20 games since Bonzo's three-month break-in period. Thus Bonzo has been a commander for just about a year ...

Um, wait just a minute here.

Three years after that, Bonzo is still commander in Salamander Army when he fights Ender in the shower. A short time before that Graff tells General Pace that if Bonzo were to be graduated now it would be "ahead of schedule" and reveal to Ender that he is being protected. However, by then Bonzo must be at least 15; he would be long overdue for graduation.

Ladies and gentlemen of this supposed jury, it does not make sense!

And it's not just Bonzo. Ender joins Rat Army a few days after his 7th birthday; at that time Dink Meeker is a toon leader in Rat, but has been promoted (and refused) commander twice. He is also still at Battle School when Ender graduates. In Ender's last battle for Salamander, the opponent is Leopard, commanded by one Pol Slattery. And in the morning of the shower fight, Ender commands Dragon against Pol Slattery's Badger Army. If it's the same Pol Slattery, he must be around 14 at that time.

Even worse things surface if we turn to Ender's Shadow. There, on the day after Ender graduates from Battle School, Bean goes to the commanders' mess and extempores a speech against the the competitive standing system. Among the senior commanders that he has to convince, we find Shen and Alai! Those two are explicitly from Ender's launch, but now they're suddenly commanders, at most a few months after Ender himself went commander at an impossibly young age.

Has Orson Scott Card no respect for chronology?

Of course he has. But, for the ansible to work, he needed to find somewhere to stow away that pesky relativity of simultaneity from SR, to wit, at Battle School. Only here it does not apply to observers with a nonzero mutual velocity; it applies to students in their respective courses of study.

P.S. Join me next week when I model the economy of Lusitania. How many full-time brickmakers can it sustain?

P.P.S. Just kidding.

P.P.P.S. Obligatory xkcd reference.