The book of Job

I've neglected to write anything here recently. Perhaps I should save some of the more self-contained comments I write in other places, to give people a better chance to tell me how mistaken I am. Here's my reaction to a recent Slacktivist post:

I've tried several times to read the Book of Job, but always had to give up about a third way in. The prose set-up is readable enough, but then the speeches start, and they make my eyes glaze over. The only content I can get from them is "a really, really verbose shouting match". The speakers assert their position with great eloquence, repetition, and doubtless masterful poetry in the original language. But while there is much asserting going on, essentially no arguments are presented. And I've not found a line where anyone even pretends to address a point their opponent has made.

The friends repeatedly implore Job to step down and make peace with God again and then everything will be alright (despite, as told in the prologue, that everything went bad while Job was behaving examplary), mixed with alternately chiding Job for complaining and hinting that it must all, somehow, be his own fault. Job, in turn, does not attempt to clear up this misunderstanding but prefers to switch between heaping big flowery loquacious abuse on God and heaping big flowery loquacious abuse on his friends for their (admittedly inexpert) attempts to cheer him up.

This goes on at least until about chapter twenty-something, at which time I admit defeat and put down the bible in exasperation.

If it's a play one could at least try to defend it as a magnificently tongue-in-cheek satire on how different religious viewpoints simply cannot communicate in any meaningful way, because they fail to listen to each other. But that somehow sounds a bit too modern of a morale.

I think I even prefer Plato. Yes, everyone Socrates speaks to is a strawman, but at least they're strawmen who pretend to care what Socrates is saying, and vice versa.

[Original comment thread].

Rindler's relativity textbook

An open letter.

Dear Professor Rindler,

I write to thank you for writing Relativity: Special, General and Cosmological. I picked it up by chance at a university bookstore several years ago, and I've found it to be very enlightening and well readable.

I'm what one might call a physics amateur – not quite a physics student, certainly nothing resembling a researcher, but possibly a step up from the "educated layman" level. I like to extend my understanding of modern physics, for my own amusement and a sense of moral duty for a thinking being to at least try to understand the world he finds himself in. Here, by "understanding" I mean something deeper than memorizing some popularizer's free-floating qualitative assertions and analogies. Luckily, as a computer scientist with a B.S. in mathematics, I am no stranger to formulae – a mathematics-free understanding of any area of physics appears to be an oxymoron.

It is not easy to find good literature for a project such as mine. There are, of course, many books that purport to explain modern physics to laymen, but they all studiously avoid presenting any mathematical content of the theories they speak of. (The only exception I have encountered is Roger Penrose's The Emperor's New Mind, which however covers so much ground that its treatment of any particular subject is very brief). Even when they manage correct qualitative descriptions of a theory, they cannot, lacking formulae, convey a good sense of the predictive character of the theory. As for general relativity, popular works tend to stop at the rubber-sheet analogy, usually without even developing it enough to make it clear whether they try to depict spatial curvature or graph gravitational potential.

On the other hand, actual university textbooks tend to be too dry for the amateur. They often dive straight into formalism, with much time spent on methods of concrete calculation and little emphasis on intuition and perspective. The amateur (meaning I) tends to have little patience with problem-solving tricks; he wants to understand the structure of the theory more than he wants to apply it in practice (though, of course, one person's clever computational shortcut can become a basic feature of another's theory – as I understand it to have been the case for quantum electrodynamics). And above all, he needs hints about intuition and perspective. Intuition without mathematics is for cocktail-party philosophers, but mathematics without intuition is for robots. Apparently most textbook authors rely on the instructor for supplying students with the big picture, which is not unreasonable but does not help for self-study.

Your book, however, is a rare gem: A text that both teaches the formalism of the theory and explains what it means intuitively. In reading some of the sections, I have followed the mathematics carefully, checking derivations and doing exercises. This gives me a solid sense of knowing what goes on. In other sections I have skipped most details of the formulae but still got a general picture from the connecting text. This general picture is, in a sense, second-hand knowledge, but feels more secure than that, because the mathematical details are right there should I ever want to check them.

It is very wonderful that the book is capable of being read both ways.

I'm convinced that this book has made me smarter. It has enabled me, in many discussions with fellow amateurs, to correct (I hope!) misconceptions and confusions caused by fuzzy and imprecise popularizations of GR and black holes. I have been recommending it left and right. I'm very happy that it exists, and that I discovered it.

Sincerely yours,

Henning Makholm

* * *

Respectfully recommended for your reading pleasure: Relativity: Special, General and Cosmological by Wolfgang Rindler (Oxford University Press, 2001; 2nd ed. 2006). This book will teach you everything you want to know about special relativity (saw the Lorentz transform in high school and thought it was all there is to it? Think again), general relativity, black holes, as well as a fair overview of cosmology and tensor calculus. The preface promises: "Anyone who knows the calculus up to partial differentiation, ordinary vectors to the point of differentiating them, and the most useful method of approximation, the binomial theorem, should be able to read this book." As far as I can tell, that is what it delivers.

Fridge logic: 2001, A Space Odyssey

– So basically we have no idea what the damned thing is for?

– Basically no.

– Or why the Chinese went and buried it under umpteen tons of moon rock?

– Well, we don't really have solid evidence that it's Chinese in the first place. It's just the working hypothesis that appeared to be least crazy at the moment.

– Hrmf. What are some of the more crazy working hypotheses?

– Natural geological formation. Aliens from outer space. Something truly evil that the NSA cooked up and have not told the rest of us about.

– Look, I know we're famous for eating little children, but could we please cease the interdepartmental potshots until we're sure the nation's security is not under imminent attack?

– Hey, he asked for crazy theories.

– Yes, and I'm sorry for that. So what I hear is that the Chinese connection is not as solid as we thought?

– Some of our analysts are pretty certain that the Chinese could not possibly have reached the spot with more than two astronauts for 5 hours without our knowing it when they went up in 1998.

– Well, personally I think it is still the least crazy theory, but I concede it is plenty crazy already.

– What about the Russians?

– Don't be silly.

– Okay, gentlemen, we know absolutely nothing. The question is, what do we do about that? We can't realistically delay briefing the President more than until tonight, and whoever goes talk to him has better have some recommendation for concrete action with him.

– Isn't that obvious? Since we don't know anything all we can do is wait until the scientists up there get us some more information.

– How is that "concrete action"?

– One thing we do have to decide is whether to go public with this or not. I'm all for putting a lid on it, but we could get into really nasty stuff if we hush it up now and then –

– I will not accept any public announcement for as long as there's a risk that this is some kind of Chinese superweapon.

– How could an inert featureless slab of whateverite be a weapon? It doesn't even point towards the earth.

– Let me tell you –

– There are rumors that it is making our people sick somehow. Some sort of bioweapon.

– Rumors, which kind of rumors? Unless I've been severely misinformed, nobody on Earth even knows the thing exists except for a few deeply trusted people who all report directly to somebody who's present in this room, and don't know who else knows. So who is spreading rumors to whom?

– Correction. The rumors do not mention this TMA thing, but there are rumors that people in Clavius are falling ill like flies.

– A natural assumption given that the base has been quarantined since yesterday afternoon. It's utterly false, but we've been discreetly encouraging it. There has to be some explanation.

– Great. We'll have the world press poking into this in a matter of hours. Then afterwards we'll have to defend not only withholding information but also lying.

– All in a day's work for you, I'd think.

– Stop that, you two. I'm more concerned about security at the site. There are two thousand people stationed on Clavius, and at least two hundred of them are aliens. The rest are civilians without any security indoctrination to speak of. I'd prefer if we –

– 1700.

– What?

– There are 1700 people in Clavius, not 2000.

– Thank you for that highly relevant correction. Now, is there any way we could get some actual military –

– Look, even if we had the ability to deploy any significant number of troops to the moon on day's notice – which I'll neither confirm nor deny even to this exclusive audience – we'd be running openly afoul of any number of international political commitments if we did. And for what good? Soldiers are not some kind of magical pixie dust that just makes everything right. We'll fight any known enemy that we can see and know how to kill, but I thought we agreed that such an enemy is simply not present on the moon right now.

– What I meant was –

– I say we pull the digging team back to base and then nuke the thing.

– WHAT?!

– I'm not even going to dignify that with a response.

– Gentlemen, please!

– Wait a moment .. I think I've got it!

– Yes?

– Let's just send a senior NASA bureaucrat to the moon and have him look at the thing in person!

– By golly! That'll solve all our problems.

– Good thinking, man.

– Excellent. We have a plan. Heywood, you're going.

– What, me?!

– Yes, you. Judging from past performance, you've contributed absolutely nothing of value so far, and you might as well continue doing that up on the moon.

– But I have to be at a tennis tournament next –

– Our hearts weep. Cancel it. I'll have one of my people put together a powerpoint for you to show to the Old Man, but you'll have to do the talking. I propose Justin go with you and provide moral support. Any other protests? Good. David, can you tell your people to start warming up a rocket or something for Dr. Floyd to go in?

* * *

Seriously, though, why did Heywood Floyd go to the moon? A fair part of 2001: A Space Odyssey is devoted to his journey, which proceeds with considerable haste and at enormous taxpayer expense. But it never becomes clear that there is anything he's uniquely qualified to do once he gets there, save for just being at the center of a Visiting VIP Tour. He does get a glowing but nonspecific introduction before he gives a peptalk on the moon base, though.

In reality his only purpose is to show us, the readers, around. He's a Watson without a Sherlock. Come to think of it, this describes many of Arthur C. Clarke's protagonists.

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.