Sunday, February 26, 2012

The Boy Who Cried Wolf

A number of political commenters have compared the current Republican contestants unfavorably with Barry Goldwater. The current crop, we are told, are religious nutcases, or possibly pretending to be. Goldwater, on the other hand, was an intelligent and reasonable man, even if not on the right side of every issue.

I have been reading my parents' autobiography, and recently got to the Goldwater campaign. Their description fits my memory. What we were being told then—by people almost none of whom could have done a competent job of explaining Goldwater's positions or the arguments for them—was that he was a dangerous madman. There was even a piece by some large number of psychiatrists, none of whom had ever examined the candidate, explaining how crazy he was. And the TV ad with the little girl, the countdown, and the mushroom cloud.

A while back I read an article attacking Bjorn Lomborg, an articulate  critic of much of the current environmental orthodoxy. It included a respectful reference to the late Julian Simon. Simon,  criticizing the population  orthodoxy, was making reasonable arguments, some of which turned out to be right. Lomborg, on the other hand ...  .

I remember that fight too—I contributed a chapter on the concept of optimal population to one of Julian Simon's books. Back when he was the front line of opposition to the then current orthodoxy, he got the same treatment Lomborg got a decade or two later.

I am not competent to judge the  climate science behind global warming, but I am suspicious of orthodoxies pushed relentlessly in the popular media, orthodoxies that claim that everyone competent agrees on an urgent problem which requires drastic action immediately if not sooner. I remember when we were being assured that it was simply a scientific fact that overpopulation was the cause of poverty and a near term threat to our own well being, if not survival. Also when we were assured that the only way to get the poor countries of the world up to our level was central planning, if possible supported by generous foreign aid.

When I see news headlines about global warming having shrunk horses to the size of cats, along with a picture comparing a cat sized horse to a modern Morgan—you have to read down a bit to discover that the ancestral horses shrank to the size of cats from the size of dogs, from 12 pounds to 8 1/2 pounds, and spent tens of thousands of years doing it—I suspect that what I am seeing is driven at least as much by what people want other people to believe as by the evidence for believing it.

Of course, going back to the beginning of this post, it's entirely possible that some of the Republican candidates are religious nutcases. With the possible exception of Ron Paul, none of them strikes me as someone I would be comfortable with as president. 

But after being told, time after time, that everyone competent to judge agrees with whatever views are currently fashionable with the academic and media elite, reasonable people stop believing it. 

Which brings me back to the title of this post.

Saturday, February 25, 2012

Richard Lindzen on Global Warming

Via a link from Eric Raymond, I've just been reading a presentation by Richard Lindzen, an MIT climate scientist critical of  current global warming arguments. His basic claims:

1. The direct effect of a doubling of atmospheric CO2 should be about a one degree C increase in global temperatures. The substantially larger effect projected in the IPCC reports depends on positive feedbacks in their models.

2. The atmosphere is a sufficiently complicated system so that predicting feedback effects on the basis of theory is difficult or impossible. Insofar as the feedbacks can be estimated empirically, they appear to be negative, not positive.

3. The historical evidence shows about a one degree increase from the past doubling. In order to make that consistent with the models it is necessary to include in the models additional features to explain a lower increase than would otherwise be predicted.

Interested readers should follow the link and look at the presentation themselves, both because my summary may not be entirely accurate--it's based on a single reading--and because there is a lot more there. 

I do not know enough about climate science to judge the argument on its merits. Lindzen sounds convincing, but it would be nice to see what sort of rebuttals people who disagree with him can offer—perhaps some readers can offer links to such. As I have commented in earlier posts, my own criticism of current global warming arguments and policy is based on the economics not the climate science. I have yet to see any convincing reason to believe that an increase in temperature of the magnitude suggested by the IPCC reports would have net negative consequences, let alone catastrophic ones. Apropos of which ... .

Human settlement and agriculture are currently limited by cold not by heat—the equator is populated, the poles are not. If global temperatures go up, more land in the northern hemisphere should become warm enough for human purposes. How big is the effect—by how many miles does the temperature contour shift? I recently did a very rough back-of-the-envelope calculation in response to someone online suggesting that the effect was larger than I was assuming, and concluded he was correct. 

I estimated the rate at which temperatures change as you move north from a page showing that day's maximum temperatures in different parts of the world. Assuming the rate of change is uniform and about the same for maximum, minimum, and average, a three degree C increase in temperature represents a shift of climate contours by more than two hundred miles—enough to more than double the effective area of Canada. Hopefully some reader can point me at a more accurate estimate, but I think that's sufficient to suggest the scale of the effect.

Freeman Dyson, in The Scientist as Rebel, argues that increased CO2 should have a larger effect on temperatures in colder areas. The argument is fairly simple. Water vapor is a strong greenhouse gas. The more water vapor in the air, the less the effect of adding CO2. The colder the climate, the less water vapor in the air. 

If he is right, then the effect on the northern limits of human habitation should be larger than my calculation shows. As far as I can see, the result is a large gain from the standpoint of human beings, via a large increase in the amount of usable land in North America and Eurasia. It would be interesting to compare the size of that increase to the size of the decrease in usable land from the sea level rise of a foot or two suggested by the IPCC models; my guess is that the decrease is much less than the increase, but I have not done the calculation.

One would also expect an increase in average temperatures to raise them at the equator—although by less, if Dyson is correct. I am not sure how large the resulting negative effects would be; people live and farm at the equator, but my guess is that temperatures are already above what would be optimal from their standpoint, hence an increase would be, for them, a loss not a gain.

Tim Lambert, in the comments, offers a link to a page with criticisms of Lindzen's position.

Tuesday, February 14, 2012

Machinery of Freedom (2d edn) is in Print

For some years, the second edition of my book The Machinery of Freedom has appeared to be out of print—shown on Amazon only at high prices from third parties who presumably had stock left over. I just spoke with someone at the publisher (Open Court), who claimed that it had never been out of print, despite Amazon not having it, and referred me to their web page. The book is indeed there, and presumably can be ordered.

Checking with the Wayback machine, I found that it was on their web page during the period when I believed, and various people told me, that it was effectively unavailable—but during much of that time it was listed as "usually ships in 4 to 6 weeks," which raises some question as to exactly what "in print" means. If anyone orders it, let me know whether it arrives in some reasonable length of time.

One reason the question is of interest to me is that I plan to do a third edition. If it has stayed in print, then Open Court still has the copyright and a new edition has to be either with them or with their permission. If it was out of print then, under my contract, the copyright reverts to me. It is not yet clear whether they would be interested in publishing a third edition or, if not, willing to permit me to do so.

I should add that for those who are happy reading books on their screen, the pdf of Machinery is available for free on my web page.

Monday, February 13, 2012

Obama's "compromise" and Behavioral Economics

If I correctly understand it—readers are welcome to correct me if I don't—Obama's "compromise" on the issue of requiring Catholic (and other) institutions to provide employees with health care that covers contraception, is that, instead of requiring them to provide health insurance that covers contraception, they are requiring them to provide health insurance with insurance companies which are required to cover contraception at no additional cost. That's a change in labeling, not substance, hence my scare quotes around "compromise."

It occurs to me that this particular deception may be inspired by the work of Cass Sunstein, now part of the administration, and Richard Thaler. In Nudges, Sunstein and Thaler discuss ways of tricking people into doing things by taking advantage of patterns of predictable irrationality, patterns themselves based on the work of Daniel Kahneman, which I discussed in an earlier post. The reality of what Obama is demanding has not changed, but the appearance has.

Leaving me curious as to whether this is one of Cass Sunstein's contributions to current policy, and if so whether he would describe it as an example of libertarian paternalism, tricking people into doing what (in his view) is in their own interest. 

I hope not.

Sunday, February 05, 2012

Obama and Catholic Voters

Just for a change from talking about my books ...  .

A recent story in the Wall Street Journal argues that Obama has made a catastrophic blunder, one likely to cost him the election, by requiring organizations run by the Catholic Church to provide their employees with health insurance that covers the cost of contraception. It's an interesting claim, and I wonder if it is true.

On the one hand, I suspect that many, probably a majority, of American Catholics do not  accept the church's position on contraception—are, for one thing, willing to use it themselves. One might expect them to accept the requirement, perhaps to approve of it. That might be what Obama is counting on.

On the other hand ...  . Human beings have a very strong aversion to being pushed around. I can easily imagine a Catholic who would be delighted if the church dropped its opposition to contraception, who is entirely willing to use contraception, but who is badly offended by having the U.S. government compel the church to pay for services that violate church doctrine.

One interesting thing about this question is that it will probably get answered. After the election, exit polls will provide fairly accurate information on how many Catholic voters supported Obama. If he does considerably worse with them than with voters in general, relative to his past performance, that will be reasonably good evidence that the Journal is right. If not, evidence that it was wrong.

"Most of us never owned slaves and never expect to,
It takes money to buy a slave and we’re most of us poor,
But we won’t lie down and let the North walk over us
About slaves or anything else."
(from John Brown's Body, Steven Vincent Benét's book length poem on the Civil War)

Saturday, February 04, 2012

No Plot Survives

contact with the characters.

That is one of the conclusions I reached from writing two novels. When I started writing Harald, I already had a complete outline, created in the process of telling the story to my daughter while putting her to bed. I had discovered in the past that she remembered my stories better than I did, which could lead to problems, as in "But Daddy, that magical device they got in the story you told me three months ago will get them out of this situation with no trouble at all." So this time, every evening after I finished telling her a chunk of the story, I went to my computer and outlined it.

Spoiler Alert for Harald

Despite which, someone who was only a minor character in the original version turned into a major character in the written version. Anne was originally the King's mistress who Harald used to feed his view of what was going on to the social set around the King, in order to put pressure on him. He did it by telling the story of how a lady of the Order had saved his life at considerable risk to her own in his first battle—and only revealing at the end that the lady was Leonora, now the lady commander of the Order, who the king had treacherously taken prisoner as part of his plan to take control of the Order. 

By the time the book was written, Anne had become the noblewoman the King was courting and a major influence in the plot. 

It may have occurred to some readers that the King was pretty stupid to fall into Harald's trap and end up his prisoner. The reason was not only that Harald was a much better general than the King. What I never explained but tried to hint at was that, at that point, the King did not much care whether he won or lost, lived or died. As he saw it, he was responsible, through treachery, for the death of a woman who had played a large part in defending his kingdom from its enemies for the past twenty years. The woman he was in love with had made it obvious that she thought he had behaved outrageously and was refusing to marry him. He was hoping that somehow, if he could capture Harald without killing him, he could put things back together, but it did not look likely.

Some of which was supposed to be signaled, for sufficiently perceptive readers, by:
The King sent a boy running for his captain. With luck, this time, …

And either way, at least it would be over.
 Which is why, when he is captured, the King's emotional state is nearer relief than despair. He no longer has to make any decisions.

What is supposed to finally signal what was going on between the King and Anne is a scene a little later, after the King has recognized his error and made his peace with Harald and Leonora, fortunately not dead after all. He encounters Anne:
Anne spoke, surprise in her voice: "You are at peace with Harald?"
"With Harald and with the Lady Commander. In their debt. You were right; I was wrong."
She spoke gravely. "Then if your question has not changed, my answer has."
It was some time before they again noticed the two Ladies.
 Later still, in her escape from the Imperial army, Anne demonstrates a very Harald-like level of ingenuity. 

All of which explains why I think of her as my stealth heroine.

Salamander was not outlined in advance, and the changes from my original plan were much more drastic. As originally conceived, there were three major characters, who I thought of as the good good mage (Durilil), the good bad mage (Coelus), and the bad bad mage (Maridon). The good bad mage invented the cascade for good reasons, not seeing its potential for misuse. The bad bad mage encouraged him, with the intention of taking control of it. The good good mage opposed both of them. The final scene, after the bad bad mage had been killed, was supposed to be a confrontation between the good bad mage, with the power of the Cascade, and the good good mage, with the power of the Salamander. The Salamander gave unlimited power but of a narrow sort; the good bad mage did not realize what he was facing and so kept trying to force his way through the magic of the opposing mage, and when he had completely exhausted his very large but not unlimited power the good good mage took over, reduced him back to a youth, eliminated his memory of everything since he had been young, and adopted him as his apprentice.

Which was an interesting idea, if a bit melodramatic, but not even close to how the plot actually turned out. 

Spoiler Alert for Salamander

By the time I was done, the good good mage had been converted to a secondary character and his place as protagonist taken by his daughter, whose existence had been only a possibility when I started. The good bad mage had seen the error of his ways part way through the book and allied with the daughter, the bad bad mage had gotten burned up, and the remaining conflicts were with people of whose existence I had been entirely ignorant when I started.

Somewhere along the way, not one but two very different love stories managed to sneak in. One was between two highly intelligent intellectuals with limited social skills, one of whom manages to not notice that he is in love for a surprisingly long time, and the other between two sophisticated and socially adept aristocrats, fencing with each other all the way to their eventual engagement.

Friday, February 03, 2012

The Map from Salamander

The map of the College is now up. Not nearly as nice as the map for Harald, which was done for me by a generous professional, but at least it shows where everything is.

Salamander and Central Planning

The central planning fallacy is the plausible, but mistaken, idea that if only all the resources of a society were under the control of some sensible person, wonderful things could be done. It is mistaken for at least three reasons:

1. All those resources are already being used by their owners for their purposes. There is no obvious reason to think that shifting them to the planner's purposes would be an improvement, and some reason to suspect the opposite.

2. Figuring out how to best use the resources of a society is a much harder problem than it seems at first glance—perhaps an insoluble problem. This was the point of the winning side of the calculation controversy, the early 20th century dispute between socialist and anti-socialist economists.

3. Once the mechanisms for central control of resources are set up, there is no reason to believe that the people who end up in control of them will use them for benevolent purposes instead of for their own benefit.

[Spoiler Warning: If you plan to read Salamander, you might want to stop here until you do.]

My original idea for Salamander was a fantasy version of that fallacy. In my imagined world, magic exists but is weak, a frustrating situation for a mage who finds that most of the things he would like to do require more power than he has to do them with. Coelus, one of my protagonists and a brilliant theorist, comes up with a solution, a magical procedure that funnels the power of a large number of mages through one mage who can then use it to do things that no single mage could do before.

The first problem is pointed out by Ellen, his equally brilliant student, when he tries to enlist her in the project of developing the Cascade. She refuses, on the grounds that he will be seizing the power of  mages without their consent.
He looked at the girl in astonishment, felt for words to explain. "You don't understand. There is so much to be done, so little power to do it with. A river floods. With enough magery in the hands of a water mage with proper skills, we could divert the water to where it would be harmless. A plague kills hundreds, mothers and fathers"—his voice faltered—"leaving behind orphaned children. Enough power in the hands of a healer could see the plague when it first struck, cure everyone before the sickness spread farther. So much to do, and we are so weak.

"You are young, sheltered. If you had seen … . I cannot make you aid me. But consider the needless deaths and misery that might happen if you do not."

She shook her head. "My mother is a healer; I have seen sickness enough. Men with gaping wounds that she has closed. When you have seized her power to shift a flood, on whose hands will be the blood of those she cannot heal?"
The second point is never made explicitly, but I hint at it earlier in the same conversation when Coelus, explaining his idea, says:
"Think how much we could do with the pooled talent of fifty mages and five hundred, or five thousand, or fifty thousand ordinary people, each adding his trifle of talent to the pool, pouring it through a trained mage. Almost unlimited power to end a plague, to heal even someone at the point of death, to build a road or monument, to do things that no single mage, whatever his talent, could do before.
The key word is "monument." Along with achieving things that are arguably more important than what mages are currently using their power for, he includes one that might be impressive but is pretty clearly less important. The point is suggested again a little later, when Coelus repeats Ellen's argument to Maridon, the one colleague who knows about his project and supports it. Maridon's reply:
"So they stop killing off bedbugs for rich innkeepers, or healing sick cattle. You know as well as I do that most mages outside the College aren’t doing anything that really matters—not to mention those inside. With this pooled power, we can do things that do matter.  
The arrogance of "things that do matter," meaning things that matter to Maridon, suggests the problem. When Coelus attempts the first full scale trial of the spell, Maridon seizes control of it—demonstrating the third point. Fortunately for Coelus and the world he lives in, something unexpected goes wrong. The Cascade taps an enormous source of fire of whose existence he is unaware, and Maridon burns up.

Coelus' experiments come to the ears of Prince Kieron, the royal official in charge of dealing with magery—himself a mage, as well as the brother and heir of the king. He sees the dangers in what Coelus has invented, both the fact that a mage, using it, might be able to kill the king and seize the throne, and the danger of its use by an enemy army. He concludes that it might be better if the spell had never been invented, but the knowledge at this point will be hard to keep secret, so best to perfect it under royal authority and keep it available just in case it is ever needed. 

By this time, however, Coelus has been convinced, by Ellen's arguments and Maridon's betrayal, that inventing the Cascade was a mistake. He refuses to cooperate in perfecting it. That sets up a conflict between the Prince on one side and Coelus and Ellen on the other. At this point the plot is reflecting a different set of issues, having to do with the dangers of scientific progress; it is not entirely accidental that the Cascade itself involves a sort of chain reaction. 

The Prince's concern, and his conclusion, are not unreasonable ones. That sets up a theme that had not occurred to me when I started writing the book, the question of to what degree the ends justify the means. In some sense, they must—with enough at stake, a reasonable person will be willing to use means that under other circumstances would be considered unacceptable. Kieron, who is fundamentally an honest man, makes that point explicitly in a conversation with Ellen's friend Mari, at a point when he is looking for Ellen as part of his attempt to keep word of the Cascade from getting out.
"If you could get a message to her, asking her to come here and assuring her of safety, would she believe you?"

"Perhaps. Would it be true?"

Another long silence, again ended by the Prince. "No. She sounds an admirable person, and one who might in time prove useful to the Kingdom; I would prefer to do her no harm. But I have obligations to my brother and to the kingdom he rules. If it turns out that the only way of keeping our enemies from learning magery that could be our ruin is to kill a charming young lady, or two, or three, I will do it."
And he makes a similar point to Ellen herself later in the story. Later still, he uses quite unscrupulous means to try to force Ellen and Coelus to cooperate in perfecting the Cascade, in order that it can be used without again killing the mage who is the focus.

The Prince is an antagonist but not a villain, a good person who finds himself trapped in a situation where he honestly believes that he is obligated to do bad things to prevent much worse things. His mistake is being too willing to take it for granted that his judgement of what needs to be done is better than that of Coelus and Ellen, even though he knows that they know more about the subject, at least the magical end of it, than he does. Arrogance not wickedness. As Ellen remarks later: "I do not think Kieron is a bad man, but he is too used to having his way."

One  side issue in the story  is related, not exactly to economics, but to my legal interests. There are traditional bounds on what mages should or should not do with their power—love potions, for instance, more generally compulsion spells of any sort, are banned. 

The traditional enforcement mechanism is a decentralized one. A mage convicted of violating the bounds by a jury of all the mages locally available is banned from the use of magic; if he violates the ban any mage may kill him. This mechanism is in the process of being gradually replaced by a centralized system under royal control, with court trials. 

One of the mages working for the Prince is caught by Ellen using a compulsion spell on her, and charged with violation of the bounds. He assumes that, since the Prince is the one in charge of enforcement under the newer system, he will be let off. The Prince explains to him that the gradual replacement of the old system by the new depends on the mages respecting the verdicts of his courts, and so having no reason to try to apply the traditional approach instead, hence he will be tried and, in all probability, convicted and banned.

At one level, the theme of the book is progress and its perils. The Cascade is made possible by a scientific breakthrough some forty years earlier that represented the first step in converting magery from a craft to a science. The shift from decentralized to centralized enforcement of the bounds is another sort of progress, possibly desirable, possibly not, probably, in the long run, inevitable. The kingdom where it is all set is post-feudal, but with feudal remnants.

One question. I have a map of the College, which is where much of book is set. Would people who have read the book like me to web it?

Wednesday, February 01, 2012

Salamander: Magic and Physics

I originally mentioned the economic element in Salamander, but one commenter asked about the relation of the magic to physics.

Part of what I was doing in the book was trying to sketch an original, interesting, and plausible version of magic. Since the story was largely set in a college training mages, I wanted something that sounded as though it had a deep enough theoretical background to be interesting.

What I came up with was modeled on the mathematics underlying quantum mechanics. As readers familiar with the subject will know, the same particle may be described by a superposition of states of exact momentum or a superposition of states of exact position. At the extremes, a particle with precisely known momentum can be represented either as a certainty of one eigenstate of momentum or as a superposition of eigenstates of position spread across the universe—hence, as per the uncertainty principle, if its momentum is known perfectly its position is entirely unknown—and similarly the other way around.

For an example of the same logic that does not depend on quantum mechanics, consider polarized light. The polarization of a beam of light can be described as a mix of vertically polarized and horizontally polarized. The same beam can be equally well described as a mix of left handed circularly polarized light and right handed circularly polarized light. In particular, vertically polarized light can be described as a mix of left and right handed with one phase relation, and horizontally as a similar mix with a different phase relation, and similarly the other way around.

That was the set of ideas on which my system of magic was based. In my back story, magic was originally thought of as based on the elements: earth, air, fire and water. What Olver, the Newton equivalent in my world who set off the shift of magic from a craft to a science, worked out, was that the elements were merely one basis star, a set of four things which could be combined in ways that describe all magic. But there are lots of other basis stars, each of which can also provide a complete description, and one point of any one star can be described as some mix of the points of any other star--just as a momentum eigenstate can be described as a mix of position eigenstates, or vertical polarization as a mix of circular polarizations. That gave me a structure sufficiently counterintuitive but coherent to work for my  purposes.

I should confess that I did not work out the whole system. In particular, while there is one throwaway reference to "phase," I don't actually know how it fits in. My objective was only to get the description deep enough into the system to be convincing, to look as though there was a real theoretical science there.

One thing that came up in writing the book was the question of how the theoretical structure got figured out. The answer was that two mages, for their own purposes, had put together a very large collection of spells.
"Then Olver showed up, and what he had been looking for was sitting in the library waiting for him. Olver didn't need powerful spells. What he needed were multiple spells doing the same thing in different ways, using different talents. If you could banish horseflies with a spell of fire and air and get exactly the same result with a spell built only on heat, that meant that in some fashion heat was fire plus air. How the spell was constructed let you figure out just how the air and fire were put together. Olver started with more than forty multiples—two or more spells that did the same thing in different ways. When he was finished he had the science of magic as we now know it—the different basis stars, the central paradox that any one star spans all of magery, and the rest. That was the first big breakthrough in three hundred years, since the Dorayans worked out the basic principles by trial and error.
"If he had a spell that used warmth he could make one using air and fire, so mages were no longer limited to using only spells that fit their particular talents. Jon is right; the library came first. The theory of magic was built on the library; the College was built on the theory of magic. The talented came here because it was the only place in the world where they could learn not only what worked but why."

In my next post I plan to explain the link to economics—the Cascade as the magical equivalent of the central planning fallacy.

More on Harald

Having received a gratifyingly positive response to my previous post, I thought I would say a little more about  my first novel, then do another post on my second. 

There are a couple of places in Harald where I mention tactics my protagonist is using to solve the problem of raising an army. One is a scene where he mentions having captured the Emperor's tent, presumably after defeating an Imperial army that the Emperor was accompanying. He talked some of his people into lugging the tent over the mountain pass that separates Kaerlia, where the battle was, from the Vales, and sets it up in his back pasture. One of the people he is telling the story to responds:
"Just what every meadow needs."

"Don't laugh. Silk hangings, tent poles banded with gold. By the time the story spread a bit, every highborn in the Imperial army had gold tent poles and chests full of silver and jewels. Made it easy to raise troops the next time."
 The other is a bit more complicated. Harald forces a large body of cavalry loyal to Iskander, one of the two princes who are competing to be their father's heir, or possibly to replace him, to surrender, and auctions off their horses to the local plains nomads. In a later campaign, he defeats a different cavalry force, loyal to the Emperor. His nomad allies return home with the horses captured in that battle—and offer to sell them to Iskander. The bargaining is between one of Harald's sons and Iskander's son Kiron, who earlier spent some time as a guest/hostage at Haraldhold.
"Name Kiron. Speak for Commander, Governor. Know you Valestalk, Tengu?"

"Getting better, but I still speak your language better than you speak mine."

A long pause.


"In the flesh. Got bored with rabbits."

"This is your army?"

Niall shook his head:

"My brother Donal is war leader for Fox Clan at the moment, four hundred clan brothers. Eagle, Bear, half this end of the plains sent someone along for the ride. Some day you try to get a couple thousand Westkin, fourteen clans, all moving in the same direction. Make running the Empire feel like a vacation."

"And you came along to … "

"Just now, to sell some horses. Thought your father might be interested; heard he was a few short. Cavalry mounts. Trained. Even have the right brand."

"How many horses--trained cavalry mounts with the Imperial brand--are you prepared to sell us? Assuming we can agree on a price."

Niall looked at him, considered.

"Sure you want to know?"

Kiron nodded.

"Four thousand. Don't expect you'll want all of them. Give you a good price, though. Market, this end of the plains, not what it used to be."
It occurred to Kiron that raising and supplying an army off the resources of a mountain farm presented difficulties to which Harald, being Harald, found his own unique answers. This one had a certain wild logic to it.
There is another feature central to the novel which is not exactly economics, although I think it is related both to my being an economist and to my being a libertarian. The central problem of the first half of the book is the attempt by a new and inexperienced king, badly advised, to convert his father's allies into subjects. Part of the reason is that he sees political structures in terms of a table of organization, a formal hierarchy, and is afraid that anyone not in allegiance to him cannot, in the long run, be relied on. 

He is opposed by Harald, the leader of one of the allies, who sees political structures in terms of personal relationships. The alliance was put together by the previous king, who first dropped his father's unenforceable claim to rule the Vales then did everything he could to help the Vales when they were faced with a famine. In the wars with the Empire, he put Harald in charge of the allied army not because Harald had any particular rank but because he was the best commander available. And the alliance was held together in part by the close personal friendship between the king, Harald, and the Lady Commander of the Order. 

During the conflict between Harald and the new king, it becomes clear that one of the most powerful of the provincial lords, the feudal level just below the king, is a de facto ally of Harald's even though nominally obedient to the king. And part of the point of the first half of the book is that Harald's real objective is not to defeat the king but to educate him, and so to recreate the old alliance.

Incidentally, for anyone interested, the book can be bought on Amazon, downloaded free from the Baen free library, or downloaded free as podcasts from the book web page.