Trackmap.net changelog

Back in 1996 when the web was young I started a website to host my collection of railway track diagrams. It eventually became trackmap.net. It has updated in fits and starts – the last time it did so was in early 2006 – but I still plan to get time to do updates in the future, such as the maps from this summer's Frankfurt trip.

Despite the irregular updates, trackmap.net was probably my main claim to Internet fame, until I wrote xcftools (which, incidentally exists solely because I needed it for producing track maps easier). Up until now, I have updated a static recent changes page whenever I did something – but seriously, nobody is going to look at that very often to see if there's any news, what with the multi-year hiatuses.

But perhaps some readers would find it useful to subscribe to an RSS/Atom feed for updates to trackmap.net and have their feed reader check it quietly for them? That sounds like a plan. So here is what I'll do: Every time I update trackmap.net (or its subsites) in the future, I'll post about it on this very blog, with the label "trackmap.net".

The label search page becomes the new changelog page, and the feed for new updates is here (Atom) or here (RSS). (Note: These feeds will show only posts related to track maps. If you select the Blogger-provided feed link in the navigation bar, you will get my full blog feed where I blather about various other topics at irregular intervals).

Old changes are still at http://dk.trackmap.net/news.

This posting serves to populate the trackmap.dk labels such that the links just given will not be empty.

Java 5.0 type inference is underspecified

Here's a program that will make your brain hurt:

class C<E> { }
class G<X,Y,Z> { }
class P { }
class Q { }

public class Test {
   static void foo(Object o) {
      System.out.print("Object ");
   }
   static <T> void foo(G<? extends T, ? extends T, ? extends T> g) {
      System.out.print("G ");
   }
   static public void main(String[] args) {
      foo(new G<C<? super P>, C<P>, C<Q>>());
      foo(new G<C<? super P>, C<Q>, C<P>>());
      foo(new G<C<P>, C<? super P>, C<Q>>());
      foo(new G<C<Q>, C<? super P>, C<P>>());
      foo(new G<C<P>, C<Q>, C<? super P>>());
      foo(new G<C<Q>, C<P>, C<? super P>>());
      System.out.println();
   }
}

Quick, what does it print? No cheating!

For what it's worth, Sun's reference javac, version 1.5.0₀₇ produces a .class file that prints

G G G G G G 

whereas Eclipse SDK 3.2.1 creates one that prints

Object Object G G Object Object 

Normally this would lead one to point at one of the compilers and shout BUG! – but after several hours of close reading the Java Language Specification I have come to the conclusion that both behaviors adhere to the letter of the specification. In other words, it is entirely up to the whims of the compiler which of the foos gets called in each of the six calls.

This is somewhat remarkable. Sun has otherwise gone to great pains specifying exactly what a Java program is supposed to mean, modulo the a few clearly defined areas where the virtual machine – not the compiler! – is explicitly given discretion. But here is a completely straightforward single-threaded program where (so I assert) the language underspecifies which method is supposed to be called.

Such nondeterminism makes it hard to do static analysis of Java source code. What happens?

Broadly speaking, generics happen. The half of generics that gets all of the press is parameterized types, but the really hairy stuff only begins to happen when we consider parameterized methods, too. The reason for this is the the programmer always needs to write down the type parameter explicitly in order to instantiate a generic type – but the designers of Java's generics decided that explicit type arguments should not be necessary for calling a generic method. It is possible to give type parameters explicitly in the code, but in the common case, the compiler must try to infer appropriate type arguments given the types of the ordinary arguments.

And this is fairly hard. In fact, because subtyping gets into play, it is so hard that the language makes no claim that the compiler can always find appropriate type arguments when you want to call a parameterized method. The language specification itself remarks, in the middle of the 16 pages of extremely technical definition of how the type inference works:

[...] type inference does not affect soundness in any way. If the types inferred are nonsensical, the invocation will yield a type error. The type inference algorithm should be viewed as a heuristic, designed to perfdorm well in practice. If it fails to infer the desired result, explicit type paramneters may be used instead.

Still, however, one would expect the inference to be deterministic such that one would not risk changing the behavior of a program just by recompiling with a new version of the compiler. But perhaps "perfdorm" and "paramneters" is a hint that this section has not received the most thorough of proofreadings before it went to press.

In the example program above, the type inference eventually computes that T should be instantiated to the "least containing invocation" of an unordered set of the three types C<? super P>, C<P>, and C<Q>. I now quote:

[...] lci, the least containing invocation is defined

lci(S) = lci(e₁, ..., e_n) where e_i in S, 1≤i≤n
lci(e₁, ..., e_n) = lci(lci(e₁, e₂), e₃, ..., e_n)
lci(G<X₁, ..., X_n>, G<Y₁, ..., Y_n>) = G<lcta(X₁, Y₁),..., lcta(X_n, Y_n)>

where lcta() is the the least containing type argument function defined (assuming U and V are type expressions) as:

lcta(U, V) = U if U = V, ? extends lub(U, V) otherwise
lcta(U, ? extends V) = ? extends lub(U, V)
lcta(U, ? super V) = ? super glb(U, V)
lcta(? extends U, ? extends V) = ? extends lub(U, V)
lcta(? extends U, ? super V) = U if U = V, ? otherwise
lcta(? super U, ? super V) = ? super glb(U, V)

[The Java Language Specification, third edition, p. 465]. Read the definition of lci carefully. The first line says that we arrange our three types in some unspecified order. The second line says to combine two types at a time using a two-argument version of lci. And the two-argument lci in the third line just distribute lcta over all the type arguments. (We know from earlier in the type inference that all arguments to lci are instances of the same parameterized type).

This would be a nice and standard construction if only lcta (and by extension the two-argument lci) were commutative and associative. It is indeed commutative – it has to be, for the cases given in the definition only make sense if we understand implicitly that we are to take their commutative closure. But it is manifestly not associative. To wit:

(? super P) lcta (P lcta Q) = (? super P) lcta (? extends Object) = ?

whereas

((? super P) lcta P) lcta Q = (? super P) lcta Q = (? super P & Q)

In the former case, the parameterized foo is not applicable to the call with T = C<?>. Therefore, compile-time overload resolution decides on the less specific but viable foo(Object) instead. But when T is C<? super P & Q>, the parameterized call is applicable.

How clever of javac always to choose the evaluation order that reaches the better result! In fact, I suspect it of cheating and using a smarter multi-argument lcta computation for each type-argument position, instead of selecting on a common order of all lci arguments. Extending the example program to test this hypothesis is left an exercise for the reader.

(Also left for the reader is to figure out the exact meaning and properties of ? super P & Q, a possibility not hinted at anywhere in the JLS except for the two occurrences of "? super glb(U,B)" in the definition of lcta).

Does P equal NP? This is not an answer.

A preprint by Sten-Åke Tärnlund, purporting to prove that P≠NP, is making its rounds on the internets. I noticed it through a blog post by Bruce Schneier; he quite sensibly notes that "these sorts of papers make the rounds regularly, and [Schneier's] advice is to not pay attention to any of them."

Still, someone has to try to pick such papers apart, if only to make sure that they are as worthless as statistics suggest. I'll volunteer for this one. (This mini-review was originally intended to be a comment to Schneier's posting, but grew a bit too large for that. Also, I want to use markup that plain-text comments cannot contain).

It is not easy to figure out what the author is getting at, because the paper is pithy to the point of sloppiness. Take, for example:

Definition 8 p(a) for c·|a|^q some c q ∈ N any a ∈ L.

By comparison with other similarly terse definitions, this apparently means

Definition 8. Let p(a) abbreviate c·|a|^q for some c and q in N, and any list a.

But what are the scope of the quantifiers on c and q? Are they constant throughout the paper or can they depend on something? What can they depend on? It makes no sense in context to let them depend on a ... Complexity theory has no lenity for those who fail to be rigorous about order and scope of quantifiers.

Formally, the paper begins to go wrong no later than Definition 13, where T(s,a,u) is defined to mean something that involve the "truth" symbol ⊨ (or |= if your font, like mine, has no native Unicode glyph for this symbol), which is not in the language of B – but in the remainder of the paper T(s,a,u) is treated as if it was a formula of B, and bogosity ensues.

Of course, a formal error does not mean that the idea behind the paper is flawed. But it does not bode well – one would think that an author who is smart enough to solve an open problem as famous and long-standing as this would be more careful. Indeed, a true flaw shows up:

As far as I understand it, the main argument in the paper goes somewhat like this: Assume that you give me a Turing machine that purports to solve SAT (i.e., decide whether a propositional formula is a tautology) in polynomial time. Then I'll try to run a sufficiently large "pigeonhole formula" PF_m through your machine. I already know that this formula is a tautology, but if your machine tells me that in polynomial time, I can extract a short proof of the formula from what the machine does. This contradicts a theorem by Haken which says that proofs (in a certain restricted form) of the pigeonhole formula are always long. Therefore, your machine either does not solve SAT or does not do it in polynomial time.

What first meets the eye here is that the paper appears to redefine SAT. The SAT we all know and love is about propositional formulas (i.e., expressions built from Boolean variables and the Boolean operators not, and, or and so forth). However, PF_m which the paper tries to use the SAT solver on is not propositional. It is defined only informally here, but for it to have any relation to Haken's theorem, it needs to contain non-Boolean variables and equality operators. Those belong to predicate calculus, not propositional logic. However, this is not in itself damning, because satisfiability in the pure first-order theory of equality is easily seen to be in NP. A valid proof that this is outside P would also solve the P=NP question.

Correction (2008-11-09): It turns out that there are indeed purely propositional formalizations of the pigeonhole principle, and the paper must be referring to one of those. I had in mind a formula such as "(a=1 or a=2) and (b=1 or b=2) and (c=1 or c=2) implies a=b or a=c or b=c". What I did not notice (and, in my defence, the paper never writes out an example of its PF_m) was that we can just expand, say, "a=b" to "(a=1 and b=1) or (a=2 and b=2)", in which case we can take things like b=2 as propositional variables.

The true fallacy here, however, is the tacit assumption (partly concealed as Definitions 13 and 14) that if we have a Turing machine that recognizes tautologies, then a short proof that this machine answers yes for a given formula corresponds to a short proof that the formula is indeed a tautology. But this is not necessarily true; it is at least conceivable that there is a fast Turing machine that recognizes tautologies but that we cannot prove that this is what it does. In that case, a trace of the Turing machine's action does not correspond to any proof that the formula is a tautology, much less a short one. And even if the machine provably recognizes tautologies, we cannot necessarily extract a short proof in a particular formalism from a short run of the machine.

There is various additional smoke and mirrors, including the central proposition which is stated thus:

Theorem 1 SAT ∉ P is true in a simply consistent extension B' of theory B.

Does this mean simply that there is some consistent extension of B in which SAT is not in P, or that SAT∉P is true in every consistent extension of B? I cannot tell. In the former case, the proposition says nothing about the standard model for B (i.e. Turing machines modeled with the standard integers, which are not necessarily a model for the extension). In the latter case, why bother speaking about extensions in the first place?

In conclusion, Schneier is right, and this can safely be ignored.

Legal consistency

Some time ago I asserted that American court opinions "are fairly accessible once one learns a few key words and turns of phrase". Suddenly I begin to doubt that.

In EEOC v. Lee's Log Cabin (7th. Cir, 2008-10-06) I read this marvellous piece of logic:

The dissent also asserts that "[i]t is undisputed that at all relevant times, Stewart was not only HIV positive . . . but she also had AIDS. So the allegation in the complaint that Stewart was 'HIV positive' is consistent with the fact that she has AIDS." Dissent, at p. 18. No, it's not, but the opposite is true. That is, an allegation that Stewart has AIDS is consistent with an allegation that she was HIV-positive, but not vice versa. If a person has AIDS she is necessarily HIV-positive; but a person who is HIV-positive does not necessarily have AIDS.

(footnote 3). In the kind of logic I was taught, "consistency" between two propositions means that it is conceivable that both can be true at the same time, or (more syntactically) that assuming both will not let you derive a self-contradiction. This is a symmetric notion. It makes no sense to assert that A is consistent with B yet B is not consistent with A.

I wonder whether there is a particular legal meaning to "consistent" which is different enough from the logical one to make the above quote senseful.

More precise than a million monkeys with typewriters

Ferdinand Foch is remembered for remarking, when the Treaty of Versailles was signed, that it was "not a peace but a 20-year armistice". This was eerily prophetic – he was right to within a handful of months. Foch must have had an unusually precise sense of the forces that make history go.

Or did he? I wonder how many would-be prophets characterized the treaty as an armistice for 10, 15 or 25 years, and were quietly forgotten by history.

It's easy to pick successful prophecies when you're allowed to wait until they come true before you decide which prophecies to point to.

Why copyright is doomed

In the beginning there was no copyright.

Books were written (and music composed) by men of independent means, or by talented men sponsored by princes and nobles, or by scholars or clerics who were fortunate enough to have the power to decide that writing a treatise on this or that just happened to be part of their own duties. Somehow world literature got along.

Then somebody invented the printing press. The press, together with other technological advances during the 1400s, made mass production of printed books a feasible alternative to hand copying of manuscripts. And this changed everything.

First and foremost, printing books is a capital-intensive undertaking. In addition to the cost of the printing press and its various paraphernalia, setting type by hand is slow and costly. It makes sense to analyze the typesetting cost as capital rather than labor, because once the type is set, you can print copies of the book very cheaply. You can make your customers pay quite a bit more than your marginal cost for each item you sell, which will allow you to break even in the end. And the customers are not going to care whether you've broken even or not, so you can still charge the high price after you break even. If there's enough demand for the title, printing books can be quite a profitable business.

Now, printers who choose to print books that turn out to be popular become rich; printers who choose badly do not. If we assume that the popularity of one title over another is due to some special talent or effort expended by its author, it begins to look quite unfair that the printer should become rich because of them and the author get nothing. That is what the first copyright laws set out to remedy, after the changes wrought by Gutenberg had had a few centuries to sink in.

Actually, it was a bit more complex than that. Publishers – who around this time were emerging as a separate trade of funders and distributors of books – also benefited from copyright: Regulation of who could print what reduced the risk that another publisher would start printing the same book, leading to a price war (which would lose money for both printers as the the price per copy dropped towards the marginal production cost). But the moral justification for having a copyright system in the first place was that it let authors get a cut from the profit when the quality of their works became the foundation of somebody else's business.

During those same centuries, medieval religious drama gave way to professional theatre, and instead of semi-improvised lines that changed with time according to audience reactions and the actors' own wit, plays came to have written-down scripts authored by named playwrights. Theatre was now a business, and a company could make a profit with a good performance of a good play – and thanks to the printing press, the playwright need not be affiliated with the theatre company.

In music, partly in response to the demands of theatre, ensembles grew in size and complexity – beyond the point where the performance could be structured by oral agreements and remembered tunes. Music notation expanded to meet the needs of orchestrally scored music. Eventually the public concert where professional orchestras performed for paying audiences was invented. Having a good work by a recognized composer on the billboard certainly helped draw in those paying audiences.

Playwrights and composers must now suffer that not only could publishers make a business of printing their work, companies and orchestras could make a business of performing them. In response, copyright expanded to cover "public performances" in addition to simply the making of physical copies.

As I have insisted above, the moral purpose of copyright was still to save creators from the indignity of seeing somebody else build a profitable business upon their work without getting a share of the success themselves. But as a side benefit, creators who did create successes got an income source and the opportunity to quit their day jobs and create yet more successes. This benefits society as a whole. It was seen as an independent motive for copyright as early as 1787, when the drafters of the American constitution allowed for federal copyright legislation "to promote the Progress of Science and useful Arts".

Sound recordings were invented in the late 1800s and quickly integrated into the basic structure of copyright. They fit well there, because it requires specialized and expensive equipment to manufacture records, and large specific costs to prepare a recording for being mass produced – exactly the qualities that made copyright the right legal tool for printed books centuries earlier. As for books, creators of successful records have been able to quit their day job, sometimes spectacularly so.

Movies also got copyright. Again, production of film prints is a specialized commercial operation, and public performances is usually organized by businesses too. This fits the philosophical framework of copyright fairly well – though in comparison to a novel or a symphony, which are usually the work of an individual genius, creating a movie is quite a team effort. Copyright fairly easily let itself be extended too deal with large team efforts.

In each of these successful cases, copyright has felt like a right and just tool, because the activity being regulated – whether printing a book, performing an opera, stamping a record, or showing a movie – was naturally and necessarily a commercial undertaking. Done by a business. For a profit, which it is only reasonable to share with a creator.

Well, well, well. Guess what is not true anymore?

We see the underlying assumption break down most clearly for recorded music. For at least a decade there has been no practical reason why copies of sound recordings need to be made by a business rather than by private individuals. The technology is cheap and ubiquitous, and the shift in public perception of copyright has been quick and pervasive. Very few people today really feel that it is morally wrong to create an unlicensed copy of a commercially released song they like. Those of us who nevertheless refrain from doing so do it for the warm fuzzy righteous feeling of complying with the law even when the law is unreasonable.

Movies are not far behind music in this development. Many kinds of books still hold out, because people like the feeling of real bound paper books better than reading from a computer screen. But if print-on-demand hardware becomes ubiquitous enough that bound paper books are not made by specialized businesses anymore (or if really acceptable ebook readers emerge), I predict that the respect for copyright of books will go the same way as that for music. And, of course, already some kinds of non-fiction books are dying breeds, being replaced by free internet versions.

Music and movie publishers everywhere know all this, and are understandably all up in arms. Their response so far is threefold:

1. Try to put the genie back into the bottle. Have copying technology outlawed or forcibly crippled. If this prevents amateur artists from creating their own works that may compete with commercial offerings, then so much the better.

   If successful this would lead to a nightmare world, but I don't think our politicians are that stupid. We have Vernor Vinge, Cory Doctorow and the EFF to explain why this shouldn't succeed; overall they do it well enough that I think it won't.

2. Lobby legislatures to introduce ever more draconian laws to enforce copyright. Hope that you can bludgeon people into following rules out of fear that they won't follow out of fairness.

   At best, this is a short-term stopgap. At worst ... well, it doesn't really seem to have the desired effect out in the real world, does it? If anything it seems to reinforce the perception of copyright as an instrument of oppression, rather than a rule that works for the common good.

3. Appeal to everybody's better nature such that we will all begin to think it is wrong to make private copies of music even if no business is involved. This is the "artists deserve compensation" argument, and it is very convincing on its face. It is also, I think, subtly flawed, and the main point of this essay is to explain what is wrong with it.

   The hidden assumption of the argument is that the creator suffers some kind of moral wrong each time someone enjoys his work, and that the purpose of royalties is to compensate him for that wrong. But what is that wrong? It cannot really be the lack of opportunity to capitalize on the copyright, because the whole point of the argument is to motivate copyright in the first place. But stripped of that explanation, the assumption is simply stupid – creators want their work to be enjoyed, and are pleased when people do so. True, they also want to quit their day job, which requires that income can somehow be derived from the work, but it does not follow that this income has to be in the form of per-copy royalties. And wanting the conclusion to be true does not make the argument hang together.

I think all three responses are likely to fail in the end. Copyright is doomed. It may take decades, or even centuries, for it to die out completely, especially because it has been entrenched in international treaties which are very difficult to change. But die out it must, for it cannot persist in a world where copying is no longer expensive and complex.

This state of affairs creates a political obligation to think ahead. We still want want the world of tomorrow to be one where talented creators can quit their day job and create more. The challenge is to think up a system that does this and still respect the technological reality.

It is tempting to take as a starting point that creators should be rewarded in proportion to the enjoyment people derive from their work. But the trouble is that enjoyment is not easily quantified. In a way, the copyright system uses "number of copies" as a proxy for "amount of enjoyment", which works rather poorly. When making and keeping a copy is cheap and easy, people are likely to keep a copy of every work that they don't actively dislike, whether that work is one of sublime genius or merely passable.

There's a movement towards using "number of listenings/readings" as a proxy for amount of joy, such that if you want to read a book again you have to pay anew. This doesn't work well either. Many a time when I sit down to read a book, it proves to cause me no enjoyment at all and I conclude that the book is horrible. And when I reread a book it may not be because I enjoyed it the first time, but because I need to look up a dry fact about it.

I doubt a working calculus of joy can be developed. How about explicit public subsidies to outstanding creators, awarded by expert committee? That is already common in countries with languages that are perceived as too small for a national literature to flourish funded entirely by copyright, such as Danish. But I don't think it is attractive as a general solution; too much power is concentrated in the hands of the committee, and even with the best of intentions the committee cannot possibly have enough information to make a really informed choice.

Despair and accept that day jobs must be had? Most likely, music and literature would continue to exist – the equipment necessary to create either is within the reach of determined hobbyists. Movies wouldn't, however; it is mindbogglingly expensive to create a movie at the technical quality modern audiences expect. Can that be covered by the box office alone? Probably not in the long run, what with the increasing quality of home AV equipment. And a plan that means that movies cannot be made is not politically viable. Exit "despair".

I am left, for the time being, with no good proposed solution. But that does not make the problem go away. It is still there, whether we like it or not, and solving it before the death throes of copyright end should be high on the list for politicians concerned with culture.

Confused? You won't be after this...

A customer needed to read some simple information out of our server software programmatically, and suggested that a "SOAP API" might be a good way to do that. To me fell the task of researching what that might mean.

SOAP is a lightweight protocol intended for exchanging structured information in a decentralized, distributed environment. Why, it says so right in the spec!

I dread to think of a protocol that the W3C would call "heavyweight".

That funny judgement with the tree

I found this judgement through a Groklaw article some time ago. Recently I desired to reread it, but it took me quite a lot of tries to remember sufficiently precise search terms to locate it again. Clearly it has not received enough link love.

It's about a young couple who bought a house and cut down a mulberry tree which leanend over the backyard but actually belonged to their new neighbour. The neighbour sued. Fairly banal case, except that it is presented with hilarious wit.

I give you Thayer v. DeWolf, memorandum order by Magistrate Judge Goodbread, who I think would make a good hacker. Respectfully recommended for your reading pleasure.

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.

Elections and geography

Some time ago I confessed that I read American court documents for fun. I cited the quality of some judges' writing as a reason for that, but a side benefit is some indirect insights into the half-continent of madness that is the United States of America. And sometimes, by contrast, into little old Denmark too.

Consider this recent case, Gonzalez v. Aurora. Several people from a western suburb of Chicago sued their city council, demanding that its voting districts be revised such that their particular racial group would be likely to get more seats on the council. Plaintiffs lost in the lower (district) court, and now they lost in the appeals court too. The court's opinion does not have the kind of dazzling rhetoric I wrote about earlier. But it made me think, about the differences and similarities between the political system it describes and the one I'm used to.

It probably ought to startle me that this matter is considered something that a court should decide at all, but it doesn't. In USA, it seems, everything is a potential matter for court intervention. Everyone who doesn't live in a cave probably heard about the 2000 presidential election.

What does trouble me a bit is that the plaintiffs' argument seems to assume that the voters in Aurora decide who to vote for using candidates' race as their first and final criterion. Such voter behavior is not unheard-of – in semi-failed post-colonial states suffused with mutual distrust between clans and ethnicities who find themselves sharing political structures by way of historical accident rather than sharing a functional society. But in a modern democracy with everybody integrated in a common economy? I know that when I go to vote, I try to vote for the candidate who shares my political views the most, rather than one who shares my complexion.

It might seem equally troubling that the appeals court willingly accepts this strange theory. But the court did find against the plaintiffs, and it makes for a stronger and more persuasive opinion if the court goes along with the losing party for the sake of the argument until the critical point where the loser's case breaks down. Implicitly, the court says "even if you were right about all this, you'd still lose because so-and-so".

But what really got me thinking was the unquestioned baseline assumption that most councilmen have to be elected in single-seat wards. Voters who happen to agree with the majority in their local ward get to be represented. Voters who are in a local minority become virtually, or nearly, disenfranchised. It doesn't matter if some political stance has a uniform 49% following everywhere; it gets zero electees because its popular support is insufficiently clumped.

I have heard people trying to justify such a system, but I've never been able to grasp their arguments. Why should geography matter? When I go to vote, I try to vote for the candidate who shares my political views the most, rather than one who by some quirk of the housing market happens to live close to me.

This would be quaint and amusing if is was a specific rarity of Aurora, Illinois. But it is sad that it is actually quite common. Most famously, perhaps, with the electoral college by which Americans chose their president. It is not a particularly American phenomenon, though. The UK House of Commons works the same way. And the way we elect the European Commission is perhaps the most indirect, convoluted and opaque of all, closely followed by the Council of Ministers which has the final political say in all matters EU.

Closer to home – in Denmark municipal councils are elected directly and proportionally, simple enough. But elections to our national parliament the Folketing, use a weird mix of geographic and proportional methods. Some members are elected in regional districts, with a number of additional at-large seats distributed afterwards such that the final party make-up of the parliament will get as proportional as possible. Then there are complex and elaborate rules for simultaneously distributing the at-large seats to ensure approximate geographical proportionality in the parliament as a body, as well as within each party.

Active politicians care about this system, because it decides which among each party's candidates win a seat, a matter of paramount importance among those running. Almost nobody else does, and look only to the final party breakdown (which, being guaranteedly proportional, can be understood without resorting to geography). When I've been a poll worker at general elections, some voters were obviously confused because the political leader of their choice was not on the ballot – he or she were running in a different district. Again, why should geography matter here? A smart voter tries to vote for the candidate who shares his political views the most, not one who happens to live in the same part of the country.

And, adding to the confusion, the district a candidate runs in does not have to be the district where he or she lives. In fact, for top politicians it is the exception more than the rule. Each party selects the running districts for its top candidates tactically, to maximize their chance of election given the above-mentioned rules that ostensibly exist to equalize the geographic origin of the MPs. Except that what it really equalizes is virtual pseudo-origins chosen solely based on the rules themselves.

Excuse me, but I fail to see that society at large benefits at all from this convoluted system.

(... now where was I? Something about a court and a city council in Illinois, I think. You mean I was supposed to have a point about that? Sorry. Still new to this blog thingie).