Bounded in a Nutshell

So there's been a push in the last few years -- principally by libertarians -- to try and break away from the traditional single-dimensional political model. (That's left vs. right.) Their proposal involves a two-dimensional space, separating economic and social freedoms into independent axes. They then put together quick little quizzes which allegedly plot your position in their policy space. (A commentator has described these as those little tests which tell you you're a libertarian.)

There's several questions you can raise regarding this proposal. One obvious one is: why should two dimensions be enough? While this description may give more explanatory room than the standard 1D model, why should it be superior to (say) a tribal description of Canadian or American politics, where people are classified/stereotyped based on demographic concerns? Or if two dimensions are better than one, why should we stop there? Why not put together large questionaires on many, many issues and then do some clustering analysis to work out how many independent axes there really seem to be?

As interesting as those might be to pursue, they're not what I'm working on right now. Rather, I'm curious about the geometric aspects of the problem. See, there's a result by Black that states that, as long as voters' preferences are single-peaked, then one can find reasonable social choice procedures. (This isn't true if preferences are allowed to vary arbitrarily; that's Arrow's Impossibility Theorem.) What single-peaked means in this context is more or less that you can plot the various candidates along a straight line, and a voter's preferences are determined strictly by their position on this line and how close they are to the different candidates. In other words, if the left/right model is actually accurate, then reasonable voting results are possible.

So what happens in this 2D space? Assuming that the libertarians' model is accurate, does it give us guarantees of reasonable social choice? Or are there now sufficient degrees of freedom that Arrow's Paradox comes into play? And if the latter is true, then under what circumstances do we need to worry?

I'll post pictures of what I'm talking about later; for now, I just thought that some of my Faithful Readers might be interested in what I'm thinking about these days.

In case you're wondering why everything all of a sudden had quote marks around it, it's because I tried closing a <q> tag with </i>. Found it, fixed it, all good AFAIK.

I was going to write about something else, but finding my stupid coding errors completely drove it from my mind. Another time, perhaps.

So in my continuing if probably futile attempts to lead a healthier lifestyle, I've decided to do something about my whole thing with fast food.

'Cause here's the deal. I tend to get distracted very easily: snatches of songs, beautiful women, the Internet, shiny objects in general, conjectures about domination in cubic graphs... I have this little trouble with focus on occasion. This is bad when one has arranged one's day in such a way that one has a very specific time period when one is supposed to be out getting lunch, because one quick distraction and all of a sudden your lunch hour's reduced to about twenty minutes. Hence, fast food. It may not be great, but it's quick and filling, and sometimes that's good enough.

Except, of course, that fast food is actually everything that's bad for you about food distilled into a mass-produced essence and then scented with chemicals from a factory in New Jersey. (I'm exaggerating, of course, but not by a whole lot. Further details can be found in Fast Food Nation.) My reliance on it as an option is a bad habit that I'd really like to do away with.

And so: my new system. Once a fast food place pisses me off, then I never patronise it ever again. By pisses me off, generally I mean they get my order wrong, which -- when one has morbid dislikes of certain common foodstuffs -- isn't that difficult to do, yet renders my food inedible.

Phase 1 started with pizza places, and so I'm now boycotting the second- and third-largest pizza chains in the U.S. Phase 2 got under way this week, and already my two most significant fast-food weaknesses have been banished. I don't know what it says about me that I don't mind eating crap in a regular basis except when the profit on my weakness goes towards incompetence, but that seems to be the case.

So I'm well into the Firefly DVDs by now. I generally consider myself someone who doesn't like TV, but that's not entirely accurate. There's no real principle that I hold against television; I just don't particularly like aspects of the distribution. Set time periods every week for shows, for instance; I have trouble with that sometimes. The fact that you only get new episodes once a week if that. And the commercials, which range from inane to, well, inane. But there is such a thing as quality programming, and I've come to feel that the best way to watch it is on DVD, a season at a time.

Anyhow, in case you blinked and missed it when it was originally broadcast in late 2002, Firefly is a space opera. The principal characters are the crew of a small independent freighter-spaceship, which takes a variety of shady jobs to stay afloat. The series is co-created by Joss Whedon, the man principally responsible for Buffy and Angel, which might give you some idea of the tone of the show.

Now, any series that starts with a premise like that just naturally invites comparisons with Star Trek and its descendants, the great-grandmother-hive-queen of all televised space opera. And there are numerous subtle ways that Firefly encourages such a comparison; for instance, there's one scene in an early episode where the ship's mechanic takes great offense at the ship being dismissed as junk, which echoes how a bar brawl got started in a Star Trek episode when someone calls the Enterprise a garbage scow to the chief engineer's face.

At the same time... Star Trek starts with the little spiel about Space, the final frontier, and yet rarely treats it as such. The Federation is civilised; humanity has by and large been tamed by their new technology. Starting a new colony world means throwing vast amounts of hi-tech at any problems until they go away. And despite all of this, despite the apparent unification of Earth, humans still cling to their ancestral cultural identities.

One of the many nice things about Firefly is that it treats the frontier like a frontier. The malcontents, the restless, the oppressed: these are the people who go out to try their luck on a different, new world. The series often invokes tropes from Western movies (much like the anime series Cowboy Bebop does), drawing comparisons between this and the old American frontier. These are juxtaposed with the use of Chinese motifs... which makes perfect sense if you start by assuming a unified human race, since English and Chinese are the two most populous languages. (Oftentimes characters will throw in bits of Chinese into their speech, particularly in places where one might otherwise supply English swear words; I'm not sure whether this is meant to suggest that they're speaking in Chinese all the time, or just that both languages are equally common to the point of being blended. Also, most of the main cast have features that suggest ethnic fusion in various combinations, which is a nice touch.)

It's not a perfect show by any means; I find the tendency to have a theme for each episode to sometimes work and sometimes not, for instance. But I'm finding it a much more honest attempt than Star Trek to project humanity a few centuries into the future.

A couple of weeks ago I was in Florida at a conference. One of the attractions of this particular conference is a certain used bookstore in town. The people who run this bookstore are well aware that every year their town is overrun by mathematicians of a certain bent, and so they make sure to be well-stocked with books that appeal to that rather limited demographic.

Oh, plus they'll ship books around the country at ridiculously low rates. So if one already has enough stuff in their luggage, one can still buy thirty pounds of books with impunity.

My own take this year includes a couple of linguistics books, a couple of treatments of applications of discrete maths in softer subjects (social sciences, ethics), and -- the prize -- a three-volume comprehensive text on polyhedral combinatorics. Eighteen hundred pages of combinatorial optimization, a significant fraction of which is bibliographic information. One of my companions picked up a recent translation of Fibonacci's Liber Abaci, which is almost too cool for words.

Between this and being lent the Firefly DVDs for the next few weeks, I can just tell that my measurable productivity is going to plummet. And I'm looking forward to it.

Just some quick notes for now, since I feel vaguely guilty about not updating this when I keep finding out that there are more and more people reading this. (I might even be up to double digits now!)

• Sarah Harmer's new album is great. The first half is killer; the rest isn't quite as strong, but still worthy.
• I've been reading Julie Czerneda's novels recently on a parental recommendation. Good characters, great settings, fairly solid stories, but sometimes the prose wanders a little bit out of control. Also, her third Trade Pact book is a little, well, a little too happily-ever-after I feel.
• The ability to read French and the ability to read graph theory combine very nicely into at least some vague facility at reading French graph theory. However, I am going to have to hunt down a dictionary and see what is has to say about quelconques; it seems to mean something like for each, and the argument makes sense reading it that way, but I'd really like to be sure.
• Arkell Best Bitter is your friend. Available at fine establishments throughout Ontario.

Back in the Midwest and still utterly exhausted, even after a truly prodigious sleep last night. The whole early-morning, late-late-night thing just didn't end up working for me after a while. Of course given the choice I know which one I'd drop, but life is apparently just not like that sometimes.

On the plane back I started reading The Stone That Never Came Down by John Brunner, and I managed to finish it after the two-plus hour drive back to the apartment. I've found Brunner to be a little hit-and-miss; he's got some truly brilliant ideas which then get joyfully pilfered by other SF writers (in fact, I was twigged on to this one by an attribution made by James Alan Gardner at the beginning of Vigilant), but sometimes his writing just can't quite support them.

Stone is from the seven- or eight- year period when Brunner wrote what most consider to be his masterpieces: Stand on Zanzibar, The Sheep Look Up, and The Shockwave Rider. All three of those books, and Stone as well, could be described as incipient dystopian futures: that is, what you're looking at isn't quite the bleak hopelessness of 1984 or Brave New World, but rather the lead-up to such a thing. The first two books on the list -- which take as their themes population pressure and ecological breakdown, respectively -- are quite pessimistic in their outlook; Rider and Stone actually offer solutions and potential escape from their nightmare scenarios, even if those solutions are more or less impractical.

The basic idea of The Stone That Never Came Down is this: what would happen if people lost their capacity to ignore? What if everything that you ever saw, heard, etc. was at your immedite recall, whether you liked it or not? And what if your reasoning abilities were accelerated enough to allow you to take advantage of this? Brunner's postulate is that the world would be a better place; he feels that most of the social (and socialised) evils in our world are only made possible by selective inattention and hypocracy.

It's an attractive theory, though a little naive. But Brunner is good enough to acknowledge that if everyone gained these addition capacities, the whole world would be changed. (He ends the book before the condition -- caused by a manufactured virus -- has the chance to spread that far, but hints at the sorts of adjustments that would be caused.) My big problem with the book is that a number of the characters are more or less undifferentiated, and almost all of them tend to talk in somewhat of a didactic manner.

Some of the same ideas were later manifested in The Shockwave Rider, which along with Vinge's True Names is probably the direct antedecent of the whole cyberpunk sub-genre. Again, we have the idea that a truly functioning society requires a free flow of information. In both Rider and Stone you have a world that's being pushed to the breaking point, and there's only a small handful of people who have the information needed to prevent catastrophe... which is done more or less by their sharing of that knowledge as far and widely as possible.

Your faithful correspondent is in Florida right now, attending an academic conference. This is supposed to be a relaxing experience, or at least that was my plan... which probably indicates how bad I am when it comes to plans and such.

In all honesty, I've never been a terrific fan of warm weather. After having flown through a Major Midwestern Airport where it was snowing on my way down, having inarguable T-shirt weather and all these bright green plants around is a moderate source of existential distress, but there's more to my general nonplussedness than just the abruptness of the transition.

In balance, I'm glad that I live full-time in a climate with a winter worth the name. Sure, there's a month or two every year that really isn't very pleasant, but then spring comes and it always feels like an accomplishment of sorts.

It's been an interesting day. One of the associate faculty at my Urban Commuter Campus resigned today for medical reasons, requiring our department chair to find people to fill his courses. Being the agreeable kind of guy I am who doesn't have a social life, I mentioned that I could probably squeeze one of them into my schedule. (It's on overload basis, which means that I get extra money. I've been wanting an iPod for a while now...)

Anyhow, so the course in question is a second calculus course: diffy-qs, Taylor series, integration, a bit of multivariate. Except for that last, it's all stuff that I was very bad at as an undergraduate. Fortunately next week is Spring Break for us, which will give me a week or so to learn all of it again... or, in some cases, for the first time.

But that's all just background. After all this was decided and a textbook was found for me somewhere, I retired to my office. A little while later a student wandered in, asked if I was taking over Dr. So-and-so's class, and then launched into a bit of a rant about how he didn't think it was fair that his class was still going to have a test tomorrow when their last class was cancelled and their instructor was going away and blah blah blah. It took about ten seconds of this for me to determine that he was talking about one of the other classes, which was being taken over by someone else.

Gently, I pointed this out to him.

He looked at me for a second, and then resumed. Well, I still don't think it's fair...

On a related note, I'd like to thank my department secretaries for their aid in my continuing quest to direct things which are Other People's Problems away from me.