Halfway down the Danube

Unusual and beautiful solutions

Unusual and beautiful solutions to the Three-Body Problem.

He has seven pages with multiple examples on each page. Take a few minutes -- they just get wilder as you go.

(Three planets chasing each other around a figure-eight orbit can be stable. Who knew?)

They Love Iran

Okay, love might be too strong. But Armenia and Iran are definitely good friends.

Triggered by this recent story:

A visiting high-ranking Iranian official thanked Armenia on Tuesday for supporting his country in the international arena just days after Yerevan refused to join Western powers in condemning Tehran’s poor human rights record.

Prime Minister Andranik Markarian’s office quoted Iran’s Agriculture Minister Mohammad Reza Iskanderi as praising the “balanced position on Iran which Armenia takes in international structures.” No further details were reported.

The remarks, made during Iskanderi’s talks with Markarian, were apparently prompted by the Armenian vote against a Western-backed resolution that was adopted by the UN General Assembly last Wednesday. It decried continuing human rights abuses in Iran, saying that persecution, torture and even execution of individuals opposed to the ruling regime in Tehran remain widespread.

Neighboring Azerbaijan was also among 47 states that voted against the resolution co-sponsored by the United States, Canada and the European Union....

Armenian leaders have similarly avoided any criticism of Tehran’s controversial nuclear program that has drawn serious concern from the West.

So what's this all about?

Well, several things.

One, just look at a map. Armenia is a landlocked country with four neighbors. To the east is hostile Azerbaijan... border closed. To the west is unfriendly Turkey... border closed. To the north is Georgia, which isn't hostile but isn't overflowing with warmth either; the Georgians have their own problems, and charge Armenia heavily for access to the sea. So, it makes simple geographical sense to stay on good terms with Iran. The last thing they need is another closed border.

Two, energy. Armenia has none... no oil, no gas, no coal. Courtesy of Brezhnev's USSR, they have a nuclear power plant that's sitting on top of a major earthquake fault line. They have that and some hydropower and that's all. Everything else has to be imported.

Armenia sits next to Azerbaijan, one of the most energy-rich countries in the world, but -- whoops -- border closed, no relations, no trade. So they have to import natural gas and oil from Russia, through Georgia. But since Russia and Georgia don't get along so well, this is not exactly a reliable source.

So they're looking south to Iran for energy. A natural gas pipeline is about 3/4 completed -- it's expected to reach Yerevan this winter -- and there are plans for a joint hydroelectric dam on the Araxes river, which runs betweeen the two countries.

Three, there's a large Armenian minority in Iran. And -- key point here -- the Armenian-Iranians are probably the most privileged of all Iran's minorities. They're allowed to exercise their faith. They're not much discriminated against. They have a couple of representatives in the Majlis, the Iranian Parliament. They're even allowed certain privileges forbidden to the Muslim minority... for instance, they can distill alcohol and own liquor stores. Unsurprisingly, a lot of them have done very well. They're more or less a model minority.

This suits the Iranians very well; whenever they're criticized for their horrible human rights record, they can point to the Armenians. See, a hundred thousand Christians, peaceful and prosperous! Oppressive fanatics and bigots? Pshaw! -- And of course, the Armenians of Armenia have a strong interest in making sure things stay sweet for the Armenians of Iran. Because it wasn't always so. Back in the 1980s, when the Islamic Revolution was still fresh, things were a lot rougher for Iran's Armenians. The peaceful coexistence is relatively recent.

Fourth and finally, the two countries' strategic interests coincide. Armenia wants to stay friends with Russia; so does Iran. Armenia is in a state of frozen conflict with Azerbaijan; Iran is coolly neutral towards Azerbaijan. Armenia is worried about Turkey; Iran is Turkey's ancient regional rival.

So, there are plenty of reasons for Armenia to stay on good terms with Teheran.

Having said that, it's rather striking just how warm the diplomatic relations are. Iran's not a broadly popular country, but they can pretty much always count on Armenia's support, in the UN and elsewhere.

Dungeons and Dragons in Armenia

It doesn't exist.

I've looked. Forums, Usenet, mailing lists, both for gamers and for Armenia. There's nothing online. I salted the local English-language university with flyers. No response.

Next step, I suppose, would be to hit the internet cafes where the fantic video gamers stay up all night. "Hey, there are other ways to kill orcs!" But that's a tactic of desperation. Really, I think there's nothing here.

Long-time readers of this blog may recall that I found D&D gamers in Serbia and Romania. Heck, there were more gamers in Bucharest than I could easily deal with. I could have quit my job and gamed sixty hours a week. I mean, um, in theory.

Anyway, no Dungeons and Dragons in Armenia. I am mildly surprised by how much I miss it.

About all I can do at this point is a post like this, which emphasizes Dungeons and Dragons in the country of Armenia. Because while Armenia has no Dungeons and Dragons now, there's always a small possibility that some person may be googling, looking for Dungeons and Dragons players right here in, yes, Armenia. And we'd all hate for that person to go away sad, right?

Right.

Woodpecker

Saw a woodpecker today.

I was walking back from dropping Alan off at the school bus. Chilly morning, just after dawn, right around freezing. Both Alan and I had been a little sluggish... sometimes our morning walks are lively, with lots of questions and conversation. Sometimes it's companionable silence. Sometimes it's just silence, because we're both not quite started yet. This had been one of the just-silence ones. Not bad, just nothing to say. Neither of us are really morning people.

We hung around the bus stop for a minute or two, the bus came, I loaded him on. Ritual: after he sits down, I go to his window, tap with my wedding ring. He looks up and smiles. I blow a kiss. Bus takes off and I walk home.

Walking home: Heard a faint sound, tok-tok-tok. Looked up at one of the two poplars in front of the neighbors house. Thought at first it was a magpie (lots of magpies around here). But... too small. And it was tapping.

Watched it for several minutes until it flew away. (Actually, a magpie showed up and scared it off.) Undulating flight. Reddish on the bottom. I'm pretty sure it was a Great Spotted Woodpecker.

Not a particularly rare bird. In fact, common as dirt all over Europe and much of Asia too. Still, I'd never seen one before, and it was a completely unexpected touch of wilderness in our very urban neighborhood. And a bright note in an otherwise glum week.

And that's all.

Astonished

An obscure passage from Plutarch’s De Stoicorum repugnantiis:

But now he [Chrysippus] says himself that the number of conjunctions produced by means of ten assertibles exceeds a million, though he had neither investigated the matter carefully by himself nor sought out the truth with the help of experts. [...] Chrysippus is refuted by all the arithmeticians, among them Hipparchus himself who proves that his error in calculation is enormous if in fact affirmation gives 103049 conjoined assertibles and negation 310952.

Hipparchus flourished in the second century BC. Today we would probably call him a mathematical physicist. Plutarch wrote some two hundred fifty years later.

In 1870, the mathematician Friedrich Wilhelm Karl Ernst Schröder showed that the number of possible ways to bracket a row of ten symbols, e.g.

(AA)(AAA(AA)A)(AA)

and not including singletons or the whole row, was equal to 103049. This is sometimes written as s(10) = 103049.

In 1994, David Hough at George Washington University noticed that these two numbers were the same.

In 1998, Habseiger, Kazarian and Lando noticed that Plutarch's second number, 310952, was very close to half the sum of the tenth and eleventh of Schröder's numbers: (s(10) + s(11))/2 = 310954.

The modern branch of mathematics which deals with enumerating combinations is called combinatorics. It was once thought that the ancient Greeks had no interest in the subject.

(Hat-tip to Alexandre Borovik, who comes from the opposite end of the Tea Road as some of my forebears. The passage from Plutarch comes from F. Acerbi, "On the Shoulders of Hipparchus: A Reappraisal of Ancient Greek Combinatorics", Arch. Hist. Exact Sci. 57 (2003) 465-502.)

Deindustrialization in real time

They're tearing up the train tracks.

The tracks run right past our house. A few months back, I posted about walking along them:

the tracks are in crappy shape. The sleepers were originally wood, but many have rotted away, or burned in brushfires. Some have been replaced by concrete sleepers, but many have not. The track bed is in visibly bad shape. Signs have fallen over or been vandalized; signals are obviously long dead.

I had vaguely noticed that the trains weren't very fast -- maybe 50 km (30 mph) tops. Now I know why...

...it was depressing. Interesting, but depressing.

The constant garbage, of course. But also, the tracks went past abandoned factories, now rusting and empty. It was evening, and windy. The red light of sunset gave the rusting metal a peculiarly dark and dreary look, while the wind sent plastic bottles jumping and bouncing along the ground. Although the tracks ran through a densely populated neighborhood, there were few people around, and the wind blocked the sound of traffic. I could have been alone in a city left empty by some catastrophe.

Well: last week I walked home from the office, and -- in the course of looking for a shorter way home -- wandered across the tracks.

And they're being torn up. Rails gone, sleepers gone. Just the bare dirt of the bed left. We hadn't heard any trains for a couple of months; we'd vaguely thought it might was because of the season. (The rail line goes up to Sevan, which is a big summer resort.) But no -- they're shutting it down altogether.

It's true that the track was in miserable condition. Still, this seems both strange and sad.

Strange: the track is no small thing. It's the only rail link going east towards Azerbaijan. It stops at Sevan, which is on the lake... but the opposite side of the lake is just a few miles from the Azeri and Karabakh frontiers. If there was another war with Azerbaijan, you'd think a rail line to the lake would come in handy.

Also, the track links forty miles of factories and warehouses like beads on a string. A few blocks from our house is a furniture factory. It was a great box of a thing, with its own spur off the line. Presumably it sold furniture all over the former USSR. Closed now. Ripping up the line is a clear statement that, no, that industry isn't coming back. Maybe that's a wise and correct economic judgment; after all, Armenia's economy is growing again. Maybe it will never need those old smokestack industries. Did someone sit down and work this out? I wonder.

Sad: We used to hear the trains go by, and mark our schedules accordingly. The morning train meant it was almost time for me to leave for the office. The evening train, all kids should be in bed.

..next to the furniture factory is a school. I assume it was for the workers' kids; the USSR did that sort of thing. Closed now, lock on the gate, weeds growing up through the playground equipment.

No more summer rides on the little electrical train up to the lake. People said the train was old and overcrowded and smelly and slow, but I used to watch it pass and, you know, it looked like a fun ride. I never got around to trying it; now I never will.

So, what will happen to the right-of-way? Well, there are rumors.

One is that it will become a road. But that doesn't seem to make a lot of sense. Parts of it could be converted, but there are other parts that are just too narrow. It switchbacks up some steep slopes. I don't see this.

Another rumor is that the Russians are buying the train line. Buy an empty bed? The Russians are buying all sorts of things around here, so maybe.

And that's all.

See Borat? I've lived it.

I'm going to spend eleven dollars on something I can experience just by calling a relative?

The Pure Product of America: That's because you're ahead of the curve! Not everyone has crazy foreign aunts who ask young teenagers if their body hair has grown in yet.

Oh God, don't remind me.

The Pure Product of America: You should get on the bandwagon! Awkwardness. Discomfort. Xenophobia. Andy Kaufman. Psychic surgery! You know about these things.

Elf-shot. Ancient Teutonic shamans would extract microliths, bits of flint from their victims' flesh. All sleight-of-hand. In the Philippines, they've upgraded it to chicken guts. That tumor is actually a gizzard.

The Pure Product of America: Don't change the subject. You could purge all that cultural ambivalence from your system. And get chicks!

What ambivalence? Believe me, it's not ambivalence. It's very very univalent.

Anyway. I've told Doug that he should at least see Borat's infamous Black Sea thong; but I suspect he's seen the non-ironic version already.

Crisp and clear

The weather turned cold this week.

Mornings are cold and clear and frosty -- walking to the bus with Alan, we can see our breath. Afternoons are warmer, but still nippy. We're definitely on the back half of autumn now.

The cold snap started on Election Day, oddly enough. We stayed up late. I took the next day off, though I had to go into the office in the afternoon. I was wrong in my predictions, but that's fine. I did win one bet.

Anyway. Our house has no thermostats, so the heat is either all on or all off. All on is pretty powerful in some parts of the house, much less so in others... our bedroom may be uncomfortably warm, while the upstairs bathroom is close to freezing. (Claudia has put little rugs on the tile floor to make it tolerable to bare feet.) Similarly, the kitchen is toasty, but the TV room is quite cool. It's a Soviet-era house, modernized only partially -- some windows have double-glazing, for instance, and some don't. Come January, we may have to close a couple of rooms off.

Meanwhile, when the heat in the master bedroom grows too stifling, someone has to turn the heat off for a while. The heating system is in a shed in the back yard, so someone has to go outside to flip the switch. This someone is not always me, but there is, shall we say, a trend.

Anyway, the shortening days are lovely. Not complaining.

Preferring the strange to the unknown

I'm going to be spending Election Night at the gym. They've got the speed bag and the heavy bag.

In breaking election coverage, Nicaraguan voters have decided to elect former Sandinista leader Daniel Ortega to that nation's presidency. His vice-president, former Contra spokesman Jaime Morales, 'decided to join Ortega's campaign because he preferred "the strange to the unknown."'

Former American president Ronald Reagan could not be reached for comment.

Update: Who the hell schedules spinning on Election Night? But the cute trainer there showed me what I was doing wrong with my lats (my horrible stiff neck).

As for the US election, Doug's prediction was +4 Senate, +18 House, and +4 Governor. Noel Maurer's was +5 Senate and +27 House. Bernard Guerrero's was +4, at most +17, and +6 (AR, CO, MA, NY, OH, MD).

At this point in time, it's at least +5 Senate, +28 House, and +6 Governor, Bernard's picks included. Plus my old allergist won! So.

Millions Now Living Will Never Learn

Many Americans and most non-Americans don't understand the pattern of religious belief in this country. But they often think they do. When that happens, they usually talk about American Puritanism. Witchhunts, prudery, et cetera.

In fact, the descendant sect of the Puritans, the Congregationalists (now part of the United Church of Christ), is today a liberal Protestant church. Social reformers, and before that, abolitionists.

And now a more ironic twist: our conservative media views the descendants of the Puritans as "too controversial" for television, because they're impolite enough to mention that they don't turn away homosexuals.

Which brings me to Ted Haggard.

Full disclosure: Haggard has set off my Straight Man's Gaydar for a while. Something about the fashion sense and the bigotry, or maybe it was cruising the Colorado Springs gay bars for converts? I forget. (On the other hand, I often Google random Republican apologist names -- e.g.: "Is Tucker Eskew gay?" -- just in case I've overlooked someone. Keeps 'em on their toes.)

Now, not all current evangelicals are raving queer-haters; and of the ones that are, I am sure there are one or two who aren't gay themselves. Franklin Graham, perhaps, who has other issues.

I had a point here to make, about how American religious discourse has been taken over by the spiritual descendants of the nineteenth-century American Protestant freakshow occult. But thinking about how Franklin Graham must trouble his father's heart, it just gets me down.

A bird, two cats

Saw something wonderful this morning.

I walk Alan to the bus stop every morning at 8:00. Last week we were walking in the dark; thanks to Daylight Savings, it's light again. Which is nice -- the sun is coming up, and we get to watch Mount Ararat turning pink.

And birds. The selection isn't huge -- we are in the middle of a city, after all -- but there are plenty of sparrows, occasional doves, once in a while a magpie.

And lots of hooded crows.

Hoodies are interesting birds. They're only found in Eastern Europe and Scandinavia, with isolated populations in Scotland and Ireland. They're basically normal crows who have put on a grey waistcoat. This gives them an odd look, at once dignified and slightly disreputable. Like an undertaker who has fallen on hard times.

Anyway. Sitting at the bus stop with Alan, I was idly watching a hoodie fly past. Suddenly the bird stopped dead in midair, dived several meters, and then bobbed up again.

I watched more closely. The bird had something in its mouth -- a bread crust, perhaps. As I watched, it tossed the crust up -- in midair, while flying -- and let it fall. Then it folded its wings and dove after it. (I had no idea crows could do that.)

It was playing.

I watched it do this three or four times, and then it flew out of sight.

High point of my morning.

In other news, we've been adopted by two half-grown cats. Claudia can give photographs and details. Short version: they showed up hanging around our house a few days ago, mewling piteously. They're obviously domestic cats -- they're not afraid of people, and they even let the boys pick them up. But they also seem to have been abandoned or something; they're a bit scrawny, and ravenously hungry.

We fed one of them and, well, you can guess the rest. The boys love them. We're trying to keep them at arms length -- no sleeping in the house, not too much feeding -- but they're pathetically insistent.

So, cats. What can you do.

Halloween

We went to the Embassy.

See, Armenians don't do Halloween. Have only the vaguest idea what it's all about. So if you want to bring your kids trick-or-treating... well, the US Embassy is where you go.

Now, the Embassy is a set of several large, blocky buildings set in a walled compound off the road to the airport. The general architectural style is... well, you know the Ronald Reagan Building in DC? Like that.

The way it works is, you come in through security, and inside there's a sort of campus arrangement of buildings around green space. (Maybe the campus of an evangelical engineering school, but never mind that.) Then you get a sheet of paper that tells you which offices to take your kids to. So you go from one building to another, riding elevators up and down, and stopping at offices where Embassy staff have volunteered to stay late and hand out candy.

Here's where the cognitive dissonance kicks in. At one level, this is pathetic and lame. The decorations are what you'd expect in government offices -- cardboard pumpkins, and such. The embassy employees are at best bemused. Few try to dress up; something about the office environment discourages it. The embassy compound is well-lit and not in the least spooky. There's no ringing of doorbells, no peering at dark doors. It's very bland and safe and a little sad.

At another level, it totally rocked.

The kids loved it. Loved it. David in particular was beside himself with delight. When you're three, it's all new. Wearing a cosutme! Other kids in costumes! Staying up after bedtime! People just GIVING HIM! CANDY! At one point he turned to me and said, "Daddy, I love this!" And he did.

Alan is a bit older but not old enough to be blase. He enjoyed going up and down in the elevators and looking into the different offices. He saw a lot of his friends. At the end we went to the Marine quarters and had soda and pizza in the lounge and they had "Shrek 2" on the big screen and, you know, it was all good.

And when it finally ended and we were going home, David turned to me, lower lip trembling, and said, "Daddy, I don't want Halloween to be over!"

So I guess it worked after all.