Tuesday, February 28, 2006

Mardi Gras by proxy






So it's cold, dark, and miserable outside in this joyless northern city of ours. Meanwhile, people half a continent away are having a grand old time, and some of them may even remember it tomorrow. But thanks to the magic of the Internet, we can get a small inkling of all the brainless and irresponsible fun we're missing out on. That may be good or bad, I'm not sure. So here's what showed up after wandering the net for a while, while waiiiiiting for my uber-overweight C++ app to recompile on a slowwwwww HP-UX box:


  • A rant about the city of New Orleans's comically failed attempt to find commercial sponsors for this year's Mardi Gras.
  • An artist/blogger from New Orleans discussing the
    glory of beads. This is where that cool frog photo comes from. As she puts it, Reason number five million and eight why New Orleans is the greatest city on Earth: in New Orleans, even the trees wear jewelry!.
  • A brief history of the culinary phenomenon that is king cake.
  • A lesson for the uninitiated about what Mardi Gras is all about, really, including a bunch of king cake photos (including the one you see here).
  • One blogger's memories of going to Mardi Gras with his buddies way back in Y2K.
  • Another Mardi Gras reminiscence, including a paean to Popeye's biscuits.
  • A post about the singular joys of bringing a fundie to Fat Tuesday.
  • The source of that "We're from Texas, you OWE us" image. The poster is sort of disgusted, and rightly so.
  • How could I not pass along this post about the local beer down New Orleans way? I mean, it's beer...
  • Yet another blogger who found a previous Mardi Gras a bit mind-boggling.
  • Seems everyone except me has a Mardi Gras story. Here's another one.
  • An interesting and unusual perspective on the holiday, coming from a Catholic seminarian in New Orleans.
  • A comedian from New Orleans has a piece about why Mardi Gras is important.
  • Of course, you can never really get away from the earnest, well-meaning people who feel nobody should have a single moment of fun until we've gotten rid of all the bad stuff going on in the world. Here's one example.
  • And the inevitable earnest documentary about how Mardi Gras beads are made in China.
  • A student whose Sociology prof gave a talk about "Ritual disrobement during Mardi Gras", which is apparently an outgrowth of the capitalist system. It's really astonishing the things you can get a grant to study these days.
  • That professor may not even be right, to top it all off. Here's at least one visitor who practices a socialist bead-throwing philosophy.
  • Someone else writing about the ongoing "gone wild" phenomeonon. You know you want to read it.
  • Holiday greetings from another blog I stumbled across. Probably not safe for work, of course depending on where you work.
  • A post aptly titled Mardi Gras Hangover, with links to numerous photos. [Added 3/1/06]


Tags: .

large & small stuff, plus current events



I've sworn a solemn oath to never use the words "" or "" in a post title ever again (and let's add "" and "" while we're at it), so today's title is about as generic as I'm likely to get. You might have noticed that I've just figured out how to do those fancy-schmancy Technorati tags, and I suppose it's possible I'm overusing the feature just a little.

Pop quiz: Of the two images here, which one is a new image of the surface of Titan, and which one is an electron microscope image of a ? Kind of hard to tell, isn't it?

I was reading a bit about recently, due to that annoying cold I had that I'm nowhere close to finished whining about just yet. I hadn't realized that there's now an ongoing effort to classify viruses and give them latin names. So that most common cold viruses fall under the family Picornaviridae, genus Rhinovirus. The little bastards.

[Note: If you really aren't that interested in my latest science-geek diversion, just scroll down the page a few paragraphs until you see the words Mardi Gras.]

Here's a good article I came across that talks about subcellular life forms. I'd been planning to talk about some of the topics in that article myself, but it's clear and well-written, and I'm lazy, so I'll just say "yeah, what he said". In particular, the discussion about is interesting. At present they aren't usually considered to be "alive", but this strikes me as an arbitrary choice. I suspect they'll eventually come to be seen as viruses that just happen to have a symbiotic, rather than a pathogenic, relationship to their host cells.

Virology is an interesting subject to me because even though a vast amount is known about viruses, the basic taxonomy is still being sorted out, and fundamental questions like "how did viruses originate" are still very open questions. It's not even known whether all viruses share a common origin or not. It's possible that at one point all life looked sort of viruslike, for example see the RNA world hypothesis, and the less-popular hypothesis that the very first life forms were based on something called peptide nucleic acid, or PNA, a robust but not very versatile cousin of RNA and DNA.

Jumping abruptly from small to large, here's a new hypothesis about what's inside gas giant planets. In the end, it's still the case that nobody really knows, and nobody's come up with a good way of finding out. The Galileo probe seems to have been less helpful than everyone expected, for example. Cassini's sent back some interesting pictures of clouds at Saturn, but still no definite word on what's under the clouds.

I personally feel that all questions about cosmology, origins, the universe, and everything, would be much easier to address if we were all to adopt the Misanthropic Principle. (Contrast that with the more widely known "", which I tend to think of as "creationism for Mensa members".)

On an unrelated, yet timely and silly note, I'd like to work the tag "" into this post somehow. And now I have. Yay. Which is about the closest I'm likely to get to a Mardi Gras celebration, as is about as non-NOLA as it's possible to get. We're all prim and proper and we can only have a good time if we hide under a dozen layers of irony and pretend we hate the whole thing. We pretend we're all having a bitter laugh at the expense of people who don't have "creative class" jobs and expensive liberal arts degrees, but secretly we all wish we were them. Portlanders think it's hee-larious to wear John Deere hats in public and guzzle PBR from an actual beer can, as if it's all a silly lark, but ask them to give 'em up, and they can't. They just can't. People here are way too insecure and pseudo-sophisticated to ever simply have a good time and leave it at that.

In addition, Portlanders have been conditioned in recent years to think that if it's a real holiday, there ought to be a government-sponsored party in Pioneer Courthouse Square, or maybe Waterfront Park, even though most of the time there isn't one. The local TV news often sets up a camera crew near the square on Fat Tuesday, St. Patrick's, and a few other big days, and there are inevitably big groups of clueless people wandering around, wondering where the government's party is at. They always look utterly lost and confused, as if a few short years of mollycoddling by the city has rendered them unable to party on their own initiative. It's just as well that the city often neglects to hold a party, since these events are inevitably dreadful "family friendly" (meaning "alcohol-free") affairs, full of smug Subaru-driving yuppies all packing strollers the size of small SUVs and the inevitable pair of black labs. If I was the mayor, and I saw how one of these events turned out, I'd immediately cancel all future ones.

Meanwhile, if you run a bar or restaurant, you can't hold a proper party for fear of incurring the wrath of the jackbooted thugs of the [PDF].

It's all a crying shame, really. Except for the evil booze police and the sheeplike, proudly general public, we've got everything we need for a good time. You need streets for parades, and we have those. We have a container ship terminal somewhere in town, so you can import entire shiploads of beads right here, directly from China. Lots of multistory buildings, some with balconies, so the whole bead-throwing thing can be done properly. We even have very lenient laws about public nudity here, so we could even pull that off as well (so to speak), in the unlikely event that the weather cooperates. Alas...


[Oh, BTW, the first picture is the viroid, the other is Titan, in case you were curious, yet not curious enough to bother clicking on either link. So now you know. And as GI Joe said, knowing is half the battle.]

Monday, February 27, 2006

olympics (pt. 3)


Just a quick addendum to pass along a few links from elsewhere in the blogosphere that didn't fit anywhere in the last post:

  • A personal favorites list at Corsairs Affairs.
  • A Dutch blogger is puzzled by the tepid way the US media and public reacted to the Olympics. Granted, he's coming from a land of rabid speed-skating fanatics, so he may be setting the bar kind of high, but he makes some interesting points.
  • A counter-perspective to my (and others') rants about NBC, from someone who argues much of the criticism is undeserved.
  • A comment discussing the weirdly hostile reaction the Olympics evoke in some people. I'd add to this the tendency I've noticed among cultural-conservative types to reject any sport that's enjoyed beyond our borders, with the possible exception of baseball. They seem to require a fantasy sports world where foreigners simply don't exist at all. NASCAR even takes it a step further, to a world where foreign cars don't exist either. If there's any chance that an American will ever lose to a foreigner, they just can't stand to watch, I guess.
  • Not to beat a dead horse, but here are three more discussions about TV coverage. Something else just occurred to me about TV coverage of the games. I seem to recall that back in the old days, when they weren't covering the sports they'd sometimes go off on an extended travelogue about the city and surrounding area hosting the games. That would've been nice, especially now in the age of HDTV. You don't need an expensive commentator or anything, just put an HD camera in a helicopter and fly around town and show us the region's points of interest, just as pure eye candy. Is that too much to ask for? Italy's a beautiful country, and we hardly got to see any of it. If all you're going to give us are closeups of pouting skiers, or speedskaters bitching about each other at news conferences, your investment in fancy HD gear was a total waste.
  • I don't usually pay attention to Bryant Gumbel, but apparently he recently made some sour comments about why he hates the Winter Olympics. So naturally people are calling him an idiot, and rightly so.
  • Another blogger coins a perfect description: Bodefreude. I wish I'd thought of that. Wasn't quite as fun as rooting against the Bad Dream Team during the Athens games, but hey. On the other hand, Mr. Miller's poor showing will no doubt impact Nike's bottom line, resulting in pay cuts for all those poor little six year olds in China who make all their shoes. I hope Bode's happy.
  • Two more bloggers who enjoy curling. I'd never watched it until these Olympics, since it's always been shunted off to some random cable channel, usually at 3 AM. I can safely say that if you want to watch something other than figure skating and hourlong tearjerking athlete bios, you're going to need cable and a DVR. Anyway, it's surprisingly fun to watch. It's all strategy and tension, and there's nothing else in the Winter games remotely like it. And then, here's someone who inexplicably doesn't like curling. Takes all kinds, I guess. :)


Incidentally, after doing a bit of blog searching lately, I've decided to take a solemn oath to never use the words "random" or "musings" in a blog entry title ever again. Ok, if I'm talking about random numbers or something I might make an exception.

olympics (pt. 2)

There are all sorts of things I love about the Olympics. Even the always-goofy opening and closing ceremonies, something I think I ought to try to explain. Olympic opening and closing ceremonies have always been a guilty pleasure: Gloriously middlebrow events full of bombastic, empty spectacle, pompous ritual, and supreme cheesiness all around. They're great that way. This year's ceremonies were great even by the usual Olympic standards. They had everything: Incomprehensible plotlines, goofy costumes, people dancing with plastic cows, a Ferrari doing donuts in the middle of the stadium, a Ricky Martin concert, poorly synchronized and unimpressive faux Cirque du Soleil routines, a survey of the greatest disco hits of the 70's while the athletes entered the stadium, giving the athletes red clown noses to wear at the closing ceremony (which almost none of them did), and so on. I think there probably was supposed to be an ultra-noble and abstract organizing theme, or concept, or at least slogan behind each ceremony, but unofficially for both of them it was the usual one: "One Damn Thing After Another". Still, after ten years nobody's yet managed to top those chrome pickup trucks back at the Atlanta games. That was just.... priceless. And am I the only person who thought having Muhammad Ali light the torch in Atlanta was actually kind of sad and painful to watch? He got that way by doing something he first became famous for in the Olympics, to top it all off.

Our local NBC affiliate had a crew in Torino, and they were interviewing people after the closing ceremony. One guy said he liked it better than the opening ceremony, which he thought was really confusing and "full of culture". You can't make up stuff like this. It's pure gold.

I'm not actually sure how much we can blame the Torino organizers for the disjointed nature of the ceremonies, since all I've seen of them is NBC's coverage. Last night's closing ceremony was especially bad that way, and it was obvious it'd been hacked up and reordered to fit NBC's own tastes. Every now and then they'd break in to the ceremony for an extended reminiscence about one of the US gold medalists, and I got the impression they were cutting large parts of the ceremony so they could fit in all the sappy instant nostalgia crap. But the worst, the absolute worst part was the near hour-long Tom Brokaw piece about how glorious World War II was. NBC seems to think that the important lesson everyone should come away with from the last two weeks is that we all need to stay perpetually misty-eyed about the exciting and wonderful world of war. Let me go out on a limb and propose that in the future, the phrase "enemy machine gun nest" should never, ever appear in any Olympic coverage, period. If you'd had company over to watch the closing ceremony, and someone had gone off on an hour-long nostalgic bender about WWII, and just wouldn't shut the hell up about it and let you watch the damn ceremony, all because he thought his own personal obsession was more important and he wanted to inflict it on everyone, I mean, you'd think that was supremely rude, wouldn't you? That Brokaw scumbag just did that to the whole country. But then, the opening ceremony commentary by his equally smarmy anchor desk replacement, Brian Williams, wasn't that much better. I guess the network decided we should have someone there to spew grim factoids and remind us all about what an ugly and violent place the world is these days. You know, to make it all "relevant", or whatever. So current events in the world are pretty terrible, yes, we all know that. Can't you people just STFU for a bit, just let us have our two weeks of fun escapism, and an imagined world where countries really do meet only on the playing field, not the battlefield? Is that just too freakin' much to ask? Bastards.

Anyway, I don't remember a lot about opening and closing ceremonies prior to '96. I'm actually not sure I watched them before that. That, or the just weren't as memorable. Or I'm getting old and starting to forget things. I do remember the bit from Barcelona (1992) where they lit the torch with a flaming arrow, although I might have just seen that clip on the news, I don't remember exactly. That was fun to watch, although it may have touched off a subsequent arms race in lighting the torch with bigger and weirder stunts. Nobody's topped the flaming arrow yet.

Some selected memories of past Olympics, summer & winter:

Montreal, 1976 The earliest Olympics I remember, and then not very clearly. I remember watching a lot of weightlifting, for some reason. I recall that one of the American competitors was black, and I made some sort of prejudiced remark about him for that reason. My parents were appalled, and wanted to know where I'd gotten those ideas. The correct answer in those days was probably "everywhere", so I'm glad now that I got a serious scolding about it at the time. An important life lesson, learned from the Olympics. Just for that, I probably merit my own human interest story on national TV next time the games roll 'round. Although since it was 1976 I think the actual important life lesson was that it's OK to hate people, just so long as their uniform says "CCCP" on it somewhere.

Lake Placid, 1980 I think I did watch the "Miracle on Ice" game, but I wasn't a hockey fan at the time, so it didn't make that big of an impression on me. No, what I cared about was Eric Heiden in his shiny gold speedskating suit. I had a new idol. I really wanted to be him, wear the gold suit, and skate super-fast. For probably the next year or so, I was convinced you could run faster if you attempted to do that side-to-side speedskating stride, and nobody could convince me otherwise. Sometimes I wonder how things would've turned out if I'd had access to ice skates at the time. But then again, this was around the time I was attempting little league and youth soccer. I was mostly OK at soccer and flat-out awful at baseball, so I wasn't exactly giving people a lot of reasons to think I had a bright athletic future ahead of me.

Los Angeles, 1984 I remember having a nasty cold during part of the Olympics, just like this year. Instead of curling and biathlon, I was curled up in bed watching a bit of cycling and a lot of equestrian stuff. I seem to recall they were playing theme music from the movie St. Elmo's Fire during one of the show jumping events. Ahh, the 80's were a dark and primitive time.

Albertville, 1992 I really miss Olympic demonstration sports. The Albertville Olympics featured a couple of fascinating events: "Ski ballet" (since renamed to the somewhat less goofy "acro"), which was the silliest thing I've ever seen on snow, period. I'm sure it's really hard and all. I've heard synchronized swimming is really hard, too. Just because something's hard doesn't make it a sport, though. And then there was speed skiing, which was about as far away as you can imagine from all the touchy-feely kiss-up-to-the-judges stuff they've been adding in recent years. It's all about top speed in a straight line, period. I don't remember it being that interesting to watch, but it had a certain geekish appeal and a "how do they do that?" quality, sort of like ski jumping. Any winter sport where you need special non-flammable pads so you don't catch on fire when you crash has got to count as reasonably "XTREME" in my book.

Torino, 2006 One thing I've always liked about the Olympics is the way that most of the athletes (various basketball and hockey "Dream Teams" excepted) seem positively giddy to be there. By now it's a familiar sight to see athletes filing into the stadium holding camcorders, taping the whole thing for posterity to show the folks back home. That never stops being endearing. During one of the US women's curling matches, there was a great moment where two US team members (both of whom looked about 17 years old) were puzzling over what shot to try next. There was a brief pause, and then one turned to the other and said in a quiet but excited voice, "We're on TV!". And they both smiled.

Perfect.

Sunday, February 26, 2006

olympics (pt. 1)

The Olympic closing ceremony's wrapping up over in the other room as I'm writing this. No, that's not quite right, they actually wrapped hours ago, but you'd never know that from the people on TV.

This isn't going to be a critique of NBC's abysmal coverage of the games. That's already been done pretty thoroughly, so instead I'll just point out a couple of good examples. I wouldn't have expected The Nation to cover the Olympics at all, but here they are, with a well-argued rant about the idiotic and chauvinistic coverage provided by NBC, a.k.a. the Neocon Bellowing Corporation. That rant references someone's blog offering a similar argument. And another example I came across. I realize I may not resemble the statistical "average" American, but I have to think that the same ideas have occurred to a lot of Olympics fans. Viewership is way down this year, and there's got to be some kind of reason behind it. Maybe viewers aren't the knuckle-draggers the TV people have them figured for, and they'd really like to see something that isn't a.) ignorant Cold War-style chest-beating nationalism, and b.) manipulative, tearjerking human interest stories about how somebody's great-grandmother passed away 15 years ago, or their dog got run over, or whatever. Enough of the moronic prepackaged storylines. Just shut up and let us watch the actual games, already, ok?

For a rather opposing perspective, the Big Old Media types at AOL present a list of ideas on how to "fix" the Olympics, gleaned by interviewing a variety of sports marketing experts. Since these are basically the people whose ideas count with the Powers That Be, I'm afraid things are going to get worse before they get better. Most of the ideas seem to focus on making the games more like the world's biggest reality show. Let the viewers vote on figure skating winners, stuff like that. Plus the authorities need to manufacture international rivalries, like USA vs. Austria in skiing, for example, because the whole point of the Olympics is to hate people from countries you can't even find on a map, I guess.

On a cheerier note, here are a trio of blog entries I came across by people who love the Olympics, each for his or her own reasons, which is great.

The Canadian blogosphere is active as well. Here are four rather interesting examples. You have to feel for the Canadians, four long years of handwringing about their men's hockey team failing to medal. That's got to sting a bit. The blame game has barely begun, so (even though I'm not Canadian) let me get my 2 cents in. The Gods of Hockey will never allow any team with Todd Bertuzzi on the roster to win an Olympic medal of any color, much less skate the Cup. If you don't believe in that sort of thing, you could also lay the blame at the feet of Joe Thornton, who apparently didn't want to be playing for Canada any more than he wanted to play for the Bruins.

A blogger in Norway is doing a bit of handwringing as well.

And finally, here's someone who argues that the Olympics turned out the way the did because Torino is a highly paranormal city. Oooh, spooooky. And it's not just because of that creepy shroud thingamajig, either.

I was going to say a few words here about why I like about the Olympics, but it's getting late, so I think I'll save that for tomorrow. So arrivederci for now...

Saturday, February 25, 2006

Greetings, Cyclotram visitor #250 (or so)!!!



I've just noticed a curious relationship: I've hit about 250 visitors here, right about the same time iTunes has hit a billion songs downloaded. So assuming that each user downloads a mere 4x10^6 songs, we're about neck and neck so far as web traffic goes. I really think that's something to take a lot of pride in, and it's certainly not a coincidence. And furthermore, Steve Jobs & Co. have been at this a bit longer than I have, so I'm going to go out on a limb and predict that I'll get my second 250 before Steve gets his second billion. And my marketshare continues to expand. Mwhahahaha!

In the interest of fiscal responsibility, I'm not actually giving out any enormous cash prizes for being the 250th visitor. What, you think the dot-com era's still going, or something? In lieu of schwag, here are a couple pictures of gibbons, because gibbons are really cool. The first image links to the Gibbon Conservation Center in Santa Clarita, CA, while the second links to the homepage of a French physicist who apparently likes gibbons.

And while we're on the topic of "lesser" apes, here's a fun column out of Alabama that pokes a bit of fun at Pat Robertson. If he didn't exist, Democrats would have to invent him. And even then, nobody would believe it. Pat Robertson is an unflattering caricature of Pat Robertson, and the inevitable riot, too, all by himself.

Friday, February 24, 2006

Short Attention Span Edition

Misc. links and comments without much of a unifying theme:

  • Our local basketball team would love a chance to wallow at the public trough, please. The Trail Blazers can't survive without taxpayer handouts, we're now being told, even though they're owned by Paul Allen, the world's 7th richest man. Right now the team isn't saying whether there's any chance they'll pull up stakes and leave town. I guess they wouldn't want to get our hopes up too much.

    Someone's put together a list of Blazers-fan blogs, if you're curious. What a dreary and depressing hobby that must be.
  • Here's another report about the sleazy petitioners behind the campaign to get rid of our fair city's shiny new public campaign financing program. I ran into several of these people myself, and my impression was about the same as hers. I'm sorry, but even if I did agree with the petition (which I didn't), there's no way I'm giving a copy of my signature to someone who looks like they're being paid in meth and stolen car stereos.
  • A funny review of a terrible new movie I have no intention of seeing.
  • Somewhat less close to home, there's another Cassini Titan flyby coming up over the weekend, if you're interested.
  • In case you've ever wondered where the hell celery comes from, today's your lucky day. Here are some images from the celery harvest in Salinas, California. Oregon State University offers some tips on successful commercial celery cultivation here in the Willamette Valley. Who knew? Not me, apparently.
  • And while we're doing a grab bag of mostly local topics, it seems the local citizenry in Portland is solidly opposed to trying to land the 2008 Republican Convention. The culture clash would be awfully fun to watch, though, you have to admit.
  • Some candidate statements from the upcoming student government elections at Portland State University. Back before there was an Internet, you couldn't enjoy all this useless blathering unless you were right on campus. But now, citizens of fledgling third-world democracies can find this stuff and learn a thing or two about how to make utterly empty and vapid campaign promises.
  • And finally, let's all raise a glass to the nice folks at the Technical University of Darmstadt, who've just unveiled their newly invented robotic bartender. The Register article is the only one that correctly places the university in Germany, not the Netherlands. Note to journalists: "Deutschland" != "Dutch". Sheesh.

Thursday, February 23, 2006

Egg and Olive Penguins


From the very beginning, it was inevitable that I'd eventually write about the egg-and-olive penguin phenomenon. It's a unique combination of two recurring themes here at Cyclotram: cute animals and horrific 60's cookbooks. As the original article notes, you can indeed assemble a semi-realistic, semi-cute, semi-edible, semi-penguin-like object out of nothing but black olives, hard-boiled eggs, and toothpicks. Does this count as "cooking", or do we file it under "hobbies and crafts"?

And to top it off, the, ah, recipe first appeared in an immortal tome titled "Meals with FOREIGN FLAIR". It's not known what country the authors had in mind, in this case. Perhaps Italy, because of the olives, you know.

I had a surprising amount of trouble locating pictures of egg-and-olive penguins. Once upon a time, they were everywhere, in every cookbook. But that was in the pre-Internet era, and they seem doomed to be one of the many things destined to disappear down our collective cultural memory hole, merely because they failed to make the leap to the latest and greatest medium. Just like all the great songs that never made the leap from 8-track to mp3. Yes, both of them.

If you'd like to compare and contrast, here's another penguin recipe. This recipe suggests they'd be perfect for a Linux get-together. Not because anyone will eat them, but a good ironic laugh will be had by all.

The page also provides a recipe for Tang Pie, but sadly there's no image to go with it. Sure, we can all laugh about it now, but when they start holding county fairs on the moon, this recipe's guaranteed to bring home a nice blue ribbon for some happy homemaker of the future.

If you tire of the whole egg-and-olive business, and you wonder what real penguins taste like, you may be out of luck, if this FAQ from NASA is to be believed. Seems the UN frowns on that sort of thing. Another FAQ page, this time from the US Antarctic Program. There seems to be a fairly widespread public interest in chowing down on penguins, which our government is valiantly struggling to discourage. Here's one rather colorful passage.

Frederick A. Cook, a doctor aboard the Belgian vessel Belgica when it was stuck in pack ice in 1898, basically regarded penguins as inedible: "If it's possible to imagine a piece of beef, odiferous cod fish and a canvas-backed duck roasted together in a pot, with blood and cod-liver oil for sauce, the illustration would be complete." But because they needed fresh meat to help combat scurvy, he told the captain of ship to regard penguins as medicinal, and swallow the meat as a duty and example to others.

You have to admit that sounds awfully discouraging. Although it's also true that most food from the 60's and 70's could be described in roughly the same way. Sometimes there was even Jello(TM) involved. Even today we aren't entirely free of icky retro-food. As one example, the one and only Emeril recently proffered a recipe for lima bean casserole, although at least he had the decency to relegate it to being a side dish and not the main course. So in theory you could feed it to the dog and nobody would notice, assuming the dog was hungry enough.

And speaking of Linux, which we were doing a minute ago becaue of the whole penguin thing, while also speaking of things that ought to disgust all civilized minds, everything's looking very very bad for SCO these days, as usual. And yet the charade continues. I just don't get it. I really don't. I mean, even back in the lawless days of the Spanish Main, you couldn't go on indefinitely in the piracy business unless you managed to turn a profit on occasion. Granted, these days SCO's more of a ghost ship than a pirate ship, but it's still amazing (and highly suspicious) how the bastards keep the damn thing afloat.

Wednesday, February 22, 2006

Generic Followup


The title of this post is a very, very poor title, according to an article I came across on how to crack the blogging "A-list". And, I mean, who wouldn't aspire to that?) Also, I need to use lots of graphics, and generally try to make people believe (rightly or wrongly) that they know and like me. Hmm. I'll take that under advisement, I guess.

But I do like graphics. Here's a French bulldog puppy for ya. Everybody and their sister loves puppies, right? See, I can pander shamelessly with the best of 'em, if I need to. If the puppies don't reel 'em in, I can always try bunnies. Evwybody wuvs bunnies!

Although (and this is the followup I mentioned) I have discovered a surefire way of my own of generating at least one or two guaranteed hits. And now I'm going to let you in on it, absolutely free. Just be sure to use the phrase pretrib rapture somewhere in your post, and bingo! The previous post's already gotten two search engine hits, and I'm guessing the first was probably the same person who left the earlier note about that "Diehards" article. Oh, goodness me, I've gone and used the phrase "pretrib rapture" again, so I'm guessing this post will pull in a hit or two as well. Hello, again!

As a followup to an earlier post of mine, but kind of still on the topic of luring unwitting visitors to this dark and remote corner of the web, I took a peek at Technorati to see if I show up there at all. Just out of idle curiosity, mind you. The answer is of course "no", and the only hit for the word "Cyclotram" is a movie review of Unknown World. Like most reviewers, he got bored and rated it a 2 out of 5. Am I the only person on the whole freakin' planet who likes this movie?

Then I decided to google for "cyclotram". Again, purely out of idle curiosity, you understand, not because I'm wallowing in vanity and neediness or anything. Lo and behold, at the moment this very blog sits squarely atop the heap. Followed closely by the FeedBurner RSS feed I set up a while back, which is odd since I'm not aware that anyone's actually using the thing, other than the occasional hit from Yahoo's blogsearch bot. But hey, at least I can say I'm down with the whole groovy RSS thing, which is about as close as I've ever gotten to being trendy. Next, after lil' ol' me, comes the movie's page in Amazon's DVD section.

Hey, whaddya know, I also show up on something called BlogShares, which claims to be some sort of fantasy blog stock market. Whatever the hell that is.

I guess I'd better get busy spending all that fantasy IPO cash I didn't realize I had, and start making brainless bizdev deals with other little-known blogs, and then post about it here, thereby driving my stock up even further. It's a new economy!!! To the moon!!!

How to suck up to me...

In a highly encouraging development, Guy Kawasaki has written a piece about how to suck up to bloggers. His thesis: Suppose you're a soulless corporate marketroid with a product to sell, and you'd really like the blogosphere to do one of those nifty viral marketing campaigns for you, gratis. Or as close to gratis as you can manage. What you want to do, in essence, is adopt a highly condescending attitude towards bloggers, and regard them as insecure little kids who respond well to, among other things:

  1. Extravagant and obviously insincere praise
  2. Random bits of token schwag straight from the bargain bin, and
  3. Smarmy marketers who pretend to be their new best friend in all the world.

As an aside, I do have a Guy Kawasaki anecdote. He was an investor in a company I worked for at one time, and he dropped by and gave a little insipirational talk, followed by a bit of Q&A. Someone mentioned they'd read a book recently that had a glowing quote of his on the cover, heaping praise on the book, going on to say they agreed with his assessment. Kawasaki then admitted he'd never actually read the book, and said that he often gives canned quotes like that out of professional courtesy. Didn't see a blessed thing wrong with that. I mean, what could possibly be wrong with deceiving the general public? After all, if you can't deceive them, who can you deceive? That was the day I decided Kawasaki was a total sleazebag.

Here are a couple of other blogger takes on the article: Marshall Sponder at WebmetricsGuru and Jeremy Zawodny.

For my part, my first reaction is to feel terribly, terribly left out. I've been doing this for a couple of months now, and I still haven't been contacted by anyone's corporate marketing department. Kawasaki at one point says "Today's egocentric, self-indulgent blogger with five page views per day may well be tomorrow's Technorati 100 stud." Couldn't agree more, although I'd like to think that I'm neither egocentric nor self-indulgent, and it's also true that five page views per day is a red-letter day here at Cyclotram, and furthermore I don't think I'm the most easily persuaded person on the planet. Still, when there's a big party going on and nobody thought to invite you, you can't help but grumble a little. It reminds me of high school, and I'd rather not be reminded of high school.

So far there's only been one instance of anyone trying to get their personal topic onto my radar. In a recent post where I ranted about the so-called "rapture", I recently got a rare user comment suggesting that I cover the topic further, particularly an article titled "Pretrib Rapture Diehards". So there, I've actually gone and linked to the original, and users can go look at it for themselves. The article takes a different perspective than I do, and seems to be arguing that it's incorrect theology. Whereas I argue that "incorrect theology" is redundant, as there's no other kind of theology. All religious beliefs are untrue, but some are harmless and others aren't. If religious people are just going to sit around navel-gazing all day, it doesn't impact me other than giving me an excuse to roll my eyes a little. But it's another matter entirely when they demand eternal war against the evil unbelievers on the other side of the planet, coupled with a gimlet-eyed book-burning theocracy here at home. Even if their theological credentials were impeccable, and they could point to passages where Jesus commanded his followers to go forth and slay the infidels in his name, or laid out God's precise wishes regarding stem cells and people in persistent vegetative states, they'd still be precisely as wrong as they are now. (As an aside, here's a good blog entry I came across discussing Thomas Jefferson's edited-down bible, where he excised all the silly and irrelevant crap about miracles and so forth.)

In any case, it turns out that the user who made this comment has made a bit of a hobby of posting similar comments around the net, encouraging people to check out the "Diehards" article. So I guess in a large sense we could consider this a marketing campaign. And I did take the bait, sort of, which ought to be really encouraging for anyone who'd like to try enlisting me in a campaign to really sell something.

I mean, personal integrity and the solemn Blogger's Oath we all take (c'mon, don't tell me you forgot about that part) both prohibit me from guaranteeing or otherwise leading people to believe that I can be bought for any price, much less that I'd stay bought thereafter. But it'd be highly entertaining and possibly lucrative if the world's top marketers and lobbyists decided to have a go at it. Why should "important" bloggers and politicians and doctors get all the goodies?

In that spirit, here are a few basic do's and dont's if you want me to blog on your behalf.

  • Golf doesn't interest me, either as a player or as a spectator. All-expenses-paid trips to St. Andrews may be enough to buy Tom DeLay's undying loyalty, but I like to think I'm a tougher nut to crack than ol' bug-boy there.
  • I don't want a freakin' polo shirt. If I wanted polo shirts, I'd go to more trade shows. Pens with your logo on 'em, maybe, but if they run out of ink or dry out quickly, you risk the infinite wrath of the blogoverse. So logo pens are probably out too. In general, anything that says "I've got a whole crate of these, and I'm handing them out to bloggers like candy" isn't going to do you a lot of good. I mean, how am I supposed to feel all warm and fuzzy and special and excited about your product unless you prove you care deeply about the real me, by getting me something a.) unique, and b.) expensive. A shiny new Lotus Elise or Exige might be a step in the right direction, so long as we're playing Dear Santa here. British Racing Green, natch.
  • If you're trying to sell crack cocaine, or Windows XP, or lite beer, or a war you'd like to start, I'm afraid you're out of luck. I have to draw the line somewhere.
  • I've mentioned that I like wine on occasion, right? Great. Although I should caution that it's not a lifestyle affectation for me, so don't make the mistake of thinking I also care about the other stuff that's supposed to be inseparable parts of the "lifestyle" (cigars, expensive Harleys, Hummers, Dockers, big shiny metal watches, er, "sports chronographs", fighter pilot fantasy camps, etc.).
  • If you have cool hardware, it might be worthwhile to ship me some and see if that helps. Be warned that if you send the bottom-of-the-barrel entry level model, I will find out. Infinite wrath of the blogoverse, remember?
  • Kawasaki's only real insight, in my mind, is the bit where he suggests Stanley Cup tickets might be helpful. Really it depends on who's playing, though. If Detroit's playing, I'll want seats close to the ice, and a generous supply of fresh octopus. You know, for throwing.
  • If one were to skip the shopping trip and just donate cash, it would make the whole transaction so much more honest, don't you agree? If you've actually read this blog at all, you'll have noticed that I often rant about people who aren't honest about their motives. No sneakiness, no wink-winks, no quid pro quo. You want a deal, put it in writing, with greenbacks behind it.
  • If you want me to use phrases or words I normally despise, like "paradigm" or "synergize", it'll cost you extra, big time. And I'll still probably put them in quotes. Readers will think it's more "authentic" that way. Trust me. We'll fool 'em all, and make millions! Mwhahahaha!
  • And I should mention that no matter what, I'll feel obligated to do the full disclosure thing and inform readers I'm shilling for someone on a paid, or semi-paid basis. It's only fair. If readers are going to get spoon-fed, they at least ought to know who's holding the spoon.


There. The cards are on the table. So if I sound like the ideal willing patsy for your unholy corporate interests, don't hesitate to drop me a line.

Thx. Mgmt.

Tuesday, February 21, 2006

Mondovino



Saw a good movie yesterday, and just this once it's not a cheesy 50's rubber monster movie. Mondovino is a documentary about wine and the impact of globalization. It's not your usual film about wine, full of pathetic rich boomers prattling on about how they simply adore everything about Tuscany. You do encounter a few of 'em, but they come off looking like complete idiots and pretentious fools, as they should. A lot of global wine industry superstars come off looking that way. When you see negative comments about the film, it seems that much of the time they're from people offended by the unflattering portrayals of their personal prophets. It's true the movie doesn't pretend to be objective. It has a clear anti-globalist agenda, and wears its heart on its sleeve. While it's ostensibly about wine, it's really a critique of wider trends in the global economy, including the creeping homogenization and dumbing-down of consumer preferences (and therefore products) across the board. I tend to agree with this critique, although I do have to note in passing that in any other industry, if the product is basically unusable for the first 25 years after it's produced, it would be considered a serious defect, not a mark of quality.

One little quarrel is that the film does tend to romanticize the lives of small wine producers in France and Italy, so anyone who's inclined to see that as a sort of ideal existence will have this attitude reinforced.

I don't mean to go off on another round of boomer-bashing, but many of the "bad guys" in the film just happen to be affluent 50-something Americans. There's something really repulsive about rich middle-aged guys who describe themselves as revolutionaries, spouting canned references to Ralph Nader and Watergate-era journalism. Yeah, buddy, after all these years you're still a rebellious outsider exactly how? Riiiight. Also, I never want to hear the phrase "our generation" ever again. Woodstock is ancient history. Ancient, silly history.

I suppose if you aren't familiar with any history (or mythology) other than your own, everything will seem like a fresh, new discovery. You can waft about the vineyards of the Mediterranean region, flaunting your money, drinking a great deal, and generally living the life of an artistic, cultured dilettante. You can go about thinking you've stumbled on a heretofore-undiscovered idyllic rural utopia that exists apart from the "modern world". You can babble on about how the light is somehow different than anywhere else on earth. You can fill entire books about how it's all so incredibly profound, which primarily means that life moves slower, and the food's pretty good. You can do all of these things, and genuinely think you're the first "generation" to ever encounter such wonders. It helps not to be aware that rich people from northern Europe have been making this same pilgrimage for centuries now. They were idiots too, but a few of them actually knew how to paint. Oh, and then there's the people who actually live there, all of whom do, in fact, live in the modern world. Some even have cell phones. How shocking!

It strikes me that the same people who swoon over rural life in Tuscany or Provence would probably cross the street to avoid meeting farmers in their home countries. Someone who'd be considered merely "rustic" overseas becomes a hopeless ingorant redneck here at home. Small towns where everyone knows everyone else's business and everyone goes to church are picturesque just so long as they're beyond our borders, otherwise they're creepy and full of hidden evil. Deeply religious and superstitious rural Italians who go on and on about the "evil eye" are charming, but when rural people here are similarly religious and superstitious, it evokes a visceral horror among the sophisticated set. Mediterranean poverty's explained away as people simply "living just as they did centuries ago", but the same thing in Appalachia marks people as poor white trash. When was the last time you saw someone heap praise on Nebraska as a utopian land of simple folk who live in joyous, perfect harmony with the seasons?

And certainly nobody ever asks the Tuscans how they feel about their region being progressively carved up for foreigners' hobby farms and turned into a sort of agrarian theme park. Welcome to Tuscanyland, the Yuppiest Place on Earth!

But enough about that. One other distinguishing characteristic of Mondovino's baddies is that nearly all of them wear polo shirts, and the good guys don't. It's like how you can always tell the bad guy in an old western because he's wearing a black hat. Before now, I really didn't think French men ever willingly wore polo shirts, but a few of them do, the same men whose French is peppered with English terms like "marketing" and "product strategy". Yikes! This is one area where the wine world has a lot in common with the computer industry. The bad guys always wear polo shirts, preferably with corporate logos on them. It's the true IT mark of the beast, the real world equivalent to "pointy hair". However, the issue's muddied a bit by the fact that geeks who don't know how to shop for themselves also wear polo shirts, or any other corporate schwag they can get for free. Give 'em corporate logo kilts instead, and they'll wear those to work.

The good guys, on the other hand, have dogs. Some of the bad guys have dogs, too, but they seem listless and unhappy compared to the good guys' happy and charismatic dogs. Dogs get a lot of screen time. I imagine they're intended to be "telling details" about the lives of the people being depicted, but it also seems pretty clear that the filmmakers just really like dogs a lot, too. Even the world's surliest French bulldog.

So anyway, all ranting aside, I highly recommend the movie. Netflix carries it, but your local chain video store probably won't. If you're like me, and you like wine but find "wine people" appalling, I think you'll enjoy it.

Monday, February 20, 2006

SuperHyperRedux

Some followup notes about my recent math-heavy Hercules vs. Hydra post. If you didn't find that one very interesting, this one will definitely bore you to tears.

  • Here's a link I ought to have included, giving an explanation of Goodstein Sequences, the basic idea behind the Hydra problem.
  • A point I don't think I made sufficiently clear in that post is that, while the basic notion of using hierarchies of functions to define ordinals is widely shared, the higher up you go the less agreement there is on what hierarchies ought to look like. There's no one natural or universally accepted representation, at least not one that's been identified to date. Veblen's phi hierarchy, introduced back in 1908, seems to have attracted general use anymore, but there's no reason you couldn't ignore it entirely and define your own equally valid representation if it suits your needs better. This recent paper discusses a number of concerns, including the ongoing problem of "proper" ordinal notation. As you can see in that paper, the state of the art as of ten years ago was well beyond anything I mentioned in that previous post. I'll try to fill that gap if I ever get a better handle on the material. Right now it's Greek to me. One interesting tidbit is that some recent notational innovations go beyond the existing trick of using 'big' ordinals (w1/Omega/aleph-1 and larger) to help describe "normal", countable ordinals (generally beyond Gamma_0), which makes some mathematicians uneasy, or at least they find the practice unsatisfying. I think the justification has something to do with the big ordinals merely being indexes into the hierarchy of functions, and not being part of the functions themselves. I think. Regardless, the state of the art moves beyond alephs into the land of large cardinals, up to at least supercompact cardinals. Which is pretty damn big, if you ask me.
  • I'd intended to spend some time pondering the relationship (if any) between ordinals and hyperreal numbers in that post, and just didn't get to it. It's not a topic I've seen a lot of discussion about, although here's a somewhat recent Usenet thread discussing the idea. I think for the most part it just doesn't come up in the course of normal mathematical work. If you're using hyperreals, you don't really need or care about ordinals, and vice versa, so positing any relationship between the two would just be unnecessary.

    To me, things would seem generally nicer and tidier if you could regard the countable ordinals as a subset of the hyperreals, for example. Or more precisely, as a subset of the hypernaturals, themselves a subset of the hyperreals. Identifying the sequence (1,2,3,...,n,...) with the ordinal omega (denoted here by 'w') doesn't seem like that big of a stretch. Venturing off to one side for a moment, the surreal numbers are intended to be all-encompassing, and it's been stated that the surreals include the class of all ordinals, plus the set of hyperreals, with the surreal number (1,2,3,...|) being explicitly identified as 'w'. Surreals and hyperreals are similar enough that it seems logical (to me) to identify the surreal 'w' with the hypernatural (1,2,3...n...), and call it 'w' as well. Further, you could identify the sequence f(n) = (a_1,a_2,a_3,...) as f(w), so that n+1 = (2,3,4,...) = w+1, n^2 = (1,4,9,16,25...) = w^2, n^^n = epsilon_0, and so forth.

    So you could do this, but let's take a step back and merely argue that ordinals and hypernaturals look pretty similar in a lot of ways, so that there may be interesting ideas to carry back and forth between them. This is because they aren't exactly the same, and you run into a few rough edges if you try to fit them together.

    Recall that arithmetic works differently on hyperreals than it does on ordinals, and then there's a third arithmetic for cardinal numbers. And further, IIRC arithmetic on surreals isn't quite the same as arithmetic on hyperreals, either. One could take the position that these are merely three different views of the same object, expressing various properties that happen to coincide and give the same answers so long as we limit ourselves to finite numbers. Because of this difference, there are several kinds of hyperreal that aren't also ordinals. Obviously infinitesimals are out (no 1/w), as are any non-"integers" (no w+pi). 2^w and w!, in hyperreal terms, both define "integers" that aren't also ordinals, since in ordinal terms both expressions are equal to 'w'. No such thing as a negative ordinal, either. And infinite numbers less than 'w' are right out, like w-1. Meanwhile, the ordinals stretch far, far past w1, the first uncountable ordinal, which appears to be the upper bound on the usual realm of hyperreals, which is why I'm limiting the discussion to countable ordinals.

    A correspondence like this does let you ask some (possibly) interesting questions, like what hyperreal sequence, in other words what function from N to N, would correspond to Gamma_0, or various other 'large' ordinals. And going the other way, one of the common objects of study in the area of function hierarchies is the so-called "slow growing hierarchy", where G_0(n) = n+1, G_m+1(n) = G_m(n)+1. Clearly, if you can increment by less than 1, you can get a hierarchy that increases much more slowly, even infinitesimally if you like, say G_0(n) = n + 1/n, G_m+1(n) = G_m(n)+ 1/G_m(n), so that I suppose you'd eventually get w+1/w, w^w+(1/w^w), Gamma_0+(1/Gamma_0), etc., unless perhaps that hierarchy converges to a limit somewhere. Either way, I don't know how useful it would really be.

    Also, it's possible everything I just said is complete nonsense.
  • On a different note, I've finally managed to piece together part of the puzzle about "supernatural numbers", for which I'd come across several apparently incompatible definitions. The PlanetMath definition just referenced doesn't mention this, but the same product-of-primes thing is used for Godel numbering. So it becomes clear that these are the same supernatural numbers that Hofstadter talks about, but doesn't properly explain or give references for, in Godel, Escher, Bach. GEB goes on to mention infinitely large supernatural numbers as an example of nonstandard arithmetic or number theory. Again, the book doesn't explain what's meant by "nonstandard", but thanks to the magic of the Internet it's possible to find out. The axioms of Peano arithmetic were intended to give a succinct, complete, and unique definition of the natural numbers, but Lowenheim-Skolem theorem demonstrates that the axioms do not, and cannot, uniquely define the natural numbers, and it's possible in principle to create sets of objects, of any cardinality you like, that fulfill precisely the same axioms. And you can't get to a unique definition by adding more axioms, or using a different set of axioms. It's just an unavoidable fact of life. Instead of freaking out or getting depressed by this result, the math world simply decided to call the desired model "standard" and all the others "nonstandard", and study all of them. The supernaturals are just one nonstandard model, one which includes the naturals as a subset. The word "nonstandard" as it appeared later in connection with hyperreals is an analogy: Nonstandard analysis is to regular analysis as nonstandard number theory is to regular number theory. Both add additional "useful" numbers to the usual set, supernaturals being "useful" because, as infinite products of primes, by definition they fall under the fundamental theorem of arithmetic, so you can do all the usual number-theoretical stuff with them, I guess. Maybe some of them are even prime themselves. That's a weird idea.

    If we're going to assume the supernaturals fit into the hyperreals (which may or may not be justifiable, see the previous discussion), I think they'd all fit within the range starting at 2^w and less than w^w, which would mean there'd be no overlap between them and the ordinals. Although again, this is just a guess.

Sunday, February 19, 2006

Concrete Cabin Fever


Ok, so I'm sick for a few days, and now it's a three day weekend. It'd be nice to get out of the house (or ultra-mod concrete pod in the sky, in my case), but it seems like we're on day Gamma_0 of a nasty cold+windy snap, so going outside is just unreasonable. It's beautiful outside, barely a cloud in the sky, and you'll need a spacesuit if you want to go out in it.

I popped outside to get some groceries a few hours ago, and I'm still thawing out. So I think I'll do a bit of aimless blogging, instead of trying that again anytime soon.

In honor of our Arctic-ish weather, today's cute animal is an Atlantic Puffin, chomping on some tasty fish. Fish has always seemed especially tasty in cold weather (to me, anyway). I'm not sure why that would be. It's probably just my opinion, not a product of evolutionary biology, since the colder it is, the more dangerous it is to go fishing, and anybody who instinctively craved fish in midwinter would be rapidly removed from the gene pool. It stands to reason, anyway.

When I was at the grocery store earlier, I picked up a chocolate bar with a photo of puffins on the wrapper, put out by the "Endangered Species Chocolate Co.". Yes, it was yet another one of those feel-good upscale "liberal" products, where what you're really buying is a temporary warm fuzzy feeling that your money's going to a good cause. And yes, it's organic chocolate, with organic sugar added. And no, it's not actually very good chocolate, but that's not really the point, is it? If you criticize the product, you must be some kind of diabolical Cheney clone who's against puffins. Not just puffins, but baby puffins. And the Baby Puffin Bar is just one product in a line of candy bars featuring a variety of charismatic megafauna. Never mind that actual puffin chicks look nothing like what's on the label. What's more, although the company's based right here in Oregon, they don't seem to be aware that puffins live along the Pacific coast as well as the Atlantic. And even the Atlantic ones are not actually endangered.

But all is not lost for local fans of actual quality chocolate. Now that Valentine's Day is over, I can mention a couple of local favorites without endangering my supply. My current favorite is Sahagun Chocolates, a tiny hole-in-the-wall storefront on NW 16th just north of Burnside downtown. The main website is more gloss than info, but the owner also has a blog here. This chocolate is amazing, wonderful stuff, but don't just take my word for it. Here's another rave about it.

Another big favorite of mine is Arioso Chocolates. They don't have a year-round store, but in warmer months they're available at local farmers' markets. Mmmm.... chocolate....

Wednesday, February 15, 2006

Common Cold Edition

I'm sitting here at home with a nasty head cold. So I've got nothing better to do than crack open a cold one at 7:30 am (hey, it's helping! honest!) and braindump a few random thoughts.

  • Now that Whittington guy's gone and had himself a heart attack, which is really inconsiderate of him, since the WH press people had just decided to start treating the whole episode as a big hearty joke, so to speak. They must be kicking themselves right now, wishing Cheney had just stuck with Plan A: finish the guy off, dump him in an unmarked shallow grave, and have the government cover the whole thing up. Unfortunately there were witnesses, and Cheney's gun was way too puny to contemplate taking them out as well.
  • On a cheerier note, the Olympics are on. Sooner or later I'm going to post about why I love the Olympics, but right now I'm in a viral-induced haze. I'm up to random thoughts and tidbits, but don't ask me to bust out multiple paragraphs on the same topic. Also, my DVR is full of curling, and it beckons to me. It calls me to come and watch the gentle art of the sliding rock and the pushbroom. And like I said, I've got nothing better to do right now. One thing though: During the opening ceremony (which was the usual parade of "one damn thing after another", but even more disjointed than most), when the Italian team marched in I noticed someone holding up a sign that said something like "Saluc Ladins". Which doesn't look Italian, exactly. Google indicates this person is a native Ladin speaker, one of a number of small linguistic minorities that cluster in the Alps in Italy and nearby countries, such as Romansch in Switzerland, and Friulian in more northeasterly parts of Italy. It's kind of fun looking at pages in Ladin, since it's obviously a romance language like Italian, Spanish and French, but it's also obviously not any of those. Still, it's kind of fascinating to look at text in a language you've never seen before and be able to make out a word or two. Not everybody's happy, though. Here's a post in an Italian skiing forum where some people seemed to think the whole incident was quite embarrassing.
  • Word on the street is that dual-core x86 iBooks may be on the way. Woohoo!
  • And the latest shenanigans in the SCO vs. Universe case. Now SCO's trying to get even more delay in their case against IBM, filing to take a bunch of depositions against third parties (Intel, Oracle, Open Group) at the very last minute. Needless to say, IBM is Not Happy About This. IBM's also making a new attempt to get most of SCO's claims about "misused material" thrown out. The filings are worth reading even if you haven't been following the case. If the filings in this case are any indication, it seems that if you can speak and write English in a clear and logical way, these days you're destined for law school. And if you can't, you're doomed to a life of journalism.

Monday, February 13, 2006

Cheney as Raskolnikov (& friends!)




No doubt you've already heard about Dick Cheney's little hunting "mishap", and every wannabe comedian out there is pretty much obligated to take a cheap shot or two (so to speak) at his expense. And yes, it is pretty funny. For those of us who already had the guy pegged as a creepy, amoral sociopath with homicidal tendencies, it's also not very surprising. The guy just doesn't seem to attach any value to human life, even that of his closest friends. So even if it was really an accident, I don't see Cheney losing any sleep over it.

And what if it wasn't really an accident? One constant theme throughout Cheney's career is that he thinks he's above the law, and deserves to be treated differently than members of the toiling classes. He didn't go to Vietnam because he had "other priorities". He didn't unload his Haliburton stock when he became VP, because he didn't want to, and nobody was willing to try to force him to. And then there's the whole bit with lying about WMDs. Let's not forget that part. His attitude is always: Do as you please, as brazenly as possible, and challenge anyone to try to lift a finger about it. You have to admit it's worked great for him so far. He's got no reason to think there's any limit whatsoever on what he can get away with.

And on top of everything else, he didn't have a license to hunt quail, it turns out. From the linked article:


Cheney has a Texas non-resident hunting license, but he failed to get a $7 stamp that's required to hunt game birds, the vice president's office said in a statement Monday night. He has since sent a check to the Texas Parks and Wildlife Department to buy the stamp, the statement said.


Another article about that pesky $7 stamp business he felt only the "little people" needed to get.

Now he's gone and shot someone, and everyone from the White House to the media to the victim himself are all rushing to say it was a regrettable but unavoidable accident. So maybe it was, and maybe it wasn't. We'll never know for sure, because they'd all close ranks and behave exactly the same way regardless of what actually happened, just because he's important and powerful and therefore deserves infinite deference and benefit of the doubt. Perhaps he just decided he wanted to shoot someone, for some reason, and so he did, because he knew for sure he was totally immune to consequences of any kind. I certainly can't believe he has moral or ethical objections to shooting people, or to anything else for that matter.

He reminds me of Raskolnikov in Crime and Punishment, who killed a couple of people because he decided they were bad and deserved to die. He, too, thought he was a law unto himself, an Übermensch outside society, entitled to kill with impunity as he saw fit. But then his conscience started to bother him, and in the end he got eight years in Siberia. This is where he and Cheney part company: Dostoyevsky (an extremely conservative and religious man, btw) hoped to demonstrate that everyone is ultimately subject to the same immutable laws and consequences. All I think he really demonstrated is that you can't get away with murder if you're an impoverished student, no matter how intellectual you are. If you're a czar, or a vice president, the rules really are different. If your czar/VP (the terms are increasingly interchangeable these days) happens to be somone like Cheney, a man who was born without a conscience, bloodshed of some kind is inevitable, and nobody will do anything about it. Nobody will even think less of him for it. After a couple of 24 hour news cycles, they won't even remember the episode ever happened, so if Dick says it didn't, they'll take his word for it.

I realize I occasionally rant about the misuse of historical analogies, but let me introduce a couple that I think are edifying. Inexact analogies, of course, but I think useful in understanding the icky Cheney mindset.

First there's the Leopold & Loeb case from way back in 1924, where a pair of rich teenagers decided to kill someone as an intellectual "experiment in sensation". They didn't get away with it, but this was back in the era when the media actually investigated things. Well, ok, it was also the era when they luridly exploited grisly crimes, too, but now and then there's an upside to that. Also, there's a big gulf between being the teenaged son of the VP of Sears, and being the VP of the whole country.

Or we can go a lot further back, all the way back to the Roman Empire. Not the end of the empire that conservatives obsess about, but its beginning, which marked the end of the centuries-old Roman Republic. An excellent popular account of that turbulent era is the recent book Rubicon: The Last Years of the Roman Republic. The lesson, in short, is that if you're ruled by men of unlimited ambition, who ignore with impunity any law or tradition that doesn't suit them, no republic can survive for long. I'm not going to compare Cheney with Julius Caesar (or Napoleon for that matter), since he (like most conservatives) would probably see that as a great compliment. Maybe he's more of a Sulla. Not in the details, perhaps, but in the larger sense, as someone who was the first to really knock the republic off its axis and make its basic institutions look vulnerable, laying the groundwork for another equally ruthless person later on down the road. President Roy Moore, anyone?

Yay. I can hardly wait.

Friday, February 10, 2006

Meanwhile, on Mars...


The twin Mars rovers are still at it. The Spirit rover's just arrived at a weird area dubbed "Home Plate", which looks very different from the usual (and rather boring, to my untrained eyes) Gusev Crater terrain. Sounds like nobody yet has a clear idea of what caused all these layered rocks, so stay tuned.

Meanwhile, here's the latest Mars Express image release, showing some funky tectonic pits and other features. Unlike their NASA counterparts, ESA researchers don't release a lot of images to the public, so any image release is a moderate-to-big occasion. ESA's still new at the whole PR game, I guess.

Meanwhile, on Earth, researchers studying a Martian meteorite have again put forth the idea there might once have been microscopic life on Mars. Something to do with veins of carbon-rich material in the meteorite. At least one of the team members was involved with the famous and still-disputed 1996 report about a different Martian meteorite. Another team member once headed the ill-fated Beagle2 project. So I don't know what to think about this. I don't really like the idea that the whole rationale for exploring Mars stands or falls solely on whether the planet ever had any microbes. People are always claiming another crucial piece of evidence for a discovery that, it's intimated, is just around the corner. And 20 years from now it'll probably still be just around the corner, and people will still be finding "crucial" bits of evidence. Do that long enough, and Congress (and the public) will start to think they're just funding a big con game. I mean, keep it on the list of things you'd like to investigate, but reserve the top couple of spots on the list for things you know actually exist, like, say, the solar system's biggest volcanoes, for example. The public loves volcanoes. Look at all the traffic the Mt. St. Helens webcam gets.

Meanwhile, elsewhere on Earth, fresh off getting fired from NASA, that slimeball George Deutsch is whining about how he's the real victim of the Big Bang Memo debacle:

"What you do have is hearsay coming from a handful of people who have clear partisan ties and they are really coming after me as a Bush appointee," he told radio station WTAW.

"I was an easy target. I was low-hanging fruit."


Un-freaking-believable, but not at all surprising. If you needed any more evidence that the guy's a total partisan apparatchik, here it is. It all boils down to partisan politics for him. In his mind, he was martyred by the hordes of commie Bush-haters, purely because of his unlimited devotion to the Glorious Leader. The notion that global warming or the Big Bang might be objectively true has never occurred to him, not even once. In today's conservative mind, it seems, there are no objective truths, just political wedge issues, just ways to scare up contributions or pander to the base. And I doubt he's the only party hack warming a cubicle at NASA HQ. In the event they ever do find unequivocal evidence of life on Mars, or anywhere else, we'll probably never hear a single word about it, since life on other planets isn't mentioned in the Bible.

Sadly, all this public wallowing in self-pity will likely turn out to be a fabulous career move for Deutschie. There's an unlimited market out there for conservative/fundie types who spin the "liberal persecution" angle and generally wallow in self-pity day after day, week after week, year after year. By now, he's probably got a seven-figure job offer from every think tank in DC. He's set for life. He'll never have to spend another minute outside the Beltway ever again, unless maybe Fox News makes him their new science editor (with extra emphasis on editor). That would be an important job in the Fox universe, since it mostly involves offering constant uninformed speculation about a variety of lurid missing-white-female-of-reproductive-age crime stories. He's already got experience at this, believe it or not, and for all we know he still thinks the Laci Peterson case was the doing of a shadowy Satanic cult.

There's an easy way NASA could've avoided this whole debacle. All they needed to do was pull Deutschie aside and tell him the President himself had given him an important, and very secret, mission. His new job: Go out and search for the edge of the flat earth, and contact HQ immediately the moment it's located. That would've kept the guy quietly occupied for the next few years. Instead, now they've gone and made him a fundie superstar.

In cheerier news, a researcher for Mars, Inc., has presented new evidence that chocolate can help prevent cancer and heart disease. As if really we needed another excuse. Seems the good Dr. Hollenberg is presenting the results at a scientific gathering known as the Cocoa Symposium. Now I know for an absolute fact that I'm wasting my life, and I picked the wrong career. Here I am, grinding out C++ code, when I could be studying chocolate instead. Of course, the symposium's put on by the National Academy of Sciences, a federally-funded institution, so it's anybody's guess what the results will look like once they've run the Deutschie-clone gauntlet. After all, chocolate tastes good and is therefore extremely sinful. I suppose these days all federally-funded researchers will be forced to say faith healing is the only real cure for any disease or ailment. Performed by a famous TV evangelist in front of a live studio audience, if at all possible.

Thursday, February 09, 2006

Glorious Victory, Or Not

So... That sleazy political commisar George Deutsch is out of a job at NASA. And on the same day, it turns out that the BLM isn't going to censor OSU's forest research after all, at least for the time being.

So I should be happy, right? Ahh, if only that were so.

I'm distressed by a trend I've noticed recently. The Oregonian, our local fishwrapper, editorialized about the OSU controversy recently, and while they argued against the attempt to censor the study, they also felt the need to tell us they personally doubted the study's conclusions. This sentiment was echoed in today's paper by various members of the Oregon and Washington congressional delegations. The Oregonian also recently offered the bland boilerplate US newspaper editorial about those notorious cartoons, defending the Danish newspaper while explaining that the cartoons themselves are oh, so very terrible. And not letting the public see 'em so they can decide for themselves, of course. That's a given.

It seems that if you stand up in defense of the principle of free expression, you're always, always supposed to turn around and offer a pious, ritualized condemnation of whatever touched off the controversy. This, I suppose, is to demonstrate that you're taking a moderate, sensible, responsible position. It was Voltaire, I think, who originated the old cliche about disagreeing with what someone says, but defending their right to say it. Which is all fine and good, so far as it goes. But defending someone's right to speak doesn't obligate you to offer any opinion whatsoever about what they said. At some point, all you're doing is showing off your own pristine ethical bona-fides. It does the target of the criticism no good whatsoever, and quite possibly a lot of harm. The target ends up with lots of vocal "defenders" but no actual allies, and these so-called defenders will go out of their way to bash the target for any petty reason they can find, just to prove they're acting purely on noble high-minded principles and aren't actually siding with anyone.

If you're a scientist whose study's just been bashed by a major regional newspaper and much of the local congressional delegation -- all of whom are confirmed non-scientists -- your careeer's bound to suffer in the future. It's not fair, but that's how it is. Furthermore, the controversy's absolutely going to have a chilling effect on any future research in the area, whether by you or by anyone else. How is it that the mainstream media folks keep celebrating one "victory" for free expression after another, and yet in practice the boundaries of what it's permissible to say keep shrinking? It doesn't seem to bother them one bit, so long as their own hands remain absolutely clean.

It feels odd to be lecturing the media about how to defend the First Amendment, but they don't seem to have much of a clue about what's at stake anymore. If everyone tut-tuts about how a certain idea ought to be off limits (while remaining legal, technically), the result is an informal ban. The effect is the same, in the end. Avoiding offering any opinion either way about a scientific study would've been the easiest thing in the world to do. They could've offered a platitude about respecting the scientific community's ability to figure things out themselves. But no. Condemning the content of speech they're busy defending is pretty much habitual at this point. And by offering uninformed opinions about someone's research, they're buying into precisely the same notion so beloved by GWB & Co, namely that there are no objective, testable truths, only political opinions. And "God" help you if you have the wrong ones.

The way to defend free expression, is to defend it, period. Don't try to split hairs or finesse the issue, don't wring your hands about it, don't look for gray areas to hide in. Don't bash anyone for going out on a limb and causing controversy; they're taking much more of a personal risk than you are. Don't concede any rhetorical points whatsoever to the would-be censors. Period. Otherwise you're fighting a rear-guard action, and constantly losing ground. You may be retreating honorably, but you're still retreating. That's just wrong. When it comes to free speech, never give an inch. Never.


I don't have as much to say about the departure of that Deutsch kid. Only that (per DC tradition) the official reason given for his departure was entirely untrue, and as usual nobody batted an eye. The real reason he's out is that he was an embarrassment and a political liability. But for some reason it's not OK to say that. It's not even OK to explicitly disavow his idiotic blather about the Big Bang and give that as the reason he's gone. I mean, that wouldn't be precisely true either; I imagine his feelings about the Big Bang mesh up precisely with GWB's opinion on the subject, and he had every reason to think he was just doing the president's bidding, in his own clumsy and inapt way. But people would've bought it. Instead we get this technicality about him allegedly lying on his resume and not having a college degree after all. Since Deutch apparently quit Texas A&M for the purpose of working in the Bush-Cheney campaign war room, they had to have known about his lack of a degree before now. And it didn't bother them one bit until the blogoverse dug it up and spread it far and wide. But the resume thing gave them a non-controversial reason to ditch the guy, and once they had their political cover, he was outta there, with the whole thing framed up as a non-political, purely HR matter.

I guess this is just how the game is played. Spokesperson gives a bland and obviously false reason for whatever just happened. It's an obvious lie and everybody knows it, but no matter. Instead of being insulted, the press happily plays along, uncritically buying whatever's being offered, and relaying the lies to the public with no analysis of any kind. Everyone goes home happy, even though not a single true word was spoken, and thus the media once again helped someone in power deceive the public. You'd think they'd be a bit more skeptical after their recent role in helping the administration lie to a mass audience about Saddam and WMDs. But that doesn't seem to have happened so far, and I'm starting to doubt it ever will.

Wednesday, February 08, 2006

Hercules vs. Hydra



While we're on the topic of Greek mythology, which we still sort of are due to the recent post about Echidnas, I recently came across a fun bit of math known as the "Battle of Hercules and the Hydra". As the ancient myth goes, one of the 12 labors of Hercules was to go kill the Hydra, a nasty creature with lots and lots of heads. When you'd cut its heads off, the Hydra would just grow more of them. It's one of the better-known Hercules stories; snakes and snake-like creatures look good in art, and they're easy to draw, so the battle's been a popular topic for artists over the centuries. Here's John Singer Sargent's take on it. Here's a version by Francisco de Zurbarán a Spanish painter of the 1630s. And one by the Italian Renaissance artist Antonio del Pollaiuolo. And that's not even the tip of the iceberg.

But the big reason I think the story's so well known is that we've all been in situations like that at some time. Well, not precisely like that, but situations where the problem seems to keep piling up and getting worse despite, or possibly because of, one's best efforts to solve it. It turns out that the situation is less hopeless than you might think, at least in theory. It turns out that Hercules always wins eventually, by simply standing there lopping off Hydra heads, if he just sticks to it long enough, and doesn't get discouraged by the rapidly mounting number of heads early on. Hercules didn't actually need that torch-wielding assistant, after all.

This paper quotes the exact mathematical definition for the Hercules vs. Hydra game:

At stage n (n a positive integer), Hercules chops one head h of the hydra H. If the predecessor of h is the root, nothing happens. Otherwise let h1 and h2 be respectively the father and the grandfather of h. The hydra sprouts n copies of the principal subtree determined by h1 without the head h from the node h2 (the the roots of the new copies are immediate successors of the node h2). Hercules wins the battle if he reduces in a finite number of attacks the hydra to its root.


Another paper mentioning the problem can be found here.

In short, most of the time you end up with more heads than before, but not always, and that's apparently enough to guarantee that Hercules will win in the end. But it'll take him a good while, but hey, he's a demigod and all, he's got the time. You'll notice that the problem as formulated isn't precisely the same as the mythological account. If anything, it's even more of a challenge, since each lopped head is replaced with two new ones. The reason for the difference is that the problem was formulated not to resolve a hair-splitting dispute over an ancient myth, but to express certain ideas in the mathematical discipline of proof theory. Namely, the battle is a "natural" example of a theorem which is true but not provable within the normal realm of addition, multiplication, and exponentiation (known in the trade as "Peano Arithmetic"), therefore requiring the use of stronger axioms. If I understand the explanation properly, anyway. The whole discipline is highly esoteric, and discussions aimed at anyone below grad student level are few and far between. And even then it seems to be assumed you've got a faculty advisor holding your hand and guiding you through the material.

It's reasonable to wonder why I'm bothering to poke around in all this mysterious abstract stuff. Well, it turns out that proof theorists are among the very few people on the planet who have a genuine need for really large infinite ordinal numbers, which is a subject I find weirdly fascinating. I'm not even going to try to explain what these numbers are used for, since I'm sure I'd bungle the attempt. For the time being, we're just interested in the numbers themselves, not so much what they're used for. Think of it as a grownup version of the playground "who can count the highest?" game.

First a quick note on notation: When you see a 'w', it's really supposed to be a lower-case 'omega', which looks sort of like a curly 'w', and which represents the first infinite ordinal. The plain vanilla one that I imagine is what everyone has in mind when they say "infinity", which is followed directly by w+1, the legendary "infinity plus one" you knew existed back on the playground in third grade, before your math teacher told you otherwise. Following typical comp-sci notation, w*2 is omega times two, and w^w is omega to the omegath power. When you see an underscore, it indicates something's a subscript. And when Greek letters are named, the naming's sort of case sensitive: "epsilon_0" indicates a lower-case epsilon with a subscripted zero, while "Gamma_0" indicates an upper-case gamma, for example.

Most discussions of ordinal numbers tail off after you get to epsilon_0, like the Wikipedia article referenced above. If you're lucky, you'll get a brief mention that there are additional epsilon numbers -- epsilon_1, epsilon_2, epsilon_w, epsilon_epsilon_0, and so forth, just to reinforce that the process goes on forever. Recall that epsilon_0 is defined as w^w^w^w... , and it's the point where you can't get any further with just finite ordinals, 'w', "+', '*' and '^'. Your system's run out of steam, and adding another w to the already-infinite stack of w's doesn't change anything. Epsilon_0 = w^epsilon_0. We've reached what's known as a fixed point. You'd think this would be a bad thing, but far from it. They're solid gold. The ordinals, even just the countable ordinals, are an unimaginably vast collection, and fixed points of various functions are among the rare guideposts in the territory. So instead of bailing out, we just introduce the new symbol epsilon_0, and we can take its successor ( epsilon_0+1) and otherwise multiply, divide, and exponentiate to our hearts' content, until we reach a new fixed point, namely epsilon_1. And so on, until the inevitable, infinitely nested epsilon_epsilon_epsilon... , also known as the first "critical epsilon number", and as phi_2(0). What you're looking at there is an example from the hierarchy of Veblen functions, which basically take the fixed point thing and abstract it up another level. Each phi function enumerates the fixed points of the previous phi function. You can start out a Veblen-style function hierarchy with whatever function you like, but classically you start out with phi_0(n) = n, i.e. 0,1,2,3...w,w+1...w^2...w^w., etc. And phi_1(n) enumerates the fixed points of phi_0(n): epsilon_1, epsilon_2, epsilon_3, and so forth, on and on and finally we hit that infinite stack of epsilons mentioned earlier. the first fixed point of phi_1(n), giving us phi_2(0). And then we've got phi_3, phi_4, phi_w, phi_(w^w), and so on.

This may be a good point to pause a moment and try to imagine, for example, the size of the gap between phi_42(666) and phi_42(667). That's 41 levels of nested fixed points, which themselves are an incredibly-widely-spaced set of little corks bobbing in a vast sea of 'normal' ordinals. Ok, maybe it's better not to try to imagine that. Perhaps the only reasonable thing to do at this point is forget that we're talking about infinity at all, and just think of it as an exercise in abstract symbol manipulation, with levels upon countless levels of nested recursion. Which is still fun to think about, at least for a computer geek like myself. We certainly aren't going to resolve the question of whether these rarefied numbers we're talking about here are "real" or not. It's not that I'm against philosophical debates, per se. It's just that I usually have very little to add. If I was forced to pick a position, I'd incline toward a sort of Platonist notion that infinitely large and small numbers are somehow reflective of an underlying reality independent of human observers. Real, but perhaps not truly graspable by anybody with a mere few pounds of grey matter to work with. But that's just a personal hunch, and I can't imagine how you'd go about testing it.

In any case, the phi_n hierarchy itself runs out of steam eventually, and its limit is the ordinal Gamma_0. Gamma_0 is a milestone in that it's the first "impredicative" ordinal. I don't really understand the implications of this very well, but I gather that at least some schools of thought hold it's something to be avoided if possible. Or at least not overly enjoyed.

Beyond Gamma_0, the landscape is less clear (to me, anyway). Well, for starters you have Gamma_0+1, I guess, and then you repeat the whole process that got you to Gamma_0 until you run out of steam again, at which point you're at Gamma_1, Gamma_2, and so forth. The subject of proper ordinal notation for "large" ordinals seems to be the subject of ongoing research and debate. A Google search on the term "ordinal notation" will bring up lots and lots of hits. Here's one somewhat comprehensible treatment of the subject. Here's a decent article titled "Transfinite Ordinals and their Notations: For the Uninitiated". [Note: Like a lot of academic papers, it's on the net in PostScript (not PDF) format, which is sort of inconvenient for most people. One way to go is save it to a file, and run it through a PS to PDF converter, like this one.]

The referenced article describes Bachmann's theta notation, which is a more powerful extension of what we've looked at so far. Theta_0(0) = 1, Theta_1(0) = epsilon_0, Theta_2(0) = phi_2(0), Theta_Omega(0) = Gamma_0, and that's just the beginning. Note the capital 'O' in Omega there. This is not a reference to the familiar 'w', the first infinite ordinal, but rather the first uncountable ordinal, a.k.a. the cardinal number Aleph_1. Note: I'd originally had a comment here saying that all depended on what you thought of the Continuum Hypothesis, but that was a momentary bit of boneheadedness on my part. Ordinals actually don't have anything to do with CH, as far as I can tell. In any case, cardinal numbers aren't important to the present topic anyway. The important, and weird, thing here is that Omega (also alternately known as w1/omega_1) is much larger than the countable, recursive ordinals we're talking about right now, but it, and even larger ordinals, are necessary as indexes into the massive Theta hierarchy. We're no longer defining numbers as combinations of smaller, simpler numbers; no, at this point to describe a given number we need to assume the existence of a vastly larger number, and use that number to help us describe the number we really care about. Some people are ok with this, others get the philosophical heebie-jeebies.

Since not everyone is comfortable with monkeying around in the higher number classes just to come up with names for plain old countable, recursive ordinals, there are a number of other approaches one can use. The simplest is just to extend the classical phi hierarchy and create ternary, or even n-place Veblen functions. The notation usually gets modified a little, dropping the function notation and subscripts and such, so it looks like you're naming a number, not a function, i.e. instead of something like phi_1(0,0) we just have phi100 -- which just happens to be yet another name for our friend Gamma_0. It might help to think of the levels of nesting as the ordinal equivalent of decimal places, except that each 'place' can be as big as we like: phi110 (= Gamma_1), phi[w]00, phi[epsilon_0]00, etc., where the square brackets are just something I'm adding for clarity since I've been trying to avoid using actual greek letters. Anything in square brackets is really a single "digit". You don't often see phi extended past 3 places, but apparently it can be done if you're so inclined. I suppose the next logical step would be to give a count of the number of places, assuming zeros for trailing "digits". This is kind of the equivalent of scientific notation, so let's say phi100 = phi1^3 (in a trivial case), with phi6^4 = phi6000, phi6.6^4 = phi6600, phi1^10, phi1^100, ad infinitum. I don't know enough about the n-place Veblen thing to be able to say if there's a limit to this madness. Can one have a non-finite number of places? Is there such a beast as phi1^w? phi1^[phi100]? phi1^[phi1^[phi1...]]]? I really don't know.

There are also more complicated notations out there: Something called "Klammersymbolen", which translates simply to "bracket symbols", for one. I don't really understand how they work, but the notation is quite complex: There's an upper and lower row, each of which specifies a sequence of ordinals, with the whole assembly surrounded with large round brackets. There's a further extension of the idea called "ordinal systems". Concrete examples of either are hard to come by, so I don't know what the equivalent Klammer notation would be for, say, phi[epsilon_0]^[10^100].

Continuing on, we run into a few semi-important ordinals: The Ackermann ordinal (Theta_Omega^2(0)), and the small (Theta_Omega^w(0)) and large (Theta_Omega^Omega(0)) Veblen ordinals. The literature varies on the exact notation for all three, and it's unclear which but either the Ackermann or the small Veblen is the limit of finite n-place Veblen notation, in other words one of the two is equal to phi1^w, but I'm not sure which one. Which does indicate that the bigger-cardinal notation is way more extensible than the idea of simply adding more places to your phi notation, all philosophical objections aside.

The next really important landmark out there is an entity known as the Howard (or Bachmann-Howard) Ordinal, not to be confused with "Bachmann Turner Overdrive", of course. A lot of the discussion I've seen treats this number like some sort of Holy Grail, without explaining why. So I know they think it's very important, for some reason, I can say that much. In the Theta notation, it's Theta_(Omega^Omega^Omega...)(0), or Theta_epsilon_(Omega+1)(0). Which really tells me nothing useful, and leaves me scratching my head, I have to say.

As an example of how the notation can trip you up, this post used to assert that the Bachmann-Howard ordinal was Theta_(Omega_Omega_Omega...)(0) rather than the correct Theta_(Omega^Omega^Omega...)(0). That may seem like a trivial difference, but the former is vastly larger, and gets us into the thrilling world of large cardinals, specifically (I think) the first inaccessible cardinal (also known as "Aleph_Aleph_Aleph...").
If we're going to take the step into large cardinal land, we can go on iterating the Theta hierarchy as long as we need to, letting the big cardinal do all the heavy lifting. Alternately, Setzer's "ordinal systems" approach is supposed to get you well beyond the Howard ordinal without ever referring to any number larger than itself. If I had examples of this, I'd show them, but I don't. I understand that the ordinal systems notation is an extension of the already-complex Klammersymbolen, so if there are any examples out there, there probably aren't any concise examples out there.

And far beyond that we have the Church-Kleene ordinal, often denoted by w1CK. This is the first non-recursive, or non-computable, ordinal, the absolute limit of what it's possible to do recursively. Think of a rough analogy with the Busy Beaver functions discussed a few days back (although BB(x) is merely an example of a noncomputable funtion, not the actual upper bound on recursive functions). Any scheme you come up with for counting really, really high is guaranteed to run out of steam before you get to w1CK. It's kind of like the lightspeed of counting. The higher you go, the harder it gets to go even higher, and you'll still never get to w1CK by counting, no matter how hard you try, no matter what clever tricks you devise. Which is not to say we're out of ordinals. Oh, no, far from it. It seems that w1CK is just the first of something called "admissible ordinals", so that there's also a w2CK, w3CK, and so on. The fundamental thing here is that while you can count countable ordinals as long as you like, the set as a whole is uncountable. Unlike the (also uncountable) real numbers, which are uncountable due to their overwhelming density everywhere on the number line, ordinals stick the uncountability out on one end. The reals you can't count anywhere, but ordinals you can count, and count, and count, and it'll just never be enough. Not only can you not count to Omega (the next higher cardinal), you can't even count to a lesser milestone on the way there (w1CK). And then there's still an unimaginably huge sea of ordinals separating w1CK and Omega.

Even then, the ordinal Omega (or omega_1) (a.k.a Aleph_1) still lies off in the distance, far, far away, and then there's omega_2, omega_3, omega_omega, stack_of_omegas, and on, and on, and on.

All of which really makes me want a beer. And I see -- in a remarkable coincidence -- it's right about time for happy hour. So I think I'll stop right here for the time being.

Updated: Two subsequent posts of mine sort of elaborate on the material here. So if you liked this one, you'll love SuperHyperRedux and No Name. To teh Megist(r)on is also somewhat related.