Statistics Canada's census data reports that Canada is home to 20,000 Jedi, mainly in British Columbia, Ontario, and Alberta (where the Conservative Alliance and the rednecks hang out). Jedi, I am pleased to report, massively outnumber Scientologists, by just over 13 to 1. In Britain, Jedi outnumber Jews: there are 390,000 Jedi, or 0.75% of the census respondents, making the Jedi way the fourth largest religion in Britain.

HogBlog has assembled a crack team of prognosticatechnicians equipped with the finest psychohistorical techniques known to modern science to bring you an exclusive look at what the census data ten years from now will reveal about our changing world. In Britain, Time Lords will become the second-largest religious group, pulling far ahead of the Anglicans. 98% of the population of New Zealand will report themselves to be Hobbits. The Church of Scientology will report that its membership exceeds the population of the Earth while in reality shrinking solely to John Travolta, while America finds itself split religiously between X-Men and Vulcans, venerating the Great Prophet Nimoy. Canada's Jedi population will grow exponentially, except in Alberta, where the unwary will be lured over to the Dark Side by Stephen Harper.

The Time Lords vs Jedi football matches will be the stuff of legend.

MoveOn.org has announced the results of its online primary. MoveOn.org had pledged to throw its support--its membership, and several million dollars' worth of proven fundraising potential; these are not small new potatoes mashed with rosemary and garlic--behind a Democratic candidate who took more than 50% of the votes in the primary. Given that there are still nine declared candidates, it seemed unlikely any candidate would win this round. I am happy to announce, however, that my man Howard Dean came close, with 43.87%! Given some more time and outreach and such, I feel a nice warm glowy confidence that Dean can capture MoveOn's support in the next round of voting. These results also show, by the way, that the wingnuts of FreeRepublic.com weren't able to bugger the voting. So ha.

You may ask yourself (where is that large automobile?) why an old-fashioned Old Labour socialist like myself would be so keen on Dean, when it is readily apparent, despite the bizarre counterfactual spins the American media like to put on things, that Dean is not remotely left-wing. He's firmly centrist, by any reasonable standard. He's pro-gun, anti-spending, in favour of the death penalty in certain cases, opposed to big defense cutbacks, essentially pro-business...Whereas I am, well, a socialist. I like nationalised utilities. Is that so wrong? And I like Canada's health care system. I like the decriminalisation of cannabis, and safe-injection sites for intravenous drug users. I like a nice rousing rendition of William Blake's 'Jerusalem'. Ideologically, I'm much closer to Kucinich than I am to Dean. Why, then, am I a Dean partisan?

Politics is the art of the possible, as someone once said.

Democracy is about compromise. There are a lot of ideologies out there, and only one president (at a time, at least). If you stick strictly to your ideological framework in every particular, you will wind up with either all of the pie, or, far more likely, none of the pie. Not even those little crumbly bits of crust people leave behind on their plates. Kucinich is, unfortunately, a no-pie sort of candidate. There are too many conservative voters in this country to make a real leftist candidate viable. Even if he were elected, the sort of policies he and I like, like socialised medicine, simply won't be passed. The health care industry wouldn't allow it. I can't have all the pie, no matter what. So I have to settle for one piece of the pie, instead. Preferably with ice cream on top. Howard Dean is willing to give me some pie. He's flexible. He's willing to change his mind. But he isn't willing to bend over. He's also willing to fight. You've probably noticed that already. Dean can motivate and impassion people; look at the grassroots support he's conjured up. He isn't a tool.

Fundamentally, I think the country would be a lot better off with Howard Dean as its president than it is now. I think a Dean presidency would defend my interests and foster an acceptably congenial national atmosphere. I think Dean would be good for civil rights, and I don't think he'd push intrusive Big Brotherly measures like TIA and PATRIOT. I think he'd be good for diplomacy; his America would be less of a bull in a china shop. And he wouldn't pursue a scorched-earth economic policy to raze Social Security and the few other bastions of socialism left in America. Admittedly, a lot of these are negatives, things he wouldn't do; Kerry or even Gephard (who I think is a tool) or most of the other Dems would also not do these things. I'd happily vote for Kerry, or somewhat less happily but still pretty darned happily vote for any other Dem, even, although here I wouldn't be very happy at all, Lieberman. But I think Dean has the most potential. Dean could make things happen. He's got the verve, the oomph, the thingy. Kerry, my second choice, has been low on thingy lately. Kucinich, alas, has no thingy at all: he favours things I like, but he couldn't make them happen. I think he could be a lot more productive staying in Congress, though I want him to stay in the presidential campaign to get his views heard and add a genuine spark of leftism.

Also, Kucinich looks like Paul Simon. If he could find a VP candidate who looked like Art Garfunkel...Well, then I'd be sold.

But until Art (who has an MA in maths from Columbia University, by the way) enters the fray, I'm sticking with Howard Dean.

I'm hungry, and Dean has the thingy to get me some pie.

Highlights from Strom Thurmond's obituary in the New York Times:

At 44, Mr. Thurmond proposed to his 20-year-old secretary, Jean Crouch, in an intraoffice memorandum he dictated to her. She consented by memorandum, and by all accounts it was a happy marriage.

Behold Billmon's Dao of American Politics. Take the time to read it all. It's a bit good.

It does tend rather to crush one's tiny delicate blossom of hope. Dialectical struggles of the sort Billmon describes, and the sort that'll be required to shove the current crop of conservatives out of power, can run to decades. Dubya and his heirs might well retain the throne until I'm old enough to run for president myself. Or longer.

(Vote Hog in 2016! A pig in every pot, and pot in every pig!)

It goes well with Ken MacLeod's first novel, The Star Fraction, with its healthy doses of Trotskyism and revolution...

Today is Appropriate Michael Savage's Name For Your Own Purposes Day! Go forth and enjoy. Before you get too carried away, though, I feel I ought to point out that Michael Savage is not at all the same as Dan Savage. They are not even cousins or anything. Do not get so caught up in the mocking of Savage Stupidity that you begin to blur the distinctions between them. If you see a Savage, the following simple guidelines will help you to determine whether it is a Michael or a Dan.

1. Dan Savage's real name is Dan Savage. Michael Savage's real name is Michael Weiner. The symbolism of this is too blatant to require comment.

2. Dan Savage is very attractive. Michael Savage is a grotesquely ugly freak.

3. Dan Savage is a broad-minded, liberal, homosexual who writes a sex-advice column. Michael Savage is a six-inch-tall monkey who flings poop.

4. Dan Savage is funny and engaging, so long as you keep him off the subject of terrorism. Michael Savage is ugly, and nobody loves him.

5. Dan Savage has an engaging prose style. Michael Savage communicates entirely through porcine grunts and flatulence.

6. Dan Savage comprehends satire. Michael Savage likes to sue people.

I hope this helps.

It's legal!

The Supreme Court has struck down Texas's anti-sodomy laws in a ruling which appears, in fact, to invalidate all anti-sodomy laws in the US, and about jolly time, too. The vote was 6-3, with, as you might expect, Rehnquist, Scalia, and Thomas dissenting. For a good look at just how creepy these three are, the AP reports Scalia as saying that the Supreme Court "has largely signed on to the so-called homosexual agenda," while Clarence Thomas believes in a strict interpretation of the Constitution and therefore finds that Americans have no right to privacy. Read the opinion here, delivered by Kennedy. Quite a good opening:

Liberty protects the person from unwarranted govern- ment intrusions into a dwelling or other private places. In our tradition the State is not omnipresent in the home. And there are other spheres of our lives and existence, outside the home, where the State should not be a domi- nant presence. Freedom extends beyond spatial bounds. Liberty presumes an autonomy of self that includes free- dom of thought, belief, expression, and certain intimate conduct. The instant case involves liberty of the person both in its spatial and more transcendent dimensions.

Perhaps, if Clarence Thomas can still claim Americans have no right to privacy, we ought to legislate one...Given programmes like Total Information Awareness and Ashcroft's PATRIOT Act, the sheer quantity of sensitive information on our citizenry held in various databases, encryption issues, RIAA lawsuits, Orrin Hatch's desire to blow up my computer, and so forth, a constitutional amendment guaranteeing a certain freedom from physical or virtual intrusion might not be a bad idea.

ASIDE: How dreadful a job have the US forces done securing Iraq's nuclear materials? Greenpeace has been rounding up and returning looted radioactives for them. This story is confirmed by the Guardian:

A team from Greenpeace handed American troops a large, abandoned canister of "yellow cake" - low-enriched uranium powder used as raw material for radioactive fuel.

Perhaps George Bush's theme song ought to be 'The Sun is Burning'...

It is said that Charles Mingus successfully trained his cat Nightlife to use the toilet.

Think about it.

ADDENDUM: Ha.

(Don't worry. It's clean.)

Horlicks: 1. A sort of malted milk beverage powder thingy consumed by old English people to help them sleep. 2. A mess. 3. What Alastair Campbell made of Britain's WMD dossiers, according to Foreign Secretary Jack Straw. 4. Insert Andrew Sullivan joke here.

Recently a conversation on the subject of free will prodded me into reading Roger Penrose's The Emperor's New Mind, dealing with consciousness, its relationship to physics, and its computability, in a sense. The thrust is, as I understand it, that the human mind is in some sense not algorithmic, and that the strong AI position is untenable: no algorithmic system is capable of true consciousness. In pushing for this conclusion Penrose treats the nature of consciousness, its connection to basic physics, and such things as the nature of time itself, which is closely connected to my conception of the free will question. Having read the book, I can say that it is well-researched, and presents its mathematical and physical background lucidly; particularly with regards to entropy. Penrose's explanation of what entropy is and how it works makes a great deal more sense to me than the one I learned as an undergraduate (though given that it was taught me by physicists and Penrose is a mathematician, this should not surprise; physicists usually can't explain things even to themselves). However, I do not think Penrose made an entirely convincing case for his philosophical theses.

I would put my own positions thus:

1. I favour the strong AI position.

2. I don't believe in time.

As a consequence of #2, I have doubts about the existence of free will. Qualified doubts. I'll attempt to explain what I mean by 'I don't believe in time' in some more detail later, but for now, I'll stick to Penrose and his anti-AI arguments.

First, his speculations on possible quantum effects in the brain, and quantum gravity, and the collapse of the wavefunction are, as he himself takes pains to stress, speculations. Much like the 'many worlds' interpretation of quantum mechanics that Penrose admits to disliking. There are other possibilities. Which of them you buy is mostly a matter of personal preference: you're free to tentatively back whichever theory that fits the currently-known facts you find most aesthetically pleasing. When more data and more robust theories enter the picture, then we can settle this. 'When' in this case may be up to several decades from now. One need not argue with Penrose on these speculations, because he admits himself there's no evidence backing him up.

There are some things I can argue with. Early on Penrose cites John Searle's Chinese Room thought experiment. Imagine if you will that you are sealed away in a closed room, with supplies for an indefinite period; all you get from the outside world are strings of Chinese symbols, which you cannot read or understand at all. You have with you a great big fat book, in English (assuming English is your native language, which is very Anglocentric of me), containing very specific instructions, which you follow without error, for manipulating the symbols sent in to you, and extracting from any given string of Chinese symbols another string of Chinese symbols, algorithmically, which you then pop into another slot and feed back to the outside world. It just so happens that the symbols you're being fed are perfectly reasonable and grammatically correct questions in Chinese, and the symbol strings you're algorithmically producing are the appropriate replies. In essence, you, the room, the slots, and your rulebook form a computer, for answering questions in Chinese. Now, Searle asks, this system is capable of responding sensibly to certain inputs; can it be said that this computer understands what it's saying, even though you, yourself, haven't the foggiest idea? The strong AI position must lead one to say that it does, which Searle and Penrose both hope you will find absurd. I don't. If you don't, then there's nothing about the Chinese Room to damage your position. It's only an effective argument if you allow yourself to be intimidated by its silliness. If you think that consciousness is a process or pattern independent of its specific hardware, then yes, this Chinese Room is a sort of mind, while you're chugging through your rulebook. I think it's a reasonable position. To think otherwise is to make consciousness into a very priviliged thingy, which seems terribly anthropocentric to me, verging on the mystical. The idea of consciousness as a 'pattern' may or may not be more general than the idea of consciousness as an algorithmic process, which Penrose argues against but is unable to refute decisively. Or it may not. It depends on what I mean by 'pattern'; I am not sure yet.

Penrose also cites Godel's Incompleteness Theorem to argue against the algorithmic nature of consciousness. Any formal system contains a statement which is not provable within the framework of the system, but which, nevertheless, a human mathematician can recognise as a true statement. Therefore, it seems, no formal system or algorithm can describe the mathematical abilities of a human mathematician. This is, I think, misleading. Firstly, it is not at all obvious that strong AI requires consciousness to be algorithmic in the sense that Penrose claims. Mathematicians, after all, have been known to be wrong. (Graduate school would be much, much easier if this were not the case.) A consistent formal system cannot make mistakes. This would seem to imply, then, as Marvin Minsky pointed out, that mathematicians are not consistent formal systems. Since we are prone to error, our mathematical abilities cannot be described in terms of a formal system to which Godel's theorem applies: we are, like everyone's favourite rogue AI, Heuristic ALgorithmic systems, not merely algorithmic.There are other arguments against this, too. Some of them appear here, in a piece by Hans Moravec. For example, suppose mathematicians are algorithmic, but require about a hojillion axioms, more than our conscious minds can store and work with. We wouldn't be able to understand our Godel statement, or even recognise it as our Godel statement, because we couldn't grasp our own axioms; we'd have to call on some more powerful mathematical force (like a big hojillion-squared-axiom computer) to tell us what it was. My favourite counter-argument, though, goes like this...Godel guarantees us that, if our system is consistent--that is, if it is never the case that both a statement and its negation can both be proven true within the system--we have a statement P in our formal system which can neither be proven nor disproven. In a clever and coded way, the statement P is, in spirit, 'P is not provable.' Therefore, in any formal system, either the system is inconsistent, or it contains such an unprovable statement P. Therefore, if we assume we're consistent, we can prove within our system the statement 'P is not provable.' This is logically equivalent to the original Godel statement P. (For more details, I invite you to consult the appropriate Wikipedia article.) There are so many holes in this argument, that Godel somehow forbids AI, that I'm frankly surprised that a man of Penrose's intelligence would use it.

It's possible that Penrose might have been drawn to the Godel argument by his fairly extreme Platonism. There's nothing wrong with Platonism; I'm a mathematical Platonist, too. I'm just...not quite as much of one as Penrose is. He seems to assert in his book that the Platonic world of pure mathematics really truly exists, and that mathematicians make contact with it somehow when they get a really good idea¹. Godel's results would live in this Platonic realm. The physical world is a sort of echo of this mathematical world, imperfectly: so one can almost convince oneself that Godel's Incompleteness Theorems should find themselves echoed in the physical world along with all that crap about differential equations, and so one might be tempted to apply them to physical things like mathematicians, forgetting, alas, that mathematicians are not mathematics...

Penrose displays great erudition in his book, and he's an extremely intelligent man, but his position is painfully weak. He's like a man arguing theology: he takes the position he does not because he has solid, objective evidence that it is the correct position, but because he believes in it so firmly. He has no compelling arguments for his own position, and he cannot offer any compelling arguments against the opposition, like strong AI or the 'many worlds' hypothesis, beyond his own credibility as an expert, which ought not to get anyone anywhere in the physical sciences.

I will spare you the obligatory closing pun on the book's title. I'm sure you can make one up on your own.

***

1. Penrose, Roger. The Emperor's New Mind. Oxford: Oxford University Press, 1989. Page 428.

If anyone wants to start a chapter of Cruising for Dean here in Seattle, I noticed as I walked past the other day that the notorious gay Turkie ¹ cruisy video sex humping bar Manray (Man-spray) has a Howard Dean poster up on its window already...It is ripe for the plucking.

***

1. Turkie (tûrk): a dirtie beast who engages in fowl and unclean activities, including, but not limited to, gobbling, the consumption of pork rinds, telemarketing, and tawdry bar hookups. See also Turkie Cock.

I explored another Seattle landmark on Friday, Freeway Park. It is a park. Built over a freeway. Perhaps you find the idea curious. So did I. That's why I went. I was in the area, after an aborted attempt to buy tickets to Blur which side-tracked me into a bookstore, from which I emerged with a fistful of Ken MacLeod...Freeway Park lurks atop a misshapen concrete platform straddling I-5; I'd noticed it countless times without ever realising what it was. Curiosity overwhelmed me.

Freeway Park is something I'll probably have nightmares about some day. It is a place of Lovecraftian evil.

It's not just passively unpleasant, a place you wouldn't want to be. It's actively grotesque: it wants you to hate it. It is designed to sicken the soul. Imagine you're an ant, crawling around between the world's ugliest Legos, the colour of urban decay. I came into it via a staircase and walkway up from Pike Street, through a twisty, zigzagging narrow walk along a sheer concrete face a storey or so above street level...It was the colour of old, bad malls. The rhododendrons looked like some kind of growth upon a corpse. There were little cul-de-sacs, leading off from the path, bending around on themselves; you couldn't see into them until you entered. You weren't sure who might be there...And that begins to alarm you. Later on it opens up into a sort of square, still framed by giant concrete blocks, like a well-tended slag heap...The trees and grass in that setting actually make you feel more isolated from nature, more like you're encased in something completely artificial and contrived...One feels a great apprehension about seeing another person, or the sort of person who'd be liable to hang out in such a place...A labyrinth of stairs and ramps runs up from this square, cramped, seeming permanently damp. It is impossible to see how they double back on themselves, where they lead, whether two branchings will meet or diverge...One wonders if it will ever end, if one will be trapped forever climbing, dogged by half-imagined steps...This labyrinth is the place in Seattle I would vote Most Likely to Harbour an Evil Dwarf who will Pull my Brains out of my Nose with a Crochet Hook. This inability to see where anything goes, these blind alleys, this air of solitude and desolation and decay...It feeds a paranoia, which waxes steadily as you go through the park. It comes as an unspeakable relief to emerge again onto the populated streets.

I am not alone in this.

Also, Nyarlathotep lives beneath it. It's true. You may think me mad...Madness would be a blessing. For I have seen things man was not meant to see. I have seen the blasphemies against man, nature and sanity that lurk in the quiet corners of the Interstate highway system.

For those of you in eastern Iowa: the Riverside Theatre Shakespeare Festival's production of Macbeth opens tonight at the Globesque theatre in Lower City Park. The director Mark Hunter's previous offerings have been a good night out indeed; this event receives the HogBlog Seal of Not Entirely Objective Approval, given that the tireless HogBlog correspondent was once in the employ of said Shakespeare Festival. As an extra bonus, Buckle Down Publishing Company has offered to make a matching donation for every ticket sold this weekend. Support your local theatre! If it is your local theatre, that is. If you're in New Zealand, you're entirely off the hook.

If you are in New Zealand, for another week or so you can still catch Circa Theatre's production of Ibsen's An Enemy of the People, about which I know nothing whatsoever; but what do you have to lose?

The thing I most want to hear an MP say during Prime Minister's Questions is:

'You're ugly and nobody loves you.'

After carrying out a number of experiments this morning, I am now in a position to answer a question that has plagued mankind since time immemorial: tea on breakfast cereal instead of milk isn't as bad as you might think. I performed my experiment with Choice organic Earl Grey; I learn from the box that Earl Grey gets its distinctive bitter-spicy bouquet from essential oil of Bergamot, a small and bitter Mediterranean citrus brought to Europe from China, once used to flavour gin.

Do not try this at home; I am a trained professional.

Why are all finite-dimensional subspaces of a Banach space closed?

I hear you shouting this question to the uncaring heavens.

At last, your curiosity will be satisfied.

I will actually prove something stronger: let M be a closed subspace of a Banach space X (over a field K). Let x be any vector in X not lying in M¹. Let N be the direct sum of M and the subspace Kx spanned by x. I put it to you that N is also closed. If N is all of X, then there's nothing to prove. So let Y=X\N, and suppose Y is nonempty. Since M is closed, by a corollary to the Hahn-Banach Theorem, for every y in Y we can find a functional f_y in X^* with f_y(y)=1 and f_y(z)=0 for all z in M. Likewise we can find a functional g with g(x)=1 and g(z)=0 for all z in M. Now let h_y=f_y-f_y(x)g. Then h_y(z)=0 for all z in M, and h_y(x)=f_y(x)-f_y(x)g(x)=0, so h_y(z)=0 for all z in N: N is contained in the kernel ker h_y, for every y. Thus N is contained in the intersection of all the ker h_y, as y ranges over Y: this is an intersection of closed sets, hence a closed set. And I put it to you that this intersection is exactly N, which will complete the proof. For suppose there existed y' in Y which lay in this intersection. Then we'd have h_y(y')=0 for all y. But then f_y(y')-f_y(x)g(y')=0, or f_y(y'-g(y')x)=0, so y'-g(y')x lies in ker f_y for all y in Y; therefore it's in the intersection of all such kernels. But the intersection of all the ker f_y is truly contained in N: for any vector in Y=X\N, we constructed an f_y which was 1 at that vector. Hence y'-g(y')x lies in N, and since x lies in N, y' lies in N, a contradiction. QED

Now, the zero subspace {0} is closed. By the above, then, any one-dimensional subspace is closed: it's the direct sum of {0} with Kx for some x. By induction, therefore, all finite-dimensional subspaces are closed.

This seemed like the natural way, to me, to prove this when it was assigned as homework in the winter: if you need a vector subspace for some reason, look at kernels of linear transformations. But for some reason, analysts don't find it especially clear. Your mileage, as the old saw goes, may vary.

***
1. I left out the last clause originally. Silly me. I tacitly assumed all along that x did not lie in M but forgot to specify that. (22 June)

Today I was thinking yet again about my lack of enthusiasm for being American. And I was thinking yet again how much nicer it would be to be British, for in Britain, despite Tony Blair's best efforts, the levels of ambient evil are still significantly lower. Or Canadian; I'd enjoy being Canadian. Even if their Prime Minister does speak out of the side of his mouth like a Prohibition Chicago gangster. (Any Canadians out there who quite reasonably think the sovereignty of the British monarch over Canada ought to end are invited to contemplate my humble self as her replacement. I'm small, I wouldn't make any fuss, and I don't cost much.)

That in turn led me to ask myself this: what, exactly, is it I find so attractive about the UK?

That being a somewhat overly broad question, I later asked myself this: what is it I look for in a country?

That too being of unmanageable size, I finally asked myself this: what ought a government do for its people? Governments don't exist for their own sake, after all. We have governments instead of anarchy because governments can do things for us that, at least at this stage in human social evolution, anarchy can't, like build roads and keep people from stealing our Playstations and so forth. Governments are utilitarian things, there to ensure we have a congenial environment to get on with our lives in. (I like to end sentences with prepositions sometimes. Also propositions.) What sort of things should a government be expected to do, then? There's the obvious stuff, like national defense, police forces, roads, post offices...But national defense gets far too much press in the US. While preventing terrorist attacks is certainly a Good Idea, there are a lot of other Good Ideas a reasonable government ought to act on, in no particular order...

1. Universal health insurance. The unemployed, the low-income, and particularly children ought to be guaranteed a reasonable level of coverage.

2. Accessible higher education. Deferred loans or outright grants ought to be available to send anyone of reasonable competence to a public university.

3. Welfare. This is not a dirty word. Even Otto von Bismarck saw the need for some provision for the unemployed, the elderly, and those unable to work.

4. Corporate regulation. Big Evil Corporations should not be able to dick over the public. For example, manufacturers shouldn't be allowed to shit into rivers. Nor should firms be allowed to dominate the media and impose their ideologies on the news. Nor should they force us to call in and activate our copies of Windows XP. See also #7. Things like water, power, and rail ought to be in the public sector, not the private.

5. Freedom to enjoy. Governments should ensure that people can rave, dance, listen to rock and roll, fornicate, drink, listen to gangsta rap, play supremely violent video games, watch porn, watch Ashton Kutcher, have sexual intercourse with frozen dead chickens, smoke reefer, watch old episodes of Doctor Who, not go to church, and generally do whatever it takes to keep themselves amused and extract a decent amount of pleasure from life, so long as this doesn't hurt anyone else. Government is not, or should not be, in the morality business.

6. Human rights. Government should be in the business of ensuring everyone gets fair and equal access to the opportunities society offers, regardless of their sex, race, religion, sexual orientation, gender identity, disabilities, body piercings, age, socialism, unpatriotic character, and other factors I haven't the time to enumerate. Women have the right to seek an abortion; gays have the right to marry and, if they cut the mustard, adopt.

7. Freedom of information, and the right to privacy. Government should also be in the business of ensuring that the free flow of information is not disrupted, either by the government itself, or by corporations; and that the citizenry are free from unreasonable intrusions into their private lives. Strong encryption should be publicly encouraged. Total Information Awareness and the DMCA should not. People have been making mix tapes for decades; what was Napster but the next logical step?

8. More grant money for mathematicians. We're cheap. A mathematician, after all, is a machine for turning controlled subtances into theorems.

This is by no means an exhuastive list, nor are Canada and Britain necessarily getting top marks on all of these. But American politicians have been showing a disturbing lack of enthusiasm for most of these ideas lately. Even my preferred presidential candidate, Howard Dean, doesn't go nearly as far as I would in support of universally healthy well-educated socially secure anti-monopolistic pot-smoking equally-protected file-sharing mathematics. Dean is solidly centrist; only in America could anyone call him 'left-wing' with a straight face. Far better a centrist, though, than a trained monkey bent on taking America back to the Gilded Age.

These are things that I consider important. America's leadership doesn't, nor does a large segment of its population. This is why my country and I don't get on very well.

This is why I'd rather be British; in Britain, socialism is not necessarily a dirty word.

Nettavisen reports:

Jan O. Karlsson, the Swedish Minister for Migration, has got himself into trouble after calling the American President «that fucking Texas geezer».

It is quite a short article, but even so, the phrase 'that fucking Texas geezer' appears as the headline and also three distinct times in the body. By my calculations, including the headline but not the by-line, the phrase 'that fucking Texas geezer' accounts for 5.44% of the total wordage of the article. If we include this sentence but nothing beyond, then the phrase 'that fucking Texas geezer' accounts for 16.33% of this posting. This does not include the headline. If anyone thinks I ought to include my headline, I am entirely likely to chance it to 'that fucking Texas geezer' just to keep my numbers up. I think it would be fun to see how often one could work the phrase 'that fucking Texas geezer' into conversation. In quotation marks, of course. If one says it out loud, one is obliged to make quotation marks in the air: 'that fucking Texas geezer.' See?

If you do not care for the phrase 'that fucking Texas geezer', I am told that the phrase 'no-talent ass-clown' is also an acceptable one.

Did you know that 'that fucking Texas geezer' is an anagram of 'acreage Fez text tug knish'? I'll bet you didn't.

This news snippet comes to me via Why Do They Call Me Mr Happy?, who also points me to another online philosophy test, Taboo. I said it was morally acceptable to have sexual intercourse with frozen dead chickens, and then eat them. I am a very bad vegetarian. But a philosophically consistent one.

Scrolling down, I find that this Mr Happy runs a heck of a fun blog. He's even got a Chris Morris quote in his sidebar.

Why couldn't I have been British?

I'm sure it's 'that fucking Texas geezer's' fault somehow.

The Canadian federal government will not appeal the Ontario Appeal Court ruling requiring it to recognise same-sex marriages.

Jean Chretien declares, beneath his somewhat disturbing portrait in the Globe and Mail:

"We won't be appealing the recent decision on the definition of marriage. Rather, we'll be proposing legislation that will protect the right of churches and religious organizations to sanctify marriage as they define it. At the same time, we will ensure that our legislation includes and legally recognize the union of same-sex couples[.]"

So there you have it. The more reactionary churches are still free to spew bile and venom and call down the wrath of God upon the unholy union of two men or women. Stockwell Day and his successors can Puritanically cry shame to their heart's content. But as far as the law is concerned, at last, in this respect, we are all equal.

They are all equal. Dammit. I forget sometimes that I'm an American. For a fleeting moment in the supermarket today, I thought a block of mozzarella cheese was priced at three pounds fifty.

More here. On gay marriage, that is; not my cheese.

Spring quarter's grades are in. It turns out that I rock. I have survived my first year of graduate school unscathed. Rock rock rock. I am the champion of the freaking world. I am a rock star.

Also, have you seen this Rube Goldberg Honda ad? It, too, rocks. Though not as much as I do.

I recently read the short story collection Stories of Your Life and Others, the first book of Seattle-area resident Ted Chiang, and my one-word summary of it would be 'rocking'. It contains some extremely excellent short science fiction, including 'Understand', which you can read for yourself online thanks to the nice folk at Infinity Plus. 'Understand' is a tale of intelligence augmentation, and it's up there in swellness with Thomas Disch's Camp Concentration. There is also, and this won the collection a special place in my heart, a story, 'Seventy-Two Letters', about golems. Also the more-or-less eponymous tale 'Story of Your Life', which reminded me of, and suggested sharp constrasts with, Kurt Vonnegut's Slaughterhouse-Five, or more accurately vice-versa, since I read Chiang first; Chiang's piece differs primarily in being much less depressing. About all this I may say more in the fullness of time, but for now I wanted to have some words about the one story in the collection that I found less than entirely satisfying: 'Division by Zero'.

The premise of 'Division by Zero' is that a gifted mathematician develops a new formalism which leads her to discover that arithmetic as a system is inconsistent: she finds a way to prove, rigourously, that all numbers are in fact equal, and thus that arithmetic, and by extension pretty much all of pure mathematics, is meaningless. It sends her into bleakest despair and basically ruins her life. Which is understandable; to a mathematician, being told that mathematics just doesn't work would be about the worst thing imaginable. The thing is, I can't bring myself to suspend my disbelief. It's hard to swallow, in a way that golems or Babylonians building a tower all the way to Heaven aren't. With golems, if you make one simple assumption--that Kabbalism can replace the physical sciences--the rest follows logically. (Which is one of the best things about Chiang: everything follows so wonderfully logically!) Here...I think that is not quite the case. Maybe I'm saying that because I am, or hope to be, a mathematician myself; the idea of maths just not being true...Well. It'd be brown trousers time, for sure.

I am, like many mathematicians, a Platonist at heart. I don't believe there is literally a world of idealised mathematics made solid floating around somewhere in the formless void, but I can't help but view mathematics more as a process of discovery than of invention; true theorems weren't any less true before they were formulated and proved, after all. If they are true now, they have always been true, and they're universally true, even multiversally true: true independently of the physical world and any of its parameters. (Modulo the appropriate definitions, of course.) So the idea of maths not holding water...It's like destroying an entire universe, albeit one I perceive only indirectly. A universe, by the way, without George Bush in it.

But I think I have some firm, logical basis for my unease, beyond my epistemological and ontological qualms. Renee, the unfortunate mathematician in the story, develops a new formalism which allows her to rewrite unspecified axiom systems, and thereby prove, in essence, that 1=2. I am not a logician (an algebraist, actually, probably a representation theorist), but I do know a little set theory (which no-one else in the department seems to enjoy, damn them) and I'm familiar with the axiomatics of arithmetic. An axiom system for workaday arithmetic, called the Peano postulates, was devised by, of all things, a chap called Peano in 1889. It's possible Renee was working with these, but unlikely: the Peano postulates aren't very fundamental. If you assume ZFC set theory (Zermelo-Fraenkel, with Choice), or an equivalent, which you're more or less obliged to do to do any modern mathematics whatsoever (unless you're some kind of silly Intuitionist) you can prove the Peano axioms as theorems about the set of natural numbers; if the Peano postulates are inconsistent, then ZFC is inconsistent as well. So Renee has discovered that ZFC is self-contradictory, that 1=2 when it is axiomatic that 1 and 2 are, by construction, very different entities. This would be bad. But not that bad. This doesn't mean that mathematics in general or arithmetic in particular are themselves, in their Platonic forms, inconsistent: it means the axiom systems Renee and I have been using are, which is not at all the same thing. You can always replace your axioms. Maths has been bitch-slapped like this before, and come out all the stronger for it. Cantor's original naive set theory was inconsistent, but that didn't destroy set theory; it just meant it needed different foundations, like ZFC. If ZFC were itself inconsistent, while I'd be quite shocked, I'd also be confident that a replacement scheme could be devised. I can't imagine it'd drive anyone to suicide...

I just don't buy it. But do buy the book. The rest is, as I said, very fine.

(And what's so implausible about transfinite induction?)

Anyone interested in learning about set theory from a naive, or non-axiomatic, perspective, which is the best way to see it first, would do well to seek out Paul Halmos's Naive Set Theory, which is accessible to the tenacious layman. For a much shorter and less comprehensive introduction with more sex in it, read on...

(Edited slightly on 17 June for clarity and extra bitch-slapping.)

The most basic area of mathematics, or the most basic interesting area, if you ask me (and I acknowledge in advance that you didn't) is set theory, which is, as you might have guessed, the study of sets. Sets are exactly what you'd think they are, things made up of other things. A set is like a box, filled with these sub-things, which mathematicians like to call elements. There are many sorts of boxes. Boxes may be wooden. They may be cardboard. They can in fact be made of metal, and if you really wanted to you could probably make some sort of a box out of crack. Sets aren't quite like that. To a mathematician, a set is completely defined by its elements, the things it contains. If you have two sets and they both have precisely the same elements, then they're the same set. It's like numbers; you can have one apple or one orange or one orgasm, , and in the real world these are (usually) very different things, but abstractly, it's still just the number one. Sets are usually written as a list of their elements between curly brackets, like this: {1,2,3,4} or as a description of their elements, also between curly brackets, like this: {all positive integers less than five}. While I've described these two sets in completely different ways, you'll notice that they are, in fact, the same set. They both have exactly the same elements: 1, 2, 3, and 4. The fancy math term for this idea, that two sets are the same if they have the same elements, is extensionality. To save time and space, sets will usually be given names, like A={1,2,3,4}, and then the symbol A can be used in any expression in which I want to talk about that set. Having said nothing more, I can already display one interesting set factoid for you: let x be anything you want, a number, a letter, a symbol, a thing. It doesn't matter. Sets don't care what you put in them. Then {x,x} and {x} are equal: they're the same set. Why? Because every element of the first set, which has to be x, is an element of the second set, and vice-versa. Repeating an element doesn't change the set, so I'll just delete any references to repeated elements in my sets. And it's entirely possible to have a set that doesn't have any elements at all: {}. This is called the empty set, and I'll name it 0: 0={}. You'll see why.

There are only a few basic things you can do with sets, according to the very strict rules laid out in the axiomatic version of the theory which I'm not going into here, but as it turns out you don't really need anything complicated. First off, if you have two sets, you can take their union. If A and B are both sets, then their union is written A U B, and this is the set whose elements are all the elements of A, together with all the elements of B, and nothing else. If A={1,2,3,4} and B={1,2,5}, then A U B = {1,2,3,4,5}, since we can ignore repeated elements. We can also take intersections, though there isn't a good way to type them out here, and I won't need intersections for my purposes. The intersection of two sets is the set of all things that are elements of both of these sets at once. You can also construct subsets; a subset of some given set A is a set whose elements are also all elements of A. With my A above, {1,2} is a subset of A, and I'll write this {1,2} < A although normally it's curvier. And we can build new sets from old ones! A set doesn't care what you stick in it, after all, so why not build a set whose elements are other sets? So {A,B} is a set...But be careful. {A,B} is not at all the same set as A U B. The elements of A U B are 1, 2, 3, 4, and 5; the elements of {A,B} are A and B.

But what do I mean by 1, anyhow? How do you know 1 isn't the same thing as this set A? And how do you know that 1 isn't the same thing as 2? It sounds at first like a silly question, but it's important. What do we mean by numbers? I can now tell you exactly what numbers are, in very concrete terms. They're sets. I already defined 0 to be the empty set, {}. It's a set with zero elements, which seems like a sensible thing for zero to be. Now, let's define 1={0}: 'one' is going to be the set whose one element is zero. And we can bootstrap ourselves onwards: let 2={0,1}, and 3={0,1,2}, and so on. If you wanted to write these out more explicitly, we'd have 1={0}={{}}; 2={0,1}={ { },{{ }} }, but that's awfully awkward. Just saying 'and so on' isn't very precise, though, so I'll put it like this: if we've defined a natural number n, define its successor, the next natural number, to be n+1 = n U {n}; the elements of n+1 are going to be all the elements of n, together with n itself. This is just what I did for 1 and 2 and 3, you'll note. And having defined all the natural numbers 0, 1, 2, ... in this way, we can define arithmetic on them, too, using more set theory, and more induction, which I've skipped over entirely and waved my hands at in the above. As I said, this isn't meant to be rigourous. Just fun. For we're right on the cusp of infinity already! Let w={0,1,2,3,...}={all natural numbers}. (This ought to be a lower-case Greek omega, in case you aren't seeing it properly.) w is a set that has infinitely many elements, by which I mean that if you took an element away, you'd still have just as many left as you started with, but w behaves almost as if it were a natural number itself. In particular, we can find its successor, just by using the definition above: w+1 = {0,1,2,3,...,w}. w+1 is the set containing all natural numbers, and also w. This is a perfectly well-defined set. It looks bigger than w, since it contains everything w does and more besides. In fact, they're precisely the same size. And what do I mean by 'size' when talking about infinite sets?

Two sets are said to have the same size, or contain the same number of elements, or, in mathspeak, have equal cardinality (the cardinality of a set is the number of elements it contains, which may be bigger than finite...), if you can cook up a function or rule for associating with each and every element of the one set precisely one element of the other set, and vice-versa: you can think up a way to pair up the elements of the two sets so that you run out of elements of both sets at the same time. For example, {1,2,3} and {5,990,5324635} have the same cardinality since I can pair up 1 and 5, 2 and 990, and 3 and 5324635, and I've used up all the elements of both sets. {1,2,3} and {1,2} do not have the same cardinality. A set is finite if, as you'd expect, it has a finite number of elements, or, to be more precise, it has the same cardinality as one of the natural numbers; that natural number is then said to be the cardinality of the set. {1,2,3} has cardinality 3, since 3={0,1,2}, and we can pair up 1 with 1, 2 with 2, and 3 with 0. If a set is too big to be paired up with any natural number, it is infinite. w and w+1 are both infinite. The cardinality (or size) of w is called À₀, alef-null (or aleph-nought, because aleph or alef is the first letter of the Hebrew alphabet, and has lots of mystic connotations, and the man who invented set theory and the idea of cardinality, Georg Cantor, was an odd sort and wound up going mad, poor chap), and À₀ is the smallest of the transfinite cardinal numbers, that is, cardinalities of infinite sets. For natural, finite numbers, n and n+1 clearly never have the same cardinality; yet infinite sets are much, much odder, and it turns out that the cardinality of w+1 is also À₀, and here's why: look at w+1={0,1,2,3,...,w} and w={0,1,2,3,...}. Pair up w and 0. Now, for each natural number n in w+1, pair it up with n+1 in w. We pair up 1 and 2, 2 and 3, and so on, and so forth. We use each and every element of both sets exactly once. Thus, they both have cardinality À₀. There are lots more...Look at the set of all even numbers, {0,2,4,6,...}. This looks like it should have only half as many elements as w does, but they're actually exactly the same size, À₀. To see this, pair up 0 and 0, 1 with 2, 2 with 4, and so on...Associate to every natural number n in w the even number 2n. Or the set of all perfect squares, {0,1,4,9,16...}. Just match up each number in w to its square in {0,1,4,9,16,...}. Or the set {1,10,100,1000,...}; match up n with 10ⁿ. In fact, any infinite subset of w has À₀ elements, just like w itself. And there are much bigger sets, too, that still have only À₀ elements. Consider the integers: {....,-2,-1,0,1,2,...}, the set of all positive and negative numbers. Pair up all the nonnegative integers with the even numbers: 0 with 0, 1 with 2, 2 with 4, and so on. Then pair up all the negative numbers with the odd numbers: -1 with 1, -2 with 3, -3 with 5, and so on...There's never any danger of running out, since there are À₀ odd number and À₀ even numbers. So there are À₀ integers, too.

One of the standard examples in set theory, a bit like Schroedinger's Cat is in physics, is called Hilbert's Hotel, since it was cooked up by a German named David Hilbert who was one of the greatest mathematicians of his time. This Hotel has À₀ rooms, you see, numbered 0, 1, 2, and so on. This hotel, let's say, is poised on a particularly green and friendly hillside in the Bavarian Alps, and one day a weary hiker comes upon it and decides to stay for their famous chocolate cake. (I'm elaborating a bit.) So the hiker goes up to the desk clerk, and asks for a room. 'I'm sorry, sir,' the clerk tells him, 'but all our rooms are full.' 'Just ask everyone to move one room up,' the hiker suggests. So the clerk sends the man in room 0 off to room 1, the couple in room 1 off to room 2, and so on, leaving room 0 vacant, which the hiker happily takes. Some time later, the entire nation of China stops in. 'I'm sorry,' the clerk says, 'but all our rooms are full.' Chairman Mao suggests that the clerk simply ask everyone to move up 1.2 billion rooms, and then there's plenty of room. And so it was. Some time later, À₀ people turn up for the universe's biggest Star Trek convention. 'Jesus Fuck!' cries the clerk, throwing up his hands. 'Can't you people read? No vacancy!' The infinite number of Trekkies confer for a moment, and then send up Leonard Nimoy. 'It would be most logical if you asked all your guests to move to the room with twice the number of their current room.' So the clerk left the televangelist and the Vaseline-smeared goat where they were in room 0, and sent the blow-up doll in room 1 to room 2, and the party of nuns in room 2 to room 4, and so on, and sure enough there were precisely À₀ rooms open, just enough to fit all the Trekkies in.

At this point you might come to suspect that all infinite sets have À₀ elements, and so where's the point in giving this cardinality a special name? This is not, in fact, true, and this is where it gets fun. Hilbert's Hotel may have infinitely many rooms, but there is a quantity of guests even it can't fit, no matter how it shuffles people around.

Consider the set of all the real numbers between 0 and 1, that is, all the decimals 0.abcde... where a, b, c, and so on are all digits, between 0 and 9. (Where I forbid you from doing anything silly like ending a decimal with an infinite string of 9s.) Suppose there were À₀ of them: then we could pair them all up with the natural numbers, without missing any decimals. Pair them up; let's write the decimal we paired up with 0 as 0.a₁₁a₁₂a₁₃... where all the a_1is are digits. And let's write the decimal we paired up with 1 as 0.a₂₁a₂₂a₂₃a₂₄..., and the decimal we paired up with n-1 as 0.a_n1a_n2a_n3..., for any n. Let's write them out in an array, one above the other, in this order:

0.a₁₁a₁₂a₁₃a₁₄...
0.a₂₁a₂₂a₂₃a₂₄...
0.a₃₁a₃₂a₃₃a₃₄...
...

Now I'm going to write out a new decimal, 0.b₁b₂b₃b₄... where all the b_js are going to be digits. I'm going to do it like this. If a₁₁ is not 6, then let's let b₁ be 6. If a₁₁ is 6, let b₁ be 0. And similarly, if a₂₂ is not 6, then let b₂ be 6, and if a₂₂ is 6, let b₂ be 0. If a_nn is not 6, let b_n be 6, and if a_nn is 6, let b_n be 0. What we get is a perfectly decent decimal number, which is certainly a real number between 0 and 1, and so it must be in our list somewhere since we listed out absolutely all the decimals possible. But it isn't our first decimal, since they have different first digits. And it isn't our second decimal, since they have different second digits. And, continuing onwards, it can't be our n^th decimal for any natural number n, since they have different n^th digits. Therefore, 0.b₁b₂b₃b₄... can't have been in our list after all, and we didn't get them all. See? No matter how we pair up decimals with natural numbers, I can always construct a decimal we missed. Therefore, the set w of natural numbers and the set (0,1) of real numbers between 0 and 1 can't have the same cardinality! There must be more real numbers than natural numbers. (This is called the Diagonal Argument, and was thought up by Cantor.) But there are infinitely many real numbers, and infinitely many natural numbers! There must be, then, different levels of infinity. There's this one infinity, called À₀, to describe the natural numbers, and there must be another, in some sense bigger infinity, called c (for 'continuum', which is what the real numbers are, continuous or without holes), to describe the real numbers...

There are in fact infinitely many different levels of infinity, or transfinite numbers. (How many? It's impossible to say.) And these transfinite numbers are ordered: given any two of them, they're either equal, or the first is bigger than the second, or the second is bigger than the first, and only one of these three possibilities can be true. And as it happens, given any transfinite cardinal number, there's always a next one, too, just like there is for natural numbers. The next larger transfinite cardinal after À₀ is called À₁, and then the next bigger level of infinity after that is called À₂, and so on, and there's an À_w beyond all of those, and so on, ad infinitum as it were. Infinite levels of infinity, all of them very, very different from the ones before or after them. And how does c fit into this hierarchy, you may ask? We know c is bigger than À₀, but how much bigger? Is c equal to À₁? À₂? Or what? That is a question called the Continuum Problem, and Georg Cantor's guess that c might be equal to À₁ is called the Continuum Hypothesis. Not only, in more than a hundred years since then, has Cantor's hypothesis never been proven to be true or false, but in fact in the '30s and '60s two mathematicians, Kurt Godel (another insane genius; he believed aliens were bombarding him with a mind-control ray, so he hid under his desk at Princeton a lot, and he wound up starving himself to death because he believed he was being poisoned; he also wouldn't open his door for his students, and made them shove their papers under the crack) and Paul Cohen, working separately, in different decades even, proved that from what we know about set theory, it is in fact impossible to prove that the Continuum Hypothesis is true or false. This is an example of the phenomenon Godel is most famous for, his Incompleteness Theorem: any logical system (like set theory) sufficiently complicated to include arithmetic, that doesn't contradict itself, must contain questions that the system isn't powerful enough to answer.

And now you know enough about set theory to read and enjoy Rudy Rucker's White Light. See? That didn't hurt at all.

Behold! Another update to HogBlog, the web's home for the word 'arsebucket'.

A shout out to all you Matthew Waterhouse fans out there: Mr Waterhouse stars in a dream I added to my Dream Log in tonight's fun-filled, action-packed update. Don't forget to catch John Goodman as the Baron Vladimir Harkonnen.

So, as I was saying...

Saturday afternoon, I decided to have a nice relaxing stroll through Volunteer Park, and perhaps sun myself and read a book. To my surprise, I found the field I had in mind was already in use. There were fat white middle-aged Christian rappers about, rapping fatly and whitely and middle-agedly about Christ. And Satan, of course. They were not good rappers. Their rhymes were not tight. They looked like a bunch of frustrated domesticated guys who wanted to relive their youth and strike a blow for Jesus; the look in their poor, sad eyes was 'Yeah! This'll be so cool! Man, I'm in a band now. Bands are so cool.'

The climax, of what I saw at least, was a boxing match between Jesus and Satan. Needless to say, Jesus won, and this rang out across the assembled multitude (of twelve or so; the pudgy men's pudgy wives, and some poor brainwashed children): 'Jesus...is...the CHAMPION!'

The sad part is, they really thought they would connect with the youth that way. Or maybe the sad part is that they chose Volunteer Park on a Saturday, when that field is invariably filled with members of Capitol Hill's bountiful homosexual population sunbathing.

They did not win many converts.

There was lots of Satan. Such a juvenile concept, Satan. Satan is the ultimate 'get out of argument free' card. If you claim something is the work of Satan, or favoured by Satan, or pleasing to Satan, what, exactly, is any putative disputant supposed to say in reply? 'No, it isn't, actually' just doesn't cut it. There's nothing you can say. Invoking Satan is as irrational as voting for Bush's tax cuts. Like comparing all bad things to Hitler, mentioning Satan is a technique specifically intended to make any rational debate impossible, in the hopes that one's opponent, not wishing to throw in with Satan, or Hitler, or, in modern American politics, terrorists, won't mention any of the perfectly sensible arguments against one's position and will slink off wordlessly to the back of the Senate and just pout. People who try to frame arguments in such absolutist terms aren't worth talking to: everyone who disagrees with them is a bad person who gives blowjobs to Satan, or Hitler, or Osama bin Laden. Which is unfortunate, when they gain access to public fora.

ASIDE: Consider the War on Drugs. Remember those ads where drug use was linked to support for terrorism? Those were funny. Exactly the same phenomenon. Exactly as silly. Especially since so much, for example, marijuana is produced domestically, by the upstanding, salt-of-the-earth family farmer. In fact, the Guardian recently reported that a majority of Britain's cannabis is grown right in dear old Blighty, too. Drugs are very democratic.

I have of late been reading, for the first time in my life, Kurt Vonnegut. I began with Cat's Cradle, followed by Slaughterhouse-Five; today, having been driven from Volunteer Park by fat white Christian rappers (about which more anon), I settled down at Victrola and consumed Deadeye Dick in the space of about three and a half hours or so.

I like Vonnegut. His style is very punchy...With punchlines, even. Odd, Tom Lehrer-esque punchlines, it's true, but still. Lengthy paragraphs describing something horrible, followed by a tiny, compact, dry, intensely cynical punchline. He's compelling; as a friend put it, his books want to be read.

At the same time, his books make you want to stop living. Not die, just...Not be alive any longer.

It's like there's this clown.

He's a good clown. He wears a baggy diamond-quilted suit of red and blue and yellow, and a big red fright wig; his face is painted white, with a big red rubber nose that honks when he squeezes it. He can fart on command, and when he does so a little flag pops out of his butt reading 'Poot!'

And someone loads this clown up into an airplane. Perhaps it's a Cessna; perhaps it's a Beechcraft. Perhaps it may even be a Learjet. It doesn't matter. And this someone takes off, and soars to a healthy attitude, and then, for reasons of their own, this someone pushes the clown out of the airplane.

Peradventure, you happen to be walking along right beneath that airplane, strolling through the balmy summer air, when that clown is shoved out. The clown lands two feet to your left, on top of your best girl (or guy), who is strolling through the balmy summer air by your side. Both of them are killed instantly, although, being on the bottom, your sweetheart is killed a little more thoroughly. There is a hiss of escaping gases from the clown's corpse, and a little flag pops up from its butt reading 'Poot!'

You then die eleven years later of cancer. Because it turns out the clown was actually radioactive, with a chunk of sentient plutonium from the planet Quazon living in its left lung. The Quazonites soon after declare war on mankind, and wipe the species out to the last gamete.

What fun.

There is a wonderful example of Vonnegut's funny-yet-not prose in Slaughterhouse-Five I'd like to quote for you:

Billy coughed when the door was opened, and when he coughed he shit thin gruel. This was in accordance with the Third Law of Motion according to Sir Isaac Newton. This law tells us that for every action there is a reaction which is equal and opposite in direction.

This can be useful in rocketry.^[1]

Incidentally, in the same book Vonnegut endears himself to me forever by using the term 'wang,' which, as you all should know, is slang for 'schlong'^[2].

Possibly the most depressing thing about Vonnegut's work is not that senselessly terrible things keep happening and that life is basically shit across the board. It's that the terribleness he describes is often so accurate. Towards the end of Deadeye Dick there's a passage that describes what it's like to live in the America of today with frightening precision:

But that didn't weaken the argument of their leaflet, to wit: that the United States of America was now ruled, evidently, by a small clique of power brokers who believed that most Americans were so boring and ungifted and small time that they could be slain by the tens of thousands without inspiring any long-term regrets on the part of anyone.^[3]

Vonnegut writes like an acerbic old man who has seen far too many people die, and knows that he's going to die, and that I'm going to die, and everyone's going to die, and the whole human race is going to die for that matter too, because he's seen it firsthand. He wrote like an acerbic old man even when he was a young man, or at most a middle-aged one. And he makes the idea lighthearted, whimsical even, but sucks the life out of you all the same as you laugh.

I enjoy that. He's an artist.

All three of his novels I've read so far seem to have a fixation on the immutability of the future, too. It's most obvious in Slaughterhouse-Five where Billy Pilgrim has come unstuck in time, and visits bits of his life at random throughout the novel, and meets aliens from Tralfamadore who have nothing to do with this unstuck-ness of his, who can see in four dimensions and to whom past, present, and future are all equally real at all times. He knows how his life is going to turn out because he's seen it. But it's there in Cat's Cradle and Deadeye Dick too, if for no other reason than that both novels are being narrated by characters after the events have all taken place. They know how it'll all turn out, too, because they've already lived it. There are echoes all through both of things that will happen eventually in the narrative, but haven't yet. Mass destruction, mainly.

We do remember the future, all of us. After it's happened.

***

1. Vonnegut, Kurt. Slaughterhouse-Five. New York: Dell, 1991. Page 80.
2. Op. cit. page 132.
3. Vonnegut, Kurt. Deadeye Dick. New York: Dell, 1985. Page 231-232.

The loonie, as of 2pm EDT today, was trading at 74.91 US cents.

Sign of the times, mate. Sign of the times.

I am faintly embarassed whenever I'm confronting a cashier at the supermarket. I think this may be because, after they ring me up, they'll know precisely what will be coming out of my butt in the days to come.

No-one should have such power.

No-one.

I am overwhelmingly fond of the Guardian's Simon Hoggart's reports on the doings of Parliament:

Poor old Gordon Brown. They laughed at him. They didn't use to do that. Once they watched him with awe, even with reverence - the Iron Chancellor, keeper of the cement piggy bank, now more like some aged Scottish dominie pursued down the street by his former pupils, jeering and tugging the tails of his coat.

It's not surprising. His statement on the euro yesterday was painful. He doesn't like the euro. The very idea makes his skin crawl. I thought of a middle-aged man asked by the neighbours if he and his good lady would like to try wife-swapping. Every instinct is against it, but he doesn't want to give offence. "Well, that sounds like a fascinating idea, but I don't know if the time is right. I find that my stamp collection is absorbing most of my leisure these days..."

...

At one point poor Iain Duncan Smith began coughing dreadfully, and you can bet some of his back benchers hoped it was Sars.

Much more entertaining than C-SPAN.

Can you imagine Tom Daschle standing up in the Senate to call George Bush a turkie-fucker?

I didn't think so.

According to Robert Baer, formerly of the CIA, in an article published in the Atlantic Monthly, the Saudi royals, who now number some 30,000, have something like $1 trillion invested in the US stock market.

You should read the article. Saudi Arabia is scary. But you probably knew that already.

Did I mention my finals are now over? I will soon be more drunk than you can possibly imagine. Here's a question people often ask me: if X is an infinite-dimensional Banach space, why is any nonempty open set in the weak^* topology on X^* unbounded in the norm topology?

Good question! Non-math-dorks may wish to look elsewhere for a moment. It gets hairy.

The weak^* topology on X^* is generated by sets of the form U_xyr={f: |f(x)-y|‹r} for x in X, y in our field K (either the reals or complex numbers), and r›0. Thus any open set is a union of finite intersections of such sets. So if any finite intersection is unbounded, any open set will be unbounded. What do the finite intersections look like? They are sets of the form O={f: |f(x_i)-y_i|‹r_i, i=1...n}. That is, we pick out a finite number of vectors, and our set consists of all linear functionals whose value at those vectors is 'sufficiently close' to the value we specify. Since there are only a finite number of these vectors, and X is itself infinite-dimensional, we can choose a vector x in X linearly independent from x₁...x_n; normalise it, so that x has norm 1. The linear subspace N spanned by the x_i is finite-dimensional, hence closed (by a pretty argument I may or may not share with you later on). Then x does not lie in N. Hence by a corollary of the Hahn-Banach Theorem, we can find a functional f in X^* with f(y)=0 for all y in N, but f(x)=1. Now, if there is some f₀ in O, let us construct a new functional g in X^* by letting, for any M›0, g=f₀+(M-f₀(x))f. Then since g agrees with f₀ on N, g certainly lies in O, yet g(x)=f₀(x)+Mf(x)-f₀(x)f(x)=Mf(x)=M. Thus ||g|| is at least M, since ||g||=sup{|g(z)|: ||z||=1}. Since M was arbitrary, O must be unbounded. QED.

The votes are in. Seattle's own feisty Dan Savage announces:

Hey, everybody: We have a winner. Savage Love readers, by a wide margin, want Sen. Rick Santorum's name to stand for... THAT FROTHY MIXTURE OF LUBE AND FECAL MATTER THAT IS SOMETIMES THE BYPRODUCT OF ANAL SEX! It was a landslide for that frothy mixture; the runner-up, farting in the face of someone who's rimming you, came in a distant second.

Spread the word. Don't spread the santorum.

Satirical roguery from Jesus' General, describing the next target in Bush's War on Terra:

One hundred and fifty years of shame The case for war against Pender Island, British Columbia (Part 1)

On June 15, 1859, those who hate America because we're free sent a pig into Lyman Cutler's garden on San Juan Island in Oregon Territory. That pig was a message. A message of disrespect for all we stand for. Lyman Cutler answered that message in the only way a true American can. He shot the pig. Thus began what became to be know as the Pig War.

...

The British terrorists moved across the Haro Strait to Pender Island. Their progeny live their today, smugly taunting America with their pigs and gardens. We may have the land, but the Pender Islanders have our stolen honor and they mean to keep it. That's why they have acquired weapons of mass destruction and have opened terrorist training camps. More on that in future installments.

Scroll up for vital information on the Pender Islanders' diabolical clams.

I think Zeus would be the kind of god who'd think it was really funny to light his farts on fire.

The Ontario Appeal Court has ruled, as have courts in British Columbia and Quebec, that denying same-sex couples the right to marry is unconstitutional. Previously, the British Columbia ruling had given the federal government until 2004 to change the laws to permit same-sex marriages. The Ontario ruling has gone slightly further.

Canada has gay marriage right now.

The City of Toronto has said it will begin issuing marriage licenses to gay and lesbian couples today. This day. Tuesday. Which is to say the day which it, in point of fact, happens, as it were, to be. Now.

The federal government has until 30 June to appeal the ruling, but it's entirely likely that it won't. None of the Liberal leadership candidates, not even Paul Martin, would appeal it.. And--get this!--a majority of Canadians, ordinary, workaday Canadians, actually support gay marriage.

It really restores your faith in humanity.

Homosexual men and women are being treated with the same dignity and respect accorded to everyone else in the eyes of the law. I think this is a wonderfully important step forwards; finally, gay people--gay Canadians at least--will be told that their relationships matter as much as anyone else's, that they can live ordinary lives and do the sort of ordinary life-y things people like doing, like falling in love, getting married, having kids, getting a dog, buying a house, getting tax breaks, and getting old, fat, and satisfied together. Being gay alone does not and should not define a person; it should not stigmatise a person, and cut them off from following whichever path they wish. Are all gays going to immediately settle down and join their local Parent-Teacher Associations? Gosh, no. But now they'll have the chance.

The message is this: being gay doesn't make one a freak; it doesn't make one less able to love; and it doesn't exile you from the mainstream of society. At last.

Some quotes from the Toronto Star:

"The existing common-law definition of marriage violates the couple's equality rights on the basis of sexual orientation under (the charter)," the 61-page written ruling said.

The court also declared the current definition invalid and demanded the law be changed. It ordered the clerk of the City of Toronto to issue marriage licences to the same-sex couples involved in the case. City Hall said in a release after the ruling it would begin issuing marriage licences today to all who meet the requirements, "including same-sex couples."

...

Heritage Minister Sheila Copps and federal leadership candidate said Ottawa should accept the ruling and not appeal it to the Supreme Court of Canada.

"You can't have a half equality," she said in Ottawa. "You can't say: `Well, you're equal, but.'

"When you're speaking about equality you're talking about allowing people to exercise all rights under the law including all rights that are available to all others."

Essentially the same story from the Globe and Mail:

Ontario's Appeal Court decision joins court rulings in British Columbia and Quebec that also back same-sex unions.

However, it differs in that it calls for the new definition to take place immediately, allowing gay and lesbian couples to marry now.

It also effectively forces Ontario to recognize the January 2001 marriage of Joe Varnell and Kevin Bourassa, who were wed in a Toronto church ceremony using an ancient Christian tradition that allowed them to avoid having to get city-issued marriage licences.

Theirs would be the first same-sex marriage in Canada.

...

Also celebrating Tuesday were Joyce Barnett and Alison Kemper, who picked up their marriage licence with Mr. Stark and Mr. Leshner and planned to wed in July 2004.

Their two children were ecstatic.

"I knew that nobody could say I didn't have a family," said Robbie, 11, who was born to Alison. "Canada has finally figured out it's unfair to deny this to anybody."

More from the CBC:

Holding their licence, Michael Leshner and Michael Stark, one of the couples involved in the court case, said they are getting married within hours.

"Today is the death of homophobia in the courtroom as we've known it," said Leshner, an Ontario Crown attorney.

"Absolute faith in Canadian values" helped him through the long court battle, said Leshner, who encouraged other countries to follow Ontario's lead.

"When we get married, we will have lit a match that hopefully illuminates the world," he said.

I am a happy man.

I realised in class on Friday that one possible acronym for the Central Limit Theorem, in probability theory, is CLiT. I hate probability theory. These are the things that come to mind when I'm sitting in lecture and absolutely not paying attention in the slightest. I doodle a lot. The number of cartoon penises appearing in my notes is inversely proportional to the quantity of attention I was paying. We also heard that same day about something called the Weiner Process, which was nicely symmetrical...

The dirtiest piece of mathematical terminology I've ever heard is 'free group action'. That ought to be a porn site. The Hairy Ball Theorem is pretty decently dirty, too.

I have decided to devote my life to formulating and proving something I will call 'the Teabagging Theorem'. I think I might actually be able to get away with it; how many professional mathematicians are liable to practice the ancient art of ball-dipping, or to have seen John Waters's Pecker?

I should be studying right now.

Probably the most enjoyable thing about having a website is finding out how visitors found it. In consulting my statistics, I find that in the month of May, people found some subset of my domain by running Internet searches on the following:

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Ithyphallophobia, in case you were wondering, is an unreasoning fear of erect penises.

Jackson Doran is a young actor in Iowa City, about whom I had several dreams.

'Pedicabo' is the first person singular future active indicative form of the Latin verb meaning 'sodomise'. It appears in a poem of Catullus I translated, albeit poorly.

Padelford Hall is where I work. It was built to withstand sieges back in the dizzay. And it shows. It's grotesquely ugly and inconvenient.

Zork, of course, was a brilliant text-based interactive adventure game thingy of which I'm massively fond. I used it as the inspiration for the page on which I archive random, mainly valueless, things I have written.

Counciltucky, also known as Councilbama, is of course Council Bluffs, Iowa, where I grew up. I am not proud of this fact.

Go bake these scones at once. And splurge; use heavy whipping cream instead of half and half, and real butter instead of margarine. I can affirm, from firsthand experience, that they rock like David Bowie, and they make the world safer from terrorism. Not even Osama bin Laden himself could remain unmoved by the sweet taste of these scones.

As you have no doubt noticed, I haven't been blogging much lately. The academic year is coming to a climax here at the University of Washington, meaning, if you happen to be an undergraduate, here or elsewhere, all of your TAs, like myself, are grotesquely overworked, and you should drop down on your knees and grovel with thanks that we have time to help you review for your final exam at all, grovel and squirm like the lowest of insects at the feet of Baphomet.

Since Memorial Day, I've been more or less oblivious to the outside world, only sporadically keeping up with news and the doings of the blogosphere and suchlike. I now find myself with a few days between my last homework assignment and my first final exam, so, for kicks, I thought I might pull my head out of sand for a moment and see what the world's been up to in my absence.

Salam Pax will be writing a column for the Guardian.

It seems increasingly likely that there really were no weapons of mass destruction in Iraq, and that, moreover, the intelligence services of the western powers knew it, and that, gosh, the Bush Administration and its allies just didn't care.

Paul Krugman is very cross.

Andrew Sullivan is still an idiot:

'One reason I find some of the grand-standing over WMDs increasingly preposterous is that it comes from people who really want to avoid the obvious: more and more it's clear that the liberation of Iraq was a moral obligation under any circumstances.'

Hold on. A large glowing rainbow has been projected across my living-room floor. Either I have just spontaneously become three times gayer than before, or something is up.

...

All is well. It's the sun refracting through my roommate's salamander tank.

As I was saying...

I think perhaps I might have figured out why it is the things Andrew Sullivan says are so often at variance with the objective external world. The crucial discovery was this: Andrew Sullivan has a beard.

Suddenly everything became ever so clear. Andrew Sullivan's complete divorce from fact and reality isn't due to his ideological blindness, lack of journalistic integrity, and burning desire to felch his way into the chummy ranks of America's ruling junta. Far from it. Andrew Sullivan is completely honest and integral and is not putting any ideological spin whatsoever on the news he reports (secondhand). It's just that he reports the news from his home universe.

It is a well-known fact that every universe has a mirror image, which physicists term a 'barbiverse', which is its complete moral opposite. In the barbiverse, the good and virtuous of our universe become evil and base; the liberator becomes the oppressor; Leonard Nimoy becomes a pop star; and of course vice-versa. Evil becomes good, and deceit becomes truth, and cynical manipulation becomes idealism. Also, and this is a dead giveaway, people have beards.

The necessary conclusion is almost too obvious to state.

Somehow, somewhere, our universe's Andrew Sullivan, a Buddhist socialist who publishes scholarly works on sociology and raises rabbits, changed places with his barbiverse double, and this double has taken up a career as a columnist and blogger, faithfully reporting all the news from his native cosmos. In his world, as I said, all things are morally inverted. George Bush is an honest, compassionate defender of liberty, and Donald Rumsfeld is a selfless servant of the people; and Iraq was actually a threat, harbouring al-Qaeda forces left and right, and aggressively pushing its nuclear weapons research programme, and threatening the United Provinces of Vinland itself with cataclysm and destruction. Just in the nick of time did Bush thwart Saddam Hussein's insane plans for world domination, which had already paralysed Europe and Asia, and in a daring last-minute action Bush himself fought the Iraqi dictator hand-to-hand to keep his finger off of the fatal button, thus saving all of mankind from utter annihilation. The UP was only too willing to fund a complete reconstruction of the afflicted land; collateral damage had been kept to an absolute minimum by the timely intervention of Vinlandic forces as the Iraqi regime began to crumble and violence and anarchy threatened to sweep the streets, museums, telephone exchanges, and water treatment plants. Freedom and democracy blossomed like daisies upon the rejoicing and prosperous land of Iraq.

Which is why Sullivan appears so confused, when he encounters media from this universe, and why he has to twist the facts so to fit what he knows to be the truth.

It's all so clear now.

Post Scriptum: I am aware that I, too, have a beard. But do not be deceived. I am not from the barbiverse; I am actually from the oculo-barbiverse. For, just as every universe has its inverted, bearded dual, so also does every universe have another, equally inverted, oculiverse double, distinguished by the presence of eyepatches. The oculi-barbiverse, being doubly inverted, is indistinguishable from the universe you and I currently inhabit, barring, of course, the beards and eyepatches. I just lost my eyepatch somewhere. I'm always losing things. Memory like a thingy, you know, full of holes. You send water through them. Thus everything I say is reliable and accurate. So there.