compulsive wrestling with mathematical monstrosities

For your amusement, here is a little glimpse into a horribly undisciplined mind.

From time to time, my brain gets tackled by some monstrous mathematical idea that dominates all my thinking for hours, days, weeks, even longer.

Early in 2005, I was innocently walking one evening (pushing my son in his stroller, trying to lull him to sleep), and thinking about something thoroughly un-mathematical, when ... suddenly, I found myself suddenly convinced that I had a counterexample to Poincaré's Conjecture. I didn't ask for this to happen. I didn't intend to ponder topology for the next two weeks. It just happened.

(Like most of the world, I was not aware at the time of Grigori Perelman's proof of the conjecture, since reviewers were still busy checking it.)

The (alleged) counterexample was "obvious". Only the fact that better minds than mine had failed to prove or disprove the conjecture for 100 years or so made me mull it over, again and again, to find out what was wrong with my idea. I figured it out eventually. (The beast in question failed, in a rather subtle (to me) way, to qualify as a manifold in the first place.)

And you wonder why I never accomplish anything...

of mountains, molehills, and misplaced "mea culpa"

Here’s a crazy story.

Summary: Webster Cook, a student at the University of Central Florida, violated Catholic church rules by failing to consume immediately his consecrated wafer. Church members tried to use physical force to take the wafer back, and Cook responded by running away – with the wafer in hand. There were complaints that he was holding the Body of Christ as a hostage.

Some people (such as Bill Donohue of the Catholic League) want Cook expelled from the university. His actions are worse than “hate speech”, according to Donohue. (As far as I know, the witch-hunt is continuing, even though Cook later returned the wafer.)

Now, let’s all calm down and get things into perspective. There is no persecution of Catholics going on here, no inciting of hatred, and no interference with anyone else’s ability to perform properly their own parts of the ritual. All we have here is a ritual gone awry, and only as it pertained to Webster Cook. Aside from offending people’s sensibilities, Cook’s actions did no harm. There is no “theft” here: Even if he had not returned the wafer, the church would not have been deprived of anything that it would normally be expected to possess. (After all, the wafer was given to Cook with the expectation that he would eat it.) And there is no mess to clean up, and therefore no vandalism. There’s also no need to worry about any harm suffered by God. (You’d think God could take care of himself.)

Notice that my arguments do not depend on contradicting Catholic theology. In fact, I agree with P Z Myers’s position (let’s not be silly here; it’s obviously just a cracker), but I have no need to base an argument on that.

I can understand a Catholic getting annoyed if another Catholic messes up their part in a ritual. But what’s the big deal if an outsider does it? If my brain is already full of blasphemous opinions (e.g., that your religion is silly), and I’m going to hell anyway (according to you), then how can it possibly matter if I get my hands on one of your consecrated wafers and do something naughty with it (like failing to eat it)?

That’s where things ought to end. I would like to be able to conclude thus: Catholics are no more affected by these events than they choose to be. There’s always the option to ignore Webster Cook, and forget that any of this happened. After all, you already knew that there are non-Catholics in this world, always saying and thinking things that any party-line Catholic would find offensive.

But it’s not that simple. I’ve left out the most disturbing part of the story.

(And no, I’m not talking about Myers’s response to the story, including his threat to deface a consecrated wafer, live on the web, if someone will send one to him. That’s a rather rude and unnecessary stunt, but it’s far less offensive than the Catholic League’s campaign to get him fired over it. Again, there’s always the option to ignore him.)

Go back to the original story (my first link above), written before the wafer was returned. Notice the words of the priest Miguel Gonzalez (emphasis added).

Gonzalez said intentionally abusing the Eucharist is classified as a mortal sin in the Catholic church, the most severe possible. If it's not returned, the community of faith will have to ask for forgiveness.

"We have to make acts of reparation," Gonzalez said. "The whole community is going to turn to prayer. We'll ask the Lord for pardon, forgiveness, peace, not only for the whole community affected by it, but also for [Cook], we offer prayers for him as well."

Holy smokes.

I can understand Catholics being annoyed at Webster Cook. But having the whole congregation wallow in guilt because of his actions? What on earth is that about?

It turns out that ordinary Catholics are victims in this story, after all. But not in the way that Bill Donohue suggests. They’re not victims of hate crimes; they’re victims of mind manipulation by their own clergy.

But I suppose that shouldn’t come as a surprise.

that missile shield in eastern Europe

I’m trying to find any reports that suggest that Iran is working on missiles capable of reaching central Europe. I haven’t found any. Yet the Bush Administration seems to think a missile shield, to protect Europe against Iranian missiles, is an urgent matter.

And they want to plant their anti-missile defences in Poland and the Czech Republic – the natural place for a shield against Iranian attack, right?

Wrong. Look at a map, for crying out loud.

If the US were really concerned about an Iranian threat against Europe – putting aside the flimsy basis for such a worry – then the natural place for anti-missile defences would be Turkey, not Poland. I’m sure the Turks would happily oblige.

So what is this missile shield really for?

There are very few countries in the world with any significant capacity to retaliate if they happen to be attacked by the US. Wouldn’t Bush et al love to change “very few countries” to “no countries”? (Of course he would. Who wouldn’t, in his position?) That’s the sort of thing that this missile shield, if it works at all, could accomplish.

So who are those “very few countries”? Hmmm. Russia comes to mind, for one.

I can’t blame the Russians for feeling threatened. The evidence is on their side. The assurances of the Bush Administration – “it’s not about you, it’s about Iran” – are worth diddly-squat.

a rambling miscellany

Many events are worth commenting on.

For example, US elections always generate a lot of talk. My take: Both sides, if they’re smart, will try to lose. The winner will be blamed, unjustly, for the upcoming economic collapse.

Here in Canada, a natural and worthy topic would be the PM’s recent historic apology to aboriginal people – a first, tiny, step in Canada’s Vergangenheitsbewältingung. (No one is yet talking about the near-impossible constitutional overhaul that will be necessary if the process is ever to be completed properly.)

Many more things.

There’s the crazy (and doomed) intervention in Iraq. There’s the somewhat more justifiable (but still doomed) intervention in Afghanistan. There’s the possibility of a completely idiotic (and doomed) attack on Iran, advanced by an utterly bogus one-size-fits-all misapplication of the Munich argument.

There’s the fact that the world’s oil is quickly running out – and that if I had any sense (which I don’t), I’d be frantically learning everything I can about gardening. When the trucks can no longer deliver to Sobey’s or Superstore, I may have nothing to eat beyond what I can grow in my own yard.

So many important things! Yet I find myself drawn to something relatively trivial.

After decades of Christianity, Øystein Elgarøy, professor of astrophysics at the University of Oslo, is now an atheist, as reported here by fritanke.no. The delicious part of this story is the role played by the weak arguments of Oxford’s Alister McGrath contra Richard Dawkins and Christopher Hitchens. (One infidel has described this as an “own goal” for McGrath.)

The mere existence of weak arguments is unremarkable. But when very bright people (like McGrath) use them, one cannot help but think that good arguments must be unavailable.

In retrospect, I date my own wake-up call to my reading of the appalling little booklet History and Christianity by John Warwick Montgomery. (I review it here.) If it were possible to argue for the traditional Christian account of the origins of the Church without stooping to such glaring fallacies and misuse of evidence, surely someone with Montgomery’s considerable intelligence and encyclopaedic knowledge would have done it.

So many possible topics to rant about. I need to find my focus.