The most familiar ideas of geometry were inspired by an ancient vision — a vision of the world as flat. From parallel lines that never meet, to the Pythagorean theorem discussed in last week’s column, these are eternal truths about an imaginary place, the two-dimensional landscape of plane geometry.

Conceived in India, China, Egypt and Babylonia more than 2,500 years ago, and codified and refined by Euclid and the Greeks, this flat-earth geometry is the main one (and often the only one) being taught in high schools today. But things have changed in the past few millennia.

In an era of globalization, Google Earth and transcontinental air travel, all of us should try to learn a little about spherical geometry and its modern generalization, differential geometry. The basic ideas here are only about 200 years old. Pioneered by Carl Friedrich Gauss and Bernhard Riemann, differential geometry underpins such imposing intellectual edifices as Einstein’s general theory of relativity. At its heart, however, are beautiful concepts that can be grasped by anyone who’s ever ridden a bicycle, looked at a globe or stretched a rubber band. And understanding them will help you make sense of a few curiosities you may have noticed in your travels.
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Touched is what I am by the number of people who thought I had vanished from this place. And especially by the number who were sorry.

I wasn’t far, having only moved laterally to go on a different stage, playing a different part: the role of Gail Collins in her dialogs with David Brooks elsewhere in Opinionator while she took a well-deserved three weeks away from that grind of two fine and hefty columns a week. A gig that has been known to crumple strong men and women.

Quite a number of Cavett-ites found me there, but for those who did not and succumbed to melancholy at my possible demise, I recommend your excavating those three columns. Even if it’s only for my granting the hinted request by David Brooks — Marx Bros. fanatic extraordinaire — to include a bit of Groucho each time.

If a touch of the strain of jangled nerves should shine through here this time, it has to do with finally and at longest last pulling out of the tunnel of— O, horrid, horrid term! — moving.
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When I can’t sleep, I think about what I’m missing. I glance over at my wife and watch her eyelids flutter. I listen to the steady rhythm of her breath. I wonder if she’s dreaming and, if so, what story she’s telling to herself to pass the time. (The mind is like a shark — it can’t ever stop swimming in thought.) And then my eyes return to the ceiling and I wonder what I would be dreaming about, if only I could fall asleep.

Why do we dream? As a chronic insomniac, I like to pretend that our dreams are meaningless narratives, a series of bad B-movies invented by the mind. I find solace in the theory that all those inexplicable plot twists are just random noise from the brain stem, an arbitrary montage of images and characters and anxieties. This suggests that I’m not missing anything when I lie awake at night — there are no insights to be wrung from our R.E.M. reveries. Read more…

If the health care reform package makes it through Congress, and we should know sometime on Sunday, much of the credit for its salvation will go to Thursday’s report from the Congressional Budget Office that, according to The Times’s David M. Herszenhorn, predicted “a $940 billion price tag for the new insurance coverage provisions in the bill, and the reduction of future federal deficits of $138 billion over 10 years.” It is an article of faith that the budget office resides, pretty much alone among government bodies, in the refined aerie of nonpartisanship, a paragon of technocratic, if not inhuman, objectivity.

In fact, according to Ezra Klein of the Washington Post, the imprimatur of the C.B.O. takes the health care debate entirely out of the messy realm of political give and take we junkies love so much. “The question people generally ask about the final health-care reform vote is, “Won’t it be politically difficult for many House Democrats to vote yes?” But with the release of the C.B.O. report … I’d flip that question a bit: Won’t it be substantively difficult for many House Democrats to vote no?”

Klein explains:

If you’re a liberal House Democrat, here’s what you’d be voting against: Legislation that covers 32 million people. … If you’re a conservative House Democrat … you also get the single most ambitious effort the government has ever made to control costs in the health-care sector. According to the Congressional Budget Office, the bill cuts deficits by $130 billion in the first 10 years, and up to $1.2 trillion in the second 10 years … Democrats got the score they needed, and now they can go to their liberals and say that this is closer to universality than we’ve ever been, and they can go to their conservatives and say this does more for deficit reduction than has ever been done, and both things will be true.

If this bill does pass on Sunday, that, and not deals or polls or rides on Air Force One, will be why.

Who ever would have thought that after more than a year of vitriol, the whole health care reform question would result in a win-win bill? Read more…

What if the biggest rewards on Wall Street went to those who thwarted dangerous and excessive risk-taking instead of to those who enabled, approved or simply ignored it?

What if every senior Wall Street executive had to worry that he could lose his entire net worth at any moment — including his mansions in Greenwich, Conn., and Palm Beach to say nothing of his job — if the revenue he was generating turned out to be unprofitable or excessively risky?

Wouldn’t that combination of potential rewards and fear of calamitous personal loss instill in every Wall Streeter a zealous desire to insist that the products his firm was peddling were safe for others to buy?

If such simple incentives had been in place on Wall Street, wouldn’t the latest crisis — as well as the multitude of others that have been perpetrated on us in the past 25 years — been largely avoided? Read more…

“I’m a sleep doctor.” Silence. There is a pause in the conversation, which is common.

Sleep medicine, as a field, is new enough that people are often taken off guard: “You do what?” The disheveled older man, who seems to have Ritz crackers woven into the fabric of his tie, leans closer. He appears to have misheard or misunderstood. (I often wonder what goes through peoples’ minds in that split second; what do they think they heard me say: “I’m a peep doctor”?) I repeat and explain that I do sleep medicine, “you know, insomnia, sleep apnea, that sort of thing.” “Oh, yes. I see.” His eyes widen with interest; now he steps really close, and a trembling hand lightly lays itself on my forearm.

I know that if I am not extremely creative and diplomatic, I will be stuck in the corner all night doing what I do all day — listening to some sad soul pour out his story of tortured, restless sleep. At a party, I am right up there in popularity with the dermatologist and plastic surgeon. Everyone needs our help and no one is embarrassed to say so. Read more…

Associated Press Dennis Kucinich leaving Air Force One on Monday.

Quite a week for Dennis Kucinich, the liberal Democratic congressman who had been threatening to do to health care what Ralph Nader did to Al Gore in 2000.

On Monday, he accompanied President Obama on Air Force One, flying to his district in Cleveland for a rally.

On Wednesday, he ended months of self-righteous defiance, deciding not to stand with every single Republican in Congress trying to block health care reform.

Until the last minute, it looked like even an executive sky ride would not move the pure heart of Dennis Kucinich. When you’ve seen a U.F.O., as Kucinich says he has, a mere lobbying session at 32,000 feet by the Leader of the Free World, urging you to join your party in a cause that has eluded Democratic presidents since Franklin Roosevelt, is a tough match.
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Reuters An Afghan boy walked near American soldiers patrolling in Now Zad in southern Afghanistan on March 7. Afghans have been returning to the town after it was secured by a Marine-led operation in December.

Last week Defense Secretary Robert Gates visited the district of Now Zad in Afghanistan’s volatile Helmand Province. To many, it probably didn’t seem like significant news. Gates reportedly went no farther than a 100 meters outside the forward operating base and there were fully armed Marines posted at short intervals not far from where he was walking. They had probably been in position for at least 24 hours before Gates arrived and the area was likely swept for explosives and insurgents multiple times in the days prior to his arrival.

This surely reeks of political theater to the skeptical, but for those of us who have experienced the brutality of Now Zad’s history first-hand this news brings us one page closer to the end of long chapter in our lives.
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Luke Sharrett/The New York Times If the future of our health care system depends on Senator Max Baucus, a Democrat from Montana, and Senator Chuck Grassley, a Republican from Iowa, the republic will surely crumble.

Gail Collins: David, when I went off on vacation I left you to converse with Dick Cavett. Really, what could be more fun? All the while I was gone I was imagining what a great time the two of you were having. Well, O.K., not all the time. But the thought definitely occurred.

Then I got back to the Internet-accessible world and discovered that you’ve been in a total funk. Your conversations with Dick were wonderful to read, but what’s gotten you into this decline-and-fall-of-the-Roman-empire depression? Every week, you got sadder and more discouraged about the country, the culture, the common good. Read more…

Last Friday night a New York Times headline underwent an online transformation. The article formerly known as “A Christian Overture to Muslims Has Its Critics” acquired a new billing: “A Dispute on Using the Koran as a Path to Jesus.”

For my money this was a big improvement, and explaining what I mean will illuminate a dirty little secret: some American Christians are fostering religious strife abroad. They mean well, but the damage they’re doing can be seen all the way from Nigeria, where Christians and Muslims are killing each other, to Malaysia, where Muslims are trying to keep Christians from using the term “Allah” for God.

The Times story is about an outreach technique that some Baptist missionaries use with Muslims. It involves stressing commonalities between the Koran and the Bible and affirming that the Allah of the Koran and the God of the Bible are one and the same.

You can see how a headline writer might call this an “overture.” And certainly the Christians who deploy the technique see it in sunny terms. Their name for it — the “Camel Method” — comes from the acronym for Chosen Angels Miracles Eternal Life.

But a more apt etymology would involve the “camel’s nose under the tent.” The “overture” — the missionary’s initial bonding with Muslims via discussion of the Koran — is precision-engineered to undermine their allegiance to Islam.
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