These posts are either "jump pages" for my weblog or posts-in-process that will eventually appear there. For what it's worth, here's an archive of these random bits. The picture to the left is by a famous comic book artist.
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This is a digitally manipulated image by Hildur Bjarnardottir, an artist living in Iceland. The source image is a traditional lace knit shawl. The picture is printed large on matte paper, mounted on an aluminum panel. According to Bjarnardottir, "since I am using traditional Icelandic shawls [my recent] exhibition earned me a nomination for the DV cultural award in Iceland." This kind of symmetrical, crystalline mirroring comes easily and naturally in the computer, so the success of an image often depends on how exotic the source is. In this case, I would never have guessed Icelandic textiles.
Mathematician Fills in a Blank for a Fresh Insight on Art
By SARA ROBINSON NY Times 7/30/02
On a flight to the Netherlands, Dr. Hendrik Lenstra, a mathematician, was leafing through an airline magazine when a picture of a lithograph by the Dutch artist M. C. Escher caught his eye.
Titled "Print Gallery," it provides a glimpse through a row of arching windows into an art gallery, where a man is gazing at a picture on the wall. The picture depicts a row of Mediterranean-style buildings with turrets and balconies, fronting a quay on the island of Malta.
As the viewer's eye follows the line of buildings to the right, it begins to bulge outward and twist downward, until it sweeps around to include the art gallery itself. In the center of the dizzying whorl of buildings, ships and sky, is a large, circular patch that Escher left blank. His signature is scrawled across it.
As Dr. Lenstra studied the print he found his attention returning again and again to that central patch, puzzling over the reason Escher had not filled it in. "I wondered whether if you continue the lines inward, if there's a mathematical problem that cannot be solved," he said. "More generally, I also wondered what the structure is behind the picture: how would I, as a mathematician, make a picture like that?"
Most people, having thought this far, might have turned the page, content to leave the puzzle unsolved. But to Dr. Lenstra, a professor at the University of California at Berkeley and the University of Leiden in the Netherlands, solving mathematical puzzles is as natural as breathing. He has been known, when walking to a friend's house, to factor the street address into prime numbers in order to better fix it in his mind.
So Dr. Lenstra continued to mull over the mystery and, within a few days of his arrival, was able to answer the questions he had posed. Then, with students and colleagues in Leiden, he began a two-year side project, resulting in a precise mathematical version of the concept Escher seemed to be intuitively expressing in his picture.
Maurits Cornelis Escher, who died in 1972, had only a high school education in mathematics and little interest in its formalities. Still, he was fascinated by visual mathematical concepts and often featured them in his art.
One well-known print, for instance, shows a line of ants, crawling around a Moebius strip, a mathematical object with only one side. Another shows people marching around a circle of stairs that manage, through a trick of geometry, to always go up. The goal of his art, Escher once wrote in a letter, is not to create something beautiful, but to inspire wonder in his audience.
Seeking insight into Escher's creative process, Dr. Lenstra turned to "The Magic Mirror of M. C. Escher," a book written (under the pen name of Bruno Ernst) by Hans de Rijk, a friend of Escher's, who visited the artist as he created "Print Gallery."
Escher's goal, wrote Mr. de Rijk, was to create a cyclic bulge "having neither beginning nor end." To achieve this, Escher first created the desired distortion with a grid of crisscrossing lines, arranging them so that, moving clockwise around the center, they gradually spread farther apart. But the trick didn't quite work with straight lines, so he curved them.
Then, starting with an undistorted rendition of the quayside scene, he used this curved grid to distort the scene one tiny square at a time.
After examining the grid, Dr. Lenstra realized that carried to its logical extent, the process would have generated an image that continually repeats itself, a picture inside a picture and so on, like a set of nested Russian wooden dolls.
Thus, the logical extension of the undistorted picture Escher started with would have shown a man in an art gallery looking at print on the wall of a quayside scene containing a smaller copy of the art gallery with the man looking at a print on the wall, and so on. The logical extension of "Print Gallery," too, would repeat itself, but in a more complicated way. As the viewer zooms in, the picture bulges outward and twists around onto itself before it repeats.
Once Dr. Lenstra understood this basic structure, the task was clear: If he could find an exact mathematical formula for the repetitive pattern, he would have a recipe for making such a picture with the missing spot filled in.
Measuring with a ruler and protractor, he was able to estimate the bulging and twisting. But to compute the distortion exactly, he resorted to elliptic curves, the hot topic of mathematical research that was behind the proof of Fermat's last theorem.
Dr. Lenstra knew he could apply elliptic curve theory only after reading a crucial sentence in Mr. de Rijk's book. For esthetic reasons, Mr. de Rijk explains, Escher fashioned his grid in such a way that "the original small squares could better retain their square appearance." Otherwise, the distortion of the picture would become too extreme, smearing individual elements like windows and people to the point that they were no longer recognizable.
"At first, I followed many false leads, but that sentence was the key," Dr. Lenstra said. "After I read that, I knew exactly what was happening."
Escher was creating a distortion with a well-known mathematical property: if you look at small regions of the distorted picture, the angles between lines have been preserved. "Conformal maps," as such distortions are known, have been extensively studied by mathematicians.
In practice, they are used in Mercator projection maps, which spread the rounded surface of the earth onto a piece of paper in such a way that although land masses are enlarged near the poles, compass directions are preserved. Conformal principles are also used to map the surface of the human brain with all the folds flattened out.
Knowing that Escher's distortion followed this principle, Dr. Lenstra was able to use elliptic curves to convert his rough approximation of the distortion into an exact mathematical recipe. He then enlisted a Leiden colleague, Bart de Smit, to manage the project and several students to help him.
First, the mathematicians had to unravel Escher's distortion to obtain the picture he started with. A student, Joost Batenburg, wrote a computer program that took Escher's picture and grid as input and reversed Escher's tedious procedure.
Once the distortion was undone, the resulting picture was incomplete. Some of the blank patch in the center of "Print Gallery" translated into a blurred swath spiraling across the top of the picture. So, the researchers hired an artist to fill in the swath with buildings, pavement and water in the spirit of Escher.
Starting with this completed picture, Dr. de Smit and Mr. Batenburg then used their computer program in a different way, to apply Dr. Lenstra's formula for generating the distortion.
Finally, they achieved their goal: a completed, idealized version of Escher's "Print Gallery."
In the center of the mathematician's version, the mysterious blank patch is filled with another, smaller copy of the distorted quayside scene, turned almost upside-down. Within that is a still smaller copy of the scene, and so on, with the remaining infinity of tiny copies disappearing into the center.
Since Escher's distortion was not perfectly conformal, the mathematician's rendition differs slightly from his in other ways as well. Away from the center, for example, the lines of some of the buildings curve the opposite way.
The researchers also used their program to create variations on Escher's idea: one in which the center bulges in the opposite direction, and even an animated version that corkscrews outward as the viewer seemingly falls into the center. After a recent talk Dr. Lenstra gave at Berkeley, the audience remained seated for several minutes, mesmerized by the spiraling scene.
While Dr. Lenstra has solved the mystery of the blank patch and more, one question remains. Did Escher know what belonged in the center and choose not to represent it, or did he leave it blank because he didn't know what to put there?
As a man of science, Dr. Lenstra said he found it impossible to put himself inside Escher's mind. "I find it most useful to identify Escher with nature," he said, "and myself with a physicist that tries to model nature."
Mr. de Rijk, now in his 70's, said he believed Escher knew his picture could continue toward the center, but did not understand precisely what should go there. "He would be astonished to experience that his print was still much more interesting than was his intention," Mr. de Rijk said. He added that while he knew of another effort to fill in Escher's picture, it was not based on an understanding of the mathematics behind it.
"He was always interested when somebody used his prints as a base for further study and applications," Mr. de Rijk said. "When they were too mathematical, he didn't understand them, but he was always proud when mathematicians did something with his work."
This post is a continuation of a discussion I'm having with Pamela, which started with drawings of Shell. The main thread begins here. Pamela, assuming you've followed the link here, I found out why your links weren't working: see Jim's comment to this post. Eventually we'll get this worked out, but in the meantime I can change the URLs you posted to links, if you want.
I checked out the greenoblivion page. I'll comment soon.
"I believe people have taken a step back and asked, ‘What’s important in life?’" said the nation’s chief executive Thursday. "You know, the bottom line and this corporate America stuff, is that important? Or is serving your neighbor, loving your neighbor like you’d like to be loved yourself?" These shards of clueless verbiage bring to mind his father’s brief but beautiful poem about economic distress, "Message: I care." --Joe Conason
As a friend of mine put it, "The steel balls are finally coming out of Captain Queeg's pocket."
12/31/01
Dear Robert Jensen,
I'm writing to thank you for the articles and essays you've written in the aftermath of 9/11. I live and work in the New York metro area and saw the North Tower collapse from a friend's window. The kneejerk calls for revenge and abrogation of international law in the immediate aftermath were appalling, and I took comfort in your brave words. Having lived in Texas for many years, I know such phrases aren't uttered without a price. These are hard times for progressives (and libertarians). The quick "success" of the Afghan bombing campaign made the left seem like doubters and naysayers, and I find myself abandoned on all sides by people I'm usually in accord with. Jacob Weisberg in Slate writes that "there is no antiwar movement"; Christopher Hitchens adroitly paints progressives as unrealistic ninnies that don't live in the real world. Susan Sontag's New Yorker piece (which I recently reread, and which seems quite sane and moderate) is routinely held up as a "traitorous" screed. As I believe you've said, it's difficult to formulate an alternative to the Bush/Pentagon plan that speaks to people. I've argued that it's a police matter, to be pursued through increased intelligence and economic pressure on our Saudi "allies," but that usually falls on deaf ears. I'm not a pacifist, but neither am I in favor of rolling out our huge military machine, across sovereign borders, every time we get angry or scared. I think William Safire's view that we can "civilize" the world at gunpoint is naive--talk about a ninny who doesn't live in the real world! That's precisely why 9/11 happened! Anyway, thanks again, and keep up the good work.
Best, Tom Moody
6/9/02
Dear Maureen Dowd,
Your column today contains a risible suggestion: "Maybe if Mr. Bush brings Rudy Giuliani in as the new cabinet officer, he can work magic." Frank Rich said much the same thing yesterday. I'd like to remind you that this is the same Giuliani who built the city's $13 million "command bunker" on the 23rd floor of 7 World Trade Center, equipped with fuel tanks that exploded and toppled the building. Does his post-9/11 "leadership" really erase this act of stupidity and hubris, which put the entire city at risk? I'd just as soon not have him operating at the national level, thanks.
Best, Tom Moody
6/8/02
Dear Frank Rich,
Your column today contains a risible suggestion: "Instead of creating a new organizational chart, Mr. Bush might have enlisted one man to hose down our security bureaucracy: Rudolph Giuliani." Are you talking about the man who built the city's $13 million "command bunker" on the 23rd floor of 7 World Trade Center? Equipped with fuel tanks that exploded and toppled the building? Oh, yes, it'd be great to have him in charge on a national level.
Best, Tom Moody
6/18/02
Dear Michael Getler [WaPo Ombudsman]:
Dana Milbank's article on George Bush's Ohio State commencent address really crosses the line between objective reporting and administration propaganda. The long list of Bush's "intellectual influences" is obvious p.r. flack puffery: it should have been pared down (or--is this too much to ask?--supported with some examples of where those thinkers' ideas appear in the former C-student's speech). More disturbing is the omission of the school's threats to arrest students for protesting, and the actual arrest of a "silent protestor," which have been documented elsewhere. Milbank creates the impression that Bush has broad popular support, but that means nothing if it's coerced. In terms of sheer newsworthiness, the "turn your back on Bush" campaign organized by the students --an unpaid, grassroots effort--is a far more compelling "story hook" than Bush's so-called journey to popularity. The former took guts and belief; the latter was conferred on Bush by tragic circumstances (which, it's looking more and more like, he actively or negligently brought into being).
Sincerely, Tom Moody
6/26/02
Dear MWO,
I've been looking at your site regularly and enjoy your alerts regarding conspicuous media prostitution. I stopped watching TV news years ago because I got tired of watching blowdried heads read government press releases. I voted for Gore, but I have no illusions about Clinton/Gore's addiction to corporate money. I always treat my friends who voted for Nader with the utmost respect, as ideological comrades-in-arms. I'm writing to say: Please stick to what you're good at, which is rooting out media complicity with government policy. Give Ralph a rest, OK??? The response by his campaign manager was reasonable and civilized. I stopped reading your reply because the tone was so nasty.
All the best, Tom Moody
"Everyone is Outraged," by Paul Krugman, NY Times
Arthur Levitt, Bill Clinton's choice to head the Securities and Exchange Commission, crusaded for better policing of corporate accounting — though he was often stymied by the power of lobbyists. George W. Bush replaced him with Harvey Pitt, who promised a "kinder and gentler" S.E.C. Even after Enron, the Bush administration steadfastly opposed any significant accounting reforms. For example, it rejected calls from the likes of Warren Buffett to require deduction of the cost of executive stock options from reported profits.
But Mr. Bush and Mr. Pitt say they are outraged about
Representative Michael Oxley, the Republican chairman of the House Financial Services Committee, played a key role in passing a 1995 law (over Mr. Clinton's veto) that, by blocking investor lawsuits, may have opened the door for a wave of corporate crime. More recently, when Merrill Lynch admitted having pushed stocks that its analysts privately considered worthless, Mr. Oxley was furious — not because the company had misled investors, but because it had agreed to pay a fine, possibly setting a precedent. But he also says he is outraged about WorldCom.
Might this sudden outbreak of moral clarity have something to do with polls showing mounting public dismay over crooked corporations?
Still, even a poll-induced epiphany is welcome. But it probably isn't genuine. As the Web site dailyenron.com put it, last week "the foxes assured Americans that they are hot on the trail of those missing chickens."
The president's supposed anger was particularly hard to take seriously. As Chuck Lewis of the nonpartisan Center for Public Integrity delicately put it, Mr. Bush "has more familiarity with troubled energy companies and accounting irregularities than probably any previous chief executive." Mr. Lewis was referring to the saga of
My last column, describing techniques of corporate fraud, omitted one method also favored by Enron: the fictitious asset sale. Returning to the ice-cream store, what you do is sell your old delivery van to XYZ Corporation for an outlandish price, and claim the capital gain as a profit. But the transaction is a sham: XYZ Corporation is actually you under another name. Before investors figure this out, however, you can sell a lot of stock at artificially high prices.
Now to the story of Harken Energy, as reported in The Wall Street Journal on March 4. In 1989 Mr. Bush was on the board of directors and audit committee of Harken. He acquired that position, along with a lot of company stock, when Harken paid $2 million for Spectrum 7, a tiny, money-losing energy company with large debts of which Mr. Bush was C.E.O. Explaining what it was buying, Harken's founder said, "His name was George Bush."
Unfortunately, Harken was also losing money hand over fist. But in 1989 the company managed to hide most of those losses with the profits it reported from selling a subsidiary, Aloha Petroleum, at a high price. Who bought Aloha? A group of Harken insiders, who got most of the money for the purchase by borrowing from Harken itself. Eventually the Securities and Exchange Commission ruled that this was a phony transaction, and forced the company to restate its 1989 earnings.
But long before that ruling — though only a few weeks before bad news that could not be concealed caused Harken's shares to tumble — Mr. Bush sold off two-thirds of his stake, for $848,000. Just for the record, that's about four times bigger than the sale that has Martha Stewart in hot water. Oddly, though the law requires prompt disclosure of insider sales, he neglected to inform the S.E.C. about this transaction until 34 weeks had passed. An internal S.E.C. memorandum concluded that he had broken the law, but no charges were filed. This, everyone insists, had nothing to do with the fact that his father was president.
Given this history — and an equally interesting history involving Dick Cheney's tenure as C.E.O. of
And if some cynic should suggest that Mr. Bush's new anger over corporate fraud is less than sincere, I know how his spokesmen will react. They'll be outraged.
Part 2: 6/7/02
"O">n Tuesday, George W. Bush is scheduled to give a speech intended to put him in front of the growing national outrage over corporate malfeasance. He will sternly lecture Wall Street executives about ethics and will doubtless portray himself as a believer in old-fashioned business probity.
Yet this pose is surreal, given the way top officials like Secretary of the Army Thomas White, Dick Cheney and Mr. Bush himself acquired their wealth. As Joshua Green says in The Washington Monthly, in a must-read article written just before the administration suddenly became such an exponent of corporate ethics: "The `new tone' that George W. Bush brought to Washington isn't one of integrity, but of permissiveness. . . . In this administration, enriching oneself while one's business goes bust isn't necessarily frowned upon."
Unfortunately, the administration has so far gotten the press to focus on the least important question about Mr. Bush's business dealings: his failure to obey the law by promptly reporting his insider stock sales. It's true that Mr. Bush's story about that failure has suddenly changed, from "the dog ate my homework" to "my lawyer ate my homework — four times." But the administration hopes that a narrow focus on the reporting lapses will divert attention from the larger point: Mr. Bush profited personally from aggressive accounting identical to the recent scams that have shocked the nation.
In 1986, one would have had to consider Mr. Bush a failed businessman. He had run through millions of dollars of other people's money, with nothing to show for it but a company losing money and heavily burdened with debt. But he was rescued from failure when
Despite these connections, Harken did badly. But for a time it concealed its failure — sustaining its stock price, as it turned out, just long enough for Mr. Bush to sell most of his stake at a large profit — with an accounting trick identical to one of the main ploys used by
That's exactly what happened at Harken. A group of insiders, using money borrowed from Harken itself, paid an exorbitant price for a Harken subsidiary, Aloha Petroleum. That created a $10 million phantom profit, which hid three-quarters of the company's losses in 1989. White House aides have played down the significance of this maneuver, saying $10 million isn't much, compared with recent scandals. Indeed, it's a small fraction of the apparent profits
Oh, and Harken's fake profits were several dozen times as large as the Whitewater land deal — though only about one-seventh the cost of the Whitewater investigation.
Mr. Bush was on the company's audit committee, as well as on a special restructuring committee; back in 1994, another member of both committees, E. Stuart Watson, assured reporters that he and Mr. Bush were constantly made aware of the company's finances. If Mr. Bush didn't know about the Aloha maneuver, he was a very negligent director.
In any case, Mr. Bush certainly found out what his company had been up to when the Securities and Exchange Commission ordered it to restate its earnings. So he can't really be shocked over recent corporate scams. His own company pulled exactly the same tricks, to his considerable benefit. Of course, what really made Mr. Bush a rich man was the investment of his proceeds from Harken in the Texas Rangers — a step that is another, equally strange story.
The point is the contrast between image and reality. Mr. Bush portrays himself as a regular guy, someone ordinary Americans can identify with. But his personal fortune was built on privilege and insider dealings — and after his Harken sale, on large-scale corporate welfare. Some people have it easy.
Submitted to Media Whores Online:
In a piece that read like it was geared towards viewers of VH1, his new employer, Salon writer Jake Tapper recently trashed Al Gore's appearance at Lot 61, an arts & entertainment oriented Manhattan bar. He quotes large-tongued Kiss singer Gene Simmons very admiringly on how great Bush is and how irrelevant Gore is. Tapper is obviously really proud to have gotten this quote: he refers to it again later in the article. He appears to be offering it as evidence that the young and the hip don't like Gore, but the only problem is Simmons is just another aging redneck at this point. The article is incredibly snide; it's obvious that soon-to-be-tanking Salon is starting the cycle of Gore-bashing all over again. Of course, Gore's cogent criticisms of the disastrous Bush regime got swallowed up in all the bile.