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'Flatland' jumps off the page

Flat World Productions
Mr. and Mrs. Square have a mealtime chat with their granddaughter Hex in Seth
Caplan's version of the two-dimensional mathematical fable "Flatland."

It's been more than 120 years since Edwin A. Abbott came out with one of mathematics' best-loved fables, "Flatland: A Romance of Many Dimensions," but the tale takes on a whole new dimension in animated retellings released direct to DVD. The cartoons turn out to be as much about today's social milieu as about math - just as the original story was back in Abbott's day.

Before this year, "Flatland" has been turned into an animated short at least a couple of times - at Harvard in 1965, and at the University of Rome in 1982. But the tale gets a 21st-century update this year in two versions - a 95-minute feature directed by Ladd Ehlinger Jr.; and a 35-minute film directed by Jeffrey Travis and produced by Seth Caplan.

You don't have to be a math geek to get the basic point behind "Flatland": Sure, the characters in the story are rather flat - but that's just because they're two-dimensional geometric figures. In fact, everything in Flatland is as two-dimensional as a street map, and the inhabitants can't possibly conceive of a world where there is an up and down as well as a north and south, east and west.

The more sides you have, the higher you rise in Flatland. This means pentagons outrank squares, hexagons outrank pentagons, and circles outrank them all. And the circle priesthood's main job is to squelch the rumors of some mysterious "third dimension" - rumors that pose a threat to public order.

The main character, A. Square, holds to the party line until he receives a visitation from a Sphere who shows him the wonders of the third dimension - going "upward and yet not northward." This leads A. Square to speculate that there's even more to the world than three dimensions - an idea that's as much of a taboo for the sphere as the concept of three dimensions was for Flatland's circles.

By the end of the story, A. Square is locked up in a Flatland prison, writing his memoirs with only the foggiest recollection of what "upward and yet not northward" meant.

Back in the 1880s, Abbott meant his thin book to be a commentary on Victorian society as well as higher-dimension mathematics. In a parallel to the plight of women in those days, the female set could rise only so far in Flatland, because they were stuck in the needle phase of development. Meanwhile, novel ideas such as spiritualism and a mysterious fourth dimension were coming into vogue in class-conscious England. Free-thinkers may well have felt as if they were hopeless squares fighting powerful circles.

I haven't had a chance to see the "Flatland" feature film - but the plot description improvises on the original text and, if anything, lays on a thicker coat of social commentary.

Flat Earth Productions
Spherius is a three-dimensional
visitor to a two-dimensional
world in "Flatland."

Seth Caplan's 35-minute "Flatland" mostly sticks to the original plot, although the ending has been changed so that it's not such a downer. And the cultural references have been updated as well. For example, A. Square works in an office "squaricle," and his precocious granddaughter Hex rides a cool two-dimensional scooter. (She's also an upwardly mobile hexagon, which goes against the original's "always a needle" rule for women.)

There's some star power behind Caplan's Hollywood project: Martin Sheen (from "The West Wing") voices A. Square, Kristen Bell (from "Veronica Mars") does Hex, and Michael York (who's been in everything from "The Three Musketeers" to "Austin Powers" and beyond) plays Spherius, the condescending sphere.

Caplan told me the DVD is selling like gangbusters on the Internet, and he says Princeton Press is putting out a movie tie-in version of Abbott's book next month.

"There's definitely a place in the marketplace for movies that can be enjoyed by the whole family and have an educational component," he said.

The story provides an entry point to a realm beyond our three spatial dimensions - a realm that may be closer to ultimate reality than the way we presently perceive the world. "That's the whole point of the movie, right? To take away this concept of the fourth dimension that we can't necessarily point to," Caplan said.

But there's a larger lesson as well: Don't always trust what the circles are telling you.

"Critical thought is so important, to always try to find new knowledge, to never just accept things as you're told they are," Caplan said. "What's often commonly accepted isn't always necessarily true, and I hope people have the courage to question what is known and search for what's next."

Caplan thinks that should apply to society at large, and particularly to young people getting into math and science.

"Math is so much more than problems on your test page," he said. "It's about your imagination."

The scientific challenges of the future will require a lot more than logarithmic tables and rote learning. Those future mathematicians, scientists and engineers will have to deal with issues ranging from global climate change to the mechanisms of life and society - not to mention the cosmic puzzle surrounding the existence of extra dimensions.

"The student who's going to solve that is probably a high school student right now, and is not going to be motivated by a standardized test," Caplan said.

Will "Flatland" be the spark for those flights of fancy - or will our conception of extra dimensions always be, as A. Square says at the end of Abbott's tale, "the baseless fabric of a dream"? Feel free to weigh in with your comments below. 

P.S.: I've gushed over "Flatland" numerous times before, but let's list it as part of the double selection for November and December in the Cosmic Log Used-Book Club. The CLUB Club notes books with cosmic themes that are generally available at your local library or used-book shop.

One of the neat things about "Flatland" is that it's widely and freely available over the Web. The same can't be said about the second selection, "The Fourth Dimension: A Guided Tour of the Higher Universes" - but it's worth seeking out Rudy Rucker's oldie-but-goodie in the library stacks or on secondhand-book Web sites. 

"The Fourth Dimension" delves into the philosophy as well as the mathematics behind extra dimensions - for example, does the soul actually reside in extra dimensions? That fueled a lot of speculation in Abbott's day, and today as well.

The fourth dimension sparked other works by Rucker, including "Spaceland," a satirical novel that transplants the idea behind "Flatland" into three-dimensional  dot-com culture.