tetracube in flatland

Tetracube in Flatland

I call our world Flatland, not because we call it so, but to make its nature clearer to you, my happy readers, who are privileged to live in Space.
—↑Edwin A. Abbott (1884:Section 1.)

Victorian society seems to be a preferred metaphor and target for scientifically and technologically inclined writers who strive to express social and cultural critique. Meanwhile I have finished “The Diamond Age, or: The Young Lady’s Illustrated Primer” (Stephenson 1996 [1995])—that second generation cyberpunk-tale wherein the Neo-Victorians feature so prominently. Both emotionally and intellectually I really enjoyed following artifex John Percival Hackworth through the post-nation-state-collapse, retro-tribalized, nano-tech infected near-future universe created by Neal Stephenson. But now I again am in savant Edward “Leviathan” Mallory’s company, enjoying—and co-suffering—his adventurous path through a Victorian alternate reality dominated by what might have been the societal consequences of Charles Babbage’s difference engine. That means I resumed my reading of Gibson & Sterling’s collaborative steampunk-novel of the same name (Gibson & Sterling 1991). In the respective context of the two novels ‘savant’ denominates the highest order of scholars, ‘artifex’ the highest order of engineers. A person thus attributed is a member of the aristocracies of said noble arts & crafts. The individual going by the adequate pseudonym—I dare not say nickname’—Seifert Surface is both a savant and an artifex. A graduate student of three dimensional topology and geometry at Stanford who creates experiencable mathematical conundrums in the virtual world of Second Life. Inspired by Robert A. Heinlein‘s short story “And He Built a Crooked House” (Heinlein 1940) he has created a house being a tesseract, which can be visited, toured, and experienced by the players within Second Life. “What’s a tesseract?” “Didn’t you go to school? A tesseract is a hypercube, a square figure with four dimensions to it, like a cube has three, and a square has two. Here, I’ll show you.” (Heinlein 1940) No, I won’t show you—please see the Wikipedia-entry Tesseract and/or the article Dimensionality at the University of Winnipeg. Via the latter article I learned about Edwin A. Abbott‘s (1838-1926) satirical novel “Flatland: A romance of Many Dimensions” (Abbott 1884), another inspiration to cyberpunk writers, especially to Rudy Rucker—by the way, in many of Rucker’s books hypercubes and all kinds of multi-dimensional space and structures star prominently … tesseracts in art and literature. Anyway, Abbott’s novel can be seen as a classical example of mathematical fiction, the author trying to help us understand the idea of dimensions through the fictional example of visiting a world with only two spatial dimensions. But there is way more to it, as “Flatland” is a story that can be interpreted in several ways:

(1) It is a satire on the staid and heartless Victorian society, a place filled with bigotry and suffocating prejudice. “Irregulars” (cripples) are put to death, women have no rights at all, and when the protagonist in the story Mr. A. Square tries to teach his fellows about the third dimension, he is imprisoned.

(2) It is a scientific work. By thinking about A. Square’s difficulties in understanding the third dimension, we become better able to deal with our own problems with the fourth

(3) At the deepest level, we can perhaps view Flatland as Abbott’s roundabout way to talk about some intense spiritual experiences.

See also Thomas F. Banchoff‘s From Flatland to Hypergraphics. And now for the feedback-twist: Mr. Surface describes what was still to do once he had figured out how to build the tetracube-house within Second Life’s gamespace: “From there, it was mostly a matter of creating the human-sized version, building a 19th century era interior with textures and furniture […] [emphasis mine]

initially via entry at boingboing