Ve tried smoothing and flattening the six points. That was easy -- but it made the eight triangles as bowed and non-Euclidean as they'd been on the original sphere. It seemed "obvious" that the points and the triangles could never be made flat simultaneously...but Yatima still couldn't pin down the reason why the two goals were irreconcilable. Ve measured the angles where four triangles met, around what had once been a point of the diamond: 90, 90, 90, 90. That much made perfect sense: to lie flat and meet nicely without any gaps, they had to add up to 360 degrees. Ve reverted to the unblunted diamond, and measured the same angles again: 60, 60, 60, 60. A total of 240 was too small to lie flat; anything less than a full circle forced the surface to roll up like the point of a cone...
That was it! That was the heart of the contradiction! Every vertex needed angles totaling 360 degrees around it, in order to lie flat...while every flat Euclidean triangle supplied just 180 degrees. Half as much. so if there'd been exactly twice as many triangles as vertices everything would have added up perfectly -- but with six vertices and only eight triangles, there wasn't enough flatness to go around.

If ve ever wanted to be a miner in vis own right -- making and testing vis own conjectures at the coal face, like Gauss and Euler, Riemann and Levi-Civita, deRham and Cartan, Radiya and Blanca -- then Yatima knew there were no shortcuts, no alternatives to exploring the Mines firsthand. Ve couldn't hope to strike out in a fresh direction, a route no one had ever chosen before, wihtout a new take on the old results. Only once ve'd constructed vis own map of the Mines -- idiosyncratically crumpled and stained, adorned and annotated like no one else's -- could ve begin to guess where the next rich vein of undiscovered truths lay buried.

"But why a 2-sphere?" Blanca duplicated the diagram, but used a circle as the standard fiber instead of a sphere. Again, no two paths through the wormhole were the same color at the cross-over point; the main difference was that they took on different colors straight from the whiteness of the surrounding space, because there were no "north and south poles" now from which they could spread out. "In two-dimensional space, you only need one extra dimension to avoid the singularity."
"That's true," the avatar conceded. "But I used a two-dimensional standard fiber because this wormhole possesses two degrees of freedom. One keeps the geodesics from colliding at the center. The other keeps the two mouths of the wormhole itself apart. If I'd used a circle as the standard fiber, then the distance between the mouths would have been fixed at precisely zero -- which would have been an absurd constraint when the whole point of the model was to mimic quantum uncertainty."

Incorporated into this novel is the short story "Wang's Carpets", which also appeared separately in some SF collections. This story is "a First Contact story about a form of life made out of (Hao) Wang tiles."

It was astonishing. Paolo hoped Elena was tapping the library, wherever she was. A colony of algae would have been more "advanced" — but this incredible primordial creature revealed infinitely more about the possibilities for the genesis of life. Carbohydrate, here, played every biochemical role: information carrier, enzyme, energy source, structural material. Nothing like it could have survived on Earth, once there were organisms capable of feeding on it?and if there were ever intelligent Orpheans, they'd be unlikely to find any trace of this bizarre ancestor.

Karpal wore a secretive smile.

Paolo said, "What?"

"Wang tiles. The carpets are made out of Wang tiles."

Hermann beat him to the library, again.

"Wang as in twentieth-century flesh mathematician, Hao Wang. Tiles as in any set of shapes which can cover the plane. Wang tiles are squares with various shaped edges, which have to fit complementary shapes on adjacent squares. You can cover the plane with a set of Wang tiles, as long as you choose the right one every step of the way. Or in the case of the carpets, grow the right one."

Karpal said, "We should call them Wang's Carpets, in honor of Hao Wang. After twenty-three hundred years, his mathematics has come to life."

Paolo liked the idea, but he was doubtful. "We may have trouble getting a two-thirds majority on that. It's a bit obscure ..."

Hermann laughed. "Who needs a two-thirds majority? If we want to call them Wang's Carpets, we can call them Wang's Carpets. There are ninety-seven lan­guages in current use in C-Z?, half of them invented since the polis was founded. I don't think we'll be exiled for coining one private name."

Paolo concurred, slightly embarrassed. The truth was, he'd completely forgotten that Hermann and Karpal weren't actually speaking Modern Roman.

The three of them instructed their exoselves to consider the name adopted: hence­forth, they'd hear "carpet" as "Wang's Carpet"? but if they used the term with anyone else, the reverse translation would apply.

This is how all Science Fiction should be, totally engaging, with well developed worlds. I consider this to be one of the best Sci Fi novels I've ever read. On every level it excels. I've read some of Egan's works previously and can't understand how I missed this one, or why no one ever recommended it.

Interesting ideas in the book, but they are not enough. And like most hard sci-fi, it becomes quickly dated. As a work of literature, it is one of the worst books I have ever read. Character motivation and development is laughable (when it isn't annoying) and clumsy. Dramatic tension is almost non-existent. I don't know why I finished this book. I almost abandoned it several times as I was reading. I wish I had - life is too short to waste on works like this one.

SEMINAL WORK. brilliant and inspiring.

I have highly ambiguous feelings about this novel. On the one hand it is clearly an intellectual work with numerous scientific and mathematical concepts and I believe that there are not nearly enough works of this type, but I'm concerned that anyone who hasn't majored in mathematics or modern physics would find it unintelligible. Furthermore, most popular scientific books are written with the intention of simplifying advanced scientific concepts for laypeople, but Mr. Egan seems to unnecessarily obfuscate the concepts embedded in this novel by needlessly resorting to scientific jargon.

This having been said, "Diaspora" posses many philosophical question that are worthy of consideration, not the least of which is the "meaning" of existence. Moreover, this work induces one to to consider the limits of scientific advancement and it's moral implications.

a good story that provokes serious thinking about truth in math, and what are the invariants of consciousness that make unique sentient individuals.

I enjoyed your section on Wang/s Carpets/Dispora by Greg Egan. He does a brilliant job. I wrote a 6000 word essay on Wang's Carpets years ago and felt like I barely scratched the surface. His ideas are brilliant. The essay is called "Strange Loops of Wonder." It first appeared in Tangent magazine and was later reprinted in Projections: Science Fiction in Literature & Film edited by Lou Anders.