Our heroes are trying to escape from `Industrial Algebra', an evil corporation that wants to use their mathematical discoveries (or perhaps supress them). Our heroes have discovered that arithmetic is inconsistent... but only when using numbers so large that no mathematician has encoutered the inconsistency (there is an undercurrent of constructivism/intuitionism running through the story). They use Luminous, a super fast computer made out of light, to verify the result, and discover an entirely different world co-existing with ours... using different rules of arithmetic."

This is the best math fiction I've read. The math is speculative, and most likely couldn't be fleshed out in reality, but it makes for a great story - lots of 'wow' factor."

"Really liked not only the mathematical background, but also writing-style of Egan. The incipit is really great. If only more sf writers write like him."

[Spectacular site, btw. I'm very grateful for all the work you've put into it.]

In your review you mentioned not understanding what space the fractal border was in, because the integers are too discrete. I'm fairly sure that it's a curve in the logical space of arithmetic propositions, not in the numbers themselves: an enormous graph with each node a true assertion and each link an inference, or in the 3d form with distance as the number of inferential steps.

For instance, the computer plotting it makes "billions of inferential loops" (valid circular deductions), and "portrayed the network of statements as an intricate lattice in three dimensions (a crude representational convention)". "At the border, every theorem you test is getting contradictory advice. From one neighbor, x-1 = y-1 . . . but from another, x+1 = y+2. And the topology of the border is so complex that a near-side theorem can have more far-side neighbors than near-side ones-and vice versa."

Anyways, it's a great story. I don't know what to say for a review, except that I've spent much more time thinking about it afterwards than I spent actually reading it. I'm only a student, but the mathematical imagery of this gives me all kinds of actual math ideas to play with (what's the distribution of the inference-count of propositions in first order logic?) And I had exactly the opposite philosophical response to you. It sounds like you took the story to be arguing for Platonism because constructivism is so absurd - I'm a firm Platonist, but the details of how constructivism like this would work have too much fun math to resist!

Thank you again for your efforts with the site, and best of luck, Brady Pelkey