A few weeks ago, I pointed
you at
David
Langford's online story
New Hope
for the Dead, whose spammer
protagonist
had been uploaded into his
virtual afterlife as an Electronic-Golem
Artificial Neurosystem or EGAN. I now want to point you
at, by a *real* Egan,
the online story Crystal
Nights. Here's
a sample:

She said, "You know what they say the modern version of Pascal's Wager is? Sucking up to as many Transhumanists as possible, just in case one of them turns into God. Perhaps your motto should be 'Treat every chatterbot kindly, it might turn out to be the deity's uncle'."

David Langford knows his science fiction. So though I cannot be certain, I suspect his EGAN is an allusion to the SF writer Greg Egan. Many of Egan's stories are about post-human characters implemented as sentient software inside vast computers. Their simulated-reality universes — unconstrained by irritating restrictions such as the need to traverse the space separating the two points one is travelling between — make possible some exotic landscapes indeed. Listen to Yann, a character in Egan's novel Schild's Ladder, telling his companion about the neighbourhood he was brought up in:

"In the scapes you grew up in," he asked, "was there a vertical?"

"In what sense?"

"I know you said once that you didn't feel gravity ... but was everything laid out and connected like it is on land? Or was it all isotropically three-dimensional — like a zero-gee space habitat, where everything can connect in any dimension?"

Yann replied affably, "My earliest memories are of CP

^{4}— that's a Kähler manifold that looks locally like a vector space with four complex directions, though the global topology's quite different. But I didn't really grow up there; I was moved around a lot when I was young, to keep my perceptions flexible. I only used to spend time in anything remotely like this" — he motioned at the surrounding more-or-less-Euclidean space — for certain special kinds of physics problems. And even most Newtonian mechanics is easier to grasp in a symplectic manifold; having a separate visible coordinate for the position and momentum of every degree of freedom makes things much clearer than when you cram everything together in a single three-dimensional space."

I enjoy Egan's stories for their optimism. True, some characters suffer varied and ingenious forms of nastiness. Mugged, in Luminous, on the streets of a People's Republic of China morphing in a thousand tiny steps from brutal totalitarian communism to brutal totalitarian capitalism; flayed, in Silver Fire, from inside by a virus that propagates by thrusting off one's skin; seared, in Diaspora, by gamma rays from colliding neutron stars; or slung, in Oracle, into a slimy pond in a Cambridge college quad.

But such mishaps aside, consider daily life in Egan's virtual landscapes. With the constraints of our physical universe removed, what is there left to do? As mathematical physicist John Baez remarks in this Egan-related thread:

Indeed, one nice thing about certain SF stories — like Riding the Crocodile, or some other things by Egan, or parts of Kim Stanley Robinson's Mars trilogy, or some of Iain M. Banks' Culture novels — is that they tackle the problems faced by people whose basic needs are all met, and who thus need to tackle the question what.s really worth doing, when you have the freedom to try anything?

That thread is in the The n-Category Café blog. And a mathematics blog is not an inappropriate place for it. Egan's novel Diaspora features a character named Yatima, whose early attempts to study mathematics are diverted by a journey through 267,904,176,383,504 universes, half of which are five-dimensional. (Five dimensions are comprehensible, it turns out, provided that you rewire your mind to insert the necessary visual primitives.) But Yatima then returns to the Truth Mines, a virtual landscape for learning mathematics. In the timeless world of the Mines' virtual tunnels, their walls studded with mathematical visualisations such as the sparks of light inside nested membranes which depict the open sets of a topological space, Yatima begins to review the mathematics learnt before the journey:

Everything else from vis life in the home universe had been diluted into insignificance by the scale of their journey, but this timeless world still made perfect sense. In the end, there was only mathematics.