Once upon a time, one of our most noted authors of ultra-hard SF wrote a novel about a bunch of aliens living in the interior of an asteroid in close orbit around a black hole. The author, Greg Egan, was so incensed by one of the reviews of this book – by Adam Roberts at *Strange Horizons* – that he wrote a detailed rebuttal on his website (*Anatomy of a Hatchet Job*).

The novel in question, Incandescence, (2008) has long passages describing how the inhabitants of *The Splinter*, the orbiting asteroid, come to an understanding of their environment through the intuitive observations they can make within the asteroid interior. The intellectual journey is that of *General Relativity* and it was a matter of fascination to Mr Egan to examine how GR might become intuitive in the intensely-curved space-time close to an event horizon.

Conventional literary criticism flounders when faced with such an extremely science-centric book. Yes, the characterization is poor; yes, there is a fair amount of exposition; yes again, the plotting is somewhat opaque. Adam Roberts (PhD in English) applied his literary indignation with a vengeance and while he was perhaps the most trenchant critic, he was by no means the only one.

Yet there were a few people, and not just the author, who observed that in science-fiction sometimes we have to modify the usual framework of criticism and make at least some concessions to the intent of the work. This more enlightened attitude is going to be tested to destruction, however, with Greg Egan’s new ‘Orthogonal’ trilogy. Even to understand what it’s about requires a physics major level of conceptual sophistication (Mr Egan tries valiantly here).

We’re all familiar with Pythagoras’ theorem: the square on the hypotenuse etc. Many science-fiction readers are aware that since Einstein we don’t consider time and space to be separate things: instead, they’re united into one four-dimensional space-time structure called Minkowski spacetime. Just as we can rotate something in our ordinary concept of space so that it points in a different direction, we can also rotate things in time. When we do that, it’s called giving it a velocity. Think of a *stationary* blob at the origin: its world line, straight up on the usual diagrams, corresponds to the time axis. Now rotate that line about the origin away from the vertical – you’ve got a blob moving away from the origin at some velocity. But rotation in time is not like rotations in space, it’s *hyperbolic* in our universe.

Consequently, the space-time ‘distance’ between two points (usually called events) in the space-time of our universe is, perhaps surprisingly, not given by Pythagoras’ theorem. You don’t add the squared differences between the x, y, z and t coordinates and then take the square root. Instead, you do the adding for the squared x, y and z spatial distances, but then *subtract* the squared time difference. Out of this sign change comes all the counter-intuitive power of special relativity: the constancy and maximal nature of the speed of light; length contraction and time dilation; the unification of mass, energy and momentum.

But suppose our universe was constructed the Pythagorean way, as everyone before Einstein actually thought. Would anyone notice the difference? This is what Greg Egan proposes to explore in his three books. Naturally he’s going to introduce characters, issues, problems and resolutions – all the machinery of fiction. But, make no mistake; it’s there just as scaffolding. Egan’s ‘*Orthogonal*’ trilogy exists to explore counterfactual physics, as he recounts in his science overview:

“For the past year or so I’ve been spending most of my waking hours in a place where light, matter, energy and time obey different laws of physics than those that rule our own universe. Studying the way things move and interact under these alternative laws reveals some familiar behaviour, some strange and eerily beautiful phenomena, and some terrifying risks.”

It’s going to be an interesting exercise reviewing this latest episode of Greg Egan’s work according to the standard he himself has set, namely in a spirit of sympathy for the science being presented. This would seem to involve mastering something like 70 pages of alternative physics posted on Egan’s website, the fruits of his year’s research. But they say travel broadens the mind: sometimes you can only really understand something familiar by seeing how it could have been done differently. Prepare to read with paper and pen beside you.

Volume 1 of the ‘*Orthogonal*’ trilogy is *The Clockwork Rocket*. Volume 2, *The Eternal Flame*, will be published in 2012.