Egan's "Orthogonal Trilogy" explains how the Peerless and its crew of scientists, mathematicians and engineers was launched in the hope if find a way to save their homeworld from destruction. A major focus is on the way physics and biology would be different in a universe where the laws of physics were different.
As you probably know, according to the theory of relativity, the crew of a space ship that traveled quickly away from Earth and back would return to find that many years had passed here at home for each year they experienced on the ship. (This theoretical prediction, by the way, has been experimentally verified. So, as strange as it may seem, it really seems to be true.)
The very basis of this series of novels is that with the change of just a single sign (replacing the minus sign in one component of the metric tensor of spacetime with a plus sign) the situation reverses. In particular, in such a universe the space travelers would experience many years for each year passed on their home world. Consequently, when it was discovered that the home planet was in danger of being destroyed in a collision (with "orthogonal matter"), it made sense to send a ship into space to try to find a solution to the problem. In particular, generations of scientists could live and work on the ship seeking a way to save the planet and yet they could return with the answer before the disaster occurred.
Another author might have been content to write a story around that one difference without considering what other changes would follow from this one little sign change, but Egan is not your average science fiction author. He does a truly spectacular job of working out the ways in which that universe would be the same and the ways in which that universe would be different. For a knowledgeable reader, then, there are several pleasures in reading this book. In addition to following the storyline as one would with any novel, we can experience the joy of discovery when a character figures something out, we can have the fun of trying to recognize and recall the analogous discovery in human history, and finally the very intellectual pleasure of comparing the two.
Of course, there is math here, otherwise I would not be listing it on my Website, but it is no more prominent than the physics and biology that are around. So, you have to look for it. In the first novel, the main mathematical content is in the mathematics that underlies their version of special relativity (and, just a little bit about quantum physics, too). There are plenty of diagrams and formulas for the reader's convenience as well.
I wholeheartedly believe that taste in fiction is subjective, and this is certainly not for everyone, but to me this novel is just the start of a threepart work of art that is truly exquisite. If this description appeals to you at all, I urge you to give it a try. (And, be sure to check out its sequels, The Eternal Flame and The Arrows of Time.)
Contributed by
Roman Juarez, UNAM
"The Clockwork Rocket" by Greg Egan is the first in his Orthogonal trilogy. As usual the author is very committed with the writing and goes the extra mile (or miles in this case) in order to achieve credibility. The story develops in an completely different universe from ours, unlike what could be argued of other Eganian literature. The events during the first part of the book lead the main character "Yalda" to become a Physicist at a renowned University in a city far away from her family. The mathematical content of the book is vast, sometimes aided by diagrams (which most of them happen to be drawn over the characters' bodies).
In a nutshell Yalda turns out to be the equivalent of Einstein in her home world (universe). By studying the Hurtlers' phenomenon (some sort of comets which appeared when she was little) she establishes (by accident) the principles of Special Relativity based on her studies of light and the mathematics that describe it, calling it Rotational Physics. This revolutionizes the scientific knowledge of her time (as expected), but also sheds light on the enormous threat the Hurtlers represent to her planet (and everything else actually), prompting the scientific community and the society to engage in the biggest project ever to get a chance of survival. A space opera on board the Peerless (a mountain turned into a spaceship) looking for the answers needed to prevent the impending catastrophe is in order.
Yalda's discovery is the geometry of her universe, a closed Riemannian manifold, where, contrary to what happens in our pseudoRiemannian situation, the metric has signature (++++). Thus the fundamental laws of physics we are familiar with become dramatically modified. Egan has put a lot of effort in this book (more than any of his previous work) and the extra material in his website proves that. More than 80,000 words in topics such as Geometry, Hamiltonian Mechanics, Wave Equations, Abstract Algebra, Electrodynamics, General Relativity and more. But what really impressed me was the way he (alone?) carried out the calculations for the speculative Physics to be consistent with his premise. In the process he obtains many interesting results worth of looking at (I would even recommend writing a paper). After going trough the mathematical details of his extra material (at least the speculative part for this book) I have yet to find any mistakes or misinterpretations (writing erroneously KleinGordan instead of KleinGordon is understandable recalling that it can be confused with the Gordan in the ClebschGordan coefficients).
At a personal level I really enjoyed the book and I'm looking forward to read the sequel, but I'm afraid this may not be a memorable lecture for everyone. Not only because the reader will necessarily need some understanding of the underlying mathematics and physics to follow the major turning points, but also due to storytelling some notions have names which can be confusing (e.g. rotational physics involves spacetime diagrams NOT classical mechanics), even doing the effort to clearly imagine Yalda's race's physiology is important as I found out after neglecting it for a couple chapters then seeing I couldn't keep reading cause my simplistic model didn't work anymore. Looks like a symmetry exercise where, based on his own commitment, the author demands a lot of commitment from the reader too. It's possible many people won't appreciate that and just go to next book in queue.

Contributed by
Andy Breslin
“Ye cannae change the laws of physics!”
So said Star Trek’s beloved Mr Scott. Or maybe he never explicitly said that on the show, and only uttered that frustrated maxim in a popular song parody . Still, it’s undeniably and unalterably true. But what if you could?
That’s exactly what Greg Egan did. He just changed the laws of physics. Sneaky bastard. And the result is a mindbending head trip. A trip taking place at infinite velocity, no less. “But that’s impossible!” you say. Ha! Didn’t you hear? Mr. Egan changed the laws of physics.
This was simultaneously both a delightful thought exercise and a real slap across my brain’s face, because unlearning what you’ve already learned is a much bigger pain than learning in the first place. Remember your introduction to relativistic physics? It was tough to grasp. You had to get all Taoist and Zen, allowing your mind to free itself from its expectations, apprehending the universe unfettered by the illusions deeply ingrained in it through a lifetime of experience. And now you’re going to have start all over again. Assume the lotus position and clear your mind. First there is a mountain, then there is no maintain, then there is . . . .
Back when you first studied relativity, you started with Einstein’s amazing, utterly counterintuitive insight that light’s velocity is always measured exactly the same, regardless of the speed of the observer. Once you were able to wrap your brain around that, everything else flowed logically and inevitably from it. The Lorentz–FitzGerald contraction. Relativistic mass. And of course, the most fun, time dilation and the consequent twin paradox. As you approach the speed of light, time slows down. At a velocity sufficiently close to the speed of light, you could take a little trip that seemed to last an hour, only to return to Earth and find that your twin brother is an old man and all your Windows updates have taken effect and your system has rebooted. Also, your cat will be dead and the library fines for your long overdue copy of The Clockwork Rocket will rival the national debt.
Not in this orthogonal universe. There is no “speed of light.” Time dilation is essentially reversed (you’ll come back an old man, and your computer will still be installing the same damn updates). And nobody has a twin, though most people have a “co.” The mathematical details of the laws of physics in this new universe are spelled out as lucidly as possible in the context of a science fiction novel. That doesn’t mean it’s easy to grasp, but that shouldn’t dissuade you from trying. If, however, it doesn’t all immediately make perfect sense, you should keep reading anyway. Besides being a fascinating speculation on the physics of a different universe, this is also just a damn good story.
Our protagonist, Yalda, is as memorable a character as you could hope to find. And not just memorable, but also relevant. A brilliant scientist such as she, taking action against a global danger that most of the population doesn’t really understand, might find our nonorthogonal universe, with its own bizarre laws of physics, surprisingly familiar. And maybe she could offer us some suggestions on how to address the global threats facing our world, where human industryinduced climate change threatens all future civilization, yet is rejected by the sorts of people who for some unfathomable reason think that their utter inability to do basic math somehow gives them an advantage over actual climate scientists.
A fine story, through and through, and not too long. You could read it in a couple of days. But, if you are pressed for time, and have looming deadlines to meet, it would be nice if, by moving at an infinite velocity, you could have all the time you want to read, with no time passing from everyone else’s perspective. Alas, that won’t work here with our laws of physics, and you cannae change them.

