For several years I taught a course in science fiction which included Greg Egan's Diaspora (1997), and was constantly fascinated by the response. Each year, the vast majority of a group of bright Literature students who were perfectly at home with the idea that reading Elizabethan drama or eighteenth-century poetry involves looking at very different ideas of literary conventions, and at least bought into the idea that some types of SF called for looking very carefully at what was on the page, were completely baffled. Inevitably, there would be one or two in each group who felt that a novel in which we—physical, gendered beings—are asked to imagine the worlds of beings who are neither physical nor gendered (unless they wanted to be) offered challenges which were particularly exhilarating and rewarding. But few of them "got" Egan—an author who very much defines a particular type of SF, and one of my own favorites.

The Arrows of Time comes with a warning which my students might have appreciated. The protagonists of the novel belong to a species whose biology, history, politics, and technology (not to mention the physics of the universe in which they exist) are so different from ours that readers are advised to read the preceding novels first. The entire sequence (Orthogonal) is serviced with apparatus on Egan's website which illuminates the nature of the physics underlying its universe, but assumes in the reader at least high-school algebra, calculus, and trigonometry. Or rather, it assumes in the reader the understanding that advanced theory about the physical universe is an exciting and thrilling domain, and that curiosity about the universe can be as central to our enjoyment as any melodramatic "plot." One of its delights as with so much of Egan (but one I certainly failed to convey well enough to my students), is the way we have to think deeply about what we are reading, and why we are finding it "difficult."

By the second chapter of The Arrows of Time, a debate is illustrated by a diagram illustrating the fundamental laws of the cosmos (and the central plot of the sequence). Unlike our universe, light has no universal speed: indeed, different wavelengths of light travel at different speeds. In this universe, if a spaceship can achieve sufficiently high speed, its journey will last many years for those on board but only a few for those left behind at home. In The Clockwork Rocket (2011) and The Eternal Flame (2012) we have seen the journey of the Peerless (not actually a spaceship, but a mountain) on its mission to save its homeworld. The diagram on p. 7 shows how this is meant to work. After six generations (mission time) the mission will turn and return, eventually decelerating (exactly how, is the task of the next six generations to work out!) and returning to the homeworld four years in its future with the secret of how to overcome the threat of the "hurtlers" which are the result of the approaching "orthogonal" system (think "anti-matter," only it's not). Collision with a "hurtler" has already destroyed one planet in the system.

The aforementioned diagram is simply one of a number scattered throughout the sequence which are reminiscent of the mathematics with which early science fiction insisted on "helping" its readers and which many readers now find alienating. (There's a possibly apocryphal maxim that any equation inserted in a book halves its sales, and that almost certainly goes for graphs.) These diagrams appear whenever characters are debating the physics of their universe—which is often, as the subplot of scientists coming to understand how their universe works is as important as the "main" adventure/saving the world plot; indeed, deciding which is the "main" and which is the "sub" plot is one of our challenges. But why, if diagrams are so alienating, should they appear so frequently? One answer is that they help the reader understand the nature of the "Riemannian" universe in which the events of the novel are set, which necessarily involves the kind of mathematics which most readers (and that includes this one) need a great deal of hand-holding to even approach understanding. A second answer, though, involves the reason why Egan is a rewarding writer rather than a simply "difficult" one. It is, simply, that his characters frequently communicate via diagrams, raised upon their bodies. These graphs and diagrams, presented as a matter of course during conversations, are not just teaching aids. They serve to remind us that these beings, while like us in some ways, are not like us in fundamental biology, physics, and chemistry. (They can absorb and protrude limbs, have eyes that give them forward and rear gaze, and they reproduce by fission, bringing an end to the life of the "mother" and leaving the "father" to rear the children: usually four, but during times of starvation normally two.)

All this, especially the very different reproductive system, means that, while we are "reading" personalities and characters we can empathize with, we are in effect translating. What we are imagining is analogy rather than representation of "people like us." This is true of much science fiction, of course, but Egan is particularly keen that we should tackle this idea of difference.

The debate with which The Arrows of Time begins is because, at this stage of the voyage of the Peerless, its crew have survived the crisis of overpopulation which was the subject of The Eternal Flame and have now divided into factions, one of which, led by a dissident named Pio, believes in forgetting all about the "ancestors" and the "home world" and looking for a home to settle. While these "migrationists" lose the vote, some among them turn to sabotage. The turning of the Peerless's direction of travel, moreover, means (for reasons due to the cosmological structure of this universe: it is explained on Egan's website) that it is now possible to build a device which will detect light from the future: raising the possibility of messages being sent back in time by the crew's future selves. The political implications of this are worrying, to say the least. To the mix of alternative physical matrices, Egan raises the question of free will: something which troubles his characters as much as us.

Ramiro, who had earlier survived a migrationist sabotage attempt, offers to take part in an expedition to see if a nearby planet, Esilio, is capable of supporting life. More strangeness takes place, for on Esilio the arrow of time is reversed. This leads not to gimmicky "counter-clock world" time reversals, but to some fascinating speculations about what it might be like to live in a world "where every step he was yet to take would be laid out before his eyes" (p. 198), but also where two "arrows" of time seem to coexist:

Ramiro . . . watched as Azelio knelt down, a trowel in one hand and the wheat plant in the other. He lowered the plant until its roots were in the hole, then he started adding soil from the surrounding mound. Some of the soil was scooped in with pressure from behind, in the ordinary manner. Some appeared to pursue the trowel, the way the dust sometimes pursued Ramiro's feet. What decided between the two? Azelio's own actions had to be consistent with the motion of the soil, but which determined which? Maybe there was no answer to that, short of the impossible act of solving in the finest detail the equations that Agata was yet to discover, revealing exactly which sequences of events were consistent with the laws of physics all the way round the cosmos. (p. 202)

A message is discovered carved in the rock in Esilio. Does it signify final victory for one or other party? Or is it a forgery, designed to manipulate action into creating a victory?

Such apparent paradoxes reflect the tensions in a novel which is part political thriller (when Ramiro and his companions return to the Peerless, there is yet another act to play in the drama which began with the original migrationist sabotage), part love-story (the tenderness of the consummation of the attraction between Ramiro and his lover Tarquinia—remember that in this species, the sexual act can result in the death of the female—is an unexpected delight), and part intellectual quest.

In part, it is an intellectual quest which involves us, the readers. Towards the end of the novel, there is a paragraph about air, in which it is suddenly clear that "air" in this cosmos is not exactly what it is in ours: the fundamental laws of matter are radically different, and this extends from the nature of time and space to chemistry and biology. The final chapter, describing the homecoming, emphasizes something similar about stars. But in a large part—from the story of Yalda in The Clockwork Rocket on—this is a novel about scientists discovering the shape of the cosmos in which they live. "The beauty is that [the cosmos] is comprehensible," declares Agata at one point, "even if its shape is unknown" (p. 181). And Agata's revelation towards the end of the book (underlined with yet more diagrams) that the cosmos has a particular shape "and that's why we exist at all: with a history, with memories, with an arrow of time" (p. 340) is one which Ramiro greets with joy.

This is the joy involved with really good hard SF: the conceptual breakthrough and the collision with the sublime. It is as valid an apotheosis as anything which involves the physical or the spiritual, made rarer because it celebrates curiosity, knowledge, and understanding.

Egan's achievement is that I follow his mathematics hardly at all; and yet he brings me to the end of the novel to share Ramiro's joy.

Andy Sawyer is librarian of the Science Fiction Foundation Collection at the University of Liverpool Library, and a widely published critic. For ten years he was Course Director of the MA in Science Fiction Studies offered by the University's School of English. He is Reviews Editor of Foundation: The International Review of Science Fiction. He recently co-edited (with David Ketterer) Plan for Chaos, a previously unpublished novel by John Wyndham, and (with Peter Wright) Teaching Science Fiction in the Palgrave "Teaching the New English" series. He was the 2008 recipient of the Clareson Award for services to science fiction.