Egan: Orthogonal Series

Orthogonal, book #1

Generally I like my SF hard, even diamond hard. I don’t disdain fantasy; some of my favorite stories are fantastic. (As I’ve said often, Terry Pratchett’s Discworld series is my #1, my proverbial desert island companion.) But I definitely lean towards harder SF.

Growing up it was, of course, the Holy Trinity, Asimov, Clarke, Heinlein, but there was also Clement, Niven, and many others who stirred a large measure of science into their fiction. More recently the list of hard SF authors includes Forward, Steele, Stephenson, and a particular favorite of mine, Greg Egan.

I can safely say his Orthogonal series is as hard as science fiction gets.

I can equally safely say it may be too hard for many readers, even fans of SF. It might even be a bit hard for fans of Egan’s work — I’m an avid fan, but I found it a bit challenging. For one thing, it’s “hard SF” in the usual sense, very science-y, but the science itself isn’t easy.

In fact, to help readers make sense of the book, Egan offers a large amount of support material on his website. Getting everything from the book that Egan put into it requires some level of familiarity with that material.

I do have vaguely mixed feelings about niche stories, and Egan’s work tends to be niche in general, and extremely so in some cases. That niche being theoretical physics in all its foundational and mathematical glory. (Not surprising; Egan is a skilled mathematician.) The Yin-Yang tension here is that art should be as accessible to all as possible, but extreme niche art has strong appeal to those in the niche. Ultimately I think if an artist accepts the consequences of niche work (poor sales), there is good value for both creating and enjoying niche art.

Hell, this blog is pretty niche (my other blog even more so). Niche is fine, but it has caveats. And now I’m going to stop saying niche, because I’m starting to feel like a Knight of Niche (bring me a small exotic cactus).


The Orthogonal trilogy takes place in a radically different physical reality than ours, and its characters are non-human in the extreme. The three books take their civilization from the equivalent of a pre-Newton view of reality to a modern science on par with, or in some ways slightly better than, ours.

Egan details their advances in great,… um, detail. So much detail.

But it’s important because the physics of their world gives them a way to gain the time needed to figure out how to save their civilization from an imminent existential threat. Recently they’ve begun to observe what they name “Hurtlers” in their skies. They come to identify these as high-velocity objects from outside their system (outside their galaxy, as it turns out).

The Hurtlers have been few and small, but seem to be increasing in number and size. One strikes Gemma, one of the other planets in their system, and sets it on fire — it becomes a new sun. They realize that a large enough Hurtler could do the same to their world. It would be a decisive end to their species.


Orthogonal, book #2

Egan has designed an interesting species. They’re something like people-sized amoeba with male and female kinds. They have a basically bipedal shape, but can reform their bodies as needed. It’s a native ability, not due to any special self knowledge.

Their reproductive cycle is striking. Women are larger and stronger than men, and families begin with mated pairs. When they decide to have children, a reproductive act in which the man issues a binding promise to the woman causes her to first reabsorb her limbs, features, and brain; and to then fission into four children, two pairs of mated female-male “cos” — both of whom eventually reproduce.

The wife is lost in the process; the husband raises the kids. Men have all the child-raising feelings and innate abilities, whereas women, who are never closer than aunts, tend to be the leaders, teachers, and world-builders. That women are lost during child-bearing is seen as unfortunate but just the way life is. Much of the social tension comes from those who rail against the hand nature dealt — women who want to go on working; men who don’t want to lose their wives.

There’s an interesting naming convention, reminiscent of Latin names. For instance, the first character we meet is Yalda, a female “solo” — someone born without a co. That’s not common, but it happens. It’s perhaps analogous to, but the opposite of, identical twins for us. Normally Yalda would have a co named Yaldo. She does have a brother-sister co-pair, Lucia and Lucio.

In reproducing by fission, it would seem there is no chance for genetic mixing. But it turns out traits (and diseases) can be passed — with light. I’ll come back to that.

If Egan was more into social issues, this alone would be a great canvas for stories about gender, and Egan does explore it, but these are just the characters that populate his larger story about a universe with a major physics twist. For one thing, the speed of light depends on its frequency. More importantly, Special Relativity works backwards!


In our reality, the faster something moves, the slower its clock appears to run to observers. Those last two words are important; our local clocks always run at one second per second, but observers in motion relative to us may see our clock tick differently (slower).

The canonical example is the Twin Paradox in which one identical twin, say Roberta, takes a fast spaceship to a distant star and then returns to Roberto, her twin who stayed back on Earth. Their ages originally matched, but now Roberta is younger than Roberto. (See: the posts in the Time & Twins section of the Special Relativity series for details.)

In the Orthogonal reality, a fast-moving clock appears to tick faster, not slower. What’s more, speed can be infinite; it isn’t limited to light speed (which varies by frequency, anyway). It’s possible to go fast enough that your motion vector is orthogonal to your previous vector through spacetime. This effectively stops time “back home” — allowing a journey of any length without time passing for those left behind.

Spacetime diagram of the loop made by the Peerless. During the horizontal segments, no time passes on Homeworld. Time only passes there during the acceleration and deceleration curves.

At the turnaround point, deceleration and acceleration back along the flight path makes you not orthogonal with Homeworld, and so time does pass there. Once re-acceleration is complete time freezes back home until you return, decelerate, and re-enter the original vector (hopefully bearing gifts).

So the opposite of the Twin Paradox happens: the travelers age as much as needed (some 12 generations), but only four years pass back home. The trip gives the travelers time to figure out how to deal with the Hurtlers and return in time to save the species.


Orthogonal, book #3

They need to figure out more than the Hurtlers, though.

The generation ship they launch, the Peerless, uses a large fraction of its fuel accelerating to orthogonality with Homeworld. Most of the remaining fuel is allocated to running the ship for the unknown generations — there is none for slowing down, let alone returning.

The story wouldn’t be much fun if they failed, so it’s no spoiler to admit they don’t. Here it was never more true that “the journey is the reward.” (A big, very detailed, reward if you find strange physics rewarding.)

They do solve the fuel problem by finding a way to implement something mythical from their sagas: the Eternal Flame — a source of energy that doesn’t burn up.

Along the way they discover they need to address their population problem. A wife and her co become four children and a father. Two become five. The father dies of old age (“goes the way of men”) but each child-pair repeats the growth cycle. They explore a number of interesting paths; the ultimate solution is a game-changer.

The first book is called The Clockwork Rocket because this civilization doesn’t have electricity. They don’t even have metal. Their constructions are made from different kinds of rock. For example, clearstone is analogous to glass or clear plastics, and hardstone is analogous to metals. Their rocket, as did early airplanes, works entirely with mechanical linkages. (As their technology improves, they’ll discover photonics.)

They power their rocket — which is a mountain, by the way; their Everest, Mt. Peerless — with sunstone, a volatile form of rock that, when powdered and combined with “liberator” (which they get from plants), provides their power source. It can light lamps, heat, do work, or fuel rockets. If not carefully managed, it explodes.

So their mission is to figure out how to survive in the mountain (which is filled with tunnels and chambers huge and small) long enough to figure out the Hurtlers problem, figure out the fuel problem, and maybe figure out how to deal with going against time’s arrow on the way back.

Things get especially interesting when it turns out the Hurtlers, because of their unusual origin, act like antimatter. They’re even more dangerous to Homeworld than imagined. It isn’t just their high velocity that’s a killer.


To enable this reality, one thing Egan does is make a key change to the spacetime metric — the view-independent way we define length (space) and time. For us that metric is:


Note the minus sign for the time dimension. It’s this Minkowski space +++- signature that’s behind the effects of Special Relativity.

Egan’s Orthogonal reality has no minus:


Making spacetime Euclidean, not Minkowskian, turns out to have a number of unusual effects. The books are an exploration of the consequences of the ++++ spacetime metric signature.

A key consequence is that it’s possible to accelerate to infinite velocity in a finite time. In our reality, constant acceleration approaches light speed asymptotically. In the Orthogonal universe, there’s no asymptote, acceleration rotates your spacetime vector linearly, and that vector can tip all the way over to horizontal — to being orthogonal in time with your original vector.

Obviously this requires knowing about how light behaves, spacetime diagrams, Lorentz transforms, and how Minkowski space differs from Euclidean space. It’s hard for me to judge how readable, let alone enjoyable, the book is without at least some foundation physics. It’s definitely for us geeks.

§ §

As such, I can only recommend it provisionally. Huge thumbs up on the reality, aliens, and ideas, but be warned Egan leans hard into the deals. The books have a lot of diagrams. A good starting place is his essay, Plus, Minus: A Gentle Introduction to the Physics of Orthogonal. It’ll give you a good idea if you want to try the books.

That said, wow, the ideas are great and why I like Egan’s writing so much. (Likewise Neal Stephenson along almost exactly the same lines.) I’ve only touched on some of them. I haven’t mentioned how (or why) plants emit light, or why rock burns, or that light works both ways in time so messages from the future are possible.

I’ll also mention I found the third book less satisfying on several counts. I didn’t care for the characters, for one thing. (Each book deals with different generations along the trip.) The major problems have been solved by then, and much of the story is about politics in the mountain, fighting factions, and some truly weird physics (the future messages stuff).

Parts of the third book are very much like scenes in the movie Tenet — situations in which time is running both ways. I find the notion so incoherent it got in the way of my fulling enjoying the movie or those parts of book three. (In fact, I think both the movie and the book illustrate just how incoherent the notion is. Egan does go further than Tenet does in trying to account for it.)

But wow, what a cool universe and aliens!

§ §

As a hard SF aside, George O. Smith (1911–1981) wrote a series of short stories about communications engineers using vacuum tubes and other 1940s electronics to build and maintain a Solar system-wide radio network. Those were also super niche, but as an electronics hobbyist, it was my niche.

Of course, IN SPACE, vacuum tubes are just… tubes.

Question: Is science fiction rife with trilogies because it has a Holy Trinity?

Stay orthogonal, my friends! Go forth and spread beauty and light.

About Wyrd Smythe

The canonical fool on the hill watching the sunset and the rotation of the planet and thinking what he imagines are large thoughts. View all posts by Wyrd Smythe

12 responses to “Egan: Orthogonal Series

  • Wyrd Smythe

    I’m halfway through re-reading Lindsey Ellis’s Axiom’s End (see my review) so I can read Truth of the Divine, the second book in her Noumena series. It was released earlier this month (I’ve had it on pre-order since earlier this year).

    • Wyrd Smythe

      Ellis warned readers that her second book might be something of a left turn. Indeed it is. She’s reminding me vaguely of Octavia Butler’s Xenogenesis series in terms of intimate human-alien relationships.

  • Wyrd Smythe

    I just realized, the first book review I wrote on this blog was for Egan’s standalone novel, Distress.

    That review mentions another novel, Incandescence, that’s a standalone story, but takes place in Egan’s Amalgam universe. Incandescence is a little bit like the Orthogonal series in being about aliens doing science. Incandescence is mainly about General Relativity along with a great dash of orbital mechanics. It’s a more accessible book; not quite so dense. The Orthogonal series is a much more sweeping physics lesson!

    • Wyrd Smythe

      I’ve written about Greg Egan more than a few times. As I said in the post, he’s a favorite of mine.

      Back in August 2019 I posted a review of his novel Quarantine, which, as hard SF, is about quantum wavefunction collapse. The quarantine in question had nothing to do with disease.

      The post got 13 hits the month it was published, and averaged less than three hits in the 17 months that followed. One month it got as high as 11. Three months had zero, though. Then in January of this year, 257 hits followed by a short tail: 20, 12, 6, 1, 1, 0, 0, 0, 0. (That last zero is October, so I suppose there could yet be a hit this month.)

      I’m pretty certain the spike was related to COVID-19, not a sudden, very brief, interest in the book. (But I could be wrong. The book does have an interesting premise.)

  • SelfAwarePatterns

    Yeah, I think I’ll have to pass on this one. It sounds like it requires way too much work. Egan says on his website that it’s valid to write a novel that requires the reader to keep a notebook off to the side to understand things. But he says it in the context of bitter complaints about a bad review of one his novels, where the reviewer obviously had different ideas.

    It’s a shame, because I do like alien societies.

    • Wyrd Smythe

      It is a shame. The ideas are wonderful and audacious, but he goes too far except for only the most dedicated or interested.

      As I said in the post, I would agree with him it’s a valid thing to do so long as he accepts how narrow his fully appreciative audience is likely to be.

      • SelfAwarePatterns

        I don’t know of any other fiction that puts that much work on the reader, although it wouldn’t surprise me to learn there is other stuff out there. It seems like as a genre it needs its own name so people know what they’re getting into when they pick up one of those books. Maybe “Workbook sci-fi” or something.

      • Wyrd Smythe

        Heh, SF-with-homework. 🙂 I’ve mentioned how a lot of my very early science education came from hard SF, but this takes it to a whole new level. I’m tantalized by his website, some great stuff there, but also a steep hill to climb in parts. Very much aligned with my interests, but when I’m reading a story I tend to want to sit comfortably or lie on the couch which makes the homework aspect a pain.

        Some readers of mystery books, I think, will do homework trying to figure out whodunnit. Take notes, make time tables and floor plans, that sort of thing. A few stories even come with a floor plan or train schedule — presumably as clues. But that’s about the most homework-y other kind of writing I can think of. Hard SF does stand out that way. The physics manual as fiction story. I’ve used the term “diamond hard” SF, but these days some marketer will no doubt call it “workbook punk” or something like that.

      • SelfAwarePatterns

        There often are nerds who really geek out on story. And it’s very cool when authors provide the material for it. So the maps and appendices in Lord of the Rings and Dune, or these days companion websites like Egan’s, allow for that.

        But it’s another thing entirely when it becomes a prerequisite. How many people would read Lord of the Rings if it required learning Elvish first? Or becoming familiar with the chronicles of Numenor, Andor, and Gondor?

        As you noted, it’s all in what audience Egan wants to aim for. But he should be prepared for critics who warn readers away from his stuff.

      • Wyrd Smythe

        In this case, I’m one of those who is warning potential readers!

        I’ve long found it an interesting art question: How much does the artist require the consumer to bring to the table? Most art is informed to one degree or another by external knowledge, but how much is required? Put the other way, how much must art stand on its own?

        As an aside: In narrative art, sequels and later books of series have that question of how much “what happened previously” they need to include and how much about the characters they need to re-explain. I’ve found it interesting how different artists handle that. I favor those who expect the reader to keep up; I dislike repetition. A key choice seems between an introductory — often skippable — “previously” section or working the necessary recap into the text somehow (often clumsily). I do prefer the former.

        The idea of needing to know Elvish made me think of Agatha Christie’s tendency to have her characters use French phrases. I suspect British readers at the time were more familiar with common French phrases, but even so it’s a good example of how an author can toss in something readers won’t necessarily understand. Surely some of her readers found at least some of the phrases as opaque as I do. (I love that ebooks let me highlight and look up words or translate phrases.)

        When authors do that, especially with made-up languages no one knows, there seems again a fork. Some have other characters react or restate to fill in the reader; others don’t. Christie often doesn’t. The reader has to go with the flow, which usually works out okay, the phrase wasn’t key. It just lends a kind of flavor to the character.

        Point being, a little mystery the reader can skate right over, but the greater the gap, especially when it’s kind of fundamental to the story, the harder that is. Might be impossible in this case.

      • SelfAwarePatterns

        All art does exist in a cultural milieu, assuming that the audience knows certain things. I just recently learned about a concept in visual art called the “beholder’s share”, what the viewer of a piece of art brings to their perception of it, something that does seem important with expressionist type pieces.

        In terms of writing, I remember when I first started reading literary science fiction. The authors assumed I understood certain things, which at first I didn’t, such as the need to both accelerate and decelerate spaceships, or that an accelerating ship has gravity while a coasting one doesn’t. All things media science fiction of the 60s and 70s gave me no clue about.

        I had a similar issue when first reading Robert E. Howard, when he referred to “the poop” on a ship or types of horses. In the 70s, early 80s, there was no internet to quickly look these things up. (Sometimes a large dictionary or an encyclopedia could help, but not always, and using them took time.)

        I think particularly in science fiction, fantasy, and historical fiction, an author has to make a lot of judgment calls on how much to explain to the reader. With SF, the usual advice is it’s better to assume some sophistication rather than talk down to them. But I’ve read some authors that are so aggressive on this that I’m often confused about what’s going on in their books.

        Of course, not explaining things can sometimes be a useful tool. If the author isn’t clear themselves on how something works, leaving it to the imagination gives the reader an opportunity to imagine plausible alternatives, without potentially messing up by being to explicit. (William Gibson noted in an interview that he always got in trouble when he was clear about a technology, like dot matrix printers, vs when he left it open to interpretation.)

        The trick is to find the right balance, to invoke and use the reader’s imagination without them perceiving it as a burden.

      • Wyrd Smythe

        It’s especially important in expressionist and abstract (and surreal and other) art, but it’s always true. Art always involves two translations: from the artist’s mind to the medium, and from the medium to the consumer’s mind. And the artist has little control over the latter!

        I experienced some of the same things about ships and horses, and it’s a good example. There is regular fiction about ships or about horse racing that also often assumes the reader knows about those subjects. Stories from bygone days can also assume the reader knows about current events or the popular topics of that day. (Christie often does that; refers to things her readers obviously knew all about, but which are now lost in the mists of time.)

        My dad once gave me a dictionary-sized book, What Things Are Called that was just labeled pictures of ships, castles, animals, clothing, and other objects. It was meant as a guide for writers. Fun book to thumb through, although I never used it seriously.

        It is a judgement call. How topic to be, how hip or slang-y, how technical. I’d rather an author write above me than below me. The former can be frustrating, but the latter is irritating. And I can do something about the former. Plus I enjoy a challenge; I don’t mind doing a little bit of work as a reader.

        I’ve either read Gibson say that or someone else say something very similar. (Or maybe you’ve mentioned that about Gibson before.) I have heard advice that one should write as timelessly as possible — avoid slang and topical references because they don’t age well. Being specific about technology seems like one of those things that can age badly. Also the rule about writing what you know — don’t describe technology in detail if you aren’t fully familiar with it!

        Totally agree the trick is balance (in so many things). It’s extra tricky when readers will have varying opinions about the proper balance point! One size does not fit all.

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