# Book review

### Orthogonal by Greg Egan

Oliver Brown
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I was inspired to write this review after watching Christopher Nolan’s movie Tenet. The central idea of Tenet is explored in the Orthogonal series (amongst many other things) but with more rigor and detail. As such, this review contains spoilers about the premise of Tenet. I won’t cover the details of Tenet’s plot, but if you were already going to watch Tenet, do that first.

Despite ostensibly being a review, this is mostly a piece designed to persuade you to read these books. It contains a fairly detailed explanation of the initial premise for the book (while avoiding spoilers for the plot), because talking about the things that are good is difficult otherwise.

### Tenet

The movie Tenet follows in the wake of Interstellar by taking a confusing scientific concept and creating a movie that can be compelling for a mainstream audience. In Interstellar this was the idea of time dilation, in Tenet it is the idea of the “arrow of time”, and whether, perhaps, it is not as immutable as it seems.

The one line conceptual spoiler for Tenet is the following: there are machines that allow people and objects to travel backwards in time, while in the same space as people traveling forwards. Interactions between normal people and “inverted” people are strange and unintuitive.

In the movie, the details of “how” are basically ignored. And although the plot is clever and demonstrates much of the oddness that would be present, there is little detail.

### Riemannian space

The premise for Orthogonal is a simple change to a single formula that defines the geometry of space-time. There is a detailed explanation by the author himself, but a summary is as follows:

• In two dimensional space, the distance between two points can be found using the Pythagorean theorem: `d = √(x² + y²)`, where `x` and `y` are the differences in the points' positions in the x-axis and y-axis respectively.
• A very similar formula also works for three (and higher) dimensions: `d = √(x² + y² + z²)`.
• General relativity combines time and space together to form a single thing called spacetime.
• It is possible to calculate the “distance” between two points in spacetime. However, in this case the formula features a minus sign: `d = √(x² + y² + z² - t²)`.

This kind of spacetime is described by the author as “Lorentzian”. That minus sign is a consequence (or a cause, depending on your philosophy) of the speed of light being constant, and appears to describe our universe.

In the universe of Orthogonal however, the spacetime is “Riemannian”. That is, the distance between two points in spacetime is just: `d = √(x² + y² + z² + t²)`.

This is summarized by saying the universes have metrics of `+, +, +, −` and `+, +, +, +` respectively.

### The Arrow of Time

This small change has a lot of consequences. The biggest is that there is no longer a universal speed limit. You can go as fast as you want, even reaching a sort of infinite velocity. Just like in our universe there is time dilation at high velocities. At “infinite velocity”, time stops passing completely for a stationary observer. In the universe of Orthogonal however, if you were to continue accelerating you would find that time has started to progress backwards for you, relative to a stationary observer.

The exact mechanics of this may sound confusing, but are explained well in the book, and it more detail on the author’s site.

### An actual review

With all the preliminaries out of the way, it’s time to explain why I think Orthogonal is so good. It basically does three things, and it probably could have stopped at the first one and still have been good.

#### 1. Hard sci-fi with a relevant plot

The story is “hard sci-fi”. It has a universe that has solid rules that are as scientifically rigorous as possible and tries to avoid deviating from them. In order to also be a good sci-fi story though (as opposed to just good science), it also needs a plot that allows the reader to explore that universe.

Orthogonal presents the main characters with a world ending disaster. Not a terribly unique idea in the abstract, but in this case the disaster is one that could only happen in the Riemannian spacetime it presents.

Very quickly, the characters devise a plan to avert disaster. In the best traditions of disaster movies, it initially sounds crazy, but it just might work. And like the disaster itself, the proposed solution would only be possible in Riemannian spacetime.

#### 2. Explore some further detail of the universe

Orthogonal is a trilogy of novels, spanning a significant time period. A lot of less apocalyptic consequences of Riemannian spacetime are explored. One of the more surprising is a running story of social development.

In the world of Orthogonal, women are not treated well. The way this manifests is very similar to our own world (so similar that it reminds me of classic allegorical Star Trek episodes). However the reason for the treatment in the story is, again, something that could only happen the world of Orthogonal (and is in fact a direct result of of the physics possible in Riemannian spacetime).

#### 3. First principles

The final thing Orthogonal does, and the thing that takes the story from being “good” to being absolutely staggering, is how the details of the world are presented.

It starts in a world with a similar level of technology to us at the beginning of the 20th century. The author makes no overt attempt to explain the world narratively. For the reader it appears initially that the characters inhabit a world that behaves very differently to our own for no reason. But, the main characters in the story are striving for knowledge (after all they soon have a world ending disaster to avert), and so they start to learn how the world works.

As the plot develops over several generations, we follow scientists and engineers as they untangle the physics of the universe. We learn with them as the details of how the Riemmannian equivalents of electromagnetism, thermodynamics, relativity and quantum mechanics work.

That is the what makes Orthogonal really special. Not only working out how this strange universe works, but coming with a plausible way that characters in the universe might be able to work it out for themselves.

### Conclusion

Stephen Hawking said that he was warned every equation added to a popular science book would halve the number of sales. Despite being a work of fiction, much of Orthogonal feels like a popular science book but the author has not let such an idea concern him. It is full of equations and diagrams. I wouldn’t say it is impossible to enjoy the book if you chose to ignore them (or at least not completely engage with them), but you would be missing out on a lot.

If, on the other hand, that kind of detailed explanation appeals to you, there is a site (all created personally by Greg Egan himself) dedicated to providing way more detail on all the physics and maths explored in the book.

Orthogonal is hard sci-fi. Conceptually it may be the least accessible of Egan’s works. It is, however, spread over three novels to avoid overwhelming the reader and plenty of time is dedicated to exploring how the characters deal with this world, and that can be enjoyed independently of understand why and how it works.

### Dichronauts

Actually, the least conceptually accessible work from Greg Egan is probably Dichronauts, a story set in a universe with the metric `+, +, −, −`. That universe is so weird that you can’t turn past ninety degrees, and as you get closer to it, you stretch towards infinity.

### Atonement (Star Trek: Voyager)

Oliver Brown
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Although the title suggests this is just a review of Atonement (and is biased towards it), this is really a review of the three Voyager novels The Protectors, Acts of Contrition, and Atonement which essentially make up a single story.

As a warning, this book (and by extension this review) contains heavy spoilers for the Destiny series, and the earlier Voyager relaunch stories (Full Circle to Eternal Tide).

Voyager and its crew and allies face some of the consequences of their first trip through the delta quadrant, while Seven of Nine struggles with the changing attitudes of the Federation following the events of Destiny.

One of the reasons I like Star Trek now is the sheer wealth of material available. The novels have been going from strength to strength, expanding the material in ways that would not have been possible while the show was still on TV. Despite this, I was a little concerned when the Voyager relaunch series began in Full Circle and immediately introduced a lot of new characters at once, and did so in a way that suggested they were going to stick around and be important. I think this trilogy has proven the idea was worth it.

At its core, there are two stories going on simultaneously, one in the Federation and one with the Full Circle fleet in the delta quadrant. Plot-wise they have nothing to do with each other and could have happily existed in separate works. Despite this, they do work well together solely because of the complicated relationships between all the characters - partly the existing ones between the characters we all know, but also significantly with the new ones introduced. Characters' actions were frequently motivated by their relationship with those in the ‘other’ story so this structure helped emphasize this in a way that would have been lost had they been separate.

The Federation storyline deals with unexpected fallout from the destruction of the Borg. Seven of Nine and Tom Paris leave the Full Circle fleet to help with this in a story centred around the ethics and morality of the Federation trying to rebuild too quickly. Both Seven and Tom have to deal with the fact that they’ve spent years with a crew who respect and trust them, but now have to face an outside world that doesn’t. After all, Seven is not only a former Borg drone, but also one of only a handful that didn’t join the Caeliar gestalt; while Tom is still regarded as rebellious (and only kept in Starfleet due to Janeway’s influence) as well as reckless because of his handling of the situation with his daughter in Unworthy.

Described broadly, this idea of characters redeeming themselves, and being better than they appear is a common plot for Star Trek. But it is also one that works well, especially because of the complex interactions with the secondary characters (The Doctor, Axum, Samantha Wildman, Icheb and Admiral Akaar all feature to varying degrees).

The Full Circle fleet storyline also follows another typical plot found in Star Trek: how the Federation deals with large powers that don’t quite match their ideals, and specifically what happens if they try to subject a member of the Federation to their own idea of justice. Unfortunately, the ultimate resolution to this ends up a bit weak, but as consolation it leaves the door open for more in the future.

Constantly switching between the two plots is a little frustrating at times, but only because each one is so engrossing. During it all, the new characters in the Full Circle fleet get enough time to get some depth and feel important (and in some cases like Liam O’Donnell, to stop feeling like one-dimensional caricatures). This didn’t blow me away like some have (like DTI: Watching the Clock or the Mirror Universe series), but it’s better than most other recent novels and is definitely the best of the Voyager relaunch and worth reading if you have any interest in Voyager. Although you should probably start at Full Circle and read them all.

### Department of Temporal Investigations: Watching the Clock

Oliver Brown
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Star Trek novels have improved a lot since I read them previously many years ago. Not necessarily the stories themselves but that there seems to be a serious concerted effort to maintain continuity between them, but without requiring too much knowledge of other books to read any given book (although there are more series now which obviously do require you to read them all for it to make sense).

With that in mind, before reading DTI: Watching the Clock you should definitely read the Destiny series and possibly the Typhon Pact series and the Titan series. Everything you need to know about them is explained in the book but it does spoil them a little if you do intend to read them at some point.

If you ever thought time travel in Star Trek didn’t make sense (and would like it to) then this book is for you. Truly awesome.

Time travel in Star Trek has always been a slightly problematic topic. Featured as the primary plot device in many episodes (and several movies), it was always handled differently and never followed any discernible rules. This book tries to straighten this all out (or as Douglas Adams once said make it, at least, firmly crooked) and on the whole, succeeds.

The book feels like a collection of short stories about time travel, tied together with an over-reaching story arc (complete with seemingly insignificant events in one “story” that become important later). Many of them are about how the DTI dealt with the aftermath of different time travel events in the show. In fact practically every Star Trek episode that dealt with time travel is mentioned (except for new Star Trek movie) and explained to some extent. A couple of the big ones (specifically Star Trek: First Contact, the Temporal Cold War and the whole of Voyager) are more central to the story.

Aside from the technical aspects of time travel, the book also devotes time to expanding the main characters, Dulmur* and Lucsly, who were introduced to us in the Deep Space 9 episode, “Trials and Tribulations”. As the blurb says: “There’s likely no more of a thankless job in the Federation than temporal investigation”. Considering how interesting the time travel elements are, I expected to find these parts more boring than I did. In fact after seeing how they deal with some of the Starfleet officers (and more specifically how the Starfleet officers deal with them) I thought about Sisko’s reaction to them and found him downright annoying.

So the bottom line is, the only reason I can think for a Star Trek fan not to read this would be that you want to read some of prerequisite books first (Destiny, Typhon Pact, Titan).

*Dulmur or Dulmer? I always thought Dulmer since their names were supposed to be anagrams of Mulder and Scully. The author however uses Dulmur consistently and there is a point in the story where the spelling confusion is referenced explicitly.