Axiomatic and Dark Integers by Greg Egan

Reviewed by Karen Burnham

Axiomatic cover

Dark Integers cover

Greg Egan has a reputation for being a very hard science fiction author. His books often contain mind-bending amounts of esoteric quantum physics and math. Schild's Ladder (2001) describes the creation of a new kind of space-time continuum that immediately starts expanding into our universe at half the speed of light. Diaspora (1997) includes a description of existence in five dimensions so thorough that for brief moments you think that you could just... almost... not quite... visualize five-dimensional space (a physical impossibility). His latest collection, Dark Integers and Other Stories, continues in this vein: in two of the stories, the main "what if" conceit involves pockets of "mathematical space" where simple arithmetic (albeit with really huge, transastronomical integers) becomes inconsistent. However, Gollancz's re-release of Egan's 1995 collection, Axiomatic, reminds us that some Egan stories are more conventionally accessible, dealing largely with ethical questions related to biotechnology. The contrast between the stories in these two collections raises the question: what makes different kinds of SF "accessible" or "hard?" Attempting to answer that question requires us to examine how we as genre readers construct our suspension of disbelief when we read.

For science fiction, suspension of disbelief can be critical to the reading experience. While this is true of all fiction, sff must work harder to achieve it. In a mainstream story we may question whether or not we believe that (just for example) a man whose wife has walked out on him and whose mistress is pregnant would really get involved with a student to burglarize the mistress' house and steal something from her husband's memorabilia collection (Wonder Boys, Michael Chabon, 1995). The question then isn't: "Are these things possible?" but instead "Would any real person do these things?" What's required is an emotional judgment about characters' emotional reactions. In science fiction, we judge whether or not the authors are "believably" describing impossible things. We have to decide whether or not we can believe characters can even do many of the things described before we can judge the validity of their actions. If we cannot suspend our disbelief, we may abandon a story, spend all our time attacking it, or simply wander through the narrative in a state of confusion. It's a very individual construction. It depends on what you already know in real life and what you've already read within the genre.

As an example of a story where suspending disbelief is relatively easy, take "Blood Sisters" (1991) from Axiomatic. It starts out describing a "blood sisters" ritual between young twins, with one pointing out that it isn't necessary and the other pointing out the importance of ritual. At this point, after half a page, we feel like we're on solid ground. We know that identical twins share their genetics. No problem there. Fast forward to their adulthood. One twin, the narrator, learns that she has a possibly fatal genetic disease "...from the micrographs of the misshapen lymphocytes proliferating in my bone marrow, to the print-out of portions of the RNA sequence of the virus that had triggered the disease, [the report was] thirty-two pages in all" (p. 87). From high-school biology and popular media, we can feel confident here. Lymphocytes are often heard of in the context of cancer, as is bone marrow. We know that RNA is genetic material a bit like DNA, and we've all heard of genetic diseases. That one sentence contains most of the technobabble in the story, and it's all that is needed. After that we get into questions about the ethics of double-blind clinical trials, questions that the narrator knows to ask because when different things happen to identical twins, something suspicious is probably going on. It's a good story, in that it shows the human cost of doing science the "right way." However, it never stops to focus on the main characters enough for us to really start to care about them, a flaw in a human-interest story.

In another story in the collection, "Learning to Be Me" (1990), the main speculative elements involve the construction of neural networks. Here Egan begins the story with the explanation that the character got when he was six:

I was six years old when my parents told me that there was a small, dark jewel inside my skull, learning to be me.
Microscopic spiders had woven a fine gold web through my brain, so that the jewel's teacher could listen to the whisper of my thoughts. The jewel itself eavesdropped on my senses, and read the chemical messages carried in my bloodstream; it saw, heard, smelt, tasted and felt the world exactly as I did, while the teacher monitored its thoughts and compared them with my own. Whenever the jewel's thoughts were wrong, the teacher—faster than thought—rebuilt the jewel slightly, altering it this way and that, seeking out the changes that would make its thoughts correct.
Why? So that when I could no longer be me, the jewel would do it for me. (p. 185)

Basically, everyone grows up with a physically robust neural network growing in their head, learning to mimic their thought processes. Then in their early thirties, when brain matter may begin to degrade, they "switch:" they have their organic brain replaced with robust plastic that can run the fully-trained neural network. Voila, functional immortality. The story gets deep into questions of identity, what makes a person and a personality, and develops a decidedly creepy edge when the narrator feels that he is being pushed aside by his own neural network. For me, it was very easy to suspend disbelief for this story. I've studied neural network architectures in school and worked with them professionally. If you grant the author the necessary tech advances (which is part of the informal contract that almost all readers of SF agree to: fans didn't critique Ringworld because we can't do the engineering yet, they critiqued it because Niven got his orbital dynamics wrong), then this story makes perfect sense, and is in fact a fascinating theoretical approach to the current difficulties of training neural networks to even approach the complexity of human thought. But would the explanations here work as well for someone unfamiliar with the field? It's difficult for me to judge.

In between those two extremes—those that might require specialist scientific knowledge and those that don't—lies a third kind of story. It's the case where we don't judge the speculation by what we know from the real world, we instead compare it to the other things we've read or seen in genre fiction. In the title story of the collection, "Axiomatic," (1990) the central conceit is that you can buy an implant that changes your brain:

The implant burrowed into the brain, sent out a swarm of nanomachines to explore, and forge links with, the relevant neural systems, and then went into active mode for the pre-determined time—anything from an hour to infinity—doing whatever it was designed to do. Enabling multiple orgasms of the left kneecap. Making the colour blue taste like the long-lost memory of mother's milk. Or, hard-wiring a premise. I will succeed. I am happy in my job. There is life after death. Nobody died in Belson. Four legs good, two legs bad... (p. 116)

As you can see, from this story and "Learning to Be Me," the idea of computer-mediated consciousness and its implication for our sense of identity is a key trope in much of Egan's work. He returns to this theme repeatedly, and it is usually at least a background element in his novels, even if it is not foregrounded.

In "Axiomatic," the narrator is haunted by the seemingly random murder of his lover. For years he's worked his way step-by-step towards a revenge scenario, always telling himself that he would never actually do anything about it. The last step is buying and uploading the "Life is cheap" implant, which is advertised as providing the belief that "People are meat. They're nothing, they're worthless." This enables him to take the final steps to revenge, but it wreaks even more havoc to his tortured psyche than he had foreseen. The ending is tragically just, in a twisted way.

Obviously, nothing like this is even remotely possible today. Science has only fuzzy notions about how beliefs are formed and none about how they could be changed by physically changing the brain. Moreover, nanotech of any sophisticated sort is continually "twenty to thirty years away." However, anyone who has spent much time reading in the genre is familiar with the basic concept: in Snowcrash (1992), the drug/computer program could hack your brain and make you a Sumerian cultist. In the Matrix movies, you can learn new things by throwing in a new CD-ROM and hitting the "upload" button. It's a concept SF readers are likely to be familiar with and find easy to accept, even if it has no current "real-world" validation.

All this speaks to the difficulty that people used to mainstream fiction have when trying to read science fiction. If they haven't been reading cyberpunk or watching (even ridiculously popular) SF action movies, the brain-hacking trope might be confusing. They wouldn't know how much credence to give it, especially if they know that it's not even theoretically possible in the world today. Going back to the "simple" example of "Blood Sisters," if people have intentionally or unintentionally forgotten their high school biology and avoided the health sections of the newspapers and TV shows, that simple paragraph of infodumping may be so much gibberish. An acquaintance of mine, a liberal arts major with a strong background in comic books and genre TV and movies found reading David Brin's Earth (1990) very difficult. She likened it to struggling with a science homework assignment. She didn't know enough about current day science or genre conventions to see how much credence she should give his near-future extrapolations.

Even long-time readers of science fiction with relevant scientific backgrounds can be driven to this state of confusion by the hardest of hard science fiction, the kind for which Egan has become famous. This brings us to "Dark Integers," (2007) the title story of the new collection. This story is paired with an earlier one, "Luminous" (1995). I had the misfortune of reading "Dark Integers" first, without the background of either the explanation set forth in "Luminous" (although that wouldn't have helped much) or the slightly more useful extra explanation in the introduction to this collection. In the introduction, Egan specifically addresses the difficulty in suspending disbelief for the concepts he presents in these two stories:

Two of the stories in this collection, "Luminous" and "Dark Integers," deal with the idea that the mathematics of ordinary numbers might be malleable. At first glance this notion seems comically surreal: what could be more solid, timeless and universal than the facts of arithmetic? Human languages and social customs vary from place to place and time to time ... But although the particular language, symbols, and medium used to express a simple fact about numbers can vary wildly, it seems inconceivable that in any epoch, or any corner of the universe, the underlying facts could be different from those with which we're familiar.
So, without giving away too much about the stories themselves, I'd like to sketch some of the context for this idea and explain why I believe that it's not as crazy as it sounds. There is a sense in which malleable mathematics would slot neatly into a perfectly respectable intellectual lineage, and while that proves nothing whatsoever about reality, I think it lifts the idea above pure whimsy to the point where it merits at least a temporary, science-fictional suspension of disbelief. (p. 7)

The plots of both stories involve a small cabal of people, having proven that there is a region of "different mathematics" out there, figuring out what to do about it. The stories have action-thriller plots that hinge on evading the shadowy off-stage bad guys from "Industrial Algebra," who would use this discovery for evil, and trying to reach an accommodation with beings whose existence hinges on these "alternative" mathematical postulates.

They aren't necessarily Egan's best stories. They both rely heavily on their plots, with very little characterization. To understand the story you have to understand what motivates the characters. But when they're all so bland, and the only thing that motivates them is the weird science, it's very hard to find a narrative toehold when the infodumping gets confusing—we don't have anything else to fall back on. When I read "Luminous" and "Dark Integers" for the first time, I spent most of the time confused. I didn't have any firm conceptual ground to stand on. The concepts he was using were completely disjoint from anything I knew about math or physics, and also from anything else I'd ever read in the genre. After reading the introduction I found them easier to read, because then I knew that my feeling of disjointedness wasn't because I was stupid, but because the stories' conceit really was completely without basis in any real-world science or genre convention.

All this begs the question: to what extent is it the author's responsibility to educate the reader, to help the audience build that suspension bridge? It's a fine line that SF authors walk. If you assume specialist knowledge, even just familiarity with words like "quantum" and "dimensions," you can write a more stream-lined story; getting to the heart of your concept without having to write a textbook along the way. However, that approach may drive many readers away. Another way to phrase the question is: if the reader abandons a work in a state of confusion, whose fault is it? The author's or the reader's? Ultimately, it is up to each author to decide for each individual piece.

It may be possible for readers to "skip over" a confusing aspect of the story and enjoy it anyway, if the author provides enough alternate motivation. I'd argue that it's more difficult to do this in a short story than in a novel. In a short story, usually the nifty "what if" device is the point of the whole exercise, and if you can't buy into it you can't enjoy the story. In a novel, enough other things are going on to see you through. People enjoy the rousing adventure tale of Ringworld (1970) even though the physics was disproven by 1971. For a less famous example, Robert Charles Wilson's Blind Lake (2003) contained technobabble dealing with two of my fields of specialty: neural networks and signal processing. I knew for a fact that what he was writing had no possible basis in reality. However, Wilson's stories aren't really about their science, they're about their people, and I was more than happy to continue reading the story on that basis.

When it comes to Greg Egan, then, it will always be a personal call as to whether you'll grant him the way-far-out-there science and simply enjoy the story, or whether instead not being able to understand the things he's obviously so excited about will ruin it for you. It's important to remember though, that not all his writing is at the top end of the difficulty spectrum. It feels as if there are two Greg Egans: one is so excited about whatever amazing piece of esoteric science he's imagined that he just can't resist writing a story about it. This more famous Egan shows up in Schild's Ladder and Diaspora as well as "Luminous" and "Dark Integers" in the Dark Integers collection, and in "Eugene," and "Into Darkness" in the Axiomatic collection. Then there's the lesser known Egan who uses straightforward extrapolation, usually of biology and computer modeling, to examine "what if" questions of identity and ethics. That realm covers "Ocean" in Dark Integers, almost every other story in Axiomatic, and at least the subtext in most of his novels . If you don't like the former Egan, you may want to remind yourself of the latter Egan before you abandon him altogether as an author.


Karen Burnham is vocationally an engineer and avocationally a speculative fiction reviewer. She lives in Long Beach, CA, and archives her reviews at www.SpiralGalaxyReviews.com. She can be emailed at karen.burnham@gmail.com.