There is a 1991 science fiction story by Ted Chiang, 'Division by Zero,' which begins with the statement: Dividing a number by zero doesn't produce an infinitely large number as an answer. The reason is that division is defined as the inverse of multiplication; if you divide by zero, and then multiply by zero, you should regain the number you. Ted Chiang 1 Dividing a number by zero doesn’t produce an infinitely large number as an answer. The reason is that division is defined as the inverse of multiplication; if you divide by zero, and then multiply by zero, you should regain the number you started with. Note the title of the last section, '9a = 9b,' and the last line - 'this was an empathy which separated rather than united them.' Underlying the story is an analogy between Carl and Renee's relationship and the relationship between the numbers on.
Number of words : 5500
Percent of complex words : 13.1
Average syllables per word : 1.5
Average words per sentence : 12.5
READABILITY INDICES
Fog : 10.3
Flesch : 63.4
Flesch-Kincaid : 7.5
PEOPLE
Stories Of Your Life Chiang
Renee NorwoodA mathematics prodigy and professor, and attempter of suicide.
Carl Norwood
A fellow patient of experience and her husband.
Mrs Rivas
Ward manipulator.
Division By Zero Worksheet
Bertrand Russell and Alfred WhiteheadWrote the Principia Mathematica.
Von Neumann
A mathematician.
Laura
Carl met her in hospital.
Peter Fabrisi
Colleague of Renee's.
David Hilbert
A mathematician.
Callahan
A Berkeley mathematician Renee consults with.
Kurt Godel
A mathematician. Demonstrated two theorems in 1931.
Gerhard Gentzen
Provided a proof of the consistency of arithmetic.
Marlene and Anne
Carl's friends.
MEDIA
Principia Mathematica
Treatise on the subject.
Marine Biology
A scientific journal.
ORGANISATIONS
Second International Congress of Mathematics in 1900
Conference on the same. David Hilbert listed what he considered to be the twenty-three most important unsolved problems of mathematics.
PLACESEdinburgh
City in Scotland.
PLOT
Renee and Carl are married suicide survivors. Renee is also a genius mathematician. It seems she has proved arithmetic is inconsistent. Her colleagues and peers have found no holes in her work. This is not doing good things for her mental state.
Carl has found he no longer loves this Renee, but is torn whether to tell her or not in the midst of this crisis.
4 out of 5
http://www.fantasticmetropolis.com/i/division/full/
I think I’ll always vividly recall watching the 2016 movie Arrival because of when I saw it: less than 48 hours after Trump’s victory in the presidential election, when it still seemed like the entire world might go tumbling off a cliff face and we were all about to die in a nuclear exchange with some country whose leader dissed The Donald on Twitter. (Not that that’s entirely out of the question now, mind you, but it’s become clear that the Trumpocalypse is a more death-by-degrees affair than a lot of people were expecting four years ago.)
A close friend and I had made the extremely unwise decision to watch the election results live even though it meant staying up into the early hours of the morning (I was in the UK at the time), both of us nervous but fully anticipating that Trump would lose. When that didn’t happen we decided to distract ourselves by watching a movie…and picked The Duke of Burgundy.
That’s, uh, not exactly escapist fiction, so the next day we went to see Arrival.
Even taking into account the atmosphere at the time playing a role, I remember being pretty profoundly affected by what the movie had to say about the importance of communication and mutual intelligibility in averting pointless conflict, and was intrigued to learn that it was adapted from a novella written by a science fiction author whose name I vaguely recognised but whose work I had never read.
That was four years ago, and I’m only now getting around to reading his two published short story collections: Stories of Your Life and Others (from which Arrival was adapted) and Exhalation, published in 2002 and 2019 respectively.
As you can gather from those publication dates, Ted Chiang is not exactly a prolific author. If anything I think that adds to the reputation of his work: despite producing only two collections over a span of almost twenty years (the individual stories were originally published over an even longer timescale), he’s won four Nebula awards, four Hugos and a smattering of other major prizes.
I’ll admit that I don’t read a lot of short fiction, something I’ve been trying to make up for recently, and I’m never sure how to approach reviewing it. Rather than go through each story one-by-one I’ll just talk through some thematic underpinnings that crop up repeatedly in both collections and pretty clearly highlight the kinds of issues and concerns that Chiang is interested in.
(To get it out of the way upfront: I loved almost everything on offer here, with maybe one story that I wasn’t too fond of. The stories I’m choosing to discuss are mostly the ones I found particularly compelling; that this is going to be a fairly long post says everything necessary about how much I like Chiang’s work.)
There’s a particular type of speculative fiction that I’ve always enjoyed, where the author imagines a universe with radically different fundamental truths to ours and then extrapolates outwards to investigate what living in that universe would actually be like.
Chiang is an absolute master of that format, as it turns out. Two of his stories, ‘Tower of Babylon’ and ‘Omphalos’, deal with alternate histories in which some form of Biblical literalism is correct: in ‘Tower’ there is a physical vault of heaven which occupies the upper reaches of the sky, towards which a colossal tower is being built; in ‘Omphalos’ the early natural philosophers who dug through the Earth’s strata found evidence confirming rather than refuting Young-Earth Creationism.
In both of these stories the protagonists are compelled to investigate the underlying truths of their world, and in both cases they make discoveries that upend what they thought they knew about the universe and their place in it. Many other writers would have ended one or both of these stories with the protagonist discovering that God is dead and the evidence of their faith was a sham all along; Chiang takes the much more interesting approach of having them find instead that God is real but may have had different intentions for his creation than they assumed.
What I particularly love about these stories is the attention to detail evident in the worldbuilding. What logistical systems would a pre-industrial society need to put in place in order to build and maintain a tower to heaven that takes months to climb? What phenomena would people experience as they ascend past the celestial spheres, climbing above the sun and moon in the process? And if Young-Earth Creationism had been correct all along, what kinds of evidence would early geologists have found when they first began to catalogue the objects that they dug out from beneath the surface?
A very similar thematic underpinning is evident in the titular ‘Exhalation’. (Incidentally, it was only while reading this story - dozens of pages into the book - that I realised the entire collection isn’t called ‘Exaltation’. I’ll assume for the sake of my ego that this is a universal experience and I’m not just a huge dumbass.)
Here Chiang presents the diary of a scientist belonging to a species of robot (essentially) that have no detailed knowledge of how they came to be or even how exactly their mechanical bodies are constructed. Our protagonist undergoes an audacious process of self-dissection, exposing their own brain to an elaborate microscope, and in doing so comes to the realisation that their universe, which is enclosed on all sides by a vast wall of metal, will eventually become incapable of sustaining the processes that drive their people’s mechanical cognition.
This is pretty clearly an allegory for entropy and the fact that, no matter how advanced humanity becomes, we are eventually doomed to die out along with the stars and all other complex structures in space. (Our extinction will probably happen much, much sooner than that, of course, but there is a very real upper limit on how long the Universe could conceivably support life. For more on the topic I suggest perusing this highly entertaining Wikipedia article.) This isn’t the first time I’ve seen this particular subject tackled in science fiction, obviously, but it is the first time I’ve seen an author take a concern that feels impossibly remote and re-contextualise it as something that it feels necessary to have an opinion about in the here and now.
The theme of a scientist accidentally making a discovery that throws their worldview into chaos continues in ‘Division by Zero’, in which a genius mathematician comes up with a proof that any number can and does equal any other number, essentially invalidating mathematics as a serious field of study. This realisation drives her to try to take her own life, echoing her husband’s own suicide attempt from twenty years earlier.
I’ll admit that I don’t 100% get what Chiang was going for with ‘Division by Zero’, but as usual he manages to merge his fairly heady SF concepts with an immersive human story. True, I may not understand what exactly the protagonist did to collapse mathematics into farce, but I believe in the dramatic effect it has on her psyche.
I don’t want to leave you with the impression that Chiang deals only in more heady speculative fiction concepts, however. Several of the stories in these collections marry more out-there concepts with completely grounded human protagonists. This is, in my opinion, best exemplified in ‘Anxiety is the Dizziness of Freedom’, which takes its title from a Kierkegaard quote.
The story takes place in the near future or an alternate present, in which the development of a kind of consumer technology known as ‘prisms’ allows people to communicate with parallel universes which branch off from our own at the moment any given prism is first activated. One could, therefore, activate a prism and then check in on its alternate-universe inhabitants every year for a decade in order to see how their life might have progressed if they had made different decisions at key moments throughout the intervening years.
This obviously has profound implications for free will and the makeup of our personalities. If my ‘paraself’ kills someone in an alternate universe, does that mean that the same bloodlust lurks just below the surface of my own psyche? Or, conversely, how widely must a timeline diverge from our own before my paraself develops into a person substantially different to me?
The actual plot of' ‘Anxiety’ follows Nat, a recovering drug addict who agrees to take part in an audacious con job by gaining possession of a prism connected to a parallel universe in which a famous movie star’s husband survived a deadly car crash. Said movie star would be willing to pay any price for a prism that lets him see his husband again, even taking into account each device’s limited lifespan. For Nat, the situation presents two main issues: is she willing to essentially extort a grieving widower, and can she be certain that the massive windfall from the scam won’t trigger a relapse?
Another review noted that of all the stories featured in Exhalation, this feels most likely to receive the Arrival treatment and be adapted into a movie, and I have to say that I agree. The plot isn’t wildly complex, but there’s enough to it that it would be easy to spin it out into a two hour movie or maybe a limited-run TV series. The story’s viewpoint is firmly grounded in a single universe’s viewpoint, but you could flip back and forth between them and add a few subplots if you really needed some extra running time.
Speaking of Arrival, what of Story of Your Life? I was slightly disappointed to find that the novella doesn’t really deal with the themes that affected me so strongly in Arrival. Yes, the exploration of communication across a species and psychology divide is there (in fascinating detail - Chiang apparently spent years researching the linguistic principles he would need to do the story justice), but the geopolitical angle that drives the plot of the movie is almost entirely absent.
I suppose it would be trite to say that the story is ‘dry’ in comparison to Arrival, but I can’t think of a more apt way of putting it. Separated from that now-famous Max Richter score and Amy Adams’ emotive voice over, the story’s central conceit lacks a certain emotional punch that the movie delivers effortlessly. What it does better than the movie, however, is get across why the Heptapods - and by extension the main character - remain participants in their own lives despite foreknowledge of everything that’s going to happen to them. Future tense becomes present tense, yes, but the act of speaking it is what causes it to happen at all.
Faced with paralytic terror at the enormity of their own insights, Chiang’s protagonists choose again and again to walk forward into futures that are foretold or circumscribed or vastly unknowable rather than give in to despair. That isn’t quite the same message that I got from Arrival, but it might just be more useful for the strange kind of universe we in the real world have found ourselves in.