Dove also wrote her thoughts on this one, and hers are better, but here’s mine.
Stories of Your Life and Others is a sci-fi short story collection, semi-punningly named after it’s most famous story “Story of Your Life” – you might know it as the movie Arrival.
Although they are all more-or-less about alternative and impossible scientific systems, the stories can be roughly divided into two classes. The first is the classic Asimov-style stuff, about how a scientist or scientifically-minded person comes to terms with a discovery that turns reality as we know it on its head. The other is more Gaiman-esque, taking a germ of an idea from religion or mythology and building a consistent universe around it.
Funny as this may sound coming from me, I think the latter are a lot better. “Tower of Babylon”, which tries to invent a plausible way to construct a miles-tall tower with Bronze Age technology and ties it into the old Biblical model of the firmament, is a fun way to start the collection, and “Seventy-Two Letters” mashes up various bits of Medieval esoterica (homunculi, golems, Kabbalah and the true name) with Malthusianism, quines and Victorian social worries into a very believable melange. Even Hell is the Absence of God, a rather weird story about a world where angels make random visitations that both cure and maim people as proof of the arbitrariness of God, has interesting things happening to interesting characters.
The science stories have the interesting things, but what they lack is interesting characters. “Understand”, the second story in the collection, is especially weak in this regard – its first-person narrator becomes superintelligent after taking a drug to cure brain damage, and the immediate problem should be obvious. Ted Chiang is a great writer, but he isn’t a godlike hyperintelligence. The protagonist therefore doesn’t really feel smart, just very obnoxious because the narrative makes him always correct (I have a similar problem with Sherlock Holmes). The mathematics of “Division By Zero” is a bit dodgy*, but that’s forgivable – what’s not so forgivable is its representation of a mathematician’s mind, which seems so alien to that of any mathematician I’ve ever met.
The odd story out in the collection is the last one, “Liking What You See: A Documentary”, about an attempt to make it mandatory for all students at a university to have a brain modification that switches off the brain’s perception of beauty, in order to prevent “lookism”. Now, when I read this, I assumed it was a really heavy-handed satire on current events – social media, debates about equality, student politics, Snapchat filters – but it turns out it was actually published in 2000. So I will give Chiang full credit – it’s a very prescient story.
Anyway, I thought the best way to explain my thoughts was to write a little pastiche in the style of Chiang. I hope this makes sense.
My students never know what to say when I explain that mathematics used to be done by humans. They don’t see how it was possible for someone to write a million page proof by hand. Ah, but maths was simpler then. A few lines was enough to derive plenty of interesting theorems, and a book could set out an entirely new field of study. Blame Appel and Haken. They forced us out of this mathematical Eden when they published their proof of the Four Colour Theorem.
Take a map. Any map. With just four crayons, you can fill it in so no two neighbouring areas have the same colour. Simple. But how do you prove it? Appel and Haken came up with a way. They systematically worked out every possible way of arranging shapes into a map – all 1,936 of them – and checked whether each one was “four-colourable”. This would have taken months to do by hand. Luckily for them, this was 1976, and they had access to something incredible – a computer. The computer ran through every combination, verified that they were all four-colourable, and hey presto, the theorem was proved. So computer-aided mathematics was born. Trouble is, can you trust a computer? You can’t double-check the whole thing, so how can you spot mistakes? It got worse when AI arrived. The computer no longer had to follow our logic – it could invent its own mathematical functions and make weird leaps of reasoning that no human ever would. It seems to work, but can you ever be sure?
In my day job, I check these ‘automated proof checkers’ to make sure they work as intended. It’s not the way they’re programmed that’s the problem, it’s how they’re compiled. Every program has to be broken down into a series of really basic binary commands if the computer is to understand it. Like a mother bird chewing up worms for her chicks. Every processor is unique – a tiny, mind-bendingly complex shard of glass and copper – with its own quirks. Sometimes they make tiny mistakes when dividing massive numbers, or interpret a command slightly differently to how you expected. Nothing that matters, until you’re trying to decipher the laws of maths. I make sure that the compiled code – assembly language, we call it – still makes sense and doesn’t contain any detail-dwelling devils.
But by night, I’m trying something else. I’ve got contacts in places it would be safer for you not to know about, and they bring me new nootropics. You know, smart drugs. I’ve been mainlining neuroregenerators as I read through Appel and Haken’s proof. I can actually feel my brain cells growing, never-ending writhing worms in my skull. I see new patterns everywhere. Ideas pop into my head unbidden, so brilliant I know in an instant that they are correct and unimprovable. The universe is flat. Everything is made of tiny magnets. Energy is equivalent to mass times the speed of light cubed. And there’s a 1,937th map that Appel and Haken and their computer never found. One that can’t be coloured with four colours no matter how you try. I’ve done it. I’ve disproved the Four Colour Theorem
It took the checker a tenth of a second to tell me that map 1,937 was map 832 under a rotation and skew. Wrong. It’s clearly totally different, and I’ll prove it as soon as I’m out of hospital. My constantly growing brain needs thousands of calories a day, and in my excitement at disproving the theorem, I missed my meals. The doctors say I’m hypoglycaemic, but I know the problem is really that my blood sugar got too low. They’re not very good, to be honest. They keep telling me that the increased neurons in my mind have caused my orbitofrontal cortex to swell, overinflating my sense of certainty and self-confidence. They’re wrong though, as of course they would be with minds so inferior to mine. I’m certain of it.
* The story concerns a mathematician who discovers a very complicated function that lets her prove 1 = 2 and sinks into a suicidal depression. The root of its inaccuracy is that it treats mathematics like a great monolith that can never be changed, and her proof as showing the whole thing as a sham. Modern mathematics has gone through fatal paradoxes before – Russell’s paradox is the most significant – and the result was that the rules of mathematics were simply rewritten to make it impossible to do the paradoxical thing (today, standard mathematics uses a system called Zermelo-Fraenkel set theory with the axiom of choice – a few mathematicians are experimenting with other systems). Most likely, Renee’s discovery would simply see a new axiom added that stopped her complicated function working. It’s also possible that her theory is something more along the lines of the Banach-Tarski paradox, which does effectively prove that 1 = 2 but which involves objects that can’t exist in the physical world, in which case it wouldn’t have any actual consequences wouldn’t be the mind-shattering calamity it appears in the story. Anyway, like getting the maths wrong is forgivable – even necessary for the story – but getting the psychology of mathematicians just wrecks it.