On Stephenson's Anathem

The Teglon beckons

Note: this article will contain spoilers for Neal Stephenson's Anathem. If you don't want to see said spoilers, it's best to leave this article unread until you've read this book. It's still a wonderful book regardless of whether you know the things I'm going to discuss here, though.

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Recently, I read Anathem, by the wonderful Neal Stephenson. I must admit to this being my first book of Stephenson's, which I now reckon to be a grave miscalculation.

This book was made for me.

Within the first hundred pages or so, the term "finite group theorics" is mentioned. I am, quite literally, finishing up my series Introduction to Group Theory; as I write this, ITGT9 is nearly finished and will be sent off to my Very Prestigious Reviewers (hi mom). If I ever do a deeper dive into group theory, going beyond the basics, I'll call the series Finite Group Theorics in honor of this book. That's how much I loved it. The vocabulary takes awhile to adjust to – monasteries are called "maths", the monks are called "avout", and a million other new words and old words used anew. Once you cross the barrier of no longer having to flip back and forth between the glossary, though, there's no going back. Rather than giving you an extensive, 5000-word breakdown of everything I loved, though, here's some highlights for why you need to read this book.

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The timescales

Those who've already read this book may be thinking, "David, what do you mean the timescales? The book takes place within a few months." Well, what really stuck out to me was how the entire setting was shaped by projects that span many human lifetimes. The opening of the books describes the massive, central clocktower in the monastery; it was constructed across hundreds, if not thousands, of years.

Photo by Evelin Tomić on Unsplash; what I imagine the clock towers in Anathem could look like.

In particular, these clocks were inspired by the Long Now project; they do some neat stuff, but their coolest project is building a 10,000-year clock in the west Texan desert. The clock is designed to keep the time for ten millennia (although the dials will not update unless visitors come to wind that part of the clock) and potentially longer. The point of the foundation is to get people to think in terms of a long now – not on the timescale of a few seconds, minutes, or hours, but to think of "now" as the next couple centuries; to see ourselves as part of something much bigger. Likewise, the characters of Anathem are continually thinking about future generations and referencing major points of their history; they all see themselves as playing but a small role in a grandiose story. This leads into my second point:

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The (not-so) subtle critique of the industrial revolution

There's this one page, around halfway through the book, that was strikingly profound when I read it:

In particular, this analysis of industrialization hit home:

Thousands of years ago, the work that people did had been broken down into jobs that were the same every day, in organizations where people were interchangeable parts. All of the story had been bled out of their lives. That was how it had to be; it was how you got a productive economy. But it would be easy to see a will at work behind this: not exactly an evil will, but a selfish will. The people who'd made the system thus were jealous, not of money and not of power but of story...The Powers That Be would not suffer others to be in stories of their own unless they were fake stories that had been made up to motivate them.

We, of course, live in a similar world. People are cogs. Gears in a machine which produces things that you don't need, for people you don't know, in ways you don't understand. There are, of course, some important benefits to this; no single person could create the computer I am typing these words on, nor could we have modern medicine if we insisted that everything be meticulously artisan-crafted on small scales. Nonetheless, people are cogs.

This is, overall, not good for humanity. Humans need story. How do I know? Look at what we fill our free time doing: listening to and making music, writing and reading fiction, going to movies and plays, playing sports...there are some hobbies which may not involve story-telling, but I would dare say most do. Even games like chess, which are not obviously story-driven, are discussed in story-telling language. "I went on a vicious attack on the kingside", or "it was a quiet game, but the tension kept building and building." Tense, vicious attack, quiet? None of these things literally apply to the game of chess. Our brains are built for story; we describe our experiences in that language. I certainly don’t want to go back to not having now-common medicine, but the crisis of meaning in our society is painful for all involved, and needs an antidote.

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Let's talk about planing

There's many little turns of phrase that Stephenson comes up with that are absolutely wonderful, but my favorite amongst them all has to be planing. The definition, as given in Anathem's glossary, is

• Plane: Used as a verb, utterly to destroy an opponent's position in the course of a Dialog.

This is such a vivid image for me; I think of either someone taking a wood plane to a tree trunk until it's paper-thin, or I see someone's arguments as a structure built on a perfectly flat, mathematical 2-D plane. To plane someone, then, is to collapse their arguments back into the plane. Completely smashed, smashed into the ground. I love this so much. It's particularly enjoyable watching

Bentham's Bulldog

plane

Amos Wollen

, and vice versa, when they get into it with each other...very cute, very philosophy twink.¹

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Platonic forms, anyone?

The nerdiest part of the book, by far, is how a major plot point in the story is people arguing in long conversations about what is essentially the platonic realm of forms. Are numbers real? Do they exert some kind of influence over our worlds (and possible other worlds?) On the two sides of this debate are the Procians, who believe that there is no such realm of forms – that is, that numbers and other such things don't exist – and the Halikaarnians, who believe that they do exist. In our world, these correspond to nominalists² and realists³ respectively. Nominalism vs. Realism is a massive philosophical debate that's been going for 2500+ years now. Even just the objections to the belief that the world exists independently of our minds – metaphysical realism, one of many possible realisms – have an SEP article that is in the tens of thousands of words. Nerds!

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Praxis

In Anathem, the word for technology is praxis. The relation of the avout – the monks – to praxis plays a sort of fundamental background role in the book; there are rules about what technology the monks can and can't use, the main character is annoyed by how distracting the equivalent of phones seem to be, things like this. In particular, anything like a computer as we think of it is completely off-limits for the avout, and must instead be handled by a separate underclass of people.

One of the most striking things here was the discussion around how, essentially, people started making bots to create false information, and a huge race was spurred between people trying to filter truth from nonsense, and people trying to create convincing nonsense. Given the way Chat-GPT and ai (intentionally lowercase) is influencing search engine results, this felt quite prescient for a 2008 novel. I don't want to say too much more about it, because it plays a meaningful role in the book.

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The Teglon

The Teglon is a puzzle (never fully described) that requires you to tile a regular decagon with certain kinds of tiles, satisfying certain conditions. While I wish Stephenson had fully described the rules of the Teglon so that I could attempt it myself, it is the inclusion of this sort of detail that makes the world come alive. When you have a puzzle that is a fundamental piece of the culture...that is going to draw a certain kind of mind in immediately. (That kind of mind is me.)

This was clearly influenced by Penrose tilings, a kind of aperiodic tiling.⁴ An aperiodic tiling of the plane is one where you can continue tiling a surface for as long as you want, but it will never repeat – it is not periodic. A discovery made two years ago by a hobbyist⁵ mathematician showed that in fact, we can find aperiodic tilings made out of only a single kind of tile.

The “hat” aperiodic monotile, discovered in 2022 by David Smith.

Before this discovery, mathematicians were unsure if such a tile could even exist at all; the solution was found by an amateur, not a professor. Can you see why I love the Teglon?

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Summary

There are a bunch of other things that I could talk about, but I want you to actually go and read the book yourself if you haven't already. So, I'll hold off on giving away anything else. If you've read the book, please leave a comment if there's something you loved that I didn't discuss! I really enjoy comparing notes with other people on books we've read.

1. If you don’t know what a twink is, no I will not explain it to you. Especially if you are my parents.

2. For an excellent explainer of nominalism in the context of mathematics (which is largely, though not exclusively, what Anathem is considering), see this article on the Stanford Encyclopedia of Philosophy.

3. Similarly, for an explainer of platonism/realism in the context of math, see this article, again on the SEP.

4. *switches into math major mode*

5. Yes, there are hobbyist mathematicians. The one who discovered the hat monotile, David Smith, is a retired print technician, not a PhD. This is part of why I love math; anyone with a writing implement and a flat surface can do it and make meaningful discoveries if they have a lot of drive and a little luck. This is in contrast with physics, where we have basically reached the point where all new discoveries require millions in lab equipment.