Crinkly and Complex (Book Three, Part 72: Numerocracy, Fractals)

Previously in The Last War in Albion: The first issue of Alan Moore and Bill Sienkiewicz’s Big Numbers was a lush and splendid object that positioned itself as a formal heir to Watchmen even as it rejected superheroes in favor of shopping malls and math.

Eventually, the snowflake’s edge becomes so crinkly and complex that its length, theoretically, is infinite. Its area, however, never exceeds the initial circle. Likewise, each new book provides fresh details, finer crenelations of the subject’s edge. Its area, however, can’t extend past the initial circle: Autumn, 1888. Whitechapel. – Alan Moore, From Hell

As with Watchmen, Moore uses a detached, omniscient perspective. Indeed, he takes it even further than he did in Watchmen, where he could use Rorschach as a pseudo-narrator. Big Numbers has no equivalent character. The closest it comes to narration is a montage at the end of the first issue in which one of the character’s poems is contrasted with a series of single panels reviewing the various characters that the book has introduced. For the most part, however, Big Numbers is told with an impassive objectivity. It takes flights into individual subjectivities, as with the dream sequence in the opening sequence or a later sequence in which Mr. World, a psychiatric patient released into the “care of the community,” fantasizes about the violent murder of a fellow bus passenger, but even these subjectivities are treated with a level of objectivity, the internal landscapes of the characters being treated as just another thing to look at.

Part of this sense of distance is simply the sheer number of characters involved. Moore’s outline for the series features thirty-one separate characters along with one group of characters, three characters from a story within a story, one ghost, and a set of people in a model railway set that will be treated as characters. In the forty pages of Big Numbers #1, twenty of these are introduced overtly, along with the ghost, and another is positioned in the background of a panel. Even though the action is centered almost entirely on Hampton, it gives the impression of a startlingly broad portrait of the town—one that, by the time the bulk of the remaining characters are introduced in the second issue, spans from the town’s rich and powerful to its underclass, with policemen, construction workers, students, sex workers, shopkeepers, and more all represented within the sweep of its worldview. And by exploring the connections among these people, as works of this sort of sprawling social realist genre inevitably do, Big Numbers displays the same sort of meticulous clockwork precision as its predecessor. The overwhelming sense of the first issue is one of inevitability; that a town in Thatcher’s Britain can only face the arrival of a massive shopping mall in one way. Moore even discussed as much, noting that “What I wanted to do was to show the fragility of human community, human relationships, and then to put this shadow of a large and inhuman shopping mall, a monolith of purely economic concerns, that would cast its shadow over that community. The market that I’m dealing in here is a market where generally the end of the book is Galactus’ spaceship touching down on Earth and he’s going to destroy everything unless the Avengers can stop him. I wanted to do something that was as powerful and as dynamic as that but which wasn’t as silly. With that first issue I wanted to create that sense of the fragility of our human relationships, and then have this ominous bass chord sound in the background which threatened all that.”

But Watchmen ultimately was not about the reasons for its own intricacy, which meant that in the end the impression it gave was that its world was the way it was because it was constructed and authored. It was not the overt metafiction of Animal Man, true, but nevertheless, at the end of the day the complexity of Watchmen is visibly something designed, most obviously in the moment late in the story where Adrian mentions dreaming of the Black Freighter, a moment that draws sharp attention to the artifice of its world. Big Numbers was no less obviously constructed, but it was much more overtly concerned with why its intricacies existed. This is only gradually made clear over the existant issues of the comic. Within the first two issues, it becomes clearest in a scene around the character Sammy Portus, described as “Skateboard Kid” in Moore’s outline. The scene begins with Sammy in class, listening to his history teacher (the husband of Christine’s school friend, who Christine is seen phoning in the previous scene) talk about the history of Hamptonshire. The lesson begins with a general overview of a place that admittedly would not have been especially familiar to the readers—a map of the town, specifically the area known as the Boroughs, and a brief overview of historical highlights: the hatching of the Gunpowder Plot, the Battle of Naseby, the institutionalizing of John Clare, and Northampton’s success in the shoe industry. And then, as the class lets out, the teacher offers a monologue about how “It’s important to have a sense of where we’re living… of when we’re living… a sense of history’s patterns… of time’s passing. I mean, that’s the important thing, isn’t it? To understand our context; the community surrounding us? If we don’t… I say, if we don’t pay any attention to the place where we are, well… then we might as well not be here.” The scene then follows Sammy home, where he talks briefly with his father about the book he’s reading, Rudy Rucker’s Mind Tools, which he summarizes by saying that “Apparently, life is a fractal in Hilbert Space.” The implications of these two statements are in no way clear in the first issue, but they nevertheless form the comic’s intended thesis.

Other elements of the theme were more oblique still. Starting from the first panel’s close-up of a train table, and continuing through train maps, bus schedules, the phone book, and a nutritional information panel on a box of cereal, the comic takes seemingly every available opportunity to zoom in on a bunch of numbers. Moore explained this as “a way of suggesting that we live in a field of numbers, without noticing them. Numbers everywhere,” but the full implications of this were things he intended to leave for later issues. Similarly opaque, at least when one only has two or three examples of them, were the issues’ title pages, which were full splash pages, drawn full bleed (as opposed to the handful of other splashes, which retain the outer white border, constraining the splash to the size of twelve panels), of various and simple scenes, captioned with a simple header—the chapter number, written out. In the first issue, this was the exploding window of the train. In the second, it was a simple close-up of a cup of coffee. The third would have been a crumpled up piece of paper. Asked about these and the decision to devote a structure-breaking splash page to them when they had no obvious plot relevance to justify that focus, Moore explained that the plot irrelevance was in many ways the point, saying that “I want [readers] to look at the milk swirling in the tea, and see it as what it is—a beautiful pattern of milk swirling in tea. I wanted to use patterns in a way that would enhance the story in different ways. They would add to the story, but not in any obvious way. They would just be expressions of an underlying pattern that we will be revealing as the story progresses. When you get to the end of the story you’ll be able to see what all of those patterns were referring to, but probably not until then.”

Pushed more on this point, Moore clarified that “What I want to show by the end of the book is that we live in a sea of numbers in a much more real and literal sense than just the ones upon our timetable. There are different sorts of order in mathematics that have a very great effect upon our lives without us being aware of them. I wanted to make people aware of the basic human maths surrounding us – big sums of money, big masses of population. Numbers are a key image in the book, largely because of the fractal math stuff that starts to slowly develop throughout the course of the novel. In these early stages I just want to suggest to people the way that we use numbers to order our lives, the way that we’re surrounded by numbers and schedules and timetables and things like that all the time, and, as the book progresses, that there’s a different way of seeing numbers.”

There are several questions one could ask about this “fractal math stuff.” The first and most obvious is “what are fractals.” This is a fairly straightforward question, at least as complex mathematical concepts go. A fractal is a shape or pattern with a level of infinite detail. One of the simplest examples—one Moore ultimately would reference in the epilogue to From Hell—is the Koch snowflake. This figure can be constructed simply. First, one draws an equilateral triangle. Then one divides each side into thirds, and draws another equilateral triangle extending out of the middle third, creating a six-pointed star. Then, on each of the twelve edges of the star, one repeats the process, dividing it into thirds and drawing a triangle coming off of the middle third. This process extends infinitely. Around the fourth iteration, one gets a shape that is distinctly snowflake-like. More to the point, if one iterates the process infinitely one gets a structure with an infinite level of detail—zoom in on a portion of a Koch snowflake and you will see a recursive pattern, the same  three-pronged toothy pattern appearing again and again ad infinitum. This striking visual effect is accompanied by a seeming paradox: as one iterates the process, the area of the shape will gradually approach 8/5 of the area of the original triangle, but never exceed that amount. But the length of the perimeter will grow infinitely large.

This latter topic was explored by the mathematician Benoît Mandelbrot in his 1967 paper “How Long is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension,” in which he examined the notion of the coastline paradox, which observed that because coastlines are profoundly irregular shapes, there is no real way to measure the length of a coastline—the length will increase depending on how precise a measurement you use. To grapple with this, Mandelbrot coined the notion of “fractional dimensions,” suggesting that things such as the Koch snowflake are neither one-dimensional nor two-dimensional, but an in between point that can be quantified. (The Koch snowflake, for instance, is roughly 1.262-dimensional.) Mandelbrot later refined the term to the far catchier “fractal.”

In 1978, the mathematicians Robert W. Brooks and Peter Matelski defined a fractal based on iteratively taking the square of a number and adding a given complex number to it, then repeating for the new number. In 1980, Mandelbrot created a visualization of the fractal and wrote a paper about it. A few years later Adrien Douady and John H. Hubbard further explored the fractal, which they named the Mandelbrot set in honor of Mandelbrot’s pioneering work in the field. This resulted in the August 1985 issue of Scientific American that featured a cover story by K. Dewdney on the Mandelbrot set. With its deliciously portentous opening, describing how “The Mandelbrot set broods in silent complexity at the center of a vast two-dimensional sheet of numbers called the complex plane,” the piece rocketed the Mandelbrot set, and fractals in general, into the popular consciousness—Morrison used it in their sixth issue of Animal Man in October 1988. If one is being honest, the fad was driven in no small part by the fact that the Mandelbrot set and other fractals made phenomenal dorm room art for a slightly more science-minded flavor of stoner; they were tailor made to appeal to the sorts of people who had very strong opinions about Pink Floyd albums. On a level of sheer practicality, the particular way in which fractal detail manifested bore a striking resemblance to the visuals experienced while taking LSD or psilocybin. These were a fantastic new vista in psychedelic art, and one that tapped directly into the rising prominence of the personal computer, and so they took off as a cool art fad. Which sets up the second, far more difficult question, namely “what did Alan Moore think fractals were?” [continued]