Blivet or not

In the June 1964 issue of Analog, which first went on sale on May 7, readers were treated to the drawing reproduced above, along with a note from editor John W. Campbell:

This outrageous piece of draftsmanship evidently escaped from the Finagle & Diddle Engineering works. If the contributor of this item—sent anonymously for some reason—will identify himself, we will happily pay $10 (ten bucks) or a two-year subscription to Analog.

A few months later, in the October issue, Campbell provided an update, although the source of the image proved frustratingly elusive:

It’s impossible to publish even a small fraction of the letters that outrageous piece of draftsmanship evoked. There were well over one hundred fifty letters on that one item alone—and while we have long been aware of the unusually high level of intelligence of Analog’s readership, the high level of honesty was a new and pleasant discovery. Not one of all those letters claimed to be the original contributor, or demanded the ten dollars!

Campbell added that readers had directed his attention to other instances of the illusion, which he said was sometimes called a “blivit” [sic], in recent issues of such publications as Road & Track, QST, The SAE Journal, “various and sundry house organs,” and textbooks on topology and psychology. And in December, he printed a letter from Edward G. Robles, Jr. of Sacramento, California, who claimed that the image had originated at the Jet Propulsion Laboratory in Pasadena.

To the best of my knowledge, the earliest verified appearance in print of the illusion most commonly known as the “blivet”—although there are anecdotal reports, as we’ll see shortly, from decades earlier—was in the March 23, 1964 issue of Aviation Week and Space Technology, in an advertisement for California Technical Industries, a company based in Belmont. The ad, a detail of which is pictured below, caught the eye of Donald Schuster, a professor of psychology at Iowa State University, who wrote in a short item in the American Journal of Psychology:

In my opinion, it is a matter of a new type of ambiguous figure. Unlike other ambiguous drawings and geometric figures…it is the shift in the optical focal point which plays a role in perception and interpretation here. If the observer focuses on the left-hand side of the figure at reading distance, he sees three legs, and the right-hand side remains blurred and fuzzy; if he focuses on the right-hand side, he sees a U-shaped object, like a chain joint/horizontal brace. Only if he looks at the middle or slowly allows his view to pass over the figure does he come to realize that he is looking at an “impossible object.”

The following year, it was featured on the March 1965 cover of Mad, which referred to it as “The Mad Poiuyt.” It inspired a flood of replies pointing out that it had previously appeared in such publications as Engineering Digest, The Airman, The Red Rag, The Society of Automotive Engineers Journal, Popular Mechanics, and the letters column of the July 1964 issue of Popular Science, from a reader who said that he first saw it in The Circulator, published by the Honeywell Regulator Company in Minneapolis. (I owe most of this information to David Singmaster’s Sources in Recreational Mathematics, an archived version of which can be found here.) It also made one last appearance in Analog, in February 1969, in which Campbell discussed the phenomenon of endlessly ascending tones, illustrated by a picture of a blivet in the form of a tuning fork.

The invention of the blivet has been convincingly attributed to the Swedish graphic artist Oscar Reutersvärd, the originator of many other impossible figures, who asserted in a letter quoted in Bruno Ernst’s The Eye Beguiled that he had drawn “figures of the devil’s fork type” in Stockholm in the thirties. For its explosion in popularity in the sixties, however, we can look a little closer to home. In the October issue of Analog that I mentioned above, Campbell printed a letter from James E. Tunnell of Industrial Camera, based in Oakland, California, which featured a blivet on its company letterhead. Tunnell wrote:

While a student in grade school some twenty years ago, I saw for the very first time, in my old red mathematics book, a drawing much as that shown in the upper-left hand corner of this letter, and very much like that in your publication.

In 1952, when we started business, this design was undertaken to serve as a logo. We have used it on our letterhead, on the back of business cards…and on the automobiles we use as you can see on close inspection of the attached photograph.

In the field of higher mathematics, this model is known as a Two-Slot, Mark 4, Blivit—origin unknown—and during the past ten years has gotten into the hands of many organizations through our business dealings with them.

For reasons that I’ll explain in a moment, the italics are mine. And I’ll just note for now that it’s only half an hour by car from Oakland to Belmont, where California Technical Industries was based.

When you put all this information together, an intriguing pattern emerges. The blivet can plausibly be said to have first been drawn in the thirties by Reutersvärd. From there, it migrated into at least one textbook, until it ended up as the logo of Industrial Camera. Various individuals and groups were thereby exposed to it over the next decade until, suddenly, it seemed to be everywhere at once—it showed up in Analog just six weeks after its appearance in Aviation Week, which seems too soon for one instance to have directly inspired the other. In other words, it went viral. And the evidence, while limited, implies that it owed its overnight emergence to many of the criteria that have been proposed for other kinds of social epidemics. It was a “sticky” image that couldn’t be forgotten after the viewer had seen it. After a long gestational period, it took root in an existing community of scientists and engineers with a network of small publications and newsletters in which it could be easily shared. There was also a geographical factor involved, since many of these organizations were based in the Bay Area. (Social epidemics have a curious way of starting in my home state. Malcolm Gladwell’s classic case study in The Tipping Point is Rebecca Wells’s novel Divine Secrets of the Ya-Ya Sisterhood, which first took hold in independent bookstores in Northern California, and I’ve elsewhere pointed to dianetics as an equally quintessential example.) The tipping point here may well have been its appearance in Analog, which was read both by a core audience of professionals and by a larger popular audience, and from there, it moved by a series of logical gradations to Mad, which, in the sixties, was an important gateway in which nerd culture passed invisibly into mass culture. It began as an inside joke, or even a meme, and before long, it became so ubiquitous that it seemed like it had always been there. If you’re looking for instances of virality, the blivet is a nice one, since it’s such a distinctive image that it doesn’t seem likely to have spread except by contagion. I don’t have the time to dig into it properly, but I offer it up to any academic who wants to trace its origins and dissemination more systematically. After all, it didn’t have just one tipping point, but two. Or maybe three. I guess it depends on how you look at it.

“This case has been a disaster…”

Note: This post is the twelfth installment in my author’s commentary for Eternal Empire, covering Chapter 13. You can read the previous installments here.

Many moviegoers probably maintain a mental list of scenes they’d like to see, as Mad Magazine did for so many years. Here’s one of mine. The maverick cop, doggedly pursuing a serial killer on his own time, is called onto the carpet by the police chief—or, even better, summoned before an administrative hearing. He calmly lays out the case against his primary suspect, ignoring the skeptical looks pointed in his direction. The chief glances at the stony faces to either side, turns back to the cop, and says:

You know what? That’s a very compelling case you’ve got there. You’ve convinced me. Tell us what you need. All the resources of the department are at your disposal.

Of course, that isn’t how it usually happens, but it would be great if it did. Not because it “subverts” a trope or convention, which isn’t always a valid reason in itself, but because it holds more dramatic potential. If it’s interesting to see a lone cop without any backup go up against the villain and fail, it would be all the more riveting to see the antagonist outsmart and outmaneuver the full weight of the police force. As I see it, if it’s a choice between reducing the hero or elevating the villain to keep the scales evenly matched, there’s no doubt as to which alternative would yield better stories.

That said, there’s a reason why even the best cop movies, from L.A. Confidential to The Departed, so often include some variation on the line: “Turn in your badge. You’re off the case.” In a way, it simply restores the protagonist to his proper place. Movies and television like to focus on cops because they’re the last members of our society who can plausibly confront violence directly: the rest of us are more inclined, without a strong reason to the contrary, to call the police. There’s a sense that the buck stops there, at least when it comes to the kinds of active heroes that we like to see. By throwing the officer off the force, we get the best of both worlds: he’s deprived of the system that supports him, while remaining the same driven guy as before—fully motivated and qualified, as most of us aren’t, to take justice into his own hands. His badge and gun get him to exactly the point in the story where he needs to be, after which they can be safely discarded. It doesn’t hurt that the scene also establishes our hero as a man who doesn’t play by the rules, which is rarely a bad thing, and sets up a conflict with a clueless authority figure. Like most good clichés, it survives because it does two or three useful things at once, and writers haven’t figured out anything better.

As a result, even when we recognize the trope, we’re likely to respond to it as Homer Simpson does while shouting at the television set: “It means he gets results, you stupid chief!” (To which Lisa wearily responds: “Dad, sit down.”) But like any convention, it can grate if it presses our buttons too insistently, especially if it’s written by someone who should know better. One of my few complaints about the Fargo miniseries revolves around the character of Bill Oswalt, played by Bob Odenkirk, who exists largely to foil the resourceful Molly as she gets closer to solving the case. Bill isn’t a bad guy, and the show takes pains to explain the reasons for his skepticism: he went to high school with Lester, the prime suspect, and doesn’t want to live in a world in which such evil exists. But their scenes together quickly start to feel monotonous: they occur like clockwork, once every episode, and instead of building to something, they’re nothing but theme and variations. They retard the story, rather than advancing it, and it’s hard to avoid the impression that they exist solely to keep Molly from moving too quickly. I can understand the rationale here: Molly is too smart to be misled by Lester for long, and once she arrests him, the story is over. But I can’t help feeling that it could have been handled a tad more subtly.

Still, I probably shouldn’t talk, since I include much the same scene in Chapter 13 of Eternal Empire. Here, it’s an administrative hearing at the Serious Organised Crime Agency, in which Wolfe is called to account in much the same fashion as countless heroines before her. (In particular, the scene reads a lot like a similar one in the novel Hannibal, which isn’t entirely an accident.) In my defense, I can say that the sequence is designed to move the story along, rather than slowing it down: I had to convey some necessary exposition about the dead body Wolfe discovers in her previous scene, as well as to remind the reader of a few important events from the last novel, and delivering it in a setting with some inherent conflict is more interesting than a dry summation of the facts. Leaving Wolfe at a low point here also sets up the next big moment, when she has too much to drink and spills a crucial secret to the last person she should have told. And I don’t linger on it more than necessary. If there’s any conclusion to draw, it’s that a hoary scene like this—like most of the familiar tools in a writer’s bag of tricks—can better justify its existence if it’s there to serve a larger purpose, rather than just to rile up the reader. And if it riles up the reader just a little bit, well, I’ll take such moments where I can…

Tracing the lessons of tracing paper

When you’re growing up, your life is filled with all kinds of paraphernalia that slowly disappear as you edge into adolescence and adulthood. All children are natural artists, both by instinct and because their inclinations are encouraged at least through the end of grade school, so a kid’s bedroom often looks like a Williamsburg studio: it’s cluttered with sketchbooks, colored pencils, crayons, watercolors, easels, construction paper, scissors, stickers, and the odds and ends necessary for collage or sculpture or origami. With schoolchildren, it’s taken for granted; for an adult, a house filled with these tools is the mark of an exceptional—or eccentric—personality, which is a little sad in itself. Half of creativity, I’m convinced, lies in remaining true to the values you had when you were eight years old, and it helps to have the right equipment at hand. (Even adults who don’t primarily work in creative fields seem to be getting the message: a lot of what Emily Matchar calls the new domesticity, with its emphasis on crafts like knitting and crochet, seems less about trying to replicate some vanished ideal of home economics than about recreating the mood of art class.)

And just as the materials an artist uses subtly shape the work at hand, the furnishings of a preschool art table carry messages of their own. Take the humble tracing pad. I haven’t seen or used tracing paper in a long time, and although I imagine it’s still used frequently in architecture and the fine arts, it’s another artifact that seemed to be everywhere I looked when I was younger, only to rapidly disappear once I’d left the playroom behind. Even in the professions that once might have used it extensively, its place has largely been taken by more mechanical forms of reproduction, assuming that the process hasn’t migrated exclusively online. Yet it’s still a fascinating medium. Anyone who has sketched on tracing paper—which is made of loosely spaced cellulose fibers, allowing the light to pass through—knows how appealing that surface can be: the page is finely toothed, so it’s perfect for taking a pencil line, and its translucency makes the image seem to float slightly above the rest of the pad. A sketch done on tracing paper simply looks a little more interesting than the same drawing on an opaque surface, and even if you’re just trying to replicate the picture underneath, you soon find that the version you’ve created takes on unexpected qualities of its own.

It’s no accident that many artists use tracing paper as a medium in its own right, both for its textural qualities and for its ability to accommodate easy revisions. The great caricaturist Gerry Gersten, for instance, whose work I remember vividly from Mad Magazine, worked exclusively on tissue paper, as I once saw described in an issue of Step-by-Step Graphics:

Gersten works in layers of tissue paper until he reaches a point where he is satisfied with the relationships between characteristics—eyes to nose, nose to mouth and so on. He continually refines his sketch by placing a new piece of tissue paper directly on top of the previous one.

For a caricaturist, finding the right proportions between elements is essential, perhaps even more so than for a conventional portraitist, and tracing paper provides a convenient means for revision and refinement to take place almost in real time. Again, the physical properties of the paper itself inform the work in surprising ways: its translucency, which reveals a ghostly version of the original against the crisper black lines of the latest variation, allows different drafts to coexist without overwhelming one another, and the work in progress takes on a kind of layered beauty.

Which is why I hope tracing paper remains part of the standard toolbox of artists—and children—of all kinds, even if its place threatens to be taken by other forms of technology. It’s easy to make a scan or a photocopy, or to work in multiple layers in a painting program, but as with most transitions from analog to digital solutions, there’s a loss of tactile serendipity along the way. When you trace a drawing by hand, whether it’s your own or someone else’s, the result isn’t just a copy, but something that subtly complements the original. It has something of the same appeal as doing revisions in red pen on a paper copy of a story: both versions are still there, vibrating against each other, in a way that seems lacking when you’re doing corrections on the screen—and tracking your changes in Word isn’t nearly the same. Being able to create something new while keeping the old constantly in view is a skill that most writers learn to value: I’m reminded a little of how the novelist Kenzaburō Ōe describes his own approach to writing, in which he repeatedly revisits the same subject matter from different angles, a process he calls “repetition with a difference.” That’s what tracing paper taught all of us, and I’m starting to think that I should keep a pad of it handy.