Ambiguity: Another Listen

The consciousness of good intentions disdains ambiguity.-Alexander Hamilton (Hamilton 1787)I was looking for a name like The Crickets that meant two things, and from Crickets I got to Beatles.-John Lennon (The Beatles 1964)1. A GiftFigure 1. An ambigram of "Gary" (after Steve Larson)(click to enlarge and rotate)[1.1] I met Steve Larson in the late 1980s at a College Music Society summer Institute for Music Theory Pedagogy in Boulder, Colorado. One day at lunch, he grabbed a napkin and wrote my first name in some elaborate script, then pushed it across the table to me. I glanced at the napkin, and as I did so he rotated the figure so that down was up and left was right. It still read "Gary." What had been a G now served as a Y. The A had become an R. And the last two letters underwent analogous complementary transformations. Unfortunately, I have no idea what became of that napkin over the years, but I recently attempted to produce something like it in my own hand, which you see in Figure 1.[1.2] What Steve had done on the fly was to create an ambigram of my name-a figure containing shapes that may be interpreted in two different ways depending on orientation and context. Note, for example, how you reinterpret parts of the "G" when they're inverted and placed at the end of the graphic. For instance, the decorative upstroke to the G takes on an essential role as part of the fork in the Y.[1.3] Steve had made a personal ambigram just for me. This essay is a small attempt to repay him for this delightful little gift, by making some very personal observations about ambiguity in two perceptual domains-visual and aural.2. Ambigrams and Multistable PerceptionFigure 2. Steve Larson's ambigram of his own name(click to enlarge and flip)Figure 3. A Necker cube(click to enlarge and animate)Figure 4. "Welche Thiere gleichen einander am meisten?" (1892): the first published image of a duck-rabbitFigure 5. Schroeder stairs(click to enlarge and rotate)[2.1] Steve had a habit of making these ambigrams (or at least did so when I was around). He seemed to enjoy the unique challenges posed by each new name, word, or phrase he'd tackle. Figure 2 shows an ambigram he made, which viewers interpret as his name when read as shown, or reversed as in a mirror.(1)[2.2] At the heart of the ambigram concept is ambiguity-the principle that something can be perceived in two or more mutually-exclusive ways. One of the purest forms of ambiguity is multistable perception, in which a single stimulus can be reinterpreted without any change to the stimulus itself (unlike the ambigram, which must be reoriented in some way). Classic examples of multistable perception include the Necker cube (Figure 3) and the duck-rabbit (Figure 4).[2.3] Another such illusion, one more appropriate for our current discussion, is the Schroeder stairs, shown in Figure 5. Most viewers tend to interpret this image as a set of stairs one could climb, moving from the lowest step on the right to the highest one on the left, with wall A towards the front and wall B towards the back. But it's also possible to see this as perhaps the underside of a set of stairs, with wall B towards the front and wall A towards the back. However, if you rotate the image that the bottom is now at the top, you'll find it easy to see wall B towards the apparent front of the image.[2.4] Cognitive psychologists use the term multistable perception because it indicates that our perception of such stimuli can be stable in more than one percept. It's important to note that this is not the same as vagueness. It's not as if we can't quite figure out just what the duck-rabbit is. It's either a duck or a rabbit.(2) Likewise, the shapes in a well-drawn ambigram should leap off the page as specific characters-for instance, a G or a Y-and should not leave us scratching our heads. …