Remembering Roger Shepard

Remembering Roger Shepard

August 12, 2022

Roger Shepard, a pioneering cognitive scientist, passed away on May 30, 2022. He is perhaps best known for his classic experiments on mental rotation, but also made foundational contributions across a broad range of topics including visual and auditory perception, mental representation, music cognition, learning, categorization and generalization. His work is characterized by a playful curiosity, and is consistently both rigorous and elegant.

More detailed accounts of his life and work are available in his obituary and in citations for his National Medal of Science and Rumelhart Prize. Below, four students, friends and colleagues share memories of Roger and thoughts about his work.


Daniel Levitin

I first met Roger Shepard in 1977 when I entered Stanford as an undergraduate transfer student from MIT, where I had taken cognitive psychology with Susan Carey. Stanford required students to choose a faculty advisor. Susan had spoken so admiringly of Roger, and I was fascinated by his mental rotation experiments. I went to his office my first day on campus and he invited me to sit down. We began a conversation that day that lasted for 45 years—often interrupted by time and place, but never broken in personal connection and mutual curiosity about the perceptual world.

Roger was frustrated by the disorder in the broad field of psychology—everyone working on disparate topics with no unifying theory that would tie together observations in social psychology, memory, attention, visual imagery, concepts & categories, decision making…the equivalent of Newton’s Law of Motions, or Boyle’s Laws of Thermodynamics, but for the mind.

We marveled at Mendeleev’s Periodic Table: arrange the known chemical elements in a table, with one feature manifesting in rows and the other in columns, and holes should appear in the table where undiscovered elements should exist.

One of our first research projects was to arrange all of the jokes in the world in some sort of table where rows would represent one dimension, columns another. Of course we knew that jokes were multi-dimensional and could not be squeezed into a 2 dimensional table. No problem—Roger had invented the data reduction techniques for representing and visualizing higher dimensional manifolds in 2 or 3 dimensions—multi-dimensional scaling. And his work on mental rotation showed that it was possible to visualize and manipulate 3 dimensional objects on the 2D plane of the mind’s inner eye. In our early work we identified six joke dimensions.

The goal of all this? If we could successfully complete a periodic table of jokes, we would find holes in it for jokes that had not yet been written. We spent hours telling each other jokes and classifying them. Jokes that ended in puns (Roger’s favorite: time flies like an arrow; fruit flies like a banana). Jokes that were funny because they were bawdy, or dealt with social taboos. Jokes that involved misunderstandings. Knock knock jokes. 

Roger had an insatiable curiosity to tease apart every nuance and facet of any problem that he came across. Can people perform mental rotation of impossible objects like Klein bottles and Escher staircases? (Does a 4th spatial dimension require more rotation time than the first 3?) Or apparent motion: flashing two lights in two different spatial locations in a dark room, milliseconds apart, causes the illusion that one of them moved. Does the color of the light matter? It does: flash a red light followed by a yellow light and viewers see a red line that passes through orange to become yellow. Can you take people with absolute pitch, who use an internal template to label musical tones, and rewrite that template by playing them distorted scales? Yes, you can.

Roger loved Groucho Marx, Bach, space exploration, and building—yes, actually building out of wood, paint, motors and ball-bearings—classroom demonstrations of visual illusions. An early computer user from his Bell Labs days in the 50s, he had equal enthusiasm for programming musical illusions that demonstrated principles of perception. But how to unify all of these various interests in findings? Could he discover a set of universal psychological laws? This is what kept him going.

Roger was the first professor who took an interest in my writing, not because it was good, but because it was terrible, and he wanted to show me how to fix it. It took thirty years.

My wife and I last visited Roger and his wife Barbaranne in Tucson in 2019 before the pandemic restrictions. He was working on a book about induction, another about the illusion of free will. And still searching for universal psychological laws when we last spoke in 2021.

Roger could be very funny and was also incredibly, unbelievably humble. At the banquet celebrating his Presidential Medal of Science award, he truly felt he had not done enough to merit it. I’m glad to be able to call him not just the supervisor of my undergraduate honors thesis, and my post-doctoral work, but my friend.


Jennifer Freyd

Roger Shepard was my dissertation advisor at Stanford. I chose Stanford for Roger, but in truth I did not know exactly why. I just knew his work had a compelling beauty. Also, it didn’t hurt that Stanford was in sunny California, so westward I went at the age of 21.

During our first months together, I learned that if Roger wanted to talk to me, he would pace in front of my office door. Although initially shy, he was always welcoming to me if I showed up at his office. I would come bouncing in with some new idea and we would talk for a long time. He would gently tell me all the reasons he thought I might be wrong, why the experiment I was proposing was unlikely to work, and then he’d invariably tell me: “You should run the experiment. I don’t think it will work,” he would remind me, “but you should try it.”

Sometimes my experiments would work, and he would follow his surprise by expressing wonderment and even delight that he was wrong. If there was any one thing that I most loved about Roger, it was that wonderment he brought to his pursuits – from his mentoring to his science to his art. He relished the possibilities and did not ever get stuck on dogma.

Although Roger was shy with me at first, as the years progressed, we developed a lasting friendship. One of my most proud moments was in 1995 when Roger Shepard invited me and three of his other former students to be among the few people who could attend his ceremony in the White House as he received the National Medal of Science.

Roger remains my most important intellectual mentor. He didn’t remember to teach me the practicalities of academia. I didn’t even know about grant proposals until I started my first academic job – money was just available as far as I knew as a grad student. But Roger taught me things that were so much more important – be creative, take intellectual risks, always be intellectually honest. Roger was a lovable, gentle and brilliant person who gave me his counsel and his support. He was my role model and my inspiration. With his deep contributions and his gentleness, he proved the vast potential of human beings.

See Jennifer talk about Roger here.


Keith Holyoak

The deepest cases of creativity, according to the philosopher Margaret Boden, involve the generation of new ideas that might seem impossible to think of. Roger Shepard, a mind with exceptional creative power, was a master of the impossible. Some of his creations were literally impossible—illusions arising out of carefully crafted ambiguity. He led us to see with our own eyes two identical tabletops with radically different shapes, as well as an elephant with perhaps four legs, perhaps none; he let us listen to a series of tones endlessly rising in pitch while forever returning to their starting point. This same playful mind could also construct meticulous experiments designed to test precise quantitative theories about the nature of mental representation, or a law governing inductive inference by humans (and pigeons) on planet earth—a law equally applicable to extraterrestrials (should such exist) we have yet to meet.

It was my privilege to pass through Roger’s gravitational field while I was a graduate student at Stanford from 1972-76. I was not one of his direct PhD advisees or collaborators (a group that includes a number of brilliant psychologists); their reflections will draw upon deeper and more extensive personal interactions with Roger. But perhaps I can add a few thoughts as one of the many others who were influenced by him more obliquely, including those who knew him only through his scientific and artistic contributions.

Roger’s own intellectual influences included Isaac Newton and Albert Einstein, as well as M. C. Escher and René Magritte. He was a modest, soft-spoken man, with a sly sense of humor, whom we graduate students viewed with awe. A conversation about the nature of the mind typically involved long pauses during which Roger was clearly “turning something over in his mind” (to borrow the title of a Scientific American article he wrote together with his renowned collaborator Lynn Cooper). I was a student in Roger’s graduate seminar, and recall our amazement at hearing the illusion of ever-rising tones, his auditory analog of Escher’s impossible figures. In one class, he told us of an experiment he was conducting on the perception of 4-dimensional forms. Of course humans can’t visualize a 4D form, but Roger had an idea for an experiment. 3D objects can be projected onto 2D images, and if a person views a series of such 2D projections from different angles, they will get a good sense of the 3D shape of the object. So by analogy, Roger took an abstract 4D form and created a series of 3D projections of it (i.e., 3D objects, all “views” of the same 4D form). He wanted to see if people who received such a set of 3D objects would be able to form a coherent sense of the abstract 4D form from which the 3D objects were derived. Alas, Roger reported that his experiment had failed. Only one human subject was able to grasp the shape of a 4D form from its 3D projections—and that was Roger himself.

Roger was the quintessential spatial thinker. His extraordinary spatial sense embraced audition and touch as well as vision. Indeed space, for Roger, was an ever-expanding frontier extending far beyond perception. He was able to abstract and generalize space into many dimensions, and by analogy map patterns of relations among semantic concepts onto the patterns of relations between entities within a space. Multidimensional scaling is usually considered as a methodological innovation, which of course it was. But it can also be viewed as a form of analogy in which a process of soft constraint satisfaction brings relations of similarity within some target domain into correspondence with relations defined within an abstract space. The resulting mapping forms an isomorphism (which Roger and Susan Chipman called “second-order” to emphasize it does not require any sort of identity between mapped elements). The English words “analog” (as in “analog representation”) and “analogy” come from the same Greek root, which roughly translates as “proportion”. Space, the ultimate source analog, is where these meanings merge.

I benefited from Roger’s guidance on the committee for my PhD thesis, which was about the role of analog representation in symbolic magnitude comparisons. After I left Stanford for my first job at Michigan, his influence lingered. By 1979 my own research had shifted along a trajectory that took me from analog representation to problem solving by analogy. That same year my fellow graduate student Arnold Glass, along with John Santa and me, published a textbook on cognitive psychology. For its cover we chose a stylized set of Shepard and Metzler figures, used in their groundbreaking experiments on mental rotation. Roger recorded in his memoir, “As I was drifting toward wakefulness early in the morning of November 16, 1968, 1 experienced a spontaneous hypnopompic image of three-dimensional objects majestically turning in space.” And indeed, his 2D renderings of nameless 3D forms resemble twisted space stations built from modular cubes. Though Roger, with his majestic mind, has now passed beyond our 3D world, he left us with visions of dimensions too high and wide for eyes to see.


Nick Chater

Roger Shepard was unusual among cognitive scientists in seeking to find laws rather than merely build models.

There is, inevitably, the question of whether we should expect such laws to exist in cognitive science. After all, the spectacular intricacy of the human mind contrasts with the simplicity of physical interactions or chemical reactions, where the search for laws has been so spectacularly fruitful. Indeed, the great majority of so-called principles and laws found in psychology textbooks turn out to be qualitative in character, rather than having an elegant mathematical form. Roger Shepard’s work illustrated how such quantitative laws may, nonetheless, be decoded, if we have sufficient ingenuity.

I first encountered Rogers Shepard’s approach as an undergraduate in the mid-1980s, learning about his pathbreaking work on the mental transformations of visual images. Most famously, of course, he and his collaborators discovered a roughly linear relationship between the transformational “distance” between images and reaction time. This regularity was most famously observed for mental rotation; but analogous results arise far more broadly, as Shepard himself, Stephen Kosslyn and others have shown. This work is remarkable both for uncovering a law-like regularity where one might least expect it (when considering the manipulation of internal mental representations); and also for opening up the domain of mental imagery, which had often been viewed as inherently open only to introspection, to objective scientific study.

Equally remarkable was Shepard’s so-called Universal Law of Generalization. Shepard hypothesised that there might be a lawful connection between the confusability of a pair of stimuli, and how “distant” they are in a hypothesized mental space. But how could we ever know the location of items in a mental space, which we cannot directly observe? Shepard’s pioneering work developing the statistical methods of non-parametric multidimensional scaling, going back to the late 1950s and 1960s provided a route forward: taking a matrix of confusability judgements across a set of items and mapping these into a low-dimensional spatial layout. Crucially, Shepard’s approach cleverly avoided building any quantitative assumptions about distance in the multidimensional scaling process. This allowed the key question to be asked: what is the relationship between distance in the reconstructed space, and the probability of confusion? Lo and behold, another law-like regularity appears: the probability of confusion is a decreasing exponential function of distance in the (reconstructed) mental space. I can still recall seeing this paper for the first time (published in the journal Science in 1987) as a graduate student in Edinburgh and being completely amazed by what Shepard had achieved. Since his work, many people in cognitive science have attempted to justify and generalize this regularity.

For me, Shepard’s specific achievements, remarkable though they are, are especially important for our discipline because they hold out the possibility that at least some areas of cognitive science may yield quantitative laws, just as in the traditional natural sciences. We have seen quantitative laws before in psychophysics (Weber’s Law being perhaps the most celebrated and robust); but we have seen, as a field, very few laws that cut so deep into abstract cognition. Shepard’s work has been a guiding star for many of us in cognitive science over many decades; but his achievements remain unmatched.





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