Roger N. Shepard, the Ray Lyman Wilbur Professor, Emeritus, in Stanford’s School of Humanities and Sciences, known for his groundbreaking research on mental imagery, died May 30 at his home in Tucson, Arizona. He was 93.

Roger Shepard, 1929-2022 (Image credit: L.A. Cicero)

Awarded the National Medal of Science in 1995, Shepard conducted pioneering research on how the mind creates internal representations of objects in the world. He introduced techniques for quantifying mental processes when cognitive science was still dominated by research based on behavioral observations. His research contributions extended to the fields of computer science, artificial intelligence, linguistics, robotics, and physics.

“I think of him as a gentle genius,” said Ewart Thomas, former dean of the School of Humanities and Sciences (1988-93) and professor emeritus of psychology, who was a friend and colleague of Shepard’s. “His scientific ideas revolutionized psychology.”

One of his most famous research projects was inspired by a vision that came to him as he awoke one fall morning in 1968, the year he joined the faculty at Stanford as a professor in the Department of Psychology. In his mind’s eye, he saw an image of three-dimensional shapes rotating in space. He proceeded to launch a series of studies that transformed how scientists understand mental imagery.

In the first study, Shepard and graduate student Jacqueline Metzler, who earned a doctorate at Stanford in 1973, showed pairs of drawings depicting 3D objects composed of cubes to participants. Some of the paired drawings were identical, some were different – but most were presented at different angles of orientation. The researchers discovered that the time it took for the participants to determine whether the shapes were the same or different was directly related to the degree of difference in their orientations. The finding suggested that the participants were rotating the objects in their minds, and that they were doing so at an average rate of about 60 degrees per second.

One of Shepard’s former undergraduate students, the neuroscientist and best-selling author Daniel Levitin (’92), considers the studies on mental rotation his mentor’s most significant work. “They demonstrated that our inner, mental processes of imagining things are constrained by the laws of physics,” Levitin said. “Uniting the subjective experience of imagination with physics is a very big deal.”

Lifelong ties to Stanford

Shepard was born Jan. 30, 1929, in Palo Alto, California. His father, Orson Shepard (who went by his middle name, Cutler), was a professor of materials science and engineering at Stanford. His mother, Grace Shepard, was a Stanford alumna and artist. By his own admission, Roger Shepard was an indifferent student as a boy; he was distracted by other interests. “I would spend many solitary hours happily tinkering with old clockworks, telephones, and parts of other appliances that I found in a vacant-lot junk pile or in the attic of my San Jose grandparents’ barn and, also, drawing and designing things geometrical and mechanical,” he wrote in Psychonomic Bulletin & Review, in 2004.

He earned a bachelor’s degree in psychology at Stanford in 1951 and a doctorate in psychology at Yale in 1955. At Yale, he met his future wife, Barbaranne Bradley, who was studying for a master’s degree in early childhood education. They married in 1952.

In 1958, Shepard joined Bell Laboratories, where he developed a mathematical method for mapping subjective data, such as how people perceive shapes, so that the distance between the data points would represent how similar they were to each other. He honed the technique, which could make complex datasets easy to visualize, with Joseph Kruskal, a colleague at Bell Labs. The technique is known as nonmetric multidimensional scaling, and today it is widely used as an analytical tool in disciplines as diverse as biology and marketing.

Shepard’s work on the scaling method was itself an outgrowth of the problem of generalization he had tackled as a graduate student at Yale. Generalization is the process through which animals, including humans, extrapolate from previous situations to make sense of new situations, and it is central to the theory of how we learn.

Laying down the law of generalization

At Stanford, Shepard returned to studying generalization, which he called “the most fundamental problem confronting learning theory.”

“Because we never encounter exactly the same total situation twice, no theory of learning can be complete without a law governing how what is learned in one situation generalizes to another,” he wrote in the Psychonomic Bulletin & Review.

In a paper published in 1987 in Science, Shepard gave the example of a bird that has consumed a particular type of caterpillar and found it either “delectable or sickening,” and which then must decide whether it should eat, or forgo eating, a similar-looking object.

In that paper, he proposed a universal law of generalization to describe the probability that an animal will understand a new stimulus, like a sound or a sight, in terms of a stimulus it has encountered before. The theory holds that the probability declines exponentially based on the distance between the stimuli – that is, how similar or different they are perceived to be.

In this optical illusion drawn by Shepard, the tabletops appear to have different lengths and widths. But they are identical. (Image credit: “Turning the Tables,” from Mind Sights (W.H. Freeman and Co., 1990))

“I remember that when I read that paper, I thought to myself that the psychological insights and mathematics were infused by the imagination of an artist,” Thomas said.

They were. Shepard was also a painter, a musician, and a poet. He called upon these talents not only to unlock mysteries of the mind, but also to show how the mind can play tricks on us. He published a book of hand-drawn illusions, called Mind Sights (W.H. Freeman and Co, 1990), that included the famous Shepard tables.

He also developed the Shepard tone, the basis of an auditory illusion in which the pitch of a scale seems to increase indefinitely, when in fact it is only repeating.

‘A legendary mentor’

Jennifer Freyd, professor emerit at the University of Oregon and founder and director of the Center for Institutional Courage, called Shepard her “most important intellectual mentor.”

“He didn’t remember to teach me the practicalities of academia – I did not even know about grant proposals until I got to Cornell,” said Freyd, who earned a doctorate in psychology at Stanford in 1983. “But he taught me things that were so much more important – be creative, take intellectual risks, always be intellectually honest.”

Shepard was awarded the National Medal of Science in 1995. (Image credit: Courtesy Shenna Shepard)

In addition to the National Medal of Science, Shepard received the David E. Rumelhart Prize from the Cognitive Science Society, the Wilbur Lucius Cross Medal from the Yale Graduate School Alumni Association, and the Distinguished Scientific Contribution Award from the American Psychological Association.

He co-authored dozens of research papers, co-wrote a book called Mental Images and Their Transformations (MIT Press, 1982), and co-edited a two-volume work called Multidimensional Scaling (Academic Press Inc., 1972).

Shepard was elected to the National Academy of Sciences in 1977 and the American Philosophical Society in 1999. He was awarded honorary degrees from Harvard University, Rutgers University, and the University of Arizona.

Before joining the Stanford faculty, he was a professor at Harvard from 1966 to 1968. He retired from Stanford in 1996 and moved to Tucson in 2002.

“Roger was a legendary mentor and a generous colleague, widely known for bringing out the best in people,” said Laura Carstensen, the Fairleigh S. Dickinson, Jr. Professor in Public Policy and former chair of the Department of Psychology. “He certainly made an impression on me when I first arrived at Stanford as an assistant professor. Not only was he brilliant, but he was also remarkably kind.”

Shepard is survived by his wife, Barbaranne Shepard, and three children: Shenna Shepard, Newland Shepard, and Todd Shepard. He also is survived by a grandchild, Alexandra Tansey.

In lieu of flowers, donations in his name may be made to the Parkinson’s Foundation.