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Holmes finds logic in peculiar movements of cockroaches

By Steven Schultz

Princeton NJ -- The slow-motion video shows a cockroach barreling full tilt across the camera's field of view. The bug catches one leg on a small obstacle and spins nearly all the way around, its six legs flying wildly. The flurry of action, however, coalesces into an amazingly rapid recovery, and an instant later the cockroach has left the screen on its original path.

Professor Philip Holmes holds a model of a cockroach

Professor Philip Holmes holds a model of a cockroach. He studies the pesky creatures for the vital information they provide on mobility.

For Professor Philip Holmes, this performance is a puzzle -- a complex, seemingly messy behavior that contains a hidden logic. With a career that has taken him from chaos theory to cockroaches, Holmes is known as a master of reducing such mysteries to their mathematical essence, then rebuilding them into general principles that are applicable to many other areas, from robotics to neuroscience.

Holmes' ability to cut through problems comes not just from his mathematical skills but also from what colleagues say is his uncommon ability to see beyond the confines of his discipline and bridge the specialized languages of different fields. He was trained as an engineer, shifted toward mathematics, then developed an interest in neurobiology. He currently is a professor of mechanical and aerospace engineering and applied and computational mathematics at Princeton. He also writes poetry, with four collections published over the last 35 years.

''He writes poetry, but he also writes great scientific papers,'' said Robert Full, a professor of integrative biology at the University of California-Berkeley who collaborates with Holmes. ''He's really the kind of person who can do these collaborations, because it takes someone who can communicate. I've talked to a lot of mathematicians and couldn't understand a word they said. But that's not the case with Phil Holmes.''

Moving beyond roots

Holmes grew up in England and attended Oxford University, where he received his bachelor's degree in engineering. He went on to earn a Ph.D. in engineering at Southampton University in 1974, but even before graduating had begun working with a group of mathematicians and refocusing himself toward their field.

For the next decade, he used his mathematical perspective to tackle engineering problems in areas including solid and fluid mechanics, turbulence and dynamics. This work helped pioneer a burgeoning field known as chaos theory, which examines phenomena, such as a hurricane moving across the ocean or water dripping from a faucet, whose behaviors are so irregular or so complex they cannot be predicted by conventional methods.

In the early 1980s, Holmes (with colleague John Guckenheimer) published a book that remains one of the standard texts in the fields of chaos theory and nonlinear dynamics. But by that time, however, he was already moving beyond these roots. In 1977, he emigrated to the United States to teach at Cornell University and soon had a chance meeting with a neurobiologist who was studying the nerve impulses involved in swimming. Holmes became fascinated with the patterns and rhythms of these impulses and created mathematical models to describe them.

This work continued through 1994 when he joined the Princeton faculty, but soon Holmes' interests were expanding again. He attended a National Science Foundation workshop on legged locomotion where he met Full and others who introduced him to the wonders of cockroaches. It turns out that these notoriously pesky creatures have some deep and potentially quite useful lessons to teach about how animals move.

''We are looking at millions of years of evolution,'' said Holmes. ''Cockroaches have been around far longer than we have, and they will be around long after we have gone -- and getting around quite nicely.''

Holmes was intrigued by Full's approach of studying the whole animal interacting with its environment and not just the isolated bursts of neurons in a Petri dish. The idea of integrating the complexities of mechanics into the neurological questions he already studied showed Holmes a way to combine his interests and bring them full circle to his roots in engineering.

Holmes is now part of a $5 million, multi-university project led by Full to study cockroaches as a model of stability and efficiency. Combining biology, robotics, neuroscience and mathematics, the researchers are achieving a broad understanding of legged motion, from each neural synapse to every joint and muscle.

''Cockroaches do not do much complicated thinking, but they do turn neural spikes into extremely efficient behavior,'' Holmes said, as he cued up the video of a cockroach running. ''He heaves up and down, he rolls, he pitches, he yaws, he wanders from side to side. It doesn't look very efficient. So one can ask: Why are the dynamics so rich?''

Holmes began to glimpse the answer by writing equations that reduced the problem to a simplified conceptual insect with just one springy leg. Working with Full, Holmes made a surprising discovery: the seemingly messy behavior helps stabilize the insect, but not because of any active control from the nervous system. The legs and body, once set in motion in a basic pattern, are a self-correcting stable mechanical system.

Getting to the essence

The researchers have begun to translate this discovery into a breed of super-stable legged robots that could be used for search and rescue missions, hunting for weapons and other difficult tasks. Collaborators at the University of Michigan have created a six-legged device that Full said is the most mobile autonomous legged vehicle ever created. ''If it hits something or flips over something, without additional sensory information it corrects itself and becomes stable again. The control is built in.''

This kind of advance would not be possible without Holmes' mathematical depiction of a cockroach, said Full. ''If you look at an organism, it has way too many neurons, way too many muscles and joints to ever figure out how in the world all this is coordinated,'' he said. Biologists have learned a lot by conducting experiments on real insects, but it is nearly impossible to derive deep principles without a simplified, virtual cockroach they can push and prod. ''Phil is the best person in the world I have ever met at being able to create these models and get them to their essence, get them simple enough so they are able to demonstrate a principle, yet sufficiently complex to incorporate the components that answer your question.''

The newly awarded five-year grant from the National Science Foundation is allowing the researchers to expand the work and further integrate the neural and mechanical aspects. Holmes also is working with graduate student Justin Seipel to develop the theories and models to function on three-dimensional terrain instead of just running over level ground.

While the subject of legged motion engrosses Holmes, it is far from the only topic that does so. He is working with researchers at Princeton's Center for the Study of Brain, Mind and Behavior as part of a major project funded by the National Institute of Mental Health. Collaborating with Professor of Psychology Jonathan Cohen, former postdoctoral researchers Rafal Bogacz and Jeff Moehlis and graduate alumnus Eric Brown, Holmes developed mathematical models that describe the strategies the brain uses to optimize the rewards in tasks that involve simple choices, such as trading off speed and accuracy when asked to quickly identify visual patterns.

''The grand challenge in these projects is understanding how the collective actions of millions of spiking neurons create behavior, whether it be escape for a cockroach, or a successful (or failed) prediction of a bet at roulette,'' Holmes said.

In the meantime, Holmes is putting his insights and communications skills to use in teaching. He has three current graduate students and has taught graduate and undergraduate courses at all levels, including a math course for nonscientists that he helped create. He currently is helping to develop a new series of applied mathematics courses to augment the undergraduate curriculum.

And he is still writing poetry. His most recent volume, ''Lighting the Steps,'' is a compilation of his poems from 1985 to 2001. Holmes began a serious effort to write poetry as an undergraduate at Oxford and for years his passion for writing overshadowed his interest in engineering. ''Had it been possible to transfer to English or the humanities, I might have done this,'' Holmes said in an interview with the newsletter of the Society of Industrial and Applied Mathematics. ''So I have the rigid British educational system to thank for keeping both worlds open. …''

In some ways, the skills Holmes brings to the two worlds are not so different. He noted that creating a useful mathematical model and writing a poem both require ''acts of creative neglect.'' Stripping the complicating issues from a question can reveal details that illuminate the big picture better than attempts to account for everything in a single equation or piece of writing.

And in the end, he said, the goals are the same: ''There's more play in literature and the arts, but artists and scientists alike are trying to come to terms with things around (and within) them.''