Poetry and cockroaches Interview with Philip Holmes, Princeton University, by Hinke Osinga, University of Bristol, UK
Philip Holmes.

Phil Holmes has got an impressive CV. Not only has he initiated many new areas of research in mathematics, he is also very much interested in literature and has published four volumes of poems. Perhaps because of this, his career path has taken him all over the world and for a long time it was not at all clear where it would lead him. Phil was born in the UK and studied Engineering Sciences at Oxford, while attending many lectures in literature at the same time. His studies formed the "middle part" of a thick-sandwich apprenticeship at Rolls Royce and he was clearly destined for a promising career in industry. Unfortunately, Phil hated working in a company, and especially the clocking in. He resolved to stop being an engineer and make another start as a poet.
		Phil Holmes with his father in 1945.

Phil Holmes at the age of three.

		In 1969, after a year of writing, he went on a hitchhiking trip through Europe, Greece and Turkey until the autumn. He stayed in Israel on a kibbutz for winter and planned to continue his trip through Turkey, Iran and Afghanistan to India. "But things took a completely different turn when I met Ruth at the kibbutz. We went back to England in 1970, got married in November, and now I needed a job!" On the basis of his first book of poems Three Sections (which was to be published in 1972), Phil tried to find a job as an English teacher, but then "a trusting far-sighted guy named Bob White at the Institute of Sound and Vibration (ISVR) in Southampton offered me a job as a lab assistant to help build experiments." The job proved far more interesting than Phil had expected. Moreover, Robert White felt that his activities were rather valuable: "You could get a PhD for this, you know. Why don't you go and pay the fee?" Phil received a PhD for his work on "The Experimental Characterisation of Vibration Transmission Using Transient Excitation" in 1974.
Raking hay with oncoming storm in northern Negev, Israel, 1970.

Despite having resolved not to become one, Phil was now an established engineer. He took a postdoctoral position under Bryan Clarkson, who was also the Director of ISVR. As a result, Phil could work on whatever he wanted. "I met David Chillingworth and David Rand, who were both in the School of Mathematics at Southampton. I took David Chillingworth's catastrophe course and David Rand and I studied the famous Utrecht preprint of Floris Takens. This is how I became fascinated with dynamical systems theory." However, Phil was also still passionate about his writing and in 1977 he published another book of poems A Place to Stand, which was written in Southampton and partially based on his travels on foot in the middle-east. "Unfortunately, due to my work in dynamical systems I had made myself unemployable in England. If I applied for an engineering job, they were surprised because I did mathematics, but if I applied for a job in mathematics, I was told that I didn't have a mathematics degree." Profiting from contacts made at a conference organised by David Rand in 1976, where Phil met John Guckenheimer, Jerry Marsden, and Nancy Kopell, he received an offer in 1977 to join the Department of Theoretical and Applied Mechanics (TAM) and the Center for Applied Mathematics at Cornell University. Phil began collaborating with Jerry Marsden before he left the UK, and he and John Guckenheimer started work on their textbook Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields during Phil's six-month visit to Berkeley in 1981. John subsequently moved to Cornell in 1985. "It was a very good environment for interdisciplinary work. TAM and Applied Mathematics did most the mathematics education at the university and this automatically got one involved in a broad range of projects." Phil stayed at Cornell until 1994, when he left for Princeton University to become Professor in Mechanics and Applied Mathematics, with joint appointments in the Department of Mechanical and Aerospace Engineering and The Program in Applied and Computational Mathematics.

Phil Holmes with his children near Ithaca in early to mid 1980s.

Common themes between mathematics and poetry

According to Phil, an applied mathematician needs to keep his or her eyes open. It is not sufficient to focus on mathematical theory; one has to know something about other things than mathematics. "Many people who made advances in science have had wide interests. Making connections requires breadth." While Phil does not believe that there are direct connections between mathematics and poetry, there are common themes. "Applied mathematics and poetry are both ways of coming to terms with something outside." In applied mathematics, the ouside is whatever you want to apply the mathematics to. In poetry, it is what the poet writes about. "My third book, The Green Road, was written at Cornell from 1977-1986. Part of it deals with the history of lead mining in Northern England, because I had lived in this lead mining area years ago. Writing a poem about lead mining means that I must adhere to poetic and literary structure. I must think about how to use language and the literary baggage that words or phrases may carry, while at the same time I consider the historical facts of a miner's life. In applied mathematics we have a similar relationship to mathematical history, in that we place our work in the context of previous literature, and we use a particular framework and techniques to come to our results." Ultimately, your interpretation depends on what you know and how you write. Of course, you want to do something original, but you still see things through a lense of what has been done and how it was presented before. "Can you ever look at something without a model of what you want to see? I try to look for a literary metaphor when choosing my mathematical approach. The fact that these things are going through my mind --- sometimes at the same time --- is not irrelevant. It helps me to realize that there are many different ways to understand something. Being interested in poetry has helped me to be a bit more humble about what mathematics can achieve."

Phil's latest poem started off with memories from his hitchhiking in Turkey. He is reworking it because his perception of the world has changed over the years. "This poem is about how your mind grows and parts of it die and how it changes." A poem gets rewritten over and over again to capture the exact image or a combination of images. "For example, you have a memory of light falling on trees, along with a memory of some nice experience, but you also worry about the kids at home. Just imagine trying to formulate this feeling using such a compact language as mathematics!" Of course, this may be a bit too far-fetched, but Phil has a seven-year collaboration going with Jonathan Cohen, Professor in Psychology and co-director of Princeton's Neuroscience Institute. "We are interested in the problem of how we can share attention among different tasks while there are a lot of demands on our brain. How can you explain how we think about things, the richness of our senses? We can use stochastic ODEs to model the accumulation of evidence in simple decision tasks, but can one mathematize the full range of experiences?" Phil is very glad to be involved in this complicated project of how humans think. "I include ideas from neuroscience and try to put in images of how things flow. It is difficult to draw it all together, but this is also a metaphor for research: it pulls you in lots of directions."

In many ways the practical criteria that we use in both poetry and mathematics are the same. The judgement of whether a phrase stays in a poem is similar in nature to the decision of which proof is more elegant. However, do such similarities still apply in dynamical systems? "I would proof a theorem whenever I can, but there is often a tension between what you can proof and the limitations you have to put on the object of study to achieve a proof, the hypotheses, etc." Hence, Phil has not been active recently in basic theory. "Too often one must impose limitations on exactly those effects that one wishes to include. It becomes a compromise, since we do resort to numerics, but still need the theory to help interpret them. Furthermore, my applied collaborators are typically not interested in proofs. They want to add even more bells and whistles, and so take away even more from the possible tractability."
		Phil Holmes in his office.

Collaborations as eye-openers

Phil has got many collaborators and he is convinced that collaborations are very important. "Especially the postgraduate students and postdocs in biology have a very broad interest --- they tend to be older than their equivalents in mathematics --- and it is nice to be involved in neurobiological applications." Phil has several long-standing research collaborators: "I have been blessed with a wonderful succession of postgraduates, postdocs and colleagues." As mentioned, there is his work with Jonathan Cohen, and he is studying insect locomotion with Bob Full (UC Berkeley), Dan Koditschek (University of Pennsylvania), and John Guckenheimer (Cornell). "My first interest in neurobiology was in central pattern generators. At Cornell, around 1980, Avis Cohen (now at the University of Maryland), Richard Rand and I started to investigate the swimming motions of lamprey. Avis and I met by chance waiting in line for the Math Department copier. More recently, we teamed up with Thelma Williams (St.George's Hospital Medical School, University of London) on muscle models, and Alexander Smits (Princeton) got involved because of his experimental work on unsteady oscillatory propulsion --- the hydrodynamics of swimming."

The common theme for all of these collaborations is to try to build integrated models from known components. "We know quite a lot about the components, in the end the mechanical motion all comes down to Newton's laws, while we have a central pattern generator for the neurobiological component. It seems important and feasible to build relatively simple models that show how all bits are integrated. It's like a marriage of neurobiology and mechanics in which the overall view is important, and breadth is critical." Phil likes going on to new things, but his three main projects share the common theme of asking how neuronal spikes get turned into behavior, how neurons make their imprints on the world. "I feel very lucky to have fallen into such an interesting area of research --- and it was by chance --- and then to have had appointments that let me explore freely, and to have had great collaborators and colleagues."

In practice, Phil tries to straddle the boundaries among proof, asymptotics, and numerics. For example, his work on insect locomotion seems to require a model describing the movements of six legs. However, insects typically use their legs in groups, so one can simplify to a two-legged model. "In the end, we reduced to an even more simplified model where we essentially deal with only one pogo stick. This meant we could actually proof stability results and it turned out that this was quite useful for interpreting numerical data from more realistic models. I believe we do want models that are as simple as possible, because going to the limits can be very helpful." Nevertheless, the current model now has six legs and muscles are being included. So, there are more components, more parameters and more inputs. It might be able to proof something for this complicated model, but Phil wonders what its value might be. "It is perhaps more elegant to come up with a nice algorithm and use numerics than an elaborate proof that does not illuminate or explain anything.

		Phil's activities span a very broad range. Not only has he used his skills in fields from solid and fluid mechanics to nonlinear optics, pattern formation, biomechanics, neuroscience and cognitive psychology, he also continues to learn about other skills from different scientific fields. "I do see a shift in what I am doing. For many years, I would have said that I was in dynamical systems, but now I am much more focused on particular applications areas. I work on building models that are simple enough to do analysis on, and I use only basic tools from mathematics. Sometimes, I feel I am not up to date with what is going on in dynamical systems..."
Phil in July 2006.

That is quite a strong statement from the chair of the SIAM Activity Group on Dynamical Systems! However, Phil points out that it is also a comment on the level of activity in the field. "Who can keep up with the flood of literature and preprints in such a vibrant field?" And he adamantly opposes the suggestion that he may not be up for the task. "I may have moved away from basic theory myself, but it is still very important. Applied mathematics is a very broad field and dynamical systems needs to maintain its coherence at the center of a range of fascinating technical problems. For example, we must export our knowledge of finite-dimensional systems to PDEs and DDEs, we should better unify the relatively new field of stochastic ODEs, and come up with general results in ergodic theory that are applicable in a wide context. It is really important to have abstract theorists ask themselves whether they can find a C³ counterexample to this or that. But for myself, I'm currently enjoying the ground work of modeling, which means lots of reading and collaboration." Phil points out that the member of SIAG/DS, and even more the participants at the biennial Snowbird meetings, come from many different areas --- not only from mathematics, but also from physics, engineering, and now biology, finance, etc. "Our community has spreading roots and a broad canopy, and that is terrific." He goes on to explain that we must take care of the coherent center and the tap root in dynamical systems theory, because otherwise the tree would fall. "Take complex systems theory, if it is a theory. How would you select a syllabus for a course, or choose a coherent textbook? It is important to realize that in dynamical systems we really do have a good view of the core discipline and we should not lose sight of that."