Martin Krieger, University of Southern California – Clusters

Martin Krieger

Martin Krieger

People cluster together in cities, by chance or by choice.

Today on The Academic Minute: Martin Krieger, professor of planning at the University of Southern California, examines how this applies to physics and whether cities behave like particles in a nucleus.

Martin Krieger’s current work is on defense and military policy, and on uncertainty and ambiguity. He has done social-science informed aural and photographic documentation of Los Angeles, including storefront houses of worship and industrial Los Angeles. Professor Krieger has won three consecutive Mellon Mentoring Awards, for mentoring undergraduates, faculty, and graduate students. Professor Krieger has worked in the fields of planning and design theory, ethics and entrepreneurship, mathematical models of urban spatial processes, and has explored the role of the humanities in planning. His nine published books describe how planning, design, and science are actually done. Professor Krieger has been a fellow at the Center for Advanced Study in the Behavioral Sciences and at the National Humanities Center, and is a Fellow of the American Physical Society. He has received grants from a variety of foundations, and has served as the Zell/Lurie Visiting Professor of Entrepreneurship at University of Michigan’s Business School. He joined the USC faculty in 1984. Professor Krieger often helps doctoral students, as well as undergraduates and masters students, focus and formulate their research projects.



Cities show spatial clustering of people and enterprise, by class, by race, by kind of industry. Sometimes that clustering is deliberate, sometimes it is by chance, or market mechanisms, or the unplanned effect of regulations.

Physical scientists understand clustering and orderliness when they think of the forces between molecules or particles. A liquid might freeze—its molecules clustering in an orderly fashion–so we have ice. Matter is modeled as a 3-d grid on which actual molecules are attached to the vertices; and, perhaps, something like electric fields may be attached to the links between vertices.

If the molecules interact with their nearest neighbors, the lattice or grid may develop clusters of like particles, in seas of unlike particles, in seas of like particles…  If the temperature is low enough, the particles form a sea of like particles, and they are said to be aligned–in effect, there is freezing. If the temperature is high enough, there is very little clustering at all. There is randomness and heterogeneity.

Those electric fields allow for new phenomena. Namely, particles become entangled with each other through those links and it becomes impossible to separate them from each other. Individuals are “confined,” so to speak, never to be on their own.

In actual cities we see orderliness, heterogeneity, and confinement—depending on social and economic conditions.

It’s not as if people behave like molecules. Rather, there are common sources for the behavior of individuals in crowds.