Martin Krieger, University of Southern California – Primes and Particles

What used to be simple, may now be more complex.

Martin Krieger, professor of planning at the University of Southern California, explains that as we look deeper into what we thought we knew, new details emerge.

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.

Primes and Particles

Whether it be prime numbers or elementary particles or atoms, again and again what we once took as elementary has proven to be composed of new “more”-elementary objects.

If we want to solve simple equations, such as x² – 2 = 0, we are forced to acknowledge numbers such as √2, and add them to the integers.  And then 3 is no longer prime, for it may be divided by (1 + √-2).

The previous generation’s elementary particles turn out to be composed of new elementary particles once we look at higher energies. Atoms are made of electrons and nuclei, protons are made of three quarks held together by gluons.

Families or symmetries organize the elementary objects. The chemists’ Periodic Table is grouped into horizontal and vertical families of elements. Physicists group particles into clans and families organized by charge, spin, and other quantum numbers. Mathematicians describe a tower of number systems, beginning with the integers.

The behavior of elementary objects is determined by their family, much as happens in society.

At each more articulated level, families break up into what might be called “nuclear families” or are discovered to be part of clans.  New elementary objects now compose what we once thought were the fundamental constituents of arithmetic and of nature. When the muon was discovered, the physicist I. I. Rabi, asked in surprise, “Who ordered that?”  The scientists’ goal is to be able to infer the existence and properties of those new elementary objects from the behavior of elementary objects at the less detailed level.