July 20, 2024

Thematic Program on the Renormalization and Universality in Mathematics and Mathematical Physics
Clay Mathematics Institute Public Lecture

Leo P. Kadanoff, University of Chicago
"Making a Splash; Breaking a Neck:
The Development of Complexity in Physical Systems"

October 24, 2005 -- 6:00 p.m.
University of Toronto, Koffler Institute
Room KP 108

Making a Splash; Breaking a Neck: The Development of Complexity in Physical Systems

The fundamental laws of physics are very simple. They can be written on the top half of an ordinary piece of paper. The world about us is very complex. Whole libraries hardly serve to describe it. Beyond this, any living organism exhibits a degree of complexity quite beyond the capacity of our libraries. This complexity has led some thinkers to suggest that living things are not the outcome of physical law but instead the creation of a (super)-intelligent design.

In this talk, we examine the development of complexity using examples drawn from studies of the flow of simple materials. Examples include splashing water, the formation of a thin neck as one mass of fluid separates into two, swirls in gases heated over a flame, and jets thrown up from beds of sand. We watch complexity develop in front of our eyes. Mostly, we are able to understand and explain what we are seeing. We do our work by following a succession of very specific situations. In following these specific problems, we soon get to broader issues: predictability and chaos, mechanisms for the generation of complexity and of simple laws, and finally the question of whether there is a natural tendency toward the formation of complex 'machines'.

Clay Public Lectures
The aim of this lecture series is to increase the awareness and understanding of mathematics — in the public at large as well as in the business, scientific and university communities.

Leo P. Kadanoff is a theoretical physicist and applied mathematician who has contributed widely to research in the properties of matter, the development of urban areas, statistical models of physical systems, and the development of chaos in simple mechanical and fluid systems.
His best-known contribution was in the development of the concepts of "scale invariance" and "universality" as they are applied to phase transitions. More recently, he has been involved in the understanding of singularities in fluid flow.

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