Life After Retirement: Kurt Kreith

In the years 1992-94, the University of California offered a golden handshake under the acronym VERIP. In 1994, having twice refused the lure, I signed up for VERIP III, making 2024 my 30th year of retirement.

Many of my early retirement activities reflected a desire to give meaning to the study of differential equations, an enterprise that had put food on the table since 1960. In 1984 world population was fast approaching 5 billion, memories of OPEC's oil embargo were still fresh in our mtinds, and spurious use of the logistic equation to predict “peak oil” was in vogue. Against this background I made contact with The American Forum for Global Education and agreed to offer a series of summer programs for New York teachers under the heading “The Mathematics of Global Change.”

These summer programs coincided with the development of new computer technology for schools. Notable here was the "systems dynamics" software named Stella whose development was closely related to the "World3" model underlying the 1972 best selling book, The Limits To Growth. Stella provides students with an icon-based format for formulating a system of differential equations whose numerical solution it then displays graphically. Not requiring mathematical understanding by its user, Stella was seen as a way of promoting “systems thinking” by students at large.

Jumping ahead to 2015 and a lessened zeal for travel, I was able to take advantage of UC Davis' program of First Year Seminars (FYS) to offer a course on “The Limits To Growth” (LTG). Meeting in a computer lab we read LTG, engaged in discussion about the use and misuse of models such as World3, and learned enough about difference equations and Excel to create our own spreadsheet versions of Stella.

This led to a mathematical discovery! By way of setting the stage for its applications of World 3, LTG describes “Four Possible Behavior Modes of the World Model” which can be termed exponential growth, logistic growth, overshoot and oscillation to equilibrium, and overshoot and crash. (See graphs at right.)

Using Excel, we were able to generate these behavior modes and found that the last three correspond to solutions of the delay logistic equation ^du/_dt = ru(t) - eu(t-d)². This realization led me to reflect on the number of times I had taught logistic growth without mention (or awareness!) of such modifications. It also led to reflections about the importance of delay differential equations in the biological and social sciences and the ease with which delays can be dealt with numerically.

Buoyed by this experience, I learned to make use of Excel's rich reservoir of built in functions to offer First Year Seminars in other areas. Here Excel's MOD function enabled us to address a variety of topics in number theory, including Fibonacci's numerical solution of the delay differential equation ^du/_dt = u(t-1) with u(0) = 1. By returning and undoing the ASCII code of a keyboard symbol, Excel's CODE and CHAR functions made possible a FYS on cryptology. Excel's COMBIN function and ability to generate random numbers enabled us to address a variety of topics from probability. In this way, First Year Seminars provided a context for continued learning as well as contact with students and the outside world.

With time, a hearing loss combined with a growing diversity in the first languages of students made instruction of First Year Seminars less satisfying. Then came COVID-19 and the need to adapt to remote instruction which I found challenging. Here I had the good fortune of obtaining the support of Al Mendle, an adventurous recently retired colleague from the School of Education who became a partner in such undertakings. Our collaboration included ways of modeling epidemics in a format appropriate for a First Year Seminar.

So what now? My colleague in the School of Education specializes in the preparation of elementary school teachers to face the challenge of teaching children basic arithmetic. A First Year Seminar on “Arithmetic In the Time of Computers” would allow us to associate the “moment of conception” of the computer age with the development of an electronic circuit for adding two binary numbers. I continue to ponder whether such insights are appropriate for future teachers of children, for students at large?

About Professor Emeritus Kurt Kreith

Having received his Ph.D. with Frantisek Wolf in Berkeley, Kurt Kreith arrived in Davis in 1960. In 1963 he accepted a position with the newly established U.S. Arms Control and Disarmament Agency, arriving just in time for the signing of the Partial Test Ban Treaty (and the Great March on Washington).

In 1965 he returned to Davis, serving as Department chair from 1970-75, and in various positions in the Academic Senate. His interest in mathematics education led to participation in the Northern California Mathematics Project, a visit to the Kolmogorov School in Moscow, and participation in COSMOS. An interest in mathematics education has marked his retirement years as well.