Kurt Roemer’s experimental course at the University of San Francisco was introduced by a physical exemplar of a string-coupled pendulum such as the one pictured here. Two identical pendula are joined by a horizontal string. When the pendulum weights’ initial displacements mirror one another, both proceed in simple harmonic motion. When only one pendulum weight is initially displaced, both proceed in bi-harmonic motion with respect to axes given by a) the line joining the pendulum’s supports and b) its perpendicular.

The economy, said Roemer, presents us with analytic challenges encapsulated by the pendulum problem. Both systems are described by a geometry: the pendulum is defined by the lengths of its strings; the economy presents us with the shapes of its production and utility tradeoffs. Both systems are actuated by a latent force: the pendulum exists in a gravitational field; the economy is motivated by natural rates of asset turnover. Both systems are to be understood in terms of the dynamics controlled by their spatial and dynamic parameters.

Emulation, Roemer taught, is the method of understanding appropriate to dynamic systems instantiated by the pendulum. He established this point by presenting his computer emulation of the pendulum’s motion to the class. We were then invited to activate the physical pendulum and its emulation with like stimuli and compare the motions that followed. Class ended with an invitation to consider whether or not we should be satisfied with such evidence that the pendulum was ‘understood’.

Roemer had intuited a solution the problem of predicting the pendulum’s movements as an undergraduate. He later proved his intuition to be correct by deriving the pendulum’s internal frequencies algebraically. These matters were committed to paper in 1975, and are available for comparison to Professor Michael J. Moloney’s accepted solution of 1978. Roemer re-drafted his earlier paper in 2013. We have updated his classroom emulator in a modern Excel workbook here. And, finally, the online emulator developed for our YouTube demonstration is posted here at SFEcon.