Random walks in active learning – from an Einstein misconception to the value of simple models in the age of AI

This talk presents discoveries made while developing a novel active-learning approach for undergraduates interested in life sciences. The materials start with the "Marble Game" - a kMC simulation of diffusion based on Brownian motion. Students discover that Fick's law is explained by the unbiased random jumping in the Marble Game. In a similar guided-inquiry environment, students apply finite difference methods to: drug elimination; radioactive decay; osmosis; ligand binding; enzyme kinetics; the Boltzmann factor; phase equilibrium; random walks; membrane voltage, the action potential; COVID-19; and Newtonian mechanics. Students discover that science is an evidence-based endeavor with testable hypotheses supported by experiment. The approach led to a new diffusive model of osmosis that remains controversial, because it's at odds with Einstein's understanding of osmotic pressure. The same approach was applied to COVID-19 and resulted in a "sloppy model." "Sloppiness" has been observed in - biochemical reaction networks, quantum Monte Carlo, empirical interatomic potentials, particle accelerator design, insect flight and machine learning. Thus, with the advent of AI, it's even more important for students to understand that the purpose of modeling is to gain insights into the behavior of the physical system. AI models can easily find a curve that goes through the points, but they don't generate the kind of human insights that can be gained using an incremental approach to mechanistic modeling.