While working on algorithms, I often thought about how to demonstrate their utility. A bench-scale setup is unlikely to capture many aspects of the complexity of industrial systems. It is too idealized and overlooks important interactions among units. Mathematical models, by contrast, can simulate much more. They can incorporate nonlinear behavior, multivariable dynamics, feedback, and uncertainty. In theory, a well-constructed simulation that captures these complexities should be more informative than an idealized lab setup.
However, over time, I came across two cases that reminded me that demonstration can matter as much as analysis.
The first was when I learned about the hydraulic model of the San Francisco Bay built in the 1950s. Engineers had already used mathematical analysis to show that the Reber Plan, which proposed damming parts of the bay, would have severe environmental consequences. The math was convincing to experts, but not to the policymakers and the public who had to act on it. To bridge that gap, the U.S. Army Corps of Engineers built a large-scale physical model of the bay. The goal wasn’t to uncover new behavior, but to demonstrate what the existing analysis already predicted. The physical model helped people see the consequences of the plan directly, and it played a key role in stopping the project.
A similar case occurred with Stuxnet. Cybersecurity researchers had already analyzed the malware and understood how it attacked centrifuge controllers. The technical reports were definitive, but not for non-experts. Ralph Langner’s team built a simple physical demonstration showing how the malware could manipulate an industrial system while hiding its activity from operators. The demo was simplistic and didn’t add anything new to the technical understanding, but it made the attack real and understandable to a broader audience.
These examples illustrate something important. Physical demonstrations may not contribute new knowledge, but they can be essential communication tools. They make abstract concepts tangible, especially for those without the background to interpret equations or read technical reports. Solving the problem is only part of the challenge. Making others understand and trust the solution is just as important for achieving impact.
The lesson is: people are more likely to believe what they see than what the math proves.