Archimedes Talks

What do a stick balanced upright on your finger and a scuba diver hovering underwater have in common? Both are attempts to stabilize an unstable state -- small disturbances grow unless you constantly correct them. But what does "unstable" actually mean, mathematically?

In this talk, we'll build a simple mathematical framework that formally captures this instability. We'll start with a hands-on challenge: can you balance a wooden dowel on your finger? From there, we'll move to a surprising second example: hovering at a fixed depth while scuba diving. It turns out that air compressing in your lungs at depth creates the same mathematical structure as the falling dowel -- a force that pushes you further from where you want to be. We'll analyze this with a simple balloon-and-weight model and use phase line diagrams to show the nature of these unstable states, how they are related, and how ongoing feedback is the only way to maintain control.

Finally, we'll put it all to the test with an interactive simulation where you try to balance a virtual pendulum -- but with an artificial delay added to what you see on screen. You'll discover firsthand why perception lag is the enemy of any unstable system.