Water Knows Something Maths Doesn’t

Swirl a cup of water and watch it. For a few seconds the water spins, and then it slows down and goes still. Nobody thinks twice about it. I hadn't either, until I read about the equations behind it.

The reason the swirl stops is viscosity, the internal friction of the liquid. Water molecules rub against each other and slowly take the energy out of the motion. The swirl fades because the water pushes back against itself.

The equations that describe this are called the Navier-Stokes equations. They are a mathematical model of how liquids and gases move.

Here is the part that surprised me. No one has been able to prove that the maths always behaves the way real water does.

The worry is something called a blow-up. On paper, a swirl could keep tightening into smaller and smaller whirls until, at a single point, the velocity becomes infinite. Real water never does this.

So reality and the model disagree, and that gap is the interesting part. When the maths predicts something nature never does, either the model is missing something or we don't yet understand the maths well enough.

This changed how I think about mathematics. For a long time I wondered why maths mattered when physics is what governs nature. Water doesn't solve an equation to decide how to swirl. It just swirls. Maths is how we describe what nature is doing, find the parameters that make it behave that way, and then use those limits to build new things.

I was 23 when I understood this. I'm glad it wasn't never.

This is just a small musing on what I've been tinkering with recently. I'll be exploring this concept in more depth.