A bacterium in a drop of water is looking for food. Around it, there's a chemical gradient: more food molecules on one side, fewer on the other. How should it move to reach the tasty spot fastest? It could steer smoothly, like a cyclist dodging a puddle. Or, like a bacterium, it could periodically stop, tumble, and swim off in a random direction.
Scientists asked: why did bacteria choose the second, seemingly clumsy approach? They modeled the search as a problem: what's the fastest way to climb a gradient if you only get a limited amount of directional information per unit time? It turns out that without precise knowledge of which way to turn, discrete actions, jerks and tumbles, beat smooth steering. When information is scarce, it pays to turn around 180 degrees: if you were heading the wrong way, you quickly get back. With more information, full tumbles with a random new direction are optimal. And with even more data, turning at a few fixed angles becomes the best strategy.
This result isn't just about microbes. It shows how nature often picks simple, discrete solutions even though the underlying physics is continuous. The bacterium doesn't compute a perfect trajectory; it follows a simple rule: "swim until things get worse, then tumble." And such a rule turns out to be nearly optimal for life in murky water.
When searching for food, E. coli tumbles about once per second, and each tumble changes its direction by a random angle.