Yes, Brownian motion can indeed stir your coffee to some extent. Brownian motion refers to the random movement of particles suspended in a fluid (like water) due to collisions with smaller particles, such as molecules. In the case of coffee, it typically contains tiny suspended particles, such as coffee grounds or sugar particles. These particles undergo Brownian motion, causing them to move randomly throughout the liquid.
While the motion caused by Brownian motion is generally very small and cannot replace the deliberate stirring you would do with a spoon, it can still lead to some mixing or dispersion of the particles in your coffee. Over time, the random movements of the particles will help distribute them more evenly throughout the liquid. However, this process is relatively slow, and for efficient mixing, it is still recommended to use a spoon or any other stirring implement.