Drop a marble. Watch it find the bottom.

Type any surface f(x,y) and it renders in 3-D, colored by height. Double-click anywhere on it to drop a marble — it always rolls in the direction of steepest descent, the negative gradient −∇f, leaving a trail until it settles in a valley. This is gradient descent: the same idea that trains every neural network, just visible for once.

Try Ripples and drop five marbles in different spots — most won't find the same pit, because gradient descent only ever sees the slope right under its feet; it has no idea a deeper valley exists three ridges over. That's local vs. global minimum in one drop. Then try Saddle: a marble dropped exactly at the center sits frozen — the gradient is zero there, yet it's not a minimum at all, just a mountain pass. Nudge it a hair off-center and watch it commit to a direction and go.