Hand gestures are examples of fast and complex motions. Computers fail to track these in fast video, but sleight of hand fools humans as well: what happens too quickly we just cannot see. We show a 3D tracker for these types of motions that relies on the recognition of familiar configurations in 2D images (classification), and fills the gaps in-between (interpolation). We illustrate this idea with experiments on hand motions similar to finger spelling. The penalty for a recognition failure is often small: if two configurations are confused, they are often similar to each other, and the illusion works well enough, for instance, to drive a graphics animation of the moving hand. We contribute advances in both feature design and classifier training: our image features are invariant to image scale, translation, and rotation, and we propose a classification method that combines VQPCA with discrimination trees.