The motor system generates time-varying commands to move our limbs and body. Conventional descriptions of motor control and learning rely on dynamical representations of our body's state (forward and inverse models), and control policies that must be integrated forward to generate feedforward time-varying commands; thus these are representations across space, but not time. Here we examine a new approach that directly represents both time-varying commands and the resulting state trajectories with a function; a representation across space and time. Since the output of this function includes time, it necessarily requires more parameters than a typical dynamical model. To avoid the problems of local minima these extra parameters introduce, we exploit recent advances in machine learning to build our function using a stacked autoencoder, or deep network. With initial and target states as inputs, this deep network can be trained to output an accurate temporal profile of the optimal command and state trajectory for a point-to-point reach of a non-linear limb model, even when influenced by varying force fields. In a manner that mirrors motor babble, the network can also teach itself to learn through trial and error. Lastly, we demonstrate how this network can learn to optimize a cost objective. This functional approach to motor control is a sharp departure from the standard dynamical approach, and may offer new insights into the neural implementation of motor control.