Slick. How smooth and attractive can it be, given our brain?

It has taken about 30 years for the notion of attractor dynamics to get the attention of the experimental neuroscience community. Now that some are beginning to investigate the more sophisticated idea of continuous attractors, where marginal stability can be used for cognitive operations such as path integration or the prediction of the consequences of one's own actions, it is time to tell the truth about continuous attractors. I will discuss a quantitative approach to the smoothness of the spatial maps that can be established in the CA3 hippocampal network, and suggest that in the space of memories, we may jump more often than slide.