Grand neuroscience projects, such as connectomics, have a recurrent tendency to overpromise and underdeliver. Here I critically assess what is done in contrast with what is claimed about such endeavors, especially when the results are “horizontal” and the conclusions “vertical”, namely, when maps of one level (synaptic connections) are conflated with mappings between levels (neural function, animal behavior, cognitive processes). I argue that to suggest that connectomics will give us the mind of a mouse, a human or even a fly is conceptually flawed. Even if we, neuroscientists, do not take our metaphors literally, we should take them seriously.