The neurosciences have developed methods that outpace most other biomedical fields in terms of acquired bytes. We review how the information content and analysis challenge of such data indicates that electron microscopy (EM)-based connectomics is an especially hard problem. Here, as in many other current machine learning applications, the need for excessive amounts of labelled data while utilizing only a small fraction of available raw image data for algorithm training illustrates the still fundamental gap between artificial and biological intelligence. Substantial improvements of label and energy efficiency in machine learning may be required to address the formidable challenge of acquiring the nanoscale connectome of a human brain.