We have studied to what extent cortical columns with their particular wiring can boost neural computation. Upon a vast survey of columnar networks performing various real-world cognitive tasks, we detect no signs of enhancement. It is on a mesoscopic–intercolumnar–scale that the existence of columns, largely irrespective of their inner organization, enhances the speed of information transfer and minimizes the total wiring length required to bind distributed columnar computations towards spatiotemporally coherent results. We suggest that brain efficiency may be related to a doubly fractal connectivity law, resulting in networks with efficiency properties beyond those by scale-free networks and we exhibit corroborating evidence for this suggestion.