Jacques Bertin's legacy extends beyond the domain of cartography, and in particular to the field of information visualization where he continues to inspire researchers and practitioners. Although in the late 20 st century his books were out of print, their re-edition around 2010 has steered a renewed interest and inspired new generations of researchers to re-interpret the principles of Semiology of Graphics and La Graphique in a time of interactive computers. In particular, the work of Jacques Bertin on the reorderable matrix has been very challenging in his time, and the quest to its automation has not been satisfactory to him. This article summarizes Bertin's approach to the reorderable matrix, underlines the limitations of fully automated reordering methods, and introduces Bertifier, a hybrid system to reorder matrices using a combination of machine assistance and human control.