Generals always prepare for the last war.—Winston ChurchillYet in the 18th century, European thinkers noticed that social transformations had been accelerating for several thousand years; subsequent historical knowledge has made this observation more graphic and global. How long can the acceleration regime continue? In 1958, John von Neumann used the mathematical ‘singularity’ concept apropos of this subject, and the sonorous term was soon accepted in the humanities.The conceptual intrigue has become still more fascinating since a series of independent calculations demonstrated that the acceleration period was not limited by human history and prehistory but embraced 4.5 billion years of biosphere evolution in tune with a simple logarithmic law. This is one of the epoch-making and surprising discoveries in the early 21st century. Continents have been drifting on Earth over billions of years, climate changing repeatedly, meteorites falling down and volcanoes blowing up—yet, the phase tra ..