objects represent the first three dimensions, but a kind of reversal of space is involved in the ascent to a fourth dimension. Steiner leads us to the brink of this new perspective―as nearly as it can be done with words, diagrams, analogies, and examples of many kinds. In doing so, he continues his lifelong project of demonstrating that our objective, everyday thinking is the lowest rung of a ladder that reaches up to literally infinite heights. The talks in this series and the selections from the question-and-answer sessions on many mathematical topics over the years are translated into English for the first time in The Fourth Dimension.