The Fifth Hammer: Pythagoras and the Disharmony of the World

Published Jan. 21, 2016

(Zone Books) The fifth hammer — the discordant hammer heard by Pythagoras after discovering the fundamental musical intervals of the octave, the fifth, and the fourth — suggests how our ability to know things about the physical universe through the development of systems and laws is limited. This book explores the concept of the fifth hammer and what it implies for Western efforts to understand and describe the cosmos. Heller-Roazen is the Arthur W. Marks ’19 Professor of Comparative Literature and the Council of the Humanities at Princeton University.

Paw in print

Image
Tod Williams ’65 *67 stands in front of the Brooklyn Bridge.
The Latest Issue

July 2026

Architect Tod Williams ’65 *67 reflects on the Obama Presidential Center; rain and revelry at Reunions.