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.

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PAW's July/August 2025 issue cover, featuring a photo of people dressed in orange and black, marching in the P-rade, and the headline: Reunions, Back in Orange & Black.
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July 2025

On the cover: Wilton Virgo ’00 and his classmates celebrate during the P-rade.