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Circles DisturbedThe Interplay of Mathematics and Narrative$
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Apostolos Doxiadis and Barry Mazur

Print publication date: 2012

Print ISBN-13: 9780691149042

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691149042.001.0001

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Structure of Crystal, Bucket of Dust

Structure of Crystal, Bucket of Dust

(p.52) Chapter 2 Structure of Crystal, Bucket of Dust
Circles Disturbed

Peter Galison

Princeton University Press

This chapter advances the idea that every mathematical argument tells a story by focusing on the biographies of two pioneers: American physicist John Archibald Wheeler and the Bourbaki collective of young French mathematicians. Wheeler viewed mathematical arguments essentially as compound machines; his is a world where instructions pull dimensionality itself out of a Borel sets that he referred to as a “bucket of dust.” Whereas Wheeler's story is a set of linked machine-stories, a hybrid of discovery accounts, speculative machine-like functions and mechanisms, Bourbaki's account is a crystal of symbols. The chapter contrasts Wheeler's way of relating the narrative of mathematics with that of Bourbaki. In particular, it considers Wheeler's machine metaphor and its rejection by Bourbaki; his mathematical physics, and especially his views on gravitational collapse; and Bourbaki's “abstract package.”

Keywords:   mathematical argument, John Archibald Wheeler, Bourbaki, compound machines, Borel sets, symbols, narrative, mathematics, machine metaphor, mathematical physics

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