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Enlightening SymbolsA Short History of Mathematical Notation and Its Hidden Powers$
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Joseph Mazur

Print publication date: 2016

Print ISBN-13: 9780691173375

Published to Princeton Scholarship Online: January 2018

DOI: 10.23943/princeton/9780691173375.001.0001

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Invisible Gorillas

Invisible Gorillas

(p.192) Chapter 22 Invisible Gorillas
Enlightening Symbols

Joseph Mazur

Princeton University Press

This chapter explains how symbols, by providing a blank background on which we may contemplate unadulterated meaning, help us see and distinguish what is essential. It first considers the claim advanced by the German naturalist Gotthilf von Schubert in the nineteenth century that we dream in a traumbildsprache (“dream visual language”), “a higher kind of algebra,” not in a verbal language. It then discusses the study of dreams by Calvin Hall and Vernon Nordby; Christopher Chabris's and Daniel Simons's “Invisible Gorilla” experiment; and experiments undertaken by Stanislas Dehaene to investigate differences in brain activity between contemplations of numbers and words. It also revisits the study done by Anthony Jansen, Kim Marriott, and Greg Yelland of Monash University to find out how experienced users of mathematics comprehend algebraic expressions. Finally, it suggests how particular notational configurations may help us recognize structure in mathematical expressions and process equations.

Keywords:   symbols, Gotthilf von Schubert, dreams, Invisible Gorilla experiment, Stanislas Dehaene, numbers, words, mathematics, algebraic expressions, notation

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