Article ID: CBB487959297

Babbage’s Guidelines for the Design of Mathematical Notations (2021)


The design of good notation is a cause that was dear to Charles Babbage’s heart throughout his career. He was convinced of the “immense power of signs” (1864, 364), both to rigorously express complex ideas and to facilitate the discovery of new ones. As a young man, he promoted the Leibnizian notation for the calculus in England, and later he developed a Mechanical Notation for designing his computational engines. In addition, he reflected on the principles that underlie the design of good mathematical notations. In this paper, we discuss these reflections, which can be found somewhat scattered in Babbage’s writings, for the first time in a systematic way. Babbage’s desiderata for mathematical notations are presented as ten guidelines pertinent to notational design and its application to both individual symbols and complex expressions. To illustrate the applicability of these guidelines in non-mathematical domains, some aspects of his Mechanical Notation are also discussed.

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Authors & Contributors
Fisch, Menachem
Gray, Jeremy
Parshall, Karen V. Hunger
Nomura, Tsunehiko
Simonov, R. A.
Morozov, B. N.
Archive for History of Exact Sciences
Studies in History and Philosophy of Science
History and Technology
科学史研究 Kagakusi Kenkyu (History of Science)
VIET: Voprosy Istorii Estestvoznaniia i Tekhniki
Rutherford Journal: The New Zealand Journal for the History and Philosophy of Science and Technology
American Mathematical Society
Princeton University Press
Cork University Press
Number notation; mathematical notation
Visual representation; visual communication
Number theory; number concept
Babbage, Charles
Peacock, George
Gregory, Duncan Farquharson
Kronecker, Leopold
Minkowski, Hermann
Dickson, Leonard Eugene
Time Periods
19th century
20th century, early
18th century
11th century
Paris (France)
Ural Mountains region (Russia)
Florence (Italy)
University of Chicago
Search for Extraterrestrial Intelligence (SETI) (Study group: U.S.)

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