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The Rise of Statistical Thinking, 1820-1900$
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Theodore M. Porter

Print publication date: 2020

Print ISBN-13: 9780691208428

Published to Princeton Scholarship Online: January 2021

DOI: 10.23943/princeton/9780691208428.001.0001

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The Errors of Art and Nature

The Errors of Art and Nature

Chapter:
(p.97) Chapter Four The Errors of Art and Nature
Source:
The Rise of Statistical Thinking, 1820-1900
Author(s):

Theodore M. Porter

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691208428.003.0005

This chapter analyzes the law of facility of errors. All the early applications of the error law could be understood in terms of a binomial converging to an exponential, as in Abrahan De Moivre's original derivation. All but Joseph Fourier's law of heat, which was never explicitly tied to mathematical probability except by analogy, were compatible with the classical interpretation of probability. Just as probability was a measure of uncertainty, this exponential function governed the chances of error. It was not really an attribute of nature, but only a measure of human ignorance—of the imperfection of measurement techniques or the inaccuracy of inference from phenomena that occur in finite numbers to their underlying causes. Moreover, the mathematical operations used in conjunction with it had a single purpose: to reduce the error to the narrowest bounds possible. With Adolphe Quetelet, all that began to change, and a wider conception of statistical mathematics became possible. When Quetelet announced in 1844 that the astronomer's error law applied also to the distribution of human features such as height and girth, he did more than add one more set of objects to the domain of this probability function; he also began to break down its exclusive association with error.

Keywords:   error law, Abrahan De Moivre, Joseph Fourier, mathematical probability, measurement techniques, mathematical operations, Adolphe Quetelet, statistical mathematics, human features

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