Gaspard de Prony
Gaspard Clair François Marie Riche de Prony (22 July 1755 – 29 July 1839) was a French mathematician and engineer, who worked on hydraulics. He was born at Chamelet, Beaujolais, France[1] and died in Asnières-sur-Seine, France.
Education and early works
He was Engineer-in-Chief of the École Nationale des Ponts et Chaussées.
The trigonometric and logarithmic tables of the cadastre
In 1791, de Prony embarked on the task of producing logarithmic and trigonometric tables for the French Cadastre. The effort was sanctioned by the French National Assembly, which, after the French Revolution wanted to bring uniformity to the multiple measurements and standards used throughout the nation. In particular, his tables were intended for precise land surveys, as part of a greater cadastre effort. The tables were vast, with values calculated to between fourteen and twenty-nine decimal places.[2]
Inspired by Adam Smith's Wealth of Nations, de Prony divided up the labor into three levels, bragging that he "could manufacture logarithms as easily as one manufactures pins."[3]:36
The first level consisted of five or six high-ranking mathematicians with sophisticated analytical skills, including Adrien-Marie Legendre and Lazare Carnot. This group chose the analytical formulas most suited to evaluation by numerical methods, and specified the number of decimals and the numerical range the tables were to cover.
The second group of lesser mathematicians, seven or eight in number, combined analytical and computational skills, and this group calculated the pivotal values using the formulas provided and the sets of starting differences. They also prepared templates for the human computers, and the first worked row of calculations, as well as the instructions for the computers to carry the sequence to completion.
The third group consisted of sixty to eighty human computers. These had no more than a rudimentary knowledge of arithmetic and carried out the most laborious and repetitive part of the process. Many were out-of-work hairdressers, because, with the guillotining of the aristocracy, the hairdressing trade, which had tended the elaborate hairstyles of the elite, was in recession. [4][5]
At the bottom were about ninety "computers" (as they were called) who were not trained in mathematics, but who followed the instructions."[3]:33–39
Due to a lack of funding from inflation following the French revolution, the tables were never published in full. The first excerpt of the table was published a century later.[6]
Enlightenment calculations
According to Prony, the project was to leave "nothing to desire with respect to exactitude" and to be "the most vast... monument to calculation ever executed or even conceived." The tables were not used for their original purpose of bringing consistent standards for measurement, as the entire cadastre project saw delays in establishing both new measurement units as well as budget cuts. In particular, these tables, which were designed for the decimal division of circles and time, turned out to be obsolete after the French had changed their measurement system. Moreover, there was no practical use for the full extent of de Prony's calculation's accuracy. Hence, these tables became more of artifacts and monuments to Enlightenment rather than objects of practical use.[7]
Influence on the meaning of calculation
By the turn of the 19th century, there was a shift in the meaning of calculation. The talented mathematicians and other intellectuals who produced creative and abstract ideas were regarded separately from those who were able to perform tedious and repetitive computations. Before the 19th century, calculation was regarded as a task for the academics, while afterwards, calculations were associated with unskilled laborers. This was accompanied by a shift in gender roles as well, as women, who were usually underrepresented in mathematics at the time, were hired to perform extensive computations for the tables as well as other computational government projects until the end of World War II. This shift in the interpretation of calculation was largely due to de Prony's calculation project during the French Revolution.[7]:186 This project was able to unite people from many different walks of life as well as mathematical abilities (in the traditional sense) and hence changed the meaning of calculation from intelligence into unskilled labor.[7]:190
Mechanizing calculation
Prony was able to have artisans (workers who excelled in mechanical arts that require intelligence) work along with mathematicians to perform the calculations. Prony noted a few interesting observations about this new dynamic. First, it was fascinating to see so many different people work on the same problem. Second, he realized that even the ones with the least intellectual ability were able to perform these computations with astonishingly few errors. Prony saw this entire system as a collection of human computers working together as a whole - a machine governed by hierarchical principles of the division of labor. In fact, Prony may have begun to amend his notion of intelligence, which he began to use to evaluate the system as a whole, rather than evaluating the intelligence of its constituents.[7]:195,6
Prony's brake
One of de Prony's important scientific inventions was the "brake" which he invented in 1821 to measure the performance of machines and engines.
He also was first to propose using a reversible pendulum to measure gravity, which was independently invented in 1817 by Henry Kater and became known as the Kater's pendulum.
Prony's estimation method
He also created a method of converting sinusoidal and exponential curves into a systems of linear equations. Prony estimation is used extensively in signal processing and finite element modelling of non linear materials.[8]
Distinctions
Prony was a member, and eventually president, of the French Academy of Science. He was also elected a foreign member of the Royal Swedish Academy of Sciences in 1810. His name is one of the 72 names inscribed on the Eiffel Tower.
See also
References
- ↑ Bradley, Margaret (1998) A career biography of Gaspard Clair Francois Marie Riche De Prony, bridge-builder, educator, and scientist, Mellen Press
- ↑ However, one must distinguish the number of places of calculation from the number of places of accuracy. These tables were not accurate to 14 and 29 places.
- 1 2 Grier, David Alan (2005) When Computers Were Human, Princeton University Press
- ↑ Grattan-Guinness, Ivor (1990). Convolutions in French Mathematics, 1800-1840: From the Calculus and Mechanics to Mathematical Analysis and Mathematical Physics. p. 179.
- ↑ David Swade, Doron. "Calculation and Tabulation in the Nineteenth Century: Airy versus Babbage, PhD Thesis" (PDF).
- ↑ The site http://locomat.loria.fr contains a detailed analysis of Prony's tables.
- 1 2 3 4 Daston, Lorraine (1994). "Enlightenment Calculations". Critical Inquiry. University of Chicago Press. 21 (1): 183–184.
- ↑ LS-DYNDA Keyword Manual. Livermore Software Technology Corporation. 2009. pp289