A History of Vector Analysis
Encyclopedia
A History of Vector Analysis (1967) is a book on the history of vector analysis by Michael J. Crowe, originally published by the University of Notre Dame Press
.
As a scholarly treatment of a reformation in technical communication
, the text is a contribution to the history of science
. In 2002, Crowe gave a talk summarizing the book, including an entertaining introduction in which he covered its publication history and related the award of a Jean Scott prize of $4000. Crowe had entered the book in a competition for "a study on the history of complex and hypercomplex numbers" twenty-five years after his book was first published.
and quaternions; the third on other 19th and 18th century vectorial systems; the fourth on the general interest in the 19th century on vectorial systems including analysis of journal publications as well as sections on major figures and their views (e.g., Peter Guthrie Tait
as an advocate of Quaternions and James Clerk Maxwell
as a critic of Quaternions); the fifth on Josiah Willard Gibbs
and Oliver Heaviside
and their development of a modern system of vector analysis.
In chapter six, "Struggle for existence",
Michael J. Crowe delves into the zeitgeist
that pruned down quaternion theory into vector analysis on three-dimensional space
. He makes clear the ambition of this effort by considering five major texts as well as a couple dozen articles authored by participants in "The Great Vector Debate". These are the books:
Twenty of the ancillary articles appeared in Nature
; others were in Philosophical Magazine
, London or Edinburgh Proceedings of the Royal Society
, Physical Review
, and Proceedings of the American Association for the Advancement of Science
. The authors included the book authors, Cargill Gilston Knott
, and a half-dozen other hands.
The "struggle for existence" is a phrase from Charles Darwin
’s Origin of Species and Crowe quotes Darwin: "…young and rising naturalists,…will be able to view both sides of the question with impartiality." After 1901 with the Gibbs/Wilson/Yale publication Vector Analysis, the question was decided in favour of the vectorialists with separate dot and cross products. The pragmatic temper of the times set aside the four-dimensional source of vector algebra.
Crowe's chapter seven is a survey of "Twelve major publications in Vector Analysis from 1894 to 1910". Of these twelve, seven are in German, two in Italian, one in Russian, and two in English. Whereas the previous chapter examined a debate in English, the final chapter notes the influence of Hertz' results with radio and the rush of German research using vectors. Joseph George Coffin of MIT and Clark University
published his Vector Analysis in 1909; it too leaned heavily into applications. Thus Crowe provides a context for Gibbs and Wilson’s famous textbook of 1901.
The eighth chapter is the author's summary and conclusions. The book relies on references in chapter endnotes instead of a bibliography section. Crowe also states that the Bibliography of the Quaternion Society, and its supplements to 1912, already listed all the primary literature for the study.
begins his 1969 review with "Since historical publications on modern developments are rare, this book is welcome." and ends with "the subtitle [,The Evolution of the Idea of a Vectorial System,] is a better description of the contents than the title proper." Then William C. Waterhouse
—picking up where Kline's review left off—writes in 1972 "Crowe's book on vector analysis seems a little anemic in comparison, perhaps because its title is misleading. ... [Crowe] does succeed in his goal of tracing the genealogy of the 3-space system, concluding that it was developed out of quaternions by physicists."
University of Notre Dame Press
The University of Notre Dame Press is a university press that is part of the University of Notre Dame in Notre Dame, Indiana, United States.-External links:*...
.
As a scholarly treatment of a reformation in technical communication
Technical communication
Technical communication is a method of researching and creating information about technical processes or products directed to an audience through media. The information must be relevant to the intended audience. Technical communicators often work collaboratively to create products for various...
, the text is a contribution to the history of science
History of science
The history of science is the study of the historical development of human understandings of the natural world and the domains of the social sciences....
. In 2002, Crowe gave a talk summarizing the book, including an entertaining introduction in which he covered its publication history and related the award of a Jean Scott prize of $4000. Crowe had entered the book in a competition for "a study on the history of complex and hypercomplex numbers" twenty-five years after his book was first published.
Summary of book
The book has eight chapters: the first on the origins of vector analysis including Ancient Greek and 16th and 17th century influences; the second on the 19th century William Rowan HamiltonWilliam Rowan Hamilton
Sir William Rowan Hamilton was an Irish physicist, astronomer, and mathematician, who made important contributions to classical mechanics, optics, and algebra. His studies of mechanical and optical systems led him to discover new mathematical concepts and techniques...
and quaternions; the third on other 19th and 18th century vectorial systems; the fourth on the general interest in the 19th century on vectorial systems including analysis of journal publications as well as sections on major figures and their views (e.g., Peter Guthrie Tait
Peter Guthrie Tait
Peter Guthrie Tait FRSE was a Scottish mathematical physicist, best known for the seminal energy physics textbook Treatise on Natural Philosophy, which he co-wrote with Kelvin, and his early investigations into knot theory, which contributed to the eventual formation of topology as a mathematical...
as an advocate of Quaternions and James Clerk Maxwell
James Clerk Maxwell
James Clerk Maxwell of Glenlair was a Scottish physicist and mathematician. His most prominent achievement was formulating classical electromagnetic theory. This united all previously unrelated observations, experiments and equations of electricity, magnetism and optics into a consistent theory...
as a critic of Quaternions); the fifth on Josiah Willard Gibbs
Josiah Willard Gibbs
Josiah Willard Gibbs was an American theoretical physicist, chemist, and mathematician. He devised much of the theoretical foundation for chemical thermodynamics as well as physical chemistry. As a mathematician, he invented vector analysis . Yale University awarded Gibbs the first American Ph.D...
and Oliver Heaviside
Oliver Heaviside
Oliver Heaviside was a self-taught English electrical engineer, mathematician, and physicist who adapted complex numbers to the study of electrical circuits, invented mathematical techniques to the solution of differential equations , reformulated Maxwell's field equations in terms of electric and...
and their development of a modern system of vector analysis.
In chapter six, "Struggle for existence",
Michael J. Crowe delves into the zeitgeist
Zeitgeist
Zeitgeist is "the spirit of the times" or "the spirit of the age."Zeitgeist is the general cultural, intellectual, ethical, spiritual or political climate within a nation or even specific groups, along with the general ambiance, morals, sociocultural direction, and mood associated with an era.The...
that pruned down quaternion theory into vector analysis on three-dimensional space
Three-dimensional space
Three-dimensional space is a geometric 3-parameters model of the physical universe in which we live. These three dimensions are commonly called length, width, and depth , although any three directions can be chosen, provided that they do not lie in the same plane.In physics and mathematics, a...
. He makes clear the ambition of this effort by considering five major texts as well as a couple dozen articles authored by participants in "The Great Vector Debate". These are the books:
- Elementary Treatise on Quaternions (1890) Peter Guthrie TaitPeter Guthrie TaitPeter Guthrie Tait FRSE was a Scottish mathematical physicist, best known for the seminal energy physics textbook Treatise on Natural Philosophy, which he co-wrote with Kelvin, and his early investigations into knot theory, which contributed to the eventual formation of topology as a mathematical...
- Elements of Vector Analysis (1881,1884) Josiah Willard GibbsJosiah Willard GibbsJosiah Willard Gibbs was an American theoretical physicist, chemist, and mathematician. He devised much of the theoretical foundation for chemical thermodynamics as well as physical chemistry. As a mathematician, he invented vector analysis . Yale University awarded Gibbs the first American Ph.D...
- Electromagnetic Theory (1893,1899,1912) Oliver HeavisideOliver HeavisideOliver Heaviside was a self-taught English electrical engineer, mathematician, and physicist who adapted complex numbers to the study of electrical circuits, invented mathematical techniques to the solution of differential equations , reformulated Maxwell's field equations in terms of electric and...
- Utility of Quaternions in Physics (1893) Alexander MacAulay
- Vector Analysis and Quaternions (1906) Alexander MacfarlaneAlexander MacfarlaneAlexander Macfarlane was a Nova Scotia lawyer and political figure. He was a member of the Canadian Senate from 1870 to 1898. His surname also appears as McFarlane in some sources....
Twenty of the ancillary articles appeared in Nature
Nature (journal)
Nature, first published on 4 November 1869, is ranked the world's most cited interdisciplinary scientific journal by the Science Edition of the 2010 Journal Citation Reports...
; others were in Philosophical Magazine
Philosophical Magazine
The Philosophical Magazine is one of the oldest scientific journals published in English. Initiated by Alexander Tilloch in 1798, in 1822 Richard Taylor became joint editor and it has been published continuously by Taylor & Francis ever since; it was the journal of choice for such luminaries as...
, London or Edinburgh Proceedings of the Royal Society
Royal Society
The Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...
, Physical Review
Physical Review
Physical Review is an American scientific journal founded in 1893 by Edward Nichols. It publishes original research and scientific and literature reviews on all aspects of physics. It is published by the American Physical Society. The journal is in its third series, and is split in several...
, and Proceedings of the American Association for the Advancement of Science
American Association for the Advancement of Science
The American Association for the Advancement of Science is an international non-profit organization with the stated goals of promoting cooperation among scientists, defending scientific freedom, encouraging scientific responsibility, and supporting scientific education and science outreach for the...
. The authors included the book authors, Cargill Gilston Knott
Cargill Gilston Knott
Cargill Gilston Knott was a Scottish physicist and mathematician who was a pioneer in seismological research. He spent his early career in Japan...
, and a half-dozen other hands.
The "struggle for existence" is a phrase from Charles Darwin
Charles Darwin
Charles Robert Darwin FRS was an English naturalist. He established that all species of life have descended over time from common ancestry, and proposed the scientific theory that this branching pattern of evolution resulted from a process that he called natural selection.He published his theory...
’s Origin of Species and Crowe quotes Darwin: "…young and rising naturalists,…will be able to view both sides of the question with impartiality." After 1901 with the Gibbs/Wilson/Yale publication Vector Analysis, the question was decided in favour of the vectorialists with separate dot and cross products. The pragmatic temper of the times set aside the four-dimensional source of vector algebra.
Crowe's chapter seven is a survey of "Twelve major publications in Vector Analysis from 1894 to 1910". Of these twelve, seven are in German, two in Italian, one in Russian, and two in English. Whereas the previous chapter examined a debate in English, the final chapter notes the influence of Hertz' results with radio and the rush of German research using vectors. Joseph George Coffin of MIT and Clark University
Clark University
Clark University is a private research university and liberal arts college in Worcester, Massachusetts.Founded in 1887, it is the oldest educational institution founded as an all-graduate university. Clark now also educates undergraduates...
published his Vector Analysis in 1909; it too leaned heavily into applications. Thus Crowe provides a context for Gibbs and Wilson’s famous textbook of 1901.
The eighth chapter is the author's summary and conclusions. The book relies on references in chapter endnotes instead of a bibliography section. Crowe also states that the Bibliography of the Quaternion Society, and its supplements to 1912, already listed all the primary literature for the study.
Summary of reviews
There were significant reviews given near the time of original publication. Morris KlineMorris Kline
Morris Kline was a Professor of Mathematics, a writer on the history, philosophy, and teaching of mathematics, and also a popularizer of mathematical subjects.Kline grew up in Brooklyn and in Jamaica, Queens...
begins his 1969 review with "Since historical publications on modern developments are rare, this book is welcome." and ends with "the subtitle [,The Evolution of the Idea of a Vectorial System,] is a better description of the contents than the title proper." Then William C. Waterhouse
William C. Waterhouse
William Charles Waterhouse is an American mathematician, a professor of Mathematics at Pennsylvania State University. His research interests include abstract algebra, number theory, group schemes, and the history of mathematics...
—picking up where Kline's review left off—writes in 1972 "Crowe's book on vector analysis seems a little anemic in comparison, perhaps because its title is misleading. ... [Crowe] does succeed in his goal of tracing the genealogy of the 3-space system, concluding that it was developed out of quaternions by physicists."
Other Sources
- A History of Vector Analysis: The Evolution of the Idea of a Vectorial System. Michael J. Crowe, University of Notre Dame Press 1967, pages xvii, 270. ASIN: B000GX2E78
- A History of Vector Analysis: The Evolution of the Idea of a Vectorial System. Michael J. Crowe, Dover Publications 1994, pages 288. ISBN 0-486-67910-1
- Morris KlineMorris KlineMorris Kline was a Professor of Mathematics, a writer on the history, philosophy, and teaching of mathematics, and also a popularizer of mathematical subjects.Kline grew up in Brooklyn and in Jamaica, Queens...
(1969) Review of A History of Vector Analysis Mathematical ReviewsMathematical ReviewsMathematical Reviews is a journal and online database published by the American Mathematical Society that contains brief synopses of many articles in mathematics, statistics and theoretical computer science.- Reviews :...
37 #5070. - William C. WaterhouseWilliam C. WaterhouseWilliam Charles Waterhouse is an American mathematician, a professor of Mathematics at Pennsylvania State University. His research interests include abstract algebra, number theory, group schemes, and the history of mathematics...
, Review, Bulletin of the American Mathematical SocietyBulletin of the American Mathematical SocietyThe Bulletin of the American Mathematical Society is a quarterly mathematical journal published by the American Mathematical Society...
, Volume 78, Number 3 (1972), 385-391.