A History of Vector Analysis: The Evolution of the Idea of a Vectorial System

Rating:
Summary: Interesting summary of the history of an important idea
Review: Although several others made important contributions, this book is primarily a study about the ideas of four people: Hamilton, Grassmann, Gibbs, and Heaviside. Hamilton's creation of the algebra of quaternions, while an important mathematical innovation, was thought of in many minds as primarily a physical tool, to be used in many of the applications that today are done by vectorial methods (and, in fact, the terms "scalar" and "vector" were invented by Hamilton, but with slightly different meanings than their present ones). Grassmann developed a quite different system, much closer to our present vector algebra, but unrecognized because of his obscurity and his books' unreadability. The true founders of modern vector analysis were the American physical chemist Josiah Willard Gibbs and the British physicist Oliver Heaviside, working independently of each other. What is interesting is that both Gibbs and Heaviside arrived at identical systems by modifying Hamilton's quaternion algebra to make it more accurately reflect the needs of physical scientists. While both Gibbs and Heaviside started with Hamilton's methods, the system they both arrived at was closer to Grassmann's in structure. And all this is clearly put forth in Crowe's book.

One other thing that the book makes clear is that J. Willard Gibbs, far more humbly than most scientists involved in priority disputes, clearly recognized that Grassmann had anticipated his ideas, although Grassmann's books had not come to Gibbs' attention until Gibbs had completely worked out his own system. And Gibbs, though he had based his ideas on Hamilton's, also recognized that Grassmann had the superior approach. (Though this may have NOT been a sign of humility, because in this regard Gibbs ended up using Grassmann's ideas to justify his own.)

Crowe's book is very readable, makes all these points quite clearly, and is highly recommended if you are interested in the subject.

Rating:
Summary: Thoughtful, Detailed History of Vector Analysis
Review: How were the concepts of vector analysis developed? How did modern vector notation become widely accepted? Who were the key players and why did quaternions fail to gain acceptance? This book is extensively documented, scholarly in its approach, sometimes a bit slow, but overall it is a fascinating look at these specific questions as well as the fundamental issue of what factors promote or delay acceptance of revolutionary ideas in science and mathematics.

I did not become immediately engaged with Crowe's style and even set the book aside after reading the prefaces and first chapter. A few months later I returned to chapter two (in part due to a previous reviewer's high rating). And what a surprise - I suddenly found myself intrigued with Crowe's discussion of Sir William Hamilton's single minded focus on quaternions, the perseverance and genius of Hermann Grassmann, the critical roles played by Peter Tait and James Maxwell, and the pragmatic way in which Josiah Gibbs and Oliver Heaviside independently extracted key vectorial concepts from Hamiliton-Tait's quaternion analysis.

Crowe's book was originally published in 1967 by University of Notre Dame, Dover reprinted it in 1985, Crowe recieved the Jean Scott Prize by the Maison des Sciences de l'Homme (Paris)in 1992, and Dover reprinted it again in 1992. Dover should be commended for making such reprints readily available at affordable prices.

The discussion of Hamilton's quaternions does not require familiarity with quaternions, but some prior acquaintance might be helpful. I encountered quaternions in another Dover reprint: Matrices and Transformations by Pettofrezzo. Section 2-3 introduces quaternion notation, simple manipulations, and shows that addition and multiplication of quaternions is isomorphic with two particular sets of matrices.

Has quaternion analysis survived? See Quaternions and Rotation Sequences: A Primer With Applications to Orbits, Aerospace, and Virtual Reality by Jack Kuipers, Aprill, 1999. The reviews by readers are all five stars.

Rating:
Summary: Thoughtful, Detailed History of Vector Analysis
Review: How were the concepts of vector analysis developed? How did modern vector notation become widely accepted? Who were the key players and why did quaternions fail to gain acceptance? This book is extensively documented, scholarly in its approach, sometimes a bit slow, but overall it is a fascinating look at these specific questions as well as the fundamental issue of what factors promote or delay acceptance of revolutionary ideas in science and mathematics.

I did not become immediately engaged with Crowe's style and even set the book aside after reading the prefaces and first chapter. A few months later I returned to chapter two (in part due to a previous reviewer's high rating). And what a surprise - I suddenly found myself intrigued with Crowe's discussion of Sir William Hamilton's single minded focus on quaternions, the perseverance and genius of Hermann Grassmann, the critical roles played by Peter Tait and James Maxwell, and the pragmatic way in which Josiah Gibbs and Oliver Heaviside independently extracted key vectorial concepts from Hamiliton-Tait's quaternion analysis.

Crowe's book was originally published in 1967 by University of Notre Dame, Dover reprinted it in 1985, Crowe recieved the Jean Scott Prize by the Maison des Sciences de l'Homme (Paris)in 1992, and Dover reprinted it again in 1992. Dover should be commended for making such reprints readily available at affordable prices.

The discussion of Hamilton's quaternions does not require familiarity with quaternions, but some prior acquaintance might be helpful. I encountered quaternions in another Dover reprint: Matrices and Transformations by Pettofrezzo. Section 2-3 introduces quaternion notation, simple manipulations, and shows that addition and multiplication of quaternions is isomorphic with two particular sets of matrices.

Has quaternion analysis survived? See Quaternions and Rotation Sequences: A Primer With Applications to Orbits, Aerospace, and Virtual Reality by Jack Kuipers, Aprill, 1999. The reviews by readers are all five stars.

Rating:
Summary: Thorough, intelligent and impeccably unprejudiced.
Review: This book is a model of science history. Crowe manages to give one a clear view of the trends and moods of the time (1840-1900), the personalities of the various figures involved (Esp. Hamilton, Grassman and Gibbs), without sacrificing his most significant asset: the facts.