Hamilton, Rodrigues, and the Quaternion Scandal

The invention of the calculus of quaternions is a step towards the knowledge of quantities related to space which can only be compared, for its importance, with the invention of triple coordinates by Descartes. The ideas of this calculus, as distinguished from its operations and symbols, are fitted to be of the greatest use in all parts of science. Such robust language as Lord Kelvin's may now be largely forgotten, but the fact remains that the man in the street is strangely averse to using quaternions. Side by side with matrices and vectors, now the lingua franca of all physical scientists, quaternions appear to exude an air of nineteenth-century decay, as a rather unsuccess- ful species in the struggle-for-life of mathematical ideas. Mathematicians, admittedly, still keep a warm place in their hearts for the remarkable algebraic properties of quaternions, but such enthusiasm means little to the harder-headed physical scientist. This article will attempt to highlight certain problems of interpretation as regards quaternions which may seriously have affected their progress, and which might explain their present parlous status. For claims were made for quaternions which quaternions could not possibly fulfil, and this made it difficult to grasp what quater- nions are excellent at, which is handling rotations and double groups. It is

[1]  George Frederick James Temple.  Cartesian tensors. An introduction. , 1960 .

[2]  William Rowan Hamilton,et al.  LXXVIII. On quaternions; or on a new system of imaginaries in Algebra: To the editors of the Philosophical Magazine and Journal , 1844 .

[3]  E. Wilson,et al.  To the Finland Station , 1940 .

[4]  Felix Klein,et al.  Vorlesungen uber die Entwicklung der Mathematik im 19. Jahrhundert , 1967 .

[5]  S. Charléty.  Histoire du Saint-Simonisme : (1825-1864) , 1931 .

[6]  A. Mackay.  The Harvest of a Quiet Eye: A Selection of Scientific Quotations , 1977 .

[7]  Edmund Taylor Whittaker,et al.  William Rowan Hamilton , 1954 .

[8]  E. Cartan,et al.  Les groupes projectifs qui ne laissent invariante aucune multiplicité plane , 1913 .

[9]  G. Vlastos,et al.  The Presocratic Philosophers , 1959 .

[10]  S. Altmann.  Rotations, Quaternions, and Double Groups , 1986 .

[11]  Jeremy Gray,et al.  Olinde Rodrigues' paper of 1840 on transformation groups , 1980 .

[12]  E. T. Bell,et al.  Men of Mathematics , 1937, Nature.

[13]  Edmund Wilson,et al.  To the Finland station : a study in the writing and acting of history : with a new introduction , 1953 .

[14]  J. Clerk-Maxwell.  Remarks on the Mathematical Classification of Physical Quantities , 1869 .

[15]  R. Graves,et al.  The Life of Sir William Rowan Hamilton , 1889, Nature.

[16]  Silvanus Phillips Thompson,et al.  The Life of William Thomson, Baron Kelvin of Largs: THE ATLANTIC TELEGRAPH: FAILURE , 1910 .

[17]  G. Weill.  Un précurseur du socialisme : Saint-Simon et son œuvre , 1894 .

[18]  J. Stepánek,et al.  I INTRODUCTION , 1961 .

[19]  Lawrence Shaw Mayo,et al.  The Harvest of a Quiet Eye , 1928 .

[20]  Saint-Simon and Saint-Simonism : a chapter in the history of Socialism in France. , 1970 .

[21]  A. S. Ramsey.  The Mathematical Papers of Sir William Rowan Hamilton , 1931, Nature.

[22]  Clifford,et al.  Applications of Grassmann's Extensive Algebra , 1878 .

[23]  Owen Barfield.  What Coleridge Thought , 1973 .

[24]  John Warren.  On the geometrical representation of the powers of quantities, whose indices involve the square roots of negative quantities , 1815 .

[25]  Pierre Larousse,et al.  Grand dictionnaire universel du XIXe siècle , 1863 .