Cargill Gilston Knott
) was born at Penicuik
. He was a pioneer in seismological
research, working in Japan
1883 – 91. His writings display a broad interest in knowledge. Knott was a student and collaborator of Peter Guthrie Tait
and later his biographer. As such he was familiar with quaternion
algebra. When the tight constraints of a single linear algebra
began to be felt in the 1890s and revisionists began publishing, Knott contributed the pivotal article "Recent Innovations in Vector Theory". As M.J. Crowe describes in his book (pp. 200-5), this paper set straight wayward theorists that expected
to find associativity
in systems like hyperbolic quaternions
. Knott wrote:
- [T]he assumption that the square of a unit vector is positive unity leads to an algebra whose characteristic quantities are non-associative.
Evidently Knott overlooked the existence of the ring of coquaternions
. Nevertheless, Crowe states (p.216) that Knott "wrote with care and thoroughness" and that "only Knott was well acquainted with his opponents system".
For a textbook on quaternions, lecturers and students relied on Tait and Kelland's Introduction to Quaternions which had editions in 1873 and 1882. It fell to C.G. Knott to prepare a third edition in 1904. By then the Universal Algebra of Alfred North Whitehead (1898) presumed some grounding in quaternions as students encountered matrix algebra. In Knott's introduction to his textbook edition he says "Analytically the quaternion is now known to take its place in the general theory of complex numbers and continuous groups,...". Thus he was aware of the diversity to be encountered in modern mathematical structures, and that quaternions stand as a milestone on the way to others.
Knott took an active social role in his community including Sunday school teaching and church affairs. He helped to found the Edinburgh Mathematical Society. When he died October 26, 1922, in mid-stride, seemingly at the height of his powers, it is apparent that the Fellows of the Royal Society of Edinburgh experienced some distress at his loss. As Whittaker wrote, they "morn the loss of one who for many years had been as General Secretary, the centre of their corporate activity."
- K.E. Bullen (1973) "Knott, Cargill Gilston" in Dictionary of Scientific Biography, C.C. Gillespie editor, published by American Council of Learned Societies.
- M.J. Crowe (1967) A History of Vector Analysis, esp. pp. 200-5 .
- C.G. Knott (1893) "Recent innovations in vector theory" Proceedings of the Royal Society of Edinburgh 9:212-37.Synopsis in Nature 47:590-3.
- E.T. Whittaker (1922) "Cargill Gilston Knott" (obituary) Proceedings of the Royal Society of Edinburgh 43:237 – 48. Includes a substantial but partial bibliography.