Hi all-
I am going to give the Oersted lecture a careful reading before
giving my explanation of what Hesthenes is proposing. I have, however,
done a bit of historical research and found that he seems to be reviving a
controversy that was settled a century ago. I quote from Chap. 32, Sec. 5
of Kline's "Mathematical Thought from Ancient to Modern Times."
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While vector analysis whas being created and afterward there was
much controversy between the proponents of quaternions and the proponents
of vectors as to which was more useful. The quaternionists were fanatical
about the value of quaternions but the proponents of vector analysis were
equally partisan. On one side were aligned the leading supporters of
quaternions such as Tait and, on the other, Gibbs and Heaviside. Apropos
of the controversy, Heaviside remarked sarcastically that for the
treatment of quaternions, quaternions are the best instrument. On the
other hand Tait described Heaviside's vector algebra as 'a sort of
hermaphrodite monster, compounded of the notations of Grassman and
Hamilton.' Gibb's book ["Elements of Vector Analysis"] proved to be of
inestimable value in promoting the vector cause.
The issue was finally settled in favor of vectors. Engineers
welcomed Gibbs's and Heaviside's vector analysis, though the
mathematicians did not. By the beginning of the present century the
physicists too were quite convinced that vector analysis was what they
wanted. Textbooks on the subject soon appeared in all countries and are
now standard. The mathematicians finally followed suit and introduced
vector methods in analytic and differential geometry.
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The quaternion algebra is closely related to the Pauli algebra,
which Hesthenes introduced around Eq. 10 of his Lecture.
I expect to discuss Hesthenes proposal strictly within the
confines of 3-dimensional introductory physics.
Regards,
Jack
--
"What did Barrow's lectures contain? Bourbaki writes with some
scorn that in his book in a hundred pages of the text there are about 180
drawings. (Concerning Bourbaki's books it can be said that in a thousand
pages there is not one drawing, and it is not at all clear which is
worse.)"
V. I. Arnol'd in
Huygens & Barrow, Newton & Hooke