Thursday, 28 June 2012

The Origin of the Word Quaternions

The following includes most of a note in the Analyst regarding Hamilton's meaning for the name Quaternions. It includes a poem it appears he wrote, which I had never seen.
Hope it is enjoyable to others.


clipped from article:

It appears from the Preface to the "Lectures" (see page 47), that the four units are the heterogeneous quantities 1, i, j and k, of which the first is the real or scalar unit, and the others correspond to three
mutually rectangular directions in space. Hamilton had in fact found that expressing directed lines in the triplex form ix +jy + kz, x, y and z being real coefficients, he was able to interpret their product as of the form w+ix+jy+kz, a quadruplex quantity, viz.?the sum of a number and line, the latter being perpendicular to the plane of the factor lines.
It seems to have been a favorite conception of Hamilton's to refer the real quantities of simple Algebra to the uni-dimensional quantity time, as in his Essay on Algebra as the Science of Pure Time; thus in the combination of line and number to which his investigations led him, he saw united the one of time and the three of space, as expressed in the sonnet below, which was published after his death in an Article upon the life and genius of Hamilton, in the North British Review.

Sonnet by the Inventor of Quaternions.
(Supposed to have been addressed to Sir John Herschel.)

The Tetractys,
Or high Matheis, with her charm severe
Of line and number, was our theme; and we
Sought to behold her unborn progeny,
And thrones reserved in Truth's celestial sphere:
While views, before attained, became more clear;
And how the One of Time, of Space the Three,
Might, in the chain of Symbol, girdled be:
And when my eager and reverted ear
Caught some faint echoes of an ancient strain,
Some shadowy outlines of old thoughts sublime,
Gently he smiled to see, revived again,
In later age, and occidental clime,
A dimly traced Pythagorean lore,
A westward floating, mystic dream of four.

From "The Analyst Vol. 7, No. 2, Mar., 1880

Thony Christie sent the following comment shortly after I posted this :
William Wordsworth who was a good friend of Hamilton's when asked for his opinion on H's poetry told him he should stick to mathematics.
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