(A Mathematical Courtship)
It was a lovely Autumn evening, and the glorious effects of chromatic
aberration were beginning to show themselves in the atmosphere as
the earth revolved away from the great western luminary, when two
lines might have been observed wending their weary way across a plain
superficies. The elder of the two had, by long practice, acquired the
art, so painful to young and impulsive loci, of lying evenly between
her extreme points; but the younger, in her girlish impetuosity, was
ever longing to diverge and become an hyperbola or some such romantic
and boundless curve.
“They had lived and loved: fate and the intervening superficies had
hitherto kept them asunder, but this was no longer to be: _a line had
intersected them, making the two interior angles together less than
two right angles_. It was a moment never to be forgotten and they
journeyed on, a whisper thrilled along the superficies in isochronous
waves of sound, ‘Yes! We shall at length meet, if continually
produced!’” (“Jacobi’s Course of Mathematics,” Chap. I.). We have
commenced with the above quotation as a striking illustration of the
advantage of introducing the human element into the hitherto barren
region of Mathematics. Who shall say what germs of romance, hitherto
not observed, may not underlie the subject? Who can tell whether the
parallelogram, which in our ignorance we have defined and drawn, and
the whole of whose properties we profess to know, may not be all the
while panting for exterior angles, sympathetic with the interior, or
sullenly repining at the fact that it cannot be inscribed in a circle?
What mathematician has ever pondered over an hyperbola, mangling
the unfortunate curve with lines of intersection here and there, in
his efforts to prove some property that perhaps after all is a mere
calumny, who has not fancied at last that the ill-used locus was
spreading out its asymptotes as a silent rebuke, or winking one focus
at him in contemptuous pity?
[36] From “The Dynamics of a Parti-cle” (1865).