Mathematical Sex

[Xipe Totec]

Oldie but goodie...

Wherein it is related how that Polygon of Womanly Virtue, your Polly Nomial
(our heroine) is accosted by that Notorious Villain Curly Pi, and factored (oh,
horror).


Once upon a time ( 1/T ), Pretty Polly Nomial was strolling across a field of
vectors when she came to the boundary of a singularly large matrix. Now Polly
was convergent and her mother had made it an absolute condition that she never
enter such an array without her brackets on. Polly, however, who had changed her
variables that morning and was feeling particularly badly behaved, ignored this
condition on the basis that it was insufficient, and made her way amongst the
complex elements. Rows and columns closed in from all sides. Tangents approached
her surface. She became tensor and tensor. Quite suddenly, two branches of a
hyperbola touched her at a single point. She oscillated violently, lost all
sense of directrix, and went completely divergent. As she reached a turning
point, she tripped over a square root that was protruding from the erf and
plunged headlong down a steep gradient. When she rounded off once more, she
found herself inverted, apparently alone, in a non-Euclidian space.
She was being watched, however. That smooth operator, Curly Pi, was lurking
innerproduct. As his eyes devoured her curvilinear coordinates, a singular
expression crossed his face. He wondered, was she still convergent? He decided
to integrate improperly at once.
Hearing a common fraction behind her, Polly rotated and saw Curly Pi
approaching with his power series extrapolated. She could see at once by his
degenerate conic and dissipative terms that he was bent on no good.
"Arcsinh," she gasped.
"Ho, ho," he said. "What a symmetric little asymptote you have. I can see
your angles have a lot of secs."
"Oh, sir," she protested, "keep away from me. I haven't got my brackets on."
"Calm yourself, My Dear," said our Suave Operator. "Your fears are purely
imaginary."
"I, I," she thought, "perhaps he's not normal but homologous."
"What order are you?" the Brute demanded.
"Seventeen," replied Polly.
Curly leered. "I suppose you've never been operated on."
"Of course not," Polly replied quite properly. "I'm absolutely convergent."
"Come, come," said Curly, "Let's off to a decimal place I know and I'll take
you to the limit."
"Never," gasped Polly.
"Abscissa," he swore, using the vilest oath he knew. His patience was gone.
Coshing her over the coefficient with a log until she was powerless, Curly
removed her discontinuities. He stared at her significant places, and began
smoothing out her points of inflection. Poor Polly. The algorithmic method was
now her only hope. She felt his hand tending to her asymptotic limit. Her
convergence would soon be gone forever.
There was no mercy, for Curly was a heavyside operator. Curly's radius
squared itself; Polly's loci quivered. He integrated by parts. He integrated by
partial fractions. After he cofactored, he performed rungecutta on her. The
complex beast even went all the way around and did a contour integration. Curly
went on operating until he had satisfied her hypothesis, then he exponentiated
and became completely orthogonal.
When Polly got home that night, her mother noticed that she was no longer
piecewise continuous, but had been truncated in several places. But is was too
late to differentiate now. As the months went by, Polly's denominator increased
monotonically. Finally, she went to the L'Hopital and generated a small but
pathological function which left surds all over the place and drove Polly to
deviation.
The moral of our sad story is this:
'If you want to keep your expressions convergent, never allow them a single
degree of freedom...'