ARM Club 1/ARM_CLUB_CD.iso/contents/sillies/silly8/P/PollyNomin

Text File | 1994-03-04 | 4KB | 100 lines

Following is a mathematical romance which I came
accross years ago.

_________________________________________________________

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).

                The tragedy of Polly Nominal
                ----------------------------

Once upon a time ( 1/T ), Pretty Polly Nomial was strolling
accross 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.

        "Sixteen," 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 . . .'

*** EOF