Posted by Israel Cohen on May 13, 2001
In Reply to: Nursery Rhymes posted by R. Berg on March 21, 2001
Richard Woodman authored:
Wherein it is related how that paragon of womanly virtue, young Polly
Nomial (our heroine), is accosted by the notorious villian, 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 singular
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 is was insufficient, and made her way in
among the complex elements. Rows and columns closed in on here 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 steed gradient. When she rounded off once
more, she found herself inverted, apparently aline, in a non-euclidian
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 an 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 lit of secs."
"Oh sir," she protested. "Keep away from me. I haven"t got my
"Calm yourself, my dear." said our suave operator. "Your fears are
"I...I" she thought. "Perhaps he's not normal but homologous."
"What order are your?" the brute demanded.
"Seventeen." replied Polly.
Curly leared, "I suppose you"ve never been operated on."
"Of course not," Polly replied quite properly. "I"m absolutely
"Come, come," said Curly. "Let"s go 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 know. His patience was
gone. Cohsing 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 heavysided operator. Curly"s
radius squared itself. Polly's loci quivered. He integrated by parts,
he integrated by partial fractions. After he cofactored, he performed
runge-kutta 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 completed
When Polly got home that night, her mother noticed that she was no
longer piecewise continuous, and had been truncated in several places,
But is was too late to differentiate how. As the months went by,
Polly's denominator increased monotonically. Finally she went to
L'hospital and generated a small but pathological function which left
surds all over the place an 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."
Journal of Irreproducible Results
Vol 27/Num 1/ 1981
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