Posted by Israel Cohen on May 13, 2001

In Reply to: Re: Nursery Rhymes posted by R. Berg on March 21, 2001

Richard Woodman authored:

IMPURE MATHEMATICS

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

pace.

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

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 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

convergent."

"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

orthogonal.

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

ISSN 0022-2038

forwarded by [email protected]