A Tale of Unknown Provenience for the Subgenius Math Freaks
Correspondent:: Tartarus Sanctus
Date: Sun, 16 Jan 2005 10:16:54 -0700
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Once upon a time (1/t), pretty little Polly Nomial was strolling across
a field of vectors when she came to the edge of a singularly large matrix.
Now Polly was convergent and her mother had made it an absolute
condition that she must 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
grounds that it was insufficient, and made her way in amongst the
complex elements.
Rows and columns enveloped her on all sides. Tangents approached her
surface. She became tensor and tensor. Suddenly two branches of a
hyperbola touched her at a single point. She oscillated violently, lost
all sense of direction, and went completely divergent. As she reached a
turning point she tripped over a square root that was protruding from
the erf, and she plunged headlong down a steep gradient. When she was
differentiated once more, she found herself, apparently alone, in a
non-Euclidean space.
She was being watched, however. That smooth operator, Curly Pi, was
lurking inner product. As he numerically analyzed her, his eyes
devoured her curvilinear coordinates, and a singular expression crossed
his face. Was she still convergent, he wondered. He decided to
integrate improperly at once.
Hearing a common fraction behind her, Polly rotated and saw Curly
approaching her with his power series expanding. She could see by his
degenerate conic that he was up to no good.
"What a symmetric little polynomial you are," he said. "I can see that
your angles have lots 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 homogeneous."
"What order are you?" the brute demanded.
"Seventeen," replied Polly.
"I suppose you've never been operated on?"
"Of course not," Polly cried indignantly. "I'm absolutely convergent."
"Come, come," said Curly. "Let's go off to a decimal place, 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 head with a log until she was powerless,
Curly removed her discontinuities. He stared at her significant places
and began smoothing her points of inflection. Poor Polly. 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
Runge-Kutta on her. The complex beast even went all the way around and
did a contour integration. Curly went on operating until he 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. 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 little surds all over the place and drove Polly to deviation.
The moral of the story is, "If you want to keep your expressions
convergent, never allow them a single degree of freedom."
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Tartarus