The Loony Bin
(
loonies@bloodaxe.demon.co.uk
)
Fri, 15 Mar 1996 18:25:31 +0000
Hiya again folks...
This may be beyond one or two of you (sorry history and drama
people...life's like that...) but the rest of you should cope...:-)
Wishes & Dreams...:-)
- ANDREA
xx
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*** THE LOONY BIN ***
*** loonies@bloodaxe.demon.co.uk ***
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**********************ANDROMEDA**********************
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IMPURE MATHEMATICS
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 touched
her surface. She became tensor and tensor. Quite suddenly,
three 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 which was protruding from the erf
and plunged down a steep gradient, landing on her
saddle-point. When she was differentiated once more, she found
herself, apparently alone, in a non-Euclidean space.
But she was being watched. That smooth operator, Curly Pi, was
lurking inner product. As his eyes alighted on her curvilinear
coordinates, a singular expression crossed his face. Was she
still convergent, he wondered. He decided to integrate
improperly at once.
Hearing a vulgar fraction behind her, Polly turned round and
saw Curly Pi approaching with his power series extrapolated.
She could see by his degenerate conic and his dissipative
terms that he was bent on doing no good.
"Eureka," she gasped.
"Ho Ho," he said. "What a symmetrical little polynomial you
are. I can see you're positively bubbling over with 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 tears
are purely imaginery."
"Aye Aye," she thought. "Perhaps he's homogenous then."
"What order are you?" the brute demanded.
"Seventeen," replied Polly.
Curly leered. "I suppose you've never been operated on yet?"
he asked.
"Of course not!" Polly cried indignantly. "I'm absolutely
convergent."
"Come, come," said Curly seductively. "Let's go off to a
decimal place I know and I'll take you to the limit."
"Never!" gasped Polly.
"Exchif!" 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 her
points of inflection. Poor Polly! All was up. She felt his
hand tending to her asymptotic limit. Her convergence would
soon be gone for ever.
There was no mercy, for Curly was a Heaviside operator. He
integrated by parts. He integrated by partial fractions. The
complex beast even went right the way round and did a double
contour integration. What a catastrophe! To be
multiplicatively connected on her first integration. Curly
went on operating until he was completely and utterly
orthogonal.
When Polly got home that evening, her mother noticed that she
had been truncated in several places, but it was too late to
differentiate now. Polly soon realised that she was no longer
periodic and that she had started to increase monotonically.
Several months later, she generated a small but pathological
function which left surds all over the place until she was
driven to distraction.
The moral of our sad story is this: if you want to keep your
expressions convergent, never allow them a single degree of
freedom.
--
David Clarke