53 lines
3.4 KiB
Plaintext
53 lines
3.4 KiB
Plaintext
Little Polly Nomial was walking through a field of vectors, when she
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came to the edge of a singularly large matrix.
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Now Polly was convergent and her mother had made it an absolute condition
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that she must NEVER enter such an array without her brackets on.
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Polly, however, who had just changed her variables that morning and was feeling
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particularly badly behaved, ignored this condition on the grounds that it was
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insufficient and made her way in amongst the complex elements.
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Rows and columns enveloped her on all sides. Tangents approached her
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surface. She became tensor and tensor. Quite suddenly, three branches of a
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hyperbola touched her at a single point. She oscillated violently, and lost
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all sense of directrix, and went completely divergent. As she reached a
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turning point, she tripped over a square root which was protruding from the
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erg and plunged headlong down a steep gradient. When she differentiated once
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more she found herself, apparently alone in a non-euclidean space.
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She was being watched, however. That smooth operator, Curly Pi, was
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lurking inner product. As his eyes devoured her curvilinear coordinates, a
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singular expression crossed his face. "Was she still convergent?", he
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wondered. He decided to integrate improperly at once.
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Hearing a vulgar fraction behind her, Polly turned around and saw
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Curly Pi approaching with his power series extrapolated. She could see at once
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by his degenerative conic and dissapative terms that he was bent on no good.
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"Ho, ho!" he said. "What a symmetric little Polly Nomial you are. I can
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see that you're absolutely bubbling over with secs."
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"O sir," she protested. "Keep away from me! I haven't got my brackets on!"
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"Calm yourself, my dear," said our suave operator. "Your fears are
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purely imaginary."
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"I, I," she thought. "Perhaps he's homogeneous, then!"
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"What order are you?" the brute demanded.
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"Seventeen, of course," replied Polly.
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Curly leered. "I suppose you've never been operated on?" he said.
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"Of course not!" Polly cried indignantly. "I'm absolutely convergent!"
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"Come, come," said Curly. "Let's go off to a decimal place I know of and
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I'll take you to the limit."
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"Never!" gasped Polly.
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"Exchlf!" he swore, using the vilest oath he knew. His patience was
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gone. Coshing her over the coefficient with a log until she was powerless,
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Curly removed her discontinuities. He stared at her significant places and
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began smoothing out her points of inflection. Poor Polly. All was up. She
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felt his hand tending toward her asymptotic limit. Her convergence would
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soon be gone forever.
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There was no mercy, for Curly was a heavyside operator. He integrated
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by parts. He integrated by partial fractions. The complex beast even went
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all the way around and did a contour integration. What an indignity to be
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multiply connected on her first integration! Curly went on operating until
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he was absolutely and completely orthogonal.
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When Polly got home that evening, her mother noticed that she had
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been truncated in several places. But it was too late to differentiate now.
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Her convergence was gone forever. As the months went by, she generated a
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small but pathological function which left surds all over the place until she
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was driven to distraction.
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The moral of our sad story is this: If you want to keep your expressions
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convergent, never allow them a single degree of freedom.
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