87 lines
3.7 KiB
Plaintext
87 lines
3.7 KiB
Plaintext
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Impure Mathematics
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by Richard A. Gibbs
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Once upon a time (1/T) pretty little Polly Nomial was strolling across a field
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of vectors when she 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 that
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she must never enter such an array without her brackets on. Polly, however,
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who had changed her variables that morning and was feeling particularly badly
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behaved, ignored this condition on the grounds that it was insufficient and
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made her way in amongst the complex elements.
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Rows and columns enveloped her on all sides. Tangents approached her surface.
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She became tensor and tensor. Quite suddenly, three branches of a hyperbola
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touched her at a single point. She oscillated violently, lost all sense of
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directrix and went completely divergent.
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As she reached a turning point she tripped over a square root which was
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protruding from the erf and plunged headlong down a steep gradient. When she
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was differentiated once more she found herself, apparently alone, in a non-
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euclidean space.
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She was being watched, however. That smooth operator, Curly Pi, was lurking
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inner product. As his eyes devoured her curvilinear coordinates, a singular
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expression crossed his face. Was she still convergent, he wondered. He
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decided to integrate improperly at once.
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Hearing a vulgar fraction behind her, Polly turned around and saw Curly Pi
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approaching with his power series extrapolated. She could see at once, by his
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degenerate conic and his dissipative terms, that he was bent on no good.
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"Eureka," she gasped.
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"Ho, ho," he said. "What a symmetric little Polynomial you are. I can see
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you're 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 purely
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imaginary."
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"I, I," she thought, "perhaps he's homogenous then."
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"What order are you," the brute demanded.
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"Seventeenth," replied Polly.
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Curly leered, "I suppose you've never been operated on yet?" he asked.
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"Of course not," Polly cried indignantly. "I'm absolutely convergent."
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"Come, come," said Curly. "Let's off to a decimal place I know and I'll take
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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 gone.
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Coshing her over the coefficient with a log until she was powerless, Curly
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removed her discontinuities.
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He stared at her significant places and began smoothing her points of
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inflexion. Poor Polly... All was up. She felt his hand tending to her
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asymptotic limit. Her convergence would soon be gone forever.
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There was no mercy, for Curly was a heavyside operator. He integrated by
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parts. He integrated by partial fractions. The complex beast even went all
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the way around and did a counter integration! What an indignity! To be
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multiply connected ON HER FIRST INTEGRATION! Curly went on operating until he
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was absolutely and completely orthogonal.
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When Polly got home that evening, her mother noticed that she had been
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truncated in several places.
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But it was too late to differentiate now. As the months went by, Polly
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increased monotonically. Finally she generated a small but pathological
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function which left surds all over the place until she was driven to
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distraction.
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The moral of our sad story is this:
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If you want to keep your expressions convergent, never allow them a
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single degree of freedom.
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(from the Best of JIR)
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