Conference rusure::math

151.0. "A Fable" by HARE::STAN () Mon Sep 17 1984 23:06

From:	ROLL::USENET       "USENET Newsgroup Distributor" 17-SEP-1984 22:05
To:	HARE::STAN
Subj:	USENET net.math newsgroup articles

Newsgroups: net.jokes,net.math
Path: decwrl!decvax!mcnc!unc!black
Subject: Impure Mathematix ... a fable.
Posted: Sun Sep 16 13:01:39 1984




	From the Michigan Technic, Mar 1979.  Author unknown.

	------------------------------------------------------


			Impure Mathematix


    Wherein it is related how that Polygon of Womanly Virtue, your Polly
 Nomial (out heroine) is accosted by that Notorious Villain 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 singularly large 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.  Pollo, 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 amongst the complex elements.  Rows and columns closed in 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 steep gradient.
 When she rounded off once more, she found herself inverted, apparently alone,
 in a non-Euclidean space.

    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 and 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 you angles have a lot 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 you?" the Brute demanded.

    "Seventeen," replied Pollo.

    Curly leered.  "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 off to a decimal place I know and I'll
 take you to the limit."

    "Never," gasped Polly.

    "Abcissa," 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 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 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 rungecutta 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 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.  But it was
 too late to differentiate now.  As the months went by, Polly's denominator
 increased monotonically.  Finally, she went to the L'Hopital and generated
 a small but pathalogical function which left surds all over the place and
 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...'