Impure Mathematics |
Once upon a time, pretty little Polly
Nominal was trolling 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. Row and columns enveloped her on all
sides. Tangents approached 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 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 character, Curly Pi, was lurking inner product. As his eyes
devoured her curvilinear co-ordinate a singular expression crossed his
face. Was she still convergent? He wondered. He decided to integrate
improperly at once. “Eureka”, she gasped. “Ho, ho” he said. “What a symmetric
little polynomial you are. I can see you’re absolutely 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 fears are purely
imaginary.” “I, I …” she thought. “Perhaps he
is homogenous then?” “What order are you?” the brute
demanded. “Seventeen”, replied
Polly. Curly leered. “Suppose you have never
been operated on yet?” he said. “Of course not”, Polly cried
indignantly. “I’m absolutely
convergent.” “Come, come”, said Curly “lets be off
to a decimal place I know and I’ll take you to the
limit”. “Never”, gasped
Polly. “EXCHLF”, he swore, using the vilest
oath he knew. His patience was gone. Coshing her over the co-efficient
with a log until she was powerless, Curly removed her discontinuities. He
stared at her significant places and began smoothing her points of
inplexion. Poor Polly. All was up. She felt his hand tending her
asymptotic limit. Her convergence would soon be gone
forever. There was no mercy, for Curly was a Heaviside operator. He integrated by parts. He integrated by partial fractions. The complex beast even went all the way round and did a contour integration. What an indignity! To be multiply connected on her first integration. Curly went on operating until he was absolutely 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. As the months went by, Polly increased monotonically. Finally she generated a small but pathological junction 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 expression convergent, never allow them a single degree of freedom. |