Date: Fri, 16 Feb 90 19:49:34 GMT From: ZDAP055@ELM.CC.KCL.ac.uk Subject: Strange loops... Sender: Traditional Nutty Stuff To: Joe Desbonnet Reply-to: ZDAP055@ELM.CC.KCL.ac.uk Comments: Warning -- original Sender: tag was zdap055@ELM.CC.KCL.AC.UK The author of this is "Pepsi"! All and any credit is due to him (as are the typo's: I can spell!) Enjoy people! 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 singlularly 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, who had changed her variables that morning, was feeling particularly badly behaved, and ignored this condition on the grounds that it was insufficient and made her way amongst the complex elements. Rows 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 direction, and went copmletely divergent. As she reached a turning point, she tripped over a square root 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 operator, Curly Pi, was lurking inner product. As his eyes devoured her curvilinear co-ordinates, 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 and saw Curly Pi approaching with his power series extrapolated. She could see at once, by his degenerate conic and his dissipative terms that he was bent on no good. "Eureka!"she gasped. "Ho, ho!"he said,"What a symmetric litle polynomial you are. I can see you are bubbling over with secs." "O Sir,"she protested,"keep away from me, I haven't got my brackets on." "Calm yourself, my dear,"said our sauve operator,"Your fears are purely imaginary." "I,I,"she thought,"perhaps he's homogeneous then." "What order are you?"the brute demanded. "Seventeen,"repiled Polly. Curly leered. "I suppose you've never been operated on yet?" he asked. "Of course not!" Polly replied indignantly. "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. "Induce the friction between Newton's Balls!" he swore, using the vilest oath he knew. His patience was gone. Coshing her over the head with a log until she was powerless, Curly removed her discontinuities. He started at her significant places and began removing her points of inflexion. Poor Polly. All was up. She felt his hand tend to her asymptotic limit. Her convergence would soon be gone forever. There was no mercy, for Curly was a heavy side operator. He integrated her by parts. He integrated her by partial fractions. The copmlex beast even went all the way round and did a contour integration. Curly went on operating until he was absolutely and completely orthogonal. When Polly got home that evening, her mother noticed that she had been truncated in several places and wondered whether her variables had been separated. But it was too late to differentiate now. As the months went by, Polly increased monotonically. Finally, she generated a small but pathological function which left surds all over the place until she was driven to distraction. The moral of this blown-out of proportion story is :"If you want to keep your expressions convergent, never allow them a single degree of freedom." ............................................................PEPSI............