[HOME - BASE Cinque - Appunti di Matematica ricreativa]

Polly Nomial e Curly Pi

Una sordida storia di matematica impura
nella quale si racconta in che modo la nostra eroina Polly Nomial, poligonale esempio di virtù femminile, sia stata avvicinata dal noto villano Curly Pi, e fattorizzata (oh, orrore!)

Michael A. Stueben

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.

Polly, however, who had changed her variables that morning and was feeling particularly badly behaved, ignored this condition on the basis that it 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-Euclidian 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 your 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 Polly.
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.
"Abscissa," 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 is 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 pathological 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...'


Un giorno la piccola Polly Nomial stava passeggiando per un campo di vettori quando si trovò sul bordo di una grande matrice singolare. Polly era ormai convergente e la madre le aveva fatto promettere come valore assoluto che non sarebbe entrata in un array senza aver su le sue parentesi.

Polly tuttavia, che quel giorno si era cambiata le variabili e si sentiva spinta a un comportamento irregolare, ignorò quelle condizioni considerandole non necessarie e si inoltrò negli elementi complessi.

Righe e colonne la avvolgevano da tutti i lati. Tangenti sfioravano le sue superfici; ella divenne sempre più tesa. Improvvisamente due rami di un'iperbole la toccarono in un punto unico. Ella oscillo violentemente, perse ogni senso di direttrice e andò completamente a divergere. Nel girare un angolo, inciampò in una radice quadrata che sporgeva dal terreno e finì a capofitto lungo un ripido gradiente. Quando si differenziò di nuovo, si trovò sola, apparentemente in uno spazio non euclideo.

C'era qualcuno che la guardava. Quel fine operatore Curly Pi, spiava il suo prodotto interno. Mentre i suoi occhi divoravano le sue coordinate curvilinee, un'espressione singolare attraversò il suo volto.

















Non ci fu pietà perché Curly era un operatore di Heaviside. Egli integrava per frazioni parziali. La bestia complessa fece tutto il circuito e un'integrazione al contorno. Che indegnità. Essere multiconnessa alla sua prima integrazione. Curly continuò a operare finché non si sentì completamente e assolutamente ortogonale ...

Quando Polly tornò a casa, quella sera, la madre notò che era troncata in diverse parti ... Man mano che i mesi passavano, Polly cresceva monotonicamente. Alla fine generò una piccola funzione patologica, che spargeva surdi dappertutto.


Traduzione parziale di Gabriele Lolli, Il riso di Talete, Boringhieri, 1998.

Ultimo aggiornamento: luglio 2005

Risposte & riflessioni

Sito Web realizzato da Gianfranco Bo