这篇文章出自Iowa Engineer杂志1968年11月号，作者不详。 个人觉得大学高等数学/线性代数的第一课如果是学习这篇文章同学们的学习积极性会提高许多，至少男同学们。

Impure Mathematics

Once upon a time (1/t), pretty little Polly Nomial（nomial - 无序的， polynomial - 多项式） was strolling across a field of vectors（vector - 矢量，向量）, when she came to the edge of a singularly large matrix（singular matrix - 降秩(矩)阵）. Now Polly was convergent(convergent - 收敛的), and her mother had made it an absolute condition that she must never enter such an array without her brackets（bracket - 括弧） on. Polly, however, had changed her variables（variable - 变量） that morning, and, feeling particularly badly behaved, she ignored this condition on the grounds that it was insufficient, and made her way in amongst the complex elements.

Rows and columns enveloped her on all sides. Tangents（Tangent - 切线） approached her surface. She became tensor and tensor（tensor - 张量）. Quite suddenly, three branches of a hyperbola（hyperbola - 双曲线） touched her at a single point. She oscillated（oscillate - 振动，振荡） violently, lost all sense of directrix（directrix - 准线）, and went completely divergent（divergent - 发散）. As she reached a turning point, she tripped over（trip over - 被绊倒） a square root（square root - 平方根） which was protruding from the erf（erf - 返回误差函数）, and plunged headlong down a steep gradient（steep gradient - 陡坡）. When she was differentiated（differentiated - 求微分） once more, she found herself, apparently alone, in a non-euclidean space（non-euclidean space - 非欧氏几何空间）.

She was being watched however. That smooth operator, Curly Pi, was lurking (lurk - 潜伏) inner product. As his eyes devoured （devoure - 贪婪地看） her curvilinear （curvilinear - 曲线的） coordinates（coordinate - 坐标）, a singular expression crossed his face. Was she still convergent, he wondered. He decided to integrate improperly at once.

Hearing a vulgar（vulgar - 粗鲁的，低级的） function（function - 函数） behind her, Polly turned round, and saw Curly Pi approaching with his power series extrapolated （extrapolate - 推算） . She could see at once, by his degenerate（degenerate - 退化的） conic（conic - 二次曲线/圆锥） and his dissipative（dissipative - 消耗的） terms, that he was bent on no good.

"Eureka（Eureka - 找到了。希腊词汇，源自 Archimedes/阿基米德在浴缸里的灵光一闪）" she gasped.

"Ho, ho!" he said. "What a symmetric（symmetric - 对称的，匀称的） little polynomial you are. I can see that you are absolutely bubbling over with secs（sec, secant，切线）".

"Sir", she said, "keep away from me. I haven't got my brackets on.

"Calm yourself my dear" said our suave（suave - 圆滑的） operator, "your fears are purely imaginary".

"i, i" she thought. "Perhaps he's homogeneous（homogeneous - 齐次的，homo - 嗯） then?".

"What order（order - 序） are you?" the brute demanded.

"Seventeen", replied Polly.

Curly leered. "I suppose you've never been operated on （咳……） yet?" he said.

"Of course not" Polly cried indignantly. "I'm absolutely convergent".

"Come, cone," said Curly. "Lets off to a decimal（decimal - 十进制的） place I know, and I'll take you to the limit（咳……）".

"Never" gasped Polly.

His patience was gone. Coshing（cosh - 双曲余弦/短棒） her over the coefficient（ coefficient - 系数） with a log（log - 圆木） until she was powerless（power - 幂，倍数）, Curly removed her discontinuities（discontinuity - 不连续性，不可微分的）. He stared at her significant places and began to smooth her points of inflexion （inflexion - 拐点）. Poor Polly. All was lost. She felt his hand bonding to her asymptotic（asymptotic - 渐近线） limit. Her convergence would be gone for ever.

There was no mercy, for Curly was a heavyside operator. He integrated by parts. He integrated by partial fractions（partial fractions - 部分分式）. The complex beast even went all the way round, and did a contour integration（contour integration - 围道积分法， contour - 轮廓）. What an indignity! Curly went on operating until he was completely and absolutely orthogonal（orthogonal - 正交，直角）.

When Polly got hone that evening, her mother noticed that she had been truncated in several places. But it was too late to differentiate now --- the seeds having been sown. As the months went by, Polly increased monotonically（monotonically - 单调地）. Finally, she generated a small, but pathological（pathological - 病态的）, function, which left surds（surd - 无理数，不尽根） all over the place, until she was driven to distraction（distraction - 错乱）.

The moral of this sad story is this: It you want to keep your expressions convergent, never allow them a single degree of freedom.