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-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 your angles have lots 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 natural 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 toward 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 her by parts. He integrated her by partial fractions. After he cofactored, he performed Runge-Cutta on her. The complex beast even went all the way around and did a coutour 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 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 expression convergent, never allow them a single degree of freedom."

A mathematical proof which explains why managers and others in authority make so much money. From your high school physics, you will recall that: 

   Work
  Power =  *** --
  Time

 From the world of business, we know that: 

 Knowledge = Power 

and also that:

 Time = Money,

 Substituting these identities into the original equation, we get: 

   Work
  Knowledge =  *** *
   Money
 

 Solving for money, we get:

   Work
  Money =   *** - *** - 
    Knowledge

Thus, Money approaches infinity as Knowledge approaches zero, regardless of the Work done. What this means is: The Less you Know, the More you Make. Taking this analysis and proof one step further, we know that: 

 Knowledge = Education x Time 

 Solving for Time:

  Knowledge
  Time =  *** - *** - 
  Education 
 

 and then substituting for Time back into the Power equation, we get:

   Work  Work x Education 
  Power = *** == *** - *** - *** * 
   Time Knowledge
 

From which we can see that the closer Knowledge gets to 0, the more power one will have.

Note: You can also increase Power through increasing either Work or Education, but it should be noted that this approach doesn't have the same type of leverage as lack of knowledge.

This equation is also known as the MANAGEMENT Equation, since it provides a clear and concise mathematical explanation of why managers, executives, politicians, defense personnel and most other highly unknowledgable individuals get paid so much.

 - Q.E.D. -

An Engineer and a Biologist were sitting next to each other on an airplane. The Engineer leans over to the Biologist and asks if he wants to play a fun game. The Biologist just wants to sleep so he politely declines, turns away and tries to sleep. The Engineer persists and explains that it's a real easy game. He explains,"I ask a question and if you don't know the answer you pay me $5. Then you ask a question and if I don't know the answer I'll pay you $5." Again the Biologist politely declines and tries to sleep. The Engineer, now somewhat agitated, says, "O.K., if you don't know the answer you pay me $5 and if I don't know the answer I pay you $50!" Now, that got the Biologist's attention, so he agrees to the game. The Engineer asks the first question, "What's the distance from the earth to the moon?" Then Biologist doesn't say a word and just hands the Engineer $5. Now, its the Biologist's turn. He asks the Engineer,"What goes up a hill on three legs and comes down on four?" The Engineer looks at him with a puzzled look, takes out his laptop computer, looks through all his references and after about an hour wakes the Biologist and hands the Biologist $50. The Biologist politely takes the $50 turns away and tries to go back to sleep. The Engineer, a little miffed, asks, "Well what's the answer to the question?" Without a word, the Biologist reaches into his wallet, hands $5 to the Engineer, turns away and goes to sleep.

Why engineers don't write recipe books:
*** - *** - *** - *** - *** - *** - *** - *** - *** *

Chocolate Chip Cookies:

1.) 532.35 cm3 gluten
2.) 4.9 cm3 NaHCO3
3.) 4.9 cm3 refined halite
4.) 236.6 cm3 partially hydrogenated tallow triglyceride
5.) 177.45 cm3 crystalline C12H22O11
6.) 177.45 cm3 unrefined C12H22O11
7.) 4.9 cm3 methyl ether of protocatechuic aldehyde
8.) Two calcium carbonate-encapsulated avian albumen-coated protein
9.) 473.2 cm3 theobroma cacao
10.) 236.6 cm3 de-encapsulated legume meats (sieve size #10)

To a 2-L jacketed round reactor vessel (reactor #1) with an overall heat transfer coefficient of about 100 Btu/F-ft2-hr, add ingredients one, two, and three with constant agitation. In a second 2-L reactor vessel with a radial flow impeller operating at 100 rpm, add ingredients four, five, six, and seven until the mixture is homogenous. To reactor #2, add ingredient eight, followed by three equal volumes of the homogenous mixture in reactor #1. Additionally, add ingredients nine and ten slowly, with constant agitation. Care must be taken at this point in the reaction to control any temperature rise that may be the result of an exothermic reaction.

Using a screw extrude attached to a #4 nodulizer, place the mixture piece-meal on a 316ss sheet (300x600mm). Heat in a 460K oven for a period of time that is in agreement with Frank & Johnston's first order rate expression (see JACOS, 21, 55), or until golden brown. Once the reaction is complete, place the sheet on a 25C heat-transfer table, allowing the product to come to equilibrium.

PS- don't try this at home.

"The concept is interesting and well-formed, but in order to earn better than a 'C,' the idea must be feasible." A Yale University management professor in response to Fred Smith's paper
proposing reliable overnight delivery service. (Smith went on to found Federal Express Corp.)

"We don't like their sound, and guitar music is on the way out." "Decca Recording Co. rejecting the Beatles, 1962."

Heavier-than-air flying machines are impossible. "Lord Kelvin, president, Royal Society, 1895."

You want to have consistent and uniform muscle development across all of your muscles? It can't be done. It's just a fact of life. You just have to accept inconsistent muscle development as an
unalterable condition of weight training. "Response to Arthur Jones, who solved the ""unsolvable"" problem by inventing Nautilus."

Drill for oil? You mean drill into the ground to try and find oil? You're crazy. Drillers who Edwin L. Drake tried to enlist to his project to drill for oil in 1859.

Stocks have reached what looks like a permanently high plateau. "Irving Fisher, Professor of Economics, Yale University, 1929." 

Everything that can be invented has been invented. "Charles H. Duell, Commissioner, U.S. Office of Patents, 1899."

Louis Pasteur's theory of germs is ridiculous fiction. "Pierre Pachet, Professor of Physiology at Toulouse, 1872"