Once upon a time (1/t) pretty little 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 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 basis that it was insufficient and made her way in amongst the complex elements. Rows and columns closed in on her from all sides. Tangents approached her surface. She became tensor and tensor. Quite suddendly 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 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 inner product. As his eyes devoured her curvilinear coordinates, a singular expression crossed his face. He wondered, "Was she still convergent?" He decided to integrate properly 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 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
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 digits 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 runge - kutta on her. The complex beast even went all the way around and did a contour integration. What an indignity - to be multiply connected on her first integration. Curly went on operating until he completely 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 to 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 expressions convergent, never allow them a single degree of freedom."
Authors: Mike J. Disney and Alan E. Wright, London University (1960s).
Hi Ole,
I have just re-read with interest the article which appears on your web pages entitled "Impure Mathematics". It says there that the origin is unknown. No longer!
The article was first penned by Mike Disney (now Prof of astronomy at the University of Wales, Cardiff and myself (now Principle Astronomer at the Parkes Observatory, Australia, while we were graduate students at London University in the mid 1960s. It was written for the Uni of London's Astronomy Society magazine and we "dared" only use our initials MJD and AEW!
As proof of our authorship the original (and still many) versions contains the "foul oath" EXCHLF which was the name of a vile computer language then current on the Uni of London's main computer!
Perhasp you might feel able to give us credit (for what is still my most widely referenced "scientific" paper (after 30 years!)
Best wishes
Alan
*================================================================* | | + | | Alan E Wright | + + | | Parkes Observatory \===O + | | ATNF, CSIRO /[] | + | | P.O. Box 276 Ph. 02 6861 1732 |HHH\| | | Parkes NSW 2870 FAX 02 6861 1730 |OHO| \__ | | AUSTRALIA awright@atnf.CSIRO.AU |HHH| | | """""""""""" | *================================================================*
1. What's the contour integral around Western Europe?
Answer: Zero, because all the Poles are in Eastern Europe!
Addendum: Actually, there ARE some Poles in Western Europe, but
they are removable!
2. An English mathematician (I forgot who) was asked by his very religious
colleague:
Do you believe in one God?
Answer: Yes, up to isomorphism!
3. What is a compact city?
It's a city that can be guarded by finitely many near-sighted
policemen!
Abdolreza Tahvildarzadeh, NYU
A: Because he left a residue at every pole.
Q: Why is it that the more accuracy you demand from an interpolation function, the more expensive it becomes to compute?
A: That's the Law of Spline Demand.
Steve Friedl, V-Systems, Inc.
\/3
/
| 2 3 x 3.14 3_
| z dz x cos( ----------) = ln (\/e )
| 9
/
1
Which, of course, translates to:
Integral z-squared dz
from 1 to the square root of 3
times the cosine
of three pi over 9
equals log of the cube root of 'e'.
And it's correct, too.
Doug Walker, SAS Institute
Later, the physicist wakes up and smells smoke. He opens his door and sees a fire in the hallway. He walks down the hall to a fire hose and after calculating the flame velocity, distance, water pressure, trajectory, etc. extinguishes the fire with the minimum amount of water and energy needed.
Later, the mathematician wakes up and smells smoke. He goes to the hall, sees the fire and then the fire hose. He thinks for a moment and then exclaims, "Ah, a solution exists!" and then goes back to bed.
Michael Plapp, NOSC
Jim Lewis, UC-Berkeley
Philippe Schnoebelen
A month later, returning, the mad scientist went to the engineer's cell and found it long empty. The engineer had constructed a can opener from pocket trash, used aluminum shavings and dried sugar to make an explosive, and escaped.
The physicist had worked out the angle necessary to knock the lids off the tin cans by throwing them against the wall. She was developing a good pitching arm and a new quantum theory.
The mathematician had stacked the unopened cans into a surprising solution to the kissing problem; his dessicated corpse was propped calmly against a wall, and this was inscribed on the floor in blood:
Theorem: If I can't open these cans, I'll die.
Proof: assume the opposite...
(name unknown), Reed College, Portland, OR
He tried a test to narrow the area of specialty. He put each man in a room with a stove, a table, and a pot of water on the table. He said "Boil the water". Both men moved the pot from the table to the stove and turned on the burner to boil the water.
Next, he put them into a room with a stove, a table, and a pot of water on the floor. Again, he said "Boil the water". The first man put the pot on the stove and turned on the burner. The counselor told him to be an Engineer, because he could solve each problem individually.
The second man moved the pot from the floor to the table, and then moved the pot from the table to the stove and turned on the burner. The counselor told him to be a mathematician because he reduced the problem to a previously solved problem.
So he leans over the basket and yells out, "Helllloooooo! Where are we?" (They hear the echo several times).
15 minutes later, they hear this echoing voice: "Helllloooooo! You're lost!!"
One of the men says, "That must have been a mathematician."
Puzzled, one of the other men asks, "Why do you say that?"
The reply: "For three reasons. (1) he took a long time to answer, (2) he was absolutely correct, and (3) his answer was absolutely useless."
So one day, some smarty-pants asked him, "Ok. Prove that you're the Pope."
He thought for a while and proclaimed, "I am one. The Pope is one. Therefore, the Pope and I are one."
Donald Chinn, UC-Berkeley
One day they looked up in the heavens and desired to reach up as far as the eye could see. So they set out in building a Mathematical edifice that was to reach up as far as "up" went. Further and further up they went ... until one night the edifice collapsed under the weight of paradox.
The following morning saw only rubble where there once was a huge structure reaching to the heavens. One by one, the Mathematicians climbed out from under the rubble. It was a miracle that nobody was killed; but when they began to speak to one another, SUPRISE of all suprises! they could not understand each other. They all spoke different languages. They all fought amongst themselves and each went about their own way. To this day the Topologists remain the original Mathematicians.
- adapted from an American Indian legend
of the Mound Of Babel
Mark William Hopkins, U. Wisconsin-Milwaukee
"What's the problem?" says Noah.
"Cut down some trees and let us live there", say the snakes.
Noah follows their advice. Several more weeks pass. Noah checks on the snakes again. Lots of little snakes, everybody is happy.
Noah asks, "Want to tell me how the trees helped?"
"Certainly", say the snakes. "We're adders, and we need logs to
multiply."
Rolan Christofferson, U.Colorado, Boulder
Physicist: Pi is 3.1415927plus or minus 0.000000005
Engineer: Pi is about 3.
David Harr, Occidental College
Proof (by induction):
Case n=1: In a set with only one horse, it is obvious that all horses
in that set are the same color.
Case n=k: Suppose you have a set of k+1 horses. Pull one of these horses out of the set, so that you have k horses. Suppose that all of these horses are the same color. Now put back the horse that you took out, and pull out a different one. Suppose that all of the k horses now in the set are the same color. Then the set of k+1 horses are all the same color. We have k true => k+1 true; therefore all horses are the same color.
Theorem: All horses have an infinite number of legs.
Proof (by intimidation):
Everyone would agree that all horses have an even number of legs. It
is also well-known that horses have forelegs in front and two legs in
back. 4 + 2 = 6 legs, which is certainly an odd number of legs for a
horse to have! Now the only number that is both even and odd is infinity;
therefore all horses have an infinite number of legs.
However, suppose that there is a horse somewhere that does not have an infinite number of legs. Well, that would be a horse of a different color; and by the Lemma, it doesn't exist.
Jerry Weldon, Livermore Labs
Of course, there are some jeers from some of his friends. The physics student then said, "I'm not sure of the validity of your proof, but I think I'll try to prove it by experiment." He continues, "Well, 1 is prime, 3 is prime, 5 is prime, 7 is prime, 9 is ... uh, 9 is an experimental error, 11 is prime, 13 is prime... Well, it seems that you're right."
The third student to try it was the engineering student, who responded, "Well, actually, I'm not sure of your answer either. Let's see... 1 is prime, 3 is prime, 5 is prime, 7 is prime, 9 is ..., 9 is ..., well if you approximate, 9 is prime, 11 is prime, 13 is prime... Well, it does seem right."
Not to be outdone, the computer science student comes along and says "Well, you two sort've got the right idea, but you'd end up taking too long doing it. I've just whipped up a program to REALLY go and prove it..." He goes over to his terminal and runs his program. Reading the output on the screen he says, "1 is prime, 1 is prime, 1 is prime, 1 is prime...."
Q: What's the title of this picture ?
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A: Hypotenuse/\ /\ /\ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /______\ /______\ /______\ || || || || || ||A: 9, tree + tree + tree
The biologist : "Look! There's a herd of zebras! And there,
in the middle : A white zebra! It's fantastic !
There are white zebra's ! We'll be famous !"
The statistician : "It's not significant. We only know there's one
white zebra."
The mathematician : "Actually, we only know there exists a zebra,
which is white on one side."
The computer scientist : "Oh, no! A special case!"
Niels Ull Jacobsen, U. of Copenhagen
1 + 1 = 3, for large values of 1
Rob Gardner, HP Ft. Collins, CO
lim ----
8-->9 \/ 8 = 3
Donald Chinn, UC-Berkeley
lim 3 = 8
w->oo
(It is more obvious when handwritten...)
/ x n
| e = f(u )
/
Naoto Kimura, Cal State-Northridge
The lawyer says: "For sure a mistress is better. If you have a wife and want a divorce, it causes all sorts of legal problems.
The doctor says: "It's better to have a wife because the sense of security lowers your stress and is good for your health.
The mathematician says: " You're both wrong. It's best to have both so that when the wife thinks you're with the mistress and the mistress thinks you're with your wife --- you can do some mathematics.
Bruce Bukiet, Los Alamos National Lab
Algebraists do it in groups.
Al Sethuraman, Calma Company, San Diego
Weiner was in fact very absent minded. The following story is told about him: When they moved from Cambridge to Newton his wife, knowing that he would be absolutely useless on the move, packed him off to MIT while she directed the move. Since she was certain that he would forget that they had moved and where they had moved to, she wrote down the new address on a piece of paper, and gave it to him. Naturally, in the course of the day, an insight occurred to him. He reached in his pocket, found a piece of paper on which he furiously scribbled some notes, thought it over, decided there was a fallacy in his idea, and threw the piece of paper away. At the end of the day he went home (to the old address in Cambridge, of course). When he got there he realized that they had moved, that he had no idea where they had moved to, and that the piece of paper with the address was long gone. Fortunately inspiration struck. There was a young girl on the street and he conceived the idea of asking her where he had moved to, saying, "Excuse me, perhaps you know me. I'm Norbert Weiner and we've just moved. Would you know where we've moved to?" To which the young girl replied, "Yes daddy, mommy thought you would forget."
The capper to the story is that I asked his daughter (the girl in the story) about the truth of the story, many years later. She said that it wasn't quite true -- that he never forgot who his children were! The rest of it, however, was pretty close to what actually happened...
Richard Harter, Computer Corp. of America, Cambridge, MA
(Logicians do it) or [not (logicians do it)].
Scott Horne
Proof:
No cat has eight tails. A cat has one tail more than no cat. Therefore, a cat has nine tails.
Arndt Jonasson
So, they decided to consult the foremost biologists and recombinant DNA technicians to build them a better cow. They assembled this team of great scientists, and gave them unlimited funding. They requested rare chemicals, weird bacteria, tons of quarantine equipment, there was a God-awful typhus epidemic they started by accident, and, 2 years later, they came back with the "new, improved cow." It had a milk production improvement of 2% over the original.
They then tried with the greatest Nobel Prize winning chemists around. They worked for six months, and, after requisitioning tons of chemical equipment, and poisoning half the small town in Colorado where they were working with a toxic cloud from one of their experiments, they got a 5% improvement in milk output.
The physicists tried for a year, and, after ten thousand cows were subjected to radiation therapy, they got a 1% improvement in output.
Finally, in desperation, they turned to the mathematicians. The foremost mathematician of his time offered to help them with the problem. Upon hearing the problem, he told the delegation that they could come back in the morning and he would have solved the problem. In the morning, they came back, and he handed them a piece of paper with the computations for the new, 300% improved milk cow.
The plans began:
"A Proof of the Attainability of Increased Milk Output from Bovines:
Consider a spherical cow......"
Chet Murthy, Cornell
Proof : Sufficient to show that for any two positive integers, A and B, A = B. Further, it is sufficient to show that for all N > 0, if A and B (positive integers) satisfy (MAX(A, B) = N) then A = B.
Proceed by induction.
If N = 1, then A and B, being positive integers, must both be 1. So A = B.
Assume that the theorem is true for some value k. Take A and B with MAX(A, B) = k+1. Then MAX((A-1), (B-1)) = k. And hence (A-1) = (B-1). Consequently, A = B.
Keith Goldfarb
He sat down at the controls and tried to figure them out. The sirens got louder and louder. Armed men surrounded the jet. The would be pilot's friends cried out, "Please, please take off now!!! Hurry!!!!!!" The experimentalist calmly replied, "Have patience. I'm just a simple pole in a complex plane."
Lyle Levine, Washington University, St. Louis
Hiawatha, mighty hunter, He could shoot ten arrows upward, Shoot them with such strength and swiftness That the last had left the bow-string Ere the first to earth descended. This was commonly regarded As a feat of skill and cunning. Several sarcastic spirits Pointed out to him, however, That it might be much more useful If he sometimes hit the target. "Why not shoot a little straighter And employ a smaller sample?" Hiawatha, who at college Majored in applied statistics, Consequently felt entitled To instruct his fellow man In any subject whatsoever, Waxed exceedingly indignant, Talked about the law of errors, Talked about truncated normals, Talked of loss of information, Talked about his lack of bias, Pointed out that (in the long run) Independent observations, Even though they missed the target, Had an average point of impact Very near the spot he aimed at, With the possible exception of a set of measure zero. "This," they said, "was rather doubtful; Anyway it didn't matter. What resulted in the long run: Either he must hit the target Much more often than at present, Or himself would have to pay for All the arrows he had wasted." Hiawatha, in a temper, Quoted parts of R. A. Fisher, Quoted Yates and quoted Finney, Quoted reams of Oscar Kempthorne, Quoted Anderson and Bancroft (practically in extenso) Trying to impress upon them That what actually mattered Was to estimate the error. Several of them admitted: "Such a thing might have its uses; Still," they said, "he would do better If he shot a little straighter." Hiawatha, to convince them, Organized a shooting contest. Laid out in the proper manner Of designs experimental Recommended in the textbooks, Mainly used for tasting tea (but sometimes used in other cases) Used factorial arrangements And the theory of Galois, Got a nicely balanced layout And successfully confounded Second order interactions. All the other tribal marksmen, Ignorant benighted creatures Of experimental setups, Used their time of preparation Putting in a lot of practice Merely shooting at the target. Thus it happened in the contest That their scores were most impressive With one solitary exception. This, I hate to have to say it, Was the score of Hiawatha, Who as usual shot his arrows, Shot them with great strength and swiftness, Managing to be unbiased, Not however with a salvo Managing to hit the target. "There!" they said to Hiawatha, "That is what we all expected." Hiawatha, nothing daunted, Called for pen and called for paper. But analysis of variance Finally produced the figures Showing beyond all peradventure, Everybody else was biased. And the variance components Did not differ from each other's, Or from Hiawatha's. (This last point it might be mentioned, Would have been much more convincing If he hadn't been compelled to Estimate his own components From experimental plots on Which the values all were missing.) Still they couldn't understand it, So they couldn't raise objections. (Which is what so often happens with analysis of variance.) All the same his fellow tribesmen, Ignorant benighted heathens, Took away his bow and arrows, Said that though my Hiawatha Was a brilliant statistician, He was useless as a bowman. As for variance components Several of the more outspoken Make primeval observations Hurtful of the finer feelings Even of the statistician. In a corner of the forest Sits alone my Hiawatha Permanently cogitating On the normal law of errors. Wondering in idle moments If perhaps increased precision Might perhaps be sometimes better Even at the cost of bias, If one could thereby now and then Register upon a target.W. E. Mientka, "Professor Leo Moser -- Reflections of a Visit" American Mathematical Monthly, Vol. 79, Number 6 (June-July, 1972)
Dave Seaman, Purdue
"What is 2 * 2 ?"
The engineer whips out his slide rule (so it's old) and shuffles it back and forth, and finally announces "3.99".
The physicist consults his technical references, sets up the problem on his computer, and announces "it lies between 3.98 and 4.02".
The mathematician cogitates for a while, oblivious to the rest of the world, then announces: "I don't what the answer is, but I can tell you, an answer exists!".
Philosopher: "But what do you _mean_ by 2 * 2 ?"
Logician: "Please define 2 * 2 more precisely."
Accountant: Closes all the doors and windows, looks around carefully, then asks "What do you _want_ the answer to be?"
Computer Hacker: Breaks into the NSA super-computer and gives the answer.
Dave Horsfall, Alcatel-STC Australia, North Sydney
John C. George, U.Illinois Urbana-Champaign
"When I was young in Poland I met the great mathematician Waclaw Sierpinski. He was old already then and rather absent-minded. Once he had to move to a new place for some reason. His wife wife didn't trust him very much, so when they stood down on the street with all their things, she said:
- Now, you stand here and watch our ten trunks, while I go and get a taxi.
She left and left him there, eyes somewhat glazed and humming absently. Some minutes later she returned, presumably having called for a taxi. Says Mr Sierpinski (possibly with a glint in his eye):
- I thought you said there were ten trunks, but I've only counted to nine.
- No, they're TEN!
- No, count them: 0, 1, 2, ..."
Kai-Mikael, Royal Inst. of Technology, Stockholm, SWEDEN
Mobius Dick.
Jeff Dalton, U. of Edinburgh, UK
Physicist: "Not quite. Physics is well on its way without those mythical `foundations'. Just give us serviceable mathematics."
Computer Scientist: "Who cares? Everything in this Universe seems to be finite anyway. Besides, I'm too busy debugging my Pascal programs."
Mathematician: "Forget all that! Just make your formulae as aesthetically pleasing as possible!"
Keitaro Yukawa, U. of Victoria, B.C, CANADA
Jogging girl scout = Brownian motion.
Ilan Vardi, Stanford
Proof: cancel the n in the numerator and denominator.
Micah Fogel, UC-Berkeley
The first one says to the second that the average person knows very little about basic mathematics.
The second one disagrees, and claims that most people can cope with a reasonable amount of math.
The first mathematicien goes off to the washroom, and in his absence the second calls over the waitress.
He tells her that in a few minutes, after his friend has returned, he will call her over and ask her a question. All she has to do is answer one third x cubed.
She repeats `one thir -- dex cue'? He repeats `one third x cubed'.
Her: `one thir dex cuebd'? Yes, that's right, he says. So she agrees, and goes off mumbling to herself, `one thir dex cuebd...'.
The first guy returns and the second proposes a bet to prove his point, that most people do know something about basic math.
He says he will ask the blonde waitress an integral, and the first laughingly agrees.
The second man calls over the waitress and asks `what is the integral of x squared?'.
The waitress says `one third x cubed' and while walking away, turns back and says over her shoulder `plus a constant'!
Lynn Marshall, Universite Catholique de Louvain, Belgium
The Penis
"It has dealings with human intelligence and sometimes displays an intelligence of its own; where a man may desire it to be stimulated it remains obstinate and follows its own course; and sometimes it moves on its own without permission or any thought by its owner. Whether one is awake or asleep, it does what it pleases; often the man is asleep and it is awake; often the man is awake and it is asleep; or the man would like it to be in action and it refuses; often it desires action and the man forbids it. That is why it seems that this creature often has a life and intelligence separate from that of the man, and it seems that man is wrong to be ashamed of giving it a name or showing it; that which he seeks to cover and hide he ought to expose solemnly like a priest at mass.
Leonardo da Vinci