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Foolproof (?) Proofs
From Bad To Verse
2 + 2 = 5 for unusually large values of 2.
42.7 percent of all statistics are made up on the spot.
7/5th of all people do not understand fractions.
A bunch of Polish scientists decided to flee their repressive government by hijacking an airliner and forcing the pilot to fly them to a western country. They drove to the airport, forced their way on board a large passenger jet, and found there was no pilot on board. Terrified, they listened as the sirens got louder. Finally, one of the scientists suggested that since he was an experimentalist, he would try to fly the aircraft. 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."
A friend was bragging to a statistician over coffee one afternoon how two-day volatility in the stock market had treated his holdings rather kindly. He chortled, "Yeah, yesterday I gained 60% but today I lost 40% for a net gain of 20%." The statistician sat in horrified silence. He finally mustered the courage and said, "My good friend I'm sorry to inform you but you had a net loss of 4%!" [My little tale above illustrates how pervasive innumeracy is in our society. Always remember, "Percent of What?"]
A hungry man went into a restaurant and noticed that the daily special was rabbit burgers, a real delicacy, for only 49 cents a burger. He was astounded at his good fortune to find such a bargain. When he inquired of the cook, the cook told him that in order to keep prices down he had to add some filler: in fact, only part of the burger was rabbit meat. The rest was horse meat. "How much of each kind of meat is in a burger?" asked the customer. The cook replied, "There is an equal amount of horse and rabbit in the burger: One horse, one rabbit."
A lazy dog is a slow pup. A slope up is an inclined plane. An ink-lined plane is a sheet of writing-paper. Therefore lazy dog is a sheet of writing-paper.
A Physics professor is walking across campus, and runs into math professor.
The physics professor has been doing an experiment, and has worked out an
empirical equation that seems to explain his data, and asks the math professor
to look at it.
A week later, they meet again, and the math professor says the equation is invalid. By then, the physics professor has used his equation to predict the results of further experiments, and he is getting excellent results, so he asks the math professor to look again.
Another week goes by, and they meet once more. The math professor tells the physics professor the equation does work, "But only in the trivial case where the numbers are real and positive."
A spider asked a frog to carry him across a river. The frog said "How do I
know you won't bite me?" The scorpion replied "Because I can't swim
and we'd just both die."
This made sense to the frog and he agreed to carry the spider across the river. Halfway across the river the spider bit the frog. Before the frog died, he asked the spider "Why in the hell did you just do that? You're going to die too!" The spider said "Hey, I'm not much of a game theorist."
A statistician can have his head in an oven and his feet in ice, and he will say that on the average he feels fine.
A statistician is a person who draws a mathematically precise line from an unwarranted assumption to a foregone conclusion.
A statistician is someone who is good with numbers but lacks the personality to be an accountant.
A statistician is someone who is skilled at drawing a precise line from an unwarranted assumption to a foregone conclusion.
A stats major was completely hung over the day of his final exam. It was a True/False test, so he decided to flip a coin for the answers. The stats professor watched the student the entire two hours as he was flipping the coin, writing the answer, flipping the coin, writing the answer. At the end of the two hours, everyone else had left the final except for the one student. The professor walks up to his desk and interrupts the student, saying: "Listen, I have seen that you did not study for this statistics test, you didn't even open the exam. If you are just flipping a coin for your answer, what is taking you so long?" The student replies bitterly (as he is still flipping the coin): "Shhh! I am checking my answers!"
A student, working on a rather long math homework assignment, discovered that
one problem was fairly easy to solve, except that it required about three pages
of fairly simple proof after the one or two difficult steps. It being rather
late at night, he did the difficult steps and left the proof undone, along with
a note: "This proof is left as an exercise for the grader."
Next week, he received his homework back. He noted that several extra pages had been stapled to the back of it. Examining the extra pages, he was surprised to find the entire proof written down step-by step. At the end, in red pen, the grader had written: "I made a minor math error. Minus 2."
A topologist walks into a bar and orders a drink. The bartender, being a number theorist, says, "I'm sorry, but we don't serve topologists here." The disgruntled topologist walks outside, but then gets an idea and performs Dahn surgery upon herself. She walks into the bar, and the bartender, who does not recognize her since she is now a different manifold, serves her a drink. However, the bartender thinks she looks familiar, or at least locally similar, and asks, "Aren't you that topologist that just came in here?" To which she responds, "No, I'm a frayed knot."
A woman walks into a bar accompanied by a dog and a cow. The bartender says, "Hey, no animals are allowed in here." The woman replies, "These are very special animals." "How so?" "They're knot theorists." The bartender raises his eyebrows and says, "I've met a number of knot theorists who I thought were animals, but never an animal that was a knot theorist." "Well, I'll prove it to you. Ask them them anything you like." So the bartender asks the dog, "Name a knot invariant." "Arf, arf" barks the dog. The bartender scowls and turns to the cow asking, "Name a topological invariant." The cow says, "Mu, mu." At this point the bartender turns to the woman, says, "Just what are you trying to pull?" and throws them out of the bar. Outside, the dog turns to the woman and asks, "Do you think I should have said the Jones polynomial?"
According to a recent poll, 51% of all Americans are in the majority.
According to Paul Erdös, a mathematician is a device for turning coffee into theorems.
Algebraic symbols are used when you do not know what you are talking about.
An actuary is someone who brings a fake bomb on a plane, because that decreases the chances that there will be another bomb on the plane.
An Indian chief had three wives, each of whom was pregnant. The first gave birth to a boy. The chief was so elated he built her a teepee made of deer hide. A few days later, the second gave birth, also to a boy. The chief was very happy. He built her a teepee made of antelope hide. The third wife gave birth a few days later, but the chief kept the details a secret. He built this one a two story teepee, made out of a hippopotamus hide. The chief then challenged the tribe to guess what had occurred. Many tried, unsuccessfully. Finally, one young brave declared that the third wife had given birth to twin boys. "Correct," said the chief. "How did you figure it out?" The warrior answered, "It's elementary. The value of the squaw of the hippopotamus is equal to the sons of the squaws of the other two hides."
Are statisticians normal?
As easy as 3.14159265358979323846264338327950288419716.
Asked how his pet parrot died, the mathematician answered "Polynomial, polygon."
At New York's Kennedy airport today, an individual later discovered to be a public school teacher, was arrested trying to board a flight while in possession of a ruler, a protractor, a set square, and a calculator. Attorney General John Ashcroft believes the man is a member of the notorious Al-gebra movement. He is being charged with carrying weapons of math instruction. Al-gebra is a very fearsome cult, indeed. They desire average solutions by means and extremes, and sometimes go off on a tangent in a search of absolute value. They consist of quite shadowy figures, with names like "x" and "y," and, although they are frequently referred to as "unknowns," we know they really belong to a common denominator and are part of the axis of medieval with coordinates in every country.
Did you hear about the statistician who was thrown in jail? He now has zero degrees of freedom.
Did you hear the one about the statistician? Probably.
Did you know that 87.166253% of all statistics claim a precision of results that is not justified by the method employed?
"Divide 14 sugar cubes into 3 cups of coffee so that each cup has an odd number of sugar cubes." "1, 1, 12." "But 12 isn't odd!" "It's an odd number of cubes to put in a cup of coffee."
Forty-three percent of all statistics are worthless.
How do you tell that you are in the hands of the Mathematical Mafia? They make you an offer that you can't understand.
How many statisticians does it take to change a light bulb? 100. One to change the bulb and n-1 to test the replacement!!!
How many statisticians does it take to screw in a light bulb? We really don't know yet. Our entire sample was skewed to the left.
I once heard that the great mathematician David Hilbert was invited to give a talk on any subject he liked during the early days of air travel. His subject: "The Proof of Fermat's Last Theorem." Needless to say, his talk was eagerly anticipated. The day arrived, the talk was given, and it was brilliant — but it had nothing at all to do with Fermat's Last Theorem. After the talk, someone asked Hilbert why he had picked a title that had nothing to do with the talk. His answer: "Oh, that title was just in case the plane crashed."
If a mathematician writes a fantasy novel, would the pages have imaginary numbers?
If Fibonacci wrote the book, the pages would be numbered 1, 1, 2, 3, 5, 8, 13, 21, . . .
In the topologic hell the beer is packed in Klein's bottles.
It is proven that the celebration of birthdays is healthy. Statistics show that those people who celebrate the most birthdays become the oldest.
It was mentioned on CNN that the new prime number discovered recently is four times bigger than the previous record.
"It's a plane figure," Tom said flatly. "99 is almost 100," said Tom roughly. "1, 3, 5, 7," Tom said oddly. "Space is an infinite set of points," Tom said distantly. "They are mirror images," reflected Tom.
Klein bottle for rent — inquire within.
Life is complex. It has real and imaginary components.
Logic is a systematic method for getting the wrong conclusion with confidence. Statistics is a systematic method for getting the wrong conclusion with 95% confidence.
Lumberjacks make good musicians because of their natural logarithms.
Math and Alcohol don't mix, so please don't drink and derive.
Mathematic puns are the first sine of madness.
My geometry teacher was sometimes acute, and sometimes obtuse, but always, he was right.
Never say "N factorial", simply scream "N" at the top of your lungs.
Numbers are like people; torture them enough and they'll tell you anything.
Old statisticians never die they just become nonsignificant.
Pie are not square. Pie are round. Cornbread are square.
REMEMBER! Data is always plural!
Several students were asked the following problem: "Prove that all odd integers are prime." The first student to try to do this was a math student. Hey says "Well, 1 is prime, 3 is prime, 5 is prime, and by induction, we have that all the odd integers are prime." The physics student then said, "I'm not sure of the validity of your proof, so I'll try to prove it by experiment. 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 was an 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 says "I've just whipped up a program to really prove it." He goes to his computer and runs his program. The output reads, "1 is prime, 1 is prime, 1 is prime, 1 is prime . . ."
She was only a mathematicians' daughter, but she knew how to multiply.
She was only the statistician's daughter, but she knew all the standard deviations.
Some say the pope is the greatest cardinal. But others insist this cannot be so, as every pope has a successor.
Statistical Analysis: Mysterious, sometimes bizarre, manipulations performed upon the collected data of an experiment in order to obscure the fact that the results have no generalizable meaning for humanity. Commonly, computers are used, lending an additional aura of unreality to the proceedings.
Statisticians are like the drunk leaning against the lamp pole — they are there for support not illumination.
Statisticians must stay away from children's toys because they regress so easily.
Statistics are like a bikini: what they reveal is suggestive but what they conceal is vital.
Statistics means never having to say you're certain.
The larger the sample size (n) the more confident you can be that your sample mean is a good representation of the population mean. In other words, the "n" justifies the means.
The last few available graves in a cemetery are called residual plots.
The law of the excluded middle either rules or does not rule, O.K.?
The limit as n goes to infinity of sin(x)/n is 6. Proof: cancel the n in the numerator and denominator.
The number you have dialed is imaginary. Please rotate your phone 90 degrees and try again.
The reason that every major university maintains a department of mathematics is that it is cheaper to do this than to institutionalize all those people.
There are 10 kinds of people in this world — those who understand binary, and those who don't.
There are three kinds of people: those who can count, and those who can't.
There is no truth to the allegation that statisticians are mean. They are just your standard normal deviates.
There was once a very smart horse. Anything that it was shown, it easily mastered, until one day, its teachers tried to teach it about rectangular coordinates and it couldn't understand them. All the horse's acquaintances and friends tried to figure out what was the matter. Then a new guy looked at the problem and said, "Of course he can't do it. Why, you're putting Descartes before the horse!"
There really are only two types of people in the world, those that don't do math, and those that take care of them.
Three men are in a hot-air balloon. Soon, they find themselves lost in a canyon somewhere. One of the three men says, "I've got an idea. We can call for help in this canyon and the echo will carry our voices far." So he leans over the basket and yells out, "Helllloooooo! Where are we?" (They hear the echo several times.) Fifteen minutes later, they hear this echoing voice: "Hello! 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."
Three statisticians are deer hunting with bows and arrows in the woods. They spot a deer and the first one shoots. His arrow goes flying ten feet off to the deer's left. The second guy takes aim and shoots, but his aim is off. His arrow goes flying ten feet to the deer's right. Suddenly the third statistician starts jumping up and down excitedly and yells, "We got him! We got him!"
Torture the data long enough and they will confess to anything.
Two male mathematicians are in a bar. 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 mathematician 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 agrees, and goes off mumbling to herself, "One third x cubed." 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?" Surprised, the waitress says, "One third x cubed," and while walking away, turns back and says over her shoulder, "plus a constant!"
Two statisticians were traveling in an airplane from LA to New York. About an hour into the flight, the pilot announced that they had lost an engine, but don't worry, there are three left. However, instead of 5 hours it would take 7 hours to get to New York. A little later, he announced that a second engine failed, and they still had two left, but it would take 10 hours to get to New York. Somewhat later, the pilot again came on the intercom and announced that a third engine had died. Never fear, he announced, because the plane could fly on a single engine. However, it would now take 18 hours to get to New York. At this point, one statistician turned to the other and said, "Gee, I hope we don't lose that last engine, or we'll be up here forever!"
What did the zero say to the 8? Nice belt!!
What do you get when you cross a mosquito with a mountain climber? Nothing. You can't cross a scaler with a vector.
What do you get when you take the circumference of your jack-o'-lantern and divide it by its diameter? Pumpkin Pi
What is "pi"? Mathematician: Pi is the number expressing the relationship between the circumference of a circle and its diameter. Physicist: Pi is 3.1415927 plus or minus 0.000000005. Engineer: Pi is about 3.
What is the difference between a statistician and a mortician? Nobody's dying to see the statistician!
What is the shortest mathematicians joke? Let epsilon be smaller than zero.
What's nonorientable and lives in the sea? Mobius Dick.
What's purple and commutes? An abelian grape.
What's yellow, and equivalent to the Axiom of Choice? Zorn's Lemon.
When she told me I was average, she was just being mean.
Why did the mathematician name his dog "Cauchy"? Because he left a residue at every pole.
Why is the number ten afraid of seven? Because seven eight nine.
Why should you never say "288" in polite conversation? Because it's two gross!
Why was the math book sad? It had so many problems.
Ya' hear about the geometer who went to the beach to catch the rays and became a tangent?
You know what seems odd to me? Numbers that aren't divisible by two.
Zenophobia: the irrational fear of convergent sequences.
Theorem: A cat has nine tails.
Proof: No cat has eight tails. A cat has one tail more than no cat. Therefore, a cat has nine tails. QED.
Theorem: All dogs have nine legs.
Proof: Would you agree that no dog has five legs? Would you agree that a dog has four legs more then no dog? 4 + 5 = 9. QED.
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.
Theorem: Consider the set of all sets that have never been considered. Hey! They're all gone!!
This is a one line proof — if we start sufficiently far to the left.
A mathematical limerick: ((12 + 144 + 20 + 3*Sqrt) / 7) + 5*11 = 9^2 + 0
A dozen, a gross and a score,
plus three times the square root of four,
divided by seven,
plus five times eleven,
equals nine squared and not a bit more!
A mathematician named Crottle
Poured water into a Klein bottle.
When asked, "Do you doubt
That some will run out?"
He replied, "No, I don't. Quite a lot'll."
There was young maiden named List
Whose mouth had a funny half-twist.
She'd turned both her lips
Into Moebius strips...
'Til she's kissed you, you haven't been kissed!
To a tightrope walker named Zekund
The 'a' due to gravity beckoned.
His performance was great
At about 9.8
Definitions of Terms Commonly Used in Higher Math
Top Ten Excuses for Not Doing Your Math Homework:
1. I accidentally divided by zero and my paper burst into flames.
2. It's Isaac Newton's birthday.
3. I could only get arbitrarily close to my textbook. I couldn't actually reach it.
4. I have the proof, but there isn't room to write it in this margin.
5. I was watching the World Series and got tied up trying to prove that it converged.
6. I have a solar powered calculator and it was cloudy.
7. I locked the paper in my trunk but a four-dimensional dog got in and ate it.
8. I couldn't figure out whether i am the square of negative one or i is the square root of negative one.
9. I took time out to snack on a doughnut and a cup of coffee. I spent the rest of the night trying to figure which one to dunk.
10. I could have sworn I put the homework inside a Klein bottle, but this morning I couldn't find it.
Top ten reasons why e is inferior to pi:
10. e is less challenging to spell than pi.
9. e ~=2.718281828459045, which can be easily memorized to its billionth place, whereas pi needs "skills" to be memorized.
8. The character for e is so cheap that it can be found on a keyboard. But pi is special (it's under "special symbols" in word processor programs.)
7. Pi is the bigger piece of pie.
6. e has an easy limit definition and infinite series. The limit definition of pi and the infinite series are much harder.
5. e you understand what it is even though you start learning it late when you're in pre-calculus. But pi, even after five or six years it's still hard to know what it really is.
4. People mistakenly confuse Euler's Number (e) with Euler's Constant (gamma). There is no confusion with the one and only pi.
3. e is named after a person, but pi stands for itself.
2. Pi is much shorter and easier to say than "Euler's Number".
1. To read pi, you don't have to know that Euler's name is really pronounced Oiler.
You might be a mathematician if ...
... you cannot refrain from blurting out counterexamples when someone claims an impossibility.
... at the age of 19 your most productive years are behind you.
... you make mistakes . . . but they are really interesting mistakes.
... you wonder how Euler pronounced "Euclid."
... your major was Mathematics, minor Caffeine.
... you know all of the Greek alphabet, but not a word of Greek.
... the solution to every problem involves counting balls into boxes.
... you can fold planar strips into regular polyhedra entirely in your head.
... doing something more than once is boring.
... you count on your fingers in binary.
... you know a six-letter word with three vowels, all of which are "y." [In case you are as ignorant as me: It is syzygy. Syzygy is the position of an object when it is in line with other objects. It is then "at syzygy".]
... your opinion of A Beautiful Mind is "been there; done that."
... you find yourself saying "there exists" instead of "there is."
... you get into heated arguments over 0.999... = 1.0...
... your retirement plans include solving the twin prime conjecture.
... you spend time helping people you don't know do their homework.
... you know the difference between a conjecture and a theorem.
... you care how people pronounce "Euler."