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Here's some math related humor obtained from various sources.
Send comments, ideas, etc. via e-mail, rather than posting to rec.humor.
New items: #9 in the Sin, Cos, Tan order mnemonics list.
The Northwestern University Marching band's "The Calculus Cheer"
Michael Cook
MLC@IBERIA.CCA.ROCKWELL.COM
Three men went to a convention. They needed a room, but all the hotels
were full. They finally found a motel that had a vacancy. They told
the Innkeeper they needed rooms. The Innkeeper said "I've only got one room
left." The three men said "We'll take it." The Innkeeper said "That'll be
$30.00." The men paid the $30.00 and went to thier room. After a while, the
Innkeeper thought to himself "I've overcharged those three men. I should give
them a discount for having to share one room." So, he called the bellboy over
and told him "Take this money to room 303 and tell the three men there I'm
giving them a discount for having to share a room." He handed the bellboy
five one dollar bills. The bellboy took off to the three men's room. On the
way, he got to thinking...How are three men going to split $5.00? He said to
himself "I can help them out by giving them just three dollars." So, the
bellboy put two dollars in his pocket. When he got to the room, he rang the
bell and when one of the men answered, he said "The Innkeeper said to tell
you he is sorry for the inconvenience, and offers this refund for your
hardship." He then handed the man three one dollar bills.
Now, if the three men paid $30.00 for the room initially... That means, t
hey each paid $10.00.
3 times 10 equals thirty
Since they got back $3.00, that means each only paid $9.00.
30 minus 3 equals 27
3 times 9 equals 27
So, now each man paid only $9.00 apiece for the room. Right?
OK three times nine is twenty seven. Right?
OK the bellboy has two dollars in his pocket. Right?
OK twenty seven plus two is twenty nine. Right?
All right they originally paid $30.00 for the room, so WHERE'S THE MISSING DOLLAR???????
Math and Alcohol don't mix, so...
PLEASE DON'T DRINK AND DERIVE
Then there's every parent's scream when their child walks into the
room dazed and staggering:
OH NO...YOU'VE BEEN TAKING DERIVATIVES!!
MADD = Mathematicians
Against
Drunk
Deriving
[This limerick was previously posted incorrectly.
The integral limit has been changed.]
Here's a limerick I picked up off the net a few years back - looks better
on paper.
3_
/3
/
| 2 3 X pi 3_
| z dz X cos(--------) = ln (/e )
| 9
/
1
Which, of course, translates to:
Integral z-squared dz
from 1 to the cube root of 3
times the cosine
of three pi over 9
equals log of the cube root of 'e'.
And it's correct, too.
This poem was written by John Saxon (an author of math textbooks).
((12 + 144 + 20 + (3 * 4^(1/2))) / 7) + (5 * 11) = 9^2 + 0
Or for those who have trouble with the poem:
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.
'Tis a favorite project of mine
A new value of pi to assign.
I would fix it at 3
For it's simpler, you see,
Than 3 point 1 4 1 5 9.
("The Lure of the Limerick" by W.S. Baring-Gould, p.5. Attributed to
Harvey L. Carter).
If inside a circle a line
Hits the center and goes spine to spine
And the line's length is "d"
the circumference will be
d times 3.14159
If (1+x) (real close to 1)
Is raised to the power of 1
Over x, you will find
Here's the value defined:
2.718281...
An engineer thinks that his equations are an approximation to reality.
A physicist thinks reality is an approximation to his equations.
A mathematician doesn't care.
Why is the number 10 afraid of seven?
-- because seven ate nine.
We use epsilons and deltas in mathematics because mathematicians tend
to make errors.
What's big, grey, and proves the uncountability of the reals?
Cantor's Diagonal Elephant!
How can you tell that Harvard was layed out by a mathematician?
The div school [divinity school] is right next to the grad school...
The Stanford Linear Accelerator Center was known as SLAC, until the
big earthquake, when it became known as SPLAC.
SPLAC? Stanford Piecewise Linear Accelerator.
Q: How many topologists does it take to change a light bulb?
A: It really doesn't matter, since they'd rather knot.
A mathematician decides he wants to learn more about practical
problems. He sees a seminar with a nice title: "The Theory of Gears."
So he goes. The speaker stands up and begins, "The theory of gears
with a real number of teeth is well known ..."
A group of scientists were doing an investigation into problem-solving
techniques, and constructed an experiment involving a physicist, an
engineer, and a mathematician.
The experimental apparatus consisted of a water spigot and two identical
pails, one of which was fastened to the ground ten feet from the spigot.
Each of the subjects was given the second pail, empty, and told to fill the
pail on the ground.
The physicist was the first subject: he carried his pail to the spigot,
filled it there, carried it full of water to the pail on the ground, and
poured the water into it. Standing back, he declared, "There: I have
solved the problem."
The engineer and the mathematician each approached the problem similarly.
Upon finishing, the engineer noted that the solution was exact, since the
volumes of the pails were equal. The mathematician merely noted that he
had proven that a solution exists.
Now, the experimenters altered the parameters of the task a bit: the pail
on the ground was still empty, but the subjects were presented with a pail
that was already half-filled with water.
The physicist immediately carried his pail over to the one on the ground,
emptied the water into it, went back to the spigot, *filled* the pail, and
finally emptied the entire contents into the pail on the ground,
overflowing it and spilling some of the water. Upon finishing, he
commented that the problem should have been better stated.
The engineer, in turn, thought for some time before going into action. He
then took his half-filled pail to the spigot, filled it to the brim, and
filled the pail on the ground from it. Again he noted that the problem had
an exact solution, which of course he had found.
The mathematician thought for a long time before stirring. At last he
stood up, emptied his pail onto the ground, and declared, "The problem has
been reduced to one already solved."
Professor Dirac, a famous Applied Mathematician-Physicist, had a horse
shoe over his desk. One day a student asked if he really believed
that a horse shoe brought luck. Professor Dirac replied, "I
understand that it brings you luck if you believe in it or not."
First of all let me make it clear that I have nothing against
contravariant functors. Some of my best friends are cohomology
theories! But now you aren't supposed to call them contravariant
anymore. It's Algebraically Correct to call them 'differently
arrowed'!!
In the same way that transcendental numbers are polynomially
challenged?
Manifolds are personifolds (humanifolds).
Neighborhoods are neighbor victims of society.
It's the Asian Remainder Theorem.
It isn't PC to use "singularity" - the function is "convergently
challenged" there.
Why did the computer scientist die in the shower?
Because he read the instructions on the shampoo bottle, "Lather,
rinse, repeat."
Why did the calculus student have so much trouble making Kool-Aid?
Because he couldn't figure out how to get a quart of water into the
little package.
Q: Why do computer scientists confuse Christmas and Halloween?
A: Because Oct 31 = Dec 25
Here are some phrases used to remember SIN, COS, and TAN.
(SIN = Opposite/Hypotenuse, COS = Adjacent/H, TAN = O/A).
1. SOHCAHTOA (sock-a-toe-a)
2. The Cat Sat
On An Orange
And Howled Hard
3. Some Old Hulks
Carry A Huge
Tub Of Ale
4. Silly Old Hitler
Caused Awful Headaches
To Our Airmen
5. Some Old Hag
Cracked All Her
Teeth On Asparagus
6. Some Old Hairy
Camels Are Hairier
Than Others Are
7. Silly Old Harry
Caught A Herring
Trawling Off America
8. SOPHY, CADHY, TOAD
9. Some Old Horse
Caught Another Horse
Taking Oats Away
--------------------------------units and dimensions-------------
2 monograms 1 diagram
8 nickles 2 paradigms
2 wharves 1 paradox
10E5 bicycles 2 megacycles
1 unit of suspense in an Agatha Christie novel 1 whod unit
Three Laws of Thermodynamics (paraphrased):
First Law: You can't get anything without working for it.
Second Law: The most you can accomplish by work is to break even.
Third Law: You can't break even.
Q: What goes "Pieces of seven! Pieces of seven!"?
A: A parroty error!!
Q: What did the circle say to the tangent line?
A: "Stop touching me!"
A mathematician is a person who says that, when 3 people are supposed
to be in a room but 5 came out, 2 have to go in so the room gets
empty...
The upgrade path to the most powerful and satisfying computer:
* Pocket calculator
* Commodore Pet / Apple II / TRS 80 / Commodore 64 / Timex Sinclair
(Choose any of the above)
* IBM PC
* Apple Macintosh
* Fastest workstation of the time (HP, DEC, IBM, SGI: your choice)
* Minicomputer (HP, DEC, IBM, SGI: your choice)
* Mainframe (IBM, Cray, DEC: your choice)
And then you reach the pinnacle of modern computing facilities:
*********************************************************
******* G R A D U A T E S T U D E N T S ********
*********************************************************
Yes, you just sit back and do all of your computing through lowly
graduate students. Imagine the advantages:
* Multi-processing, with as many processes as you have
students. You can easily add more power by promising more
desperate undergrads that they can indeed escape college
through your guidance. Special student units can even
handle several tasks *on*their*own*!
* Full voice recognition interface. Never touch a keyboard or
mouse again. Just mumble commands and they *will* be
understood (or else!).
* No hardware upgrades and no installation required. Every
student comes complete with all hardware necessary. Never
again fry a chip or $10,000 board by improper installation!
Just sit that sniveling student at a desk, give it writing
utensils (making sure to point out which is the dangerous
end) and off it goes.
* Low maintenance. Remember when that hard disk crashed in
your Beta 9900, causing all of your work to go the great bit
bucket in the sky? This won't happen with grad. students.
All that is required is that you give them a good *whack!*
upside the head when they are acting up, and they will run
good as new.
* Abuse module. Imagine yelling expletives at your computer.
Doesn't work too well, because your machine just sits there
and ignores you. Through the grad student abuse module you
can put the fear of god in them, and get results to boot!
* Built-in lifetime. Remember that awful feeling two years
after you bought your GigaPlutz mainframe when the new
faculty member on the block sneered at you because his
FeelyWup workstation could compute rings around your
dinosaur? This doesn't happen with grad. students. When
they start wearing and losing productivity, simply give them
the PhD and boot them out onto the street to fend for
themselves. Out of sight, out of mind!
* Cheap fuel: students run on Coca Cola (or the high-octane
equivalent -- Jolt Cola) and typically consume hot spicy
chinese dishes, cheap taco substitutes, or completely
synthetic macaroni replacements. It is entirely unnecessary
to plug the student into the wall socket (although this does
get them going a little faster from time to time).
* Expansion options. If your grad. students don't seem to be
performing too well, consider adding a handy system manager
or software engineer upgrade. These guys are guaranteed to
require even less than a student, and typically establish
permanent residence in the computer room. You'll never know
they are around! (Which you certainly can't say for an
AXZ3000-69 150gigahertz space-heater sitting on your desk
with its ten noisy fans....) [Note however that the
engineering department still hasn't worked out some of the
idiosyncratic bugs in these expansion options, such as
incessant muttering at nobody in particular, occasionaly
screaming at your grad. students, and posting ridiculous
messages on world-wide bulletin boards.]
So forget your Babbage Engines and abacuses (abaci?) and PortaBooks
and DEK 666-3D's and all that other silicon garbage. The wave of the
future is in wetware, so invest in graduate students today! You'll never
go back!
If I have seen farther than others, it is because I was
standing on the shoulder of giants.
-- Isaac Newton
If I have not seen as far as others, it is because giants
were standing on my shoulders.
-- Hal Abelson
In computer science, we stand on each other's feet.
-- Brian K. Reid
He thinks he's really smooth, but he's only C^1.
He's always going off on a tangent.
A mathematician and a physicist agree to a psychological experiment.
The mathematician is put in a chair in a large empty room and a
beautiful naked woman is placed on a bed at the other end of the room.
The psychologist explains, "You are to remain in your chair. Every
five minutes, I will move your chair to a position halfway between its
current location and the woman on the bed." The mathematician looks
at the psychologist in disgust. "What? I'm not going to go through
this. You know I'll never reach the bed!" And he gets up and storms
out. The psychologist makes a note on his clipboard and ushers the
physicist in. He explains the situation, and the physicist's eyes
light up and he starts drooling. The psychologist is a bit confused.
"Don't you realize that you'll never reach her?" The physicist smiles
and replied, "Of course! But I'll get close enough for all practical
purposes!"
Dean, to the physics department. "Why do I always have to give you
guys so much money, for laboratories and expensive equipment and
stuff. Why couldn't you be like the math department - all they need
is money for pencils, paper and waste-paper baskets. Or even better,
like the philosophy department. All they need are pencils and paper."
An engineer, physicist, and mathematician are all challenged with a
problem: to fry an egg when there is a fire in the house. The
engineer just grabs a huge bucket of water, runs over to the fire, and
puts it out. The physicist thinks for a long while, and then measures
a precise amount of water into a container. He takes it over to the
fire, pours it on, and with the last drop the fire goes out. The
mathematician pores over pencil and paper. After a few minutes he
goes "Aha! A solution exists!" and goes back to frying the egg.
Sequel: This time they are asked simply to fry an egg (no fire). The
engineer just does it, kludging along; the physicist calculates
carefully and produces a carefully cooked egg; and the mathematician
lights a fire in the corner, and says "I have reduced it to the
previous problem."
A physicist and a mathematician setting in a faculty lounge.
Suddenly, the coffee machine catches on fire. The physicist grabs a
bucket and leaps towards the sink, fills the bucket with water and
puts out the fire. The second day, the same two sit in the same
lounge. Again, the coffee machine catches on fire. This time, the
mathematician stands up, gets a bucket, hands the bucket to the
physicist, thus reducing the problem to a previously solved one.
An engineer, a mathematician, and a physicist are staying in three
adjoining cabins at a decrepit old motel.
First the engineer's coffee maker catches fire on the bathroom vanity.
He smells the smoke, wakes up, unplugs it, throws it out the window,
and goes back to sleep.
Later that night the physicist smells smoke too. He wakes up and sees
that a cigarette butt has set the trash can on fire. He says to
himself, "Hmm. How does one put out a fire? One can reduce the
temperature of the fuel below the flash point, isolate the burning
material from oxygen, or both. This could be accomplished by applying
water." So he picks up the trash can, puts it in the shower stall,
turns on the water, and, when the fire is out, goes back to sleep.
The mathematician, of course, has been watching all this out the
window. So later, when he finds that his pipe ashes have set the
bedsheet on fire, he is not in the least taken aback. He immediately
sees that the problem reduces to one that has already been solved and
goes back to sleep.
A mathematician and a physicist were asked the following question:
Suppose you walked by a burning house and saw a hydrant and
a hose not connected to the hydrant. What would you do?
P: I would attach the hose to the hydrant, turn on the water, and put out
the fire.
M: I would attach the hose to the hydrant, turn on the water, and put out
the fire.
Then they were asked this question:
Suppose you walked by a house and saw a hose connected to
a hydrant. What would you do?
P: I would keep walking, as there is no problem to solve.
M: I would disconnect the hose from the hydrant and set the house on fire,
reducing the problem to a previously solved form.
There were two men trying to decide what to do for a living. They
went to see a counselor, and he decided that they had good problem
solving skills.
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 a mathematician, an engineer, and a physicist are out hunting
together. They spy a deer(*) in the woods.
The physicist calculates the velocity of the deer and the effect of
gravity on the bullet, aims his rifle and fires. Alas, he misses; the
bullet passes three feet behind the deer. The deer bolts some yards,
but comes to a halt, still within sight of the trio.
"Shame you missed," comments the engineer, "but of course with an
ordinary gun, one would expect that." He then levels his special
deer-hunting gun, which he rigged together from an ordinary rifle, a
sextant, a compass, a barometer, and a bunch of flashing lights which
don't do anything but impress onlookers, and fires. Alas, his bullet
passes three feet in front of the deer, who by this time wises up and
vanishes for good.
"Well," says the physicist, "your contraption didn't get it either."
"What do you mean?" pipes up the mathematician. "Between the two of
you, that was a perfect shot!"
----------
(*) How they knew it was a deer:
The physicist observed that it behaved in a deer-like manner, so it
must be a deer.
The mathematician asked the physicist what it was, thereby reducing it
to a previously solved problem.
The engineer was in the woods to hunt deer, therefore it was a deer.
A computer scientist, mathematician, a physicist, and an engineer were
travelling through Scotland when they saw a black sheep through the
window of the train.
"Aha," says the engineer, "I see that Scottish sheep are black."
"Hmm," says the physicist, "You mean that some Scottish sheep are
black."
"No," says the mathematician, "All we know is that there is at least
one sheep in Scotland, and that at least one side of that one sheep is
black!"
"Oh, no!" shouts the computer scientist, "A special case!"
A Mathematician (M) and an Engineer (E) attend a lecture by a
Physicist. The topic concerns Kulza-Klein theories involving physical
processes that occur in spaces with dimensions of 11, 12 and even
higher. The M is sitting, clearly enjoying the lecture, while the E
is frowning and looking generally confused and puzzled. By the end
the E has a terrible headache. At the end, the M comments about the
wonderful lecture. The E says "How do you understand this stuff?"
M: "I just visualize the process."
E: "How can you POSSIBLY visualize something that occurs in
11-dimensional space?"
M: "Easy, first visualize it in N-dimensional space, then let N go to 11."
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 0.00000005
Engineer: Pi is about 3.
When considering the behaviour of a howitzer:
A mathematician will be able to calculate where the shell will land.
A physicist will be able to explain how the shell gets there.
An engineer will stand there and try to catch it.
An engineer, a physicist and a mathematician find themselves in an
anecdote, indeed an anecdote quite similar to many that you have no
doubt already heard. After some observations and rough calculations
the engineer realizes the situation and starts laughing. A few
minutes later the physicist understands too and chuckles to himself
happily as he now has enough experimental evidence to publish a paper.
This leaves the mathematician somewhat perplexed, as he had observed
right away that he was the subject of an anecdote, and deduced quite
rapidly the presence of humour from similar anecdotes, but considers
this anecdote to be too trivial a corollary to be significant, let
alone funny.
Q: What's purple and commutes?
A: An abelian grape.
Q: Why did the mathematician name his dog "Cauchy"?
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.
Q: How many mathematicians does it take to screw in a lightbulb?
A: One, who gives it to six Californians, thereby reducing it to an
earlier riddle.
-- from a button I bought at Nancy Lebowitz's table at Boskone
Q: What do a mathematician and a physicist [or engineer, or musician,
or whatever the profession of the person addressed] have in common?
A: They are both stupid, with the exception of the mathematician.
Q: What do you call a teapot of boiling water on top of mount everest?
A: A high-pot-in-use
Q: What do you call a broken record?
A: A Decca-gone
Q: What do you get when you cross 50 female pigs and 50 male deer?
A: One hundred sows-and-bucks
Q: Why did the chicken cross the Moebius strip?
A: To get to the other ... er, um ...
Q: What is the world's longest song?
A: "Aleph-nought Bottles of Beer on the Wall."
Q: What does a mathematician do when he's constipated?
A: He works it out with a pencil.
Q: What's yellow and equivalent to the Axiom of Choice.
A: Zorn's Lemon.
Q: What do you get if you cross an elephant with a zebra.
A: Elephant zebra sin theta.
Q: What do you get if you cross an elephant with a mountain climber.
A: You can't do that. A mountain climber is a scalar.
Q: What do you get when you cross an elephant with a banana?
A: Elephant banana sine theta in a direction mutually perpendicular to
the two as determined by the right hand rule.
Q: To what question is the answer "9W."
A: "Dr. Wiener, do you spell your name with a V?"
A somewhat advanced society has figured how to package basic knowledge
in pill form.
A student, needing some learning, goes to the pharmacy and asks what
kind of knowledge pills are available. The pharmacist says "Here's a
pill for English literature." The student takes the pill and swallows
it and has new knowledge about English literature!
"What else do you have?" asks the student.
"Well, I have pills for art history, biology, and world history,"
replies the pharmacist.
The student asks for these, and swallows them and has new knowledge
about those subjects.
Then the student asks, "Do you have a pill for math?"
The pharmacist says "Wait just a moment", and goes back into the
storeroom and brings back a whopper of a pill and plunks it on the
counter.
"I have to take that huge pill for math?" inquires the student.
The pharmacist replied "Well, you know math always was a little hard
to swallow."
"A mathematician is a device for turning coffee into theorems"
-- P. Erdos
Three standard Peter Lax jokes (heard in his lectures) :
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!
"Algebraic symbols are used when you do not know what you are talking about."
Heisenberg might have slept here.
Moebius always does it on the same side.
Statisticians probably do it
Algebraists do it in groups.
(Logicians do it) or [not (logicians do it)].
A promising PhD candidate was presenting his thesis at his final
examination. He proceeded with a derivation and ended up with
something like:
F = -MA
He was embarrassed, his supervising professor was embarrassed, and the
rest of the committee was embarrassed. The student coughed nervously
and said "I seem to have made a slight error back there somewhere."
One of the mathematicians on the committee replied dryly, "Either that
or an odd number of them!"
There was a mad scientist ( a mad ...social... scientist ) who
kidnapped three colleagues, an engineer, a physicist, and a
mathematician, and locked each of them in seperate cells with plenty
of canned food and water but no can opener.
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 desiccated 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...
Problem: To Catch a Lion in the Sahara Desert.
(Hunting lions in Africa was originally published as "A contribution
to the mathematical theory of big game hunting" in the American
Mathematical Monthly in 1938 by "H. Petard, of Princeton NJ"
Not a joke, but a humorous ditty I heard from some guys in an
engineering fraternity (to the best of my recollection):
I'll do it phonetically:
ee to the ex dee ex,
ee to the why dee why,
sine x, cosine x,
natural log of y,
derivative on the left
derivative on the right
integrate, integrate,
fight! fight! fight!
The Programmers' Cheer --
Shift to the left, shift to the right!
Pop up, push down, byte, byte, byte!
Other cheers:
E to the x dx dy
radical transcendental pi
secant cosine tangent sine
3.14159
2.71828
come on folks let's integerate!!
----------
E to the i dx dy
E to y dy
cosine secant log of pi
disintegrate em RPI !!!
----------
square root, tangent
hyperbolic sine,
3.14159
e to the x, dy, dx,
sliderule, slipstick, TECH TECH TECH!
----------
e to the u, du/dx
e to the x dx
cosine, secant, tangent, sine,
3.14159
integral, radical, u dv,
slipstick, slide rule, MIT!
----------
E to the X
D-Y, D-X
E to the X
D-X.
Cosine, Secant, Tangent, Sine
3.14159
E-I, Radical, Pi
Fight'em, Fight'em, WPI!
Go Worcester Polytechnic Institute!!!!!!
----------
Northwestern University Marching band's "The Calculus Cheer":
e to the x, dx/dy
e to the y, dy
cosine, tangent, inverse sine
add an asymptotic line
come on Wildcats, hold that line!
Words in {} should be interpreted as greek letters:
Q: I M A {pi}{rho}Maniac. R U 1,2?
o [- read as "U-not"
A: Y ?
o
("I am a pyromaniac. Are you not one, too?" "Why not?")
F U {can} {read} Ths U {Mst} {use} TeX
("If you can read this, you must use TeX")
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.)
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."
Actually, I prefer the IBM version of this joke...
A small, 14-seat plane is circling for a landing in Atlanta. It's
totally fogged in, zero visibility, and suddenly there's a small
electrical fire in the cockpit which disables all of the instruments
and the radio. The pilot continues circling, totally lost, when
suddenly he finds himself flying next to a tall office building.
He rolls down the window (this particular airplane happens to have
roll-down windows) and yells to a person inside the building, "Where
are we?"
The person responds "In an airplane!"
The pilot then banks sharply to the right, circles twice, and makes a
perfect landing at Atlanta International.
As the passengers emerge, shaken but unhurt, one of them says to the
pilot, "I'm certainly glad you were able to land safely, but I don't
understand how the response you got was any use."
"Simple," responded the pilot. "I got an answer that was completely
accurate and totally irrelevant to my problem, so I knew it had to be
the IBM building."
(I'm not sure if the following one is a true story or not)
The great logician Bertrand Russell (or was it A.N. Whitehead?)
once claimed that he could prove anything if given that 1+1=1.
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."
[NOTE: The following is from merritt@Gendev.slc.paramax.com (Merritt).
The story about 1+1=1 causing ridiculous consequences was, I believe,
originally the product of a conversation at the Trinity High Table.
It is recorded in Sir Harold Jeffreys' Scientific Inference, in a note
to chapter one. Jeffreys remarks that the fact that everything
followed from a single contradiction had been noticed by Aristotle (I
doubt this way of putting it is quite correct, but that is beside the
point). He goes on to say that McTaggart denied the consequence: "if
2+2=5, how can you prove that I am the pope?" Hardy is supposed to
have replied: "if 2+2=5, 4=5; subtract 3; then 1=2; but McTaggart and
the pope are two; therefore McTaggart and the pope are one." When I
consider this story, I am astonished at how much more brilliant some
people are than I (quite independent of the fallacies in the
argument).
Since McTaggart, Hardy, Whitehead, and Russell (the last two of whom
were credited with a variant of Hardy's argument in your post) were
all fellows of Trinity and Jeffreys (their exact contemporary) was a
fellow of St. Johns, I suspect that (whatever the truth of Jeffreys'
story) it is very unlikely that Whitehead or Russell had anything to do
with it. The extraordinary point to me about the story is that Hardy
was able to snap this argument out between mouthfuls, so to speak, and
he was not even a logician at all. This is probably why it came in
some people's minds to be attributed to one or other of the famous
Trinity logicians.
THE STORY OF BABEL:
In the beginning there was only one kind of Mathematician, created by
the Great Mathematical Spirit form the Book: the Topologist. And they
grew to large numbers and prospered.
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
surprises! 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
Methods of Mathematical Proof
This is from _A Random Walk in Science_ (by Joel E. Cohen?):
To illustrate the various methods of proof we give an example of a
logical system.
THE PEJORATIVE CALCULUS
Lemma 1. All horses are the same colour.
(Proof by induction)
Proof. It is obvious that one horse is the same colour. Let us assume
the proposition P(k) that k horses are the same colour and use this to
imply that k+1 horses are the same colour. Given the set of k+1 horses,
we remove one horse; then the remaining k horses are the same colour,
by hypothesis. We remove another horse and replace the first; the k
horses, by hypothesis, are again the same colour. We repeat this until
by exhaustion the k+1 sets of k horses have been shown to be the same
colour. It follows that since every horse is the same colour as every
other horse, P(k) entails P(k+1). But since we have shown P(1) to be
true, P is true for all succeeding values of k, that is, all horses are
the same colour.
Theorem 1. Every horse has an infinite number of legs.
(Proof by intimidation.)
Proof. Horses have an even number of legs. Behind they have two legs
and in front they have fore legs. This makes six legs, which is cer-
tainly an odd number of legs for a horse. But the only number that is
both odd and even is infinity. Therefore horses have an infinite num-
ber of legs. Now to show that this is general, suppose that somewhere
there is a horse with a finite number of legs. But that is a horse of
another colour, and by the lemma that does not exist.
Corollary 1. Everything is the same colour.
Proof. The proof of lemma 1 does not depend at all on the nature of the
object under consideration. The predicate of the antecedent of the uni-
versally-quantified conditional 'For all x, if x is a horse, then x is
the same colour,' namely 'is a horse' may be generalized to 'is anything'
without affecting the validity of the proof; hence, 'for all x, if x is
anything, x is the same colour.'
Corollary 2. Everything is white.
Proof. If a sentential formula in x is logically true, then any parti-
cular substitution instance of it is a true sentence. In particular
then: 'for all x, if x is an elephant, then x is the same colour' is
true. Now it is manifestly axiomatic that white elephants exist (for
proof by blatant assertion consult Mark Twain 'The Stolen White Ele-
phant'). Therefore all elephants are white. By corollary 1 everything
is white.
Theorem 2. Alexander the Great did not exist and he had an infinite
number of limbs.
Proof. We prove this theorem in two parts. First we note the obvious
fact that historians always tell the truth (for historians always take
a stand, and therefore they cannot lie). Hence we have the historically
true sentence, 'If Alexander the Great existed, then he rode a black
horse Bucephalus.' But we know by corollary 2 everything is white;
hence Alexander could not have ridden a black horse. Since the conse-
quent of the conditional is false, in order for the whole statement to
be true the antecedent must be false. Hence Alexander the Great did not
exist.
We have also the historically true statement that Alexander was warned
by an oracle that he would meet death if he crossed a certain river. He
had two legs; and 'forewarned is four-armed.' This gives him six limbs,
an even number, which is certainly an odd number of limbs for a man.
Now the only number which is even and odd is infinity; hence Alexander
had an infinite number of limbs. We have thus proved that Alexander the
Great did not exist and that he had an infinite number of limbs.
Several students were asked the following problem:
Prove that all odd integers are prime.
Well, the first student to try to do this was a math student. Hey
says "Hmmm... Well, 1 is prime, 3 is prime, 5 is prime, and by
induction, we have that all the odd integers are prime."
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...."
Mathematician: 3 is a prime, 5 is a prime, 7 is a prime,
9 is not a prime - counter-example - claim is false.
Physicist: 3 is a prime, 5 is a prime, 7 is a prime,
9 is an experimental error, 11 is a prime, ...
Engineer: 3 is a prime, 5 is a prime, 7 is a prime,
9 is a prime, 11 is a prime, ...
Computer scientist: 3's a prime, 5's a prime, 7's a prime, 7's a prime,
7's a prime, ...
Computer scientist using Unix: 3's a prime, 5's a prime, 7's a prime,
segmentation fault
Gosh, they all overlooked that even 2's a prime!!
I figure that 2 is the oddest prime of all, because it's the
only one that's even!
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.
My geometry teacher was sometimes acute, and sometimes
obtuse, but always, he was right.
And now, for some really bad picture jokes (that I heard at Cal Poly SLO) :
Q: What's the title of this picture ?
.. .. ____ .. ..
\===/======\==
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|| ( ||
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A: Hypotenuse
-------
Q: What quantity is represented by this ?
/ / /
/ / /
/ / /
/ / /
/ / /
/______ /______ /______
|| || ||
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A: 9, tree + tree + tree
Q: A dust storm blows through, now how much do you have ?
A: 99, dirty tree + dirty tree + dirty tree
Q: Some birds go flying by and leave their droppings,
one per tree, how many is that ?
A: 100, dirty tree and a turd + dirty tree and a turd
+ dirty tree and a turd
I saw the following scrawled on a math office blackboard in college:
1 + 1 = 3, for large values of 1
lim ----
8-]9 / 8 = 3
Along the same lines:
lim sqrt (3) = 2
3-]4
Asked how his pet parrot died, the mathematician answered
"Polynomial. Polygon."
Lumberjacks make good musicians because of their natural logarithms.
Q: What is Quayle-o-phobia?
A: The fear of natural logarithms.
(Hint: Quayle and the letter "e" made news.)
Pie are not square. Pie are round. Cornbread are square.
"The integral of e to the x is equal to f of the quantity
u to the n."
/ x n
| e = f(u )
/
A physics joke:
"Energy equals milk chocolate square"
Russell to Whitehead: "My Godel is killing me!"
A doctor, a lawyer and a mathematician were discussing the relative
merits of having a wife or a mistress.
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.
Von Neumann and Norbert Wiener were both the subject of many dotty
professor stories. Von Neumann supposedly had the habit of simply
writing answers to homework assignments on the board (the method of
solution being, of course, obvious) when he was asked how to solve
problems. One time one of his students tried to get more helpful
information by asking if there was another way to solve the problem.
Von Neumann looked blank for a moment, thought, and then answered,
"Yes".
Wiener 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 Wiener 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...
The USDA once wanted to make cows produce milk faster, to improve the
dairy industry.
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 horrible 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......"
An engineer, a mathematician, and a physicist went to the races one
Saturday and laid their money down. Commiserating in the bar after
the race, the engineer says, "I don't understand why I lost all my
money. I measured all the horses and calculated their strength and
mechanical advantage and figured out how fast they could run..."
The physicist interrupted him: "...but you didn't take individual
variations into account. I did a statistical analysis of their
previous performances and bet on the horses with the highest
probability of winning..."
"...so if you're so hot why are you broke?" asked the engineer. But
before the argument can grow, the mathematician takes out his pipe and
they get a glimpse of his well-fattened wallet. Obviously here was a
man who knows something about horses. They both demanded to know his
secret.
"Well," he says, between puffs on the pipe, "first I assumed all the
horses were identical and spherical..."
Theorem : All positive integers are equal.
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.
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 group of Polish tourists is flying on a small airplane through the
Grand Canyon on a sightseeing tour. The tour guide announces: "On the
right of the airplane, you can see the famous Bright Angle Falls."
The tourists leap out of their seats and crowd to the windows on the
right side. This causes a dynamic imbalance, and the plane violently
rolls to the side and crashes into the canyon wall. All aboard are
lost. The moral to this episode is: always keep your poles off the
right side of the plane.
Caveat: While this joke mentions Polish people, it is not, in my
opinion, in the category of the infamous Polish jokes. I hope no one
is offended but only humored.
Hiawatha Designs an Experiment
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)
See also "Applied Dynamic Programming" by Bellman and Dreyfuss, prior to 1962.
An assemblage of the most gifted minds in the world were all posed the
following question:
"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.
Economist: Someone who is good with numbers but lacks the personality
to be an accountant.
Old mathematicians never die; they just lose some of their functions.
During a class of calculus my lecturer suddenly checked himself and
stared intently at the table in front of him for a while. Then he
looked up at us and explained that he thought he had brought six piles
of papers with him, but "no matter how he counted" there was only five
on the table. Then he became silent for a while again and then told
the following story:
"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, ..."
What's non-orientable and lives in the sea?
Mobius Dick.
Philosopher: "Resolution of the continuum hypothesis will have
profound implications to all of science."
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!"
Definition:
Jogging girl scout = Brownian motion.
lim sin(x)
n --> oo ------ = 6
n
Proof: cancel the n in the numerator and denominator.
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
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