2595 lines
104 KiB
Plaintext
2595 lines
104 KiB
Plaintext
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Several students were asked the following problem:
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Prove that all odd integers are prime.
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Well, the first student to try to do this was a math student. Hey
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says "Hmmm... Well, 1 is prime, 3 is prime, 5 is prime, and by
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induction, we have that all the odd integers are prime."
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Of course, there are some jeers from some of his friends. The physics
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student then said, "I'm not sure of the validity of your proof, but I
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think I'll try to prove it by experiment." He continues, "Well, 1 is
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prime, 3 is prime, 5 is prime, 7 is prime, 9 is ... uh, 9 is an
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experimental error, 11 is prime, 13 is prime... Well, it seems that
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you're right."
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The third student to try it was the engineering student, who
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responded, "Well, actually, I'm not sure of your answer either. Let's
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see... 1 is prime, 3 is prime, 5 is prime, 7 is prime, 9 is ..., 9 is
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..., well if you approximate, 9 is prime, 11 is prime, 13 is prime...
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Well, it does seem right."
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Not to be outdone, the computer science student comes along and says
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"Well, you two sort've got the right idea, but you'd end up taking too
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long doing it. I've just whipped up a program to REALLY go and prove
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it..." He goes over to his terminal and runs his program. Reading
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the output on the screen he says, "1 is prime, 1 is prime, 1 is prime,
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1 is prime...."
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-----------------------------------------------------------------------------
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Mathematician: 3 is a prime, 5 is a prime, 7 is a prime,
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9 is not a prime - counter-example - claim is false.
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Physicist: 3 is a prime, 5 is a prime, 7 is a prime,
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9 is an experimental error, 11 is a prime, ...
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Engineer: 3 is a prime, 5 is a prime, 7 is a prime,
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9 is a prime, 11 is a prime, ...
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Computer scientist: 3's a prime, 5's a prime, 7's a prime, 7's a prime,
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7's a prime, ...
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Computer scientist using Unix: 3's a prime, 5's a prime, 7's a prime,
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segmentation fault
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Gosh, they all overlooked that even 2's a prime!!
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I figure that 2 is the oddest prime of all, because it's the
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only one that's even!
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------------------------------------------------------------------------------
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An engineer, a physicist and a mathmetician were driving in the country
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when they came upon pasture after pasture with only black cows in them.
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The engineer said, "There seem to be only cows colored black in this
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area." The physicist said, "That doesn't quite follow. The only cows we
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have seen are black." Then the mathemetician said, "I don't think you
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are right there. The only cows we have seen are black on one side."
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(Submitted by Ed Howland, ehowland@cyber.net)
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------------------------------------------------------------------------------
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Factorials were invented to make math look more exciting.
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(Submitted by Steven Wright, afelson@rmii.com)
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------------------------------------------------------------------------------
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Theorem: a cat has nine tails.
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Proof:
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No cat has eight tails. A cat has one tail more than no cat.
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Therefore, a cat has nine tails.
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------------------------------------------------------------------------------
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My geometry teacher was sometimes acute, and sometimes
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obtuse, but always, he was right.
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------------------------------------------------------------------------------
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And now, for some really bad picture jokes (that I heard at Cal Poly SLO) :
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Q: What's the title of this picture ?
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.. .. ____ .. ..
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\\===/======\\==
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A: Hypotenuse
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-------
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Q: What quantity is represented by this ?
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/\ /\ /\
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/ \ / \ / \
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/ \ / \ / \
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/ \ / \ / \
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/ \ / \ / \
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/______\ /______\ /______\
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A: 9, tree + tree + tree
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Q: A dust storm blows through, now how much do you have ?
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A: 99, dirty tree + dirty tree + dirty tree
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Q: Some birds go flying by and leave their droppings,
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one per tree, how many is that ?
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A: 100, dirty tree and a turd + dirty tree and a turd
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+ dirty tree and a turd
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------------------------------------------------------------------------------
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I saw the following scrawled on a math office blackboard in college:
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1 + 1 = 3, for large values of 1
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------------------------------------------------------------------------------
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lim ----
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8->9 \/ 8 = 3
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Along the same lines:
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lim sqrt (3) = 2
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3->4
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------------------------------------------------------------------------------
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Asked how his pet parrot died, the mathematician answered
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"Polynomial. Polygon."
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------------------------------------------------------------------------------
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Lumberjacks make good musicians because of their natural logarithms.
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------------------------------------------------------------------------------
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Q: What is Quayle-o-phobia?
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A: The fear of natural logarithms.
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(Hint: Quayle and the letter "e" made news.)
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------------------------------------------------------------------------------
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Pie are not square. Pie are round. Cornbread are square.
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------------------------------------------------------------------------------
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"The integral of e to the x is equal to f of the quantity
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u to the n."
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/ x n
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| e = f(u )
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/
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------------------------------------------------------------------------------
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A physics joke:
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"Energy equals milk chocolate square"
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------------------------------------------------------------------------------
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Russell to Whitehead: "My Godel is killing me!"
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------------------------------------------------------------------------------
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A doctor, a lawyer and a mathematician were discussing the relative
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merits of having a wife or a mistress.
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The lawyer says: "For sure a mistress is better. If you have a wife
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and want a divorce, it causes all sorts of legal problems.
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The doctor says: "It's better to have a wife because the sense of
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security lowers your stress and is good for your health.
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The mathematician says: " You're both wrong. It's best to have both so
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that when the wife thinks you're with the mistress and the mistress
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thinks you're with your wife --- you can do some mathematics.
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------------------------------------------------------------------------------
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Von Neumann and Norbert Wiener were both the subject of many dotty
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professor stories. Von Neumann supposedly had the habit of simply
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writing answers to homework assignments on the board (the method of
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solution being, of course, obvious) when he was asked how to solve
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problems. One time one of his students tried to get more helpful
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information by asking if there was another way to solve the problem.
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Von Neumann looked blank for a moment, thought, and then answered,
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"Yes".
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Wiener was in fact very absent minded. The following story is told
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about him: When they moved from Cambridge to Newton his wife, knowing
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that he would be absolutely useless on the move, packed him off to MIT
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while she directed the move. Since she was certain that he would
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forget that they had moved and where they had moved to, she wrote down
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the new address on a piece of paper, and gave it to him. Naturally,
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in the course of the day, an insight occurred to him. He reached in
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his pocket, found a piece of paper on which he furiously scribbled
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some notes, thought it over, decided there was a fallacy in his idea,
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and threw the piece of paper away. At the end of the day he went home
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(to the old address in Cambridge, of course). When he got there he
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realized that they had moved, that he had no idea where they had moved
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to, and that the piece of paper with the address was long gone.
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Fortunately inspiration struck. There was a young girl on the street
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and he conceived the idea of asking her where he had moved to, saying,
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"Excuse me, perhaps you know me. I'm Norbert Wiener and we've just
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moved. Would you know where we've moved to?" To which the young girl
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replied, "Yes daddy, mommy thought you would forget."
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The capper to the story is that I asked his daughter (the girl in the
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story) about the truth of the story, many years later. She said that
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it wasn't quite true -- that he never forgot who his children were!
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The rest of it, however, was pretty close to what actually happened...
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------------------------------------------------------------------------------
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The USDA once wanted to make cows produce milk faster, to improve the
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dairy industry.
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So, they decided to consult the foremost biologists and recombinant
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DNA technicians to build them a better cow. They assembled this team
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of great scientists, and gave them unlimited funding. They requested
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rare chemicals, weird bacteria, tons of quarantine equipment, there
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was a horrible typhus epidemic they started by accident, and, 2 years
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later, they came back with the "new, improved cow." It had a milk
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production improvement of 2% over the original.
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They then tried with the greatest Nobel Prize winning chemists around.
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They worked for six months, and, after requisitioning tons of chemical
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equipment, and poisoning half the small town in Colorado where they
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were working with a toxic cloud from one of their experiments, they
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got a 5% improvement in milk output.
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The physicists tried for a year, and, after ten thousand cows were
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subjected to radiation therapy, they got a 1% improvement in output.
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Finally, in desperation, they turned to the mathematicians. The
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foremost mathematician of his time offered to help them with the
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problem. Upon hearing the problem, he told the delegation that they
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could come back in the morning and he would have solved the problem.
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In the morning, they came back, and he handed them a piece of paper
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with the computations for the new, 300% improved milk cow.
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The plans began:
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"A Proof of the Attainability of Increased Milk Output from Bovines:
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Consider a spherical cow......"
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------------------------------------------------------------------------------
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An engineer, a mathematician, and a physicist went to the races one
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Saturday and laid their money down. Commiserating in the bar after
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the race, the engineer says, "I don't understand why I lost all my
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money. I measured all the horses and calculated their strength and
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mechanical advantage and figured out how fast they could run..."
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The physicist interrupted him: "...but you didn't take individual
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variations into account. I did a statistical analysis of their
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previous performances and bet on the horses with the highest
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probability of winning..."
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"...so if you're so hot why are you broke?" asked the engineer. But
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before the argument can grow, the mathematician takes out his pipe and
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they get a glimpse of his well-fattened wallet. Obviously here was a
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man who knows something about horses. They both demanded to know his
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secret.
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"Well," he says, between puffs on the pipe, "first I assumed all the
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horses were identical and spherical..."
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------------------------------------------------------------------------------
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Theorem : All positive integers are equal.
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Proof : Sufficient to show that for any two positive integers, A and B,
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A = B. Further, it is sufficient to show that for all N > 0, if A
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and B (positive integers) satisfy (MAX(A, B) = N) then A = B.
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Proceed by induction.
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If N = 1, then A and B, being positive integers, must both be 1.
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So A = B.
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Assume that the theorem is true for some value k. Take A and B
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with MAX(A, B) = k+1. Then MAX((A-1), (B-1)) = k. And hence
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(A-1) = (B-1). Consequently, A = B.
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------------------------------------------------------------------------------
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A bunch of Polish scientists decided to flee their repressive
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government by hijacking an airliner and forcing the pilot to fly them
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to a western country. They drove to the airport, forced their way on
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board a large passenger jet, and found there was no pilot on board.
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Terrified, they listened as the sirens got louder. Finally, one of
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the scientists suggested that since he was an experimentalist, he
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would try to fly the aircraft.
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He sat down at the controls and tried to figure them out. The sirens
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got louder and louder. Armed men surrounded the jet. The would be
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pilot's friends cried out, "Please, please take off now!!!
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Hurry!!!!!!"
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The experimentalist calmly replied, "Have patience. I'm just a simple
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pole in a complex plane."
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------------------------------------------------------------------------------
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A group of Polish tourists is flying on a small airplane through the
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Grand Canyon on a sightseeing tour. The tour guide announces: "On the
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right of the airplane, you can see the famous Bright Angle Falls."
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The tourists leap out of their seats and crowd to the windows on the
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right side. This causes a dynamic imbalance, and the plane violently
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rolls to the side and crashes into the canyon wall. All aboard are
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lost. The moral to this episode is: always keep your poles off the
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right side of the plane.
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------------------------------------------------------------------------------
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Hiawatha Designs an Experiment
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Hiawatha, mighty hunter,
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He could shoot ten arrows upward,
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Shoot them with such strength and swiftness
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That the last had left the bow-string
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Ere the first to earth descended.
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This was commonly regarded
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As a feat of skill and cunning.
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Several sarcastic spirits
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Pointed out to him, however,
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That it might be much more useful
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If he sometimes hit the target.
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"Why not shoot a little straighter
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And employ a smaller sample?"
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Hiawatha, who at college
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Majored in applied statistics,
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Consequently felt entitled
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To instruct his fellow man
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In any subject whatsoever,
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Waxed exceedingly indignant,
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Talked about the law of errors,
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Talked about truncated normals,
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Talked of loss of information,
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Talked about his lack of bias,
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Pointed out that (in the long run)
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Independent observations,
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Even though they missed the target,
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Had an average point of impact
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Very near the spot he aimed at,
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With the possible exception
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of a set of measure zero.
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"This," they said, "was rather doubtful;
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Anyway it didn't matter.
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What resulted in the long run:
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Either he must hit the target
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Much more often than at present,
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Or himself would have to pay for
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All the arrows he had wasted."
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Hiawatha, in a temper,
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Quoted parts of R. A. Fisher,
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Quoted Yates and quoted Finney,
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Quoted reams of Oscar Kempthorne,
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Quoted Anderson and Bancroft
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(practically in extenso)
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Trying to impress upon them
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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 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'!
|
||
|
|
|
||
|
|
------------------------------------------------------------------------------
|
||
|
|
This was made by Mike Bender and Sarah Herr:
|
||
|
|
|
||
|
|
MATHEMATICS PURITY TEST
|
||
|
|
|
||
|
|
Count the number of yes's, subtract from 60, and divide by 0.6.
|
||
|
|
|
||
|
|
----------
|
||
|
|
|
||
|
|
The Basics
|
||
|
|
|
||
|
|
1) Have you ever been excited about math?
|
||
|
|
2) Had an exciting dream about math?
|
||
|
|
3) Made a mathematical calculation?
|
||
|
|
4) Manipulated the numerator of an equation?
|
||
|
|
5) Manipulated the denominator of an equation?
|
||
|
|
6) On your first problem set?
|
||
|
|
7) Worked on a problem set past 3:00 a.m.?
|
||
|
|
8) Worked on a problem set all night?
|
||
|
|
9) Had a hard problem?
|
||
|
|
10) Worked on a problem continuously for more than 30 minutes?
|
||
|
|
11) Worked on a problem continuously for more than four hours?
|
||
|
|
12) Done more than one problem set on the same night (i.e. both
|
||
|
|
started and finished them)?
|
||
|
|
13) Done more than three problem sets on the same night?
|
||
|
|
14) Taken a math course for a full year?
|
||
|
|
15) Taken two different math courses at the same time?
|
||
|
|
16) Done at least one problem set a week for more than four months?
|
||
|
|
17) Done at least one problem set a night for more than one month
|
||
|
|
(weekends excluded)?
|
||
|
|
18) Done a problem set alone?
|
||
|
|
19) Done a problem set in a group of three or more?
|
||
|
|
20) Done a problem set in a group of 15 or more?
|
||
|
|
21) Was it mixed company?
|
||
|
|
22) Have you ever inadvertently walked in upon people doing a problem set?
|
||
|
|
23) And joined in afterwards?
|
||
|
|
24) Have you ever used food doing a problem set?
|
||
|
|
25) Did you eat it all?
|
||
|
|
26) Have you ever had a domesticated pet or animal walk over you while you
|
||
|
|
were doing a problem set?
|
||
|
|
27) Done a problem set in a public place where you might be discovered?
|
||
|
|
28) Been discovered while doing a problem set?
|
||
|
|
|
||
|
|
|
||
|
|
Kinky Stuff
|
||
|
|
|
||
|
|
29) Have you ever applied your math to a hard science?
|
||
|
|
30) Applied your math to a soft science?
|
||
|
|
31) Done an integration by parts?
|
||
|
|
32) Done two integration by parts in a single problem?
|
||
|
|
33) Bounded the domain and range of your function?
|
||
|
|
34) Used the domination test for improper integrals?
|
||
|
|
35) Done Newton's Method?
|
||
|
|
36) Done the Method of Frobenius?
|
||
|
|
37) Used the Sandwich Theorem?
|
||
|
|
38) Used the Mean Value Theorem?
|
||
|
|
39) Used a Gaussian surface?
|
||
|
|
40) Used a foreign object on a math problem (eg: calculator)?
|
||
|
|
41) Used a program to improve your mathematical technique (eg: MACSYMA)?
|
||
|
|
42) Not used brackets when you should have?
|
||
|
|
43) Integrated a function over its full period?
|
||
|
|
44) Done a calculation in three-dimensional space?
|
||
|
|
45) Done a calculation in n-dimensional space?
|
||
|
|
46) Done a change of bases?
|
||
|
|
47) Done a change of bases specifically in order to magnify your vector?
|
||
|
|
48) Worked through four complete bases in a single night (eg: using the
|
||
|
|
Graham-Schmidt method)?
|
||
|
|
49) Inserted a number into an equation?
|
||
|
|
50) Calculated the residue of a pole?
|
||
|
|
51) Scored perfectly on a math test?
|
||
|
|
52) Swallowed everything your professor gave you?
|
||
|
|
53) Used explicit notation in your problem set?
|
||
|
|
54) Purposefully omitted important steps in your problem set?
|
||
|
|
55) Padded your own problem set?
|
||
|
|
56) Been blown away on a test?
|
||
|
|
57) Blown away your professor on a test?
|
||
|
|
58) Have you ever multiplied 23 by 3?
|
||
|
|
59) Have you ever bounded your Bessel function so that the membrane
|
||
|
|
did not shoot to infinity?
|
||
|
|
69) Have you ever understood the following quote:
|
||
|
|
"The relationship between Z^0 to C_0, B_0, and H_0
|
||
|
|
is an example of a general principle which we have
|
||
|
|
encountered: the kernel of the adjoint of a linear
|
||
|
|
transformation is both the annihilator space of the
|
||
|
|
image of the transformation and also the dual space
|
||
|
|
of the quotient of the space of which the image is
|
||
|
|
a subspace by the image subspace."
|
||
|
|
(Sternberg & Bamberg's _A "Course" in Mathematics for
|
||
|
|
Students of Physics_, vol. 2)
|
||
|
|
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
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" [actually
|
||
|
|
the late Ralph Boas]. It has been reprinted several times.
|
||
|
|
|
||
|
|
1. Mathematical Methods
|
||
|
|
|
||
|
|
1.1 The Hilbert (axiomatic) method
|
||
|
|
|
||
|
|
We place a locked cage onto a given point in the desert. After that
|
||
|
|
we introduce the following logical system:
|
||
|
|
Axiom 1: The set of lions in the Sahara is not empty.
|
||
|
|
Axiom 2: If there exists a lion in the Sahara, then there exists a
|
||
|
|
lion in the cage.
|
||
|
|
Procedure: If P is a theorem, and if the following is holds:
|
||
|
|
"P implies Q", then Q is a theorem.
|
||
|
|
Theorem 1: There exists a lion in the cage.
|
||
|
|
|
||
|
|
1.2 The geometrical inversion method
|
||
|
|
|
||
|
|
We place a spherical cage in the desert, enter it and lock it from
|
||
|
|
inside. We then perform an inversion with respect to the cage. Then
|
||
|
|
the lion is inside the cage, and we are outside.
|
||
|
|
|
||
|
|
1.3 The projective geometry method
|
||
|
|
|
||
|
|
Without loss of generality, we can view the desert as a plane surface.
|
||
|
|
We project the surface onto a line and afterwards the line onto an
|
||
|
|
interior point of the cage. Thereby the lion is mapped onto that same
|
||
|
|
point.
|
||
|
|
|
||
|
|
1.4 The Bolzano-Weierstrass method
|
||
|
|
|
||
|
|
Divide the desert by a line running from north to south. The lion is
|
||
|
|
then either in the eastern or in the western part. Let's assume it is
|
||
|
|
in the eastern part. Divide this part by a line running from east to
|
||
|
|
west. The lion is either in the northern or in the southern part.
|
||
|
|
Let's assume it is in the northern part. We can continue this process
|
||
|
|
arbitrarily and thereby constructing with each step an increasingly
|
||
|
|
narrow fence around the selected area. The diameter of the chosen
|
||
|
|
partitions converges to zero so that the lion is caged into a fence of
|
||
|
|
arbitrarily small diameter.
|
||
|
|
|
||
|
|
1.5 The set theoretical method
|
||
|
|
|
||
|
|
We observe that the desert is a separable space. It therefore
|
||
|
|
contains an enumerable dense set of points which constitutes a
|
||
|
|
sequence with the lion as its limit. We silently approach the lion in
|
||
|
|
this sequence, carrying the proper equipment with us.
|
||
|
|
|
||
|
|
1.6 The Peano method
|
||
|
|
|
||
|
|
In the usual way construct a curve containing every point in the
|
||
|
|
desert. It has been proven [1] that such a curve can be traversed in
|
||
|
|
arbitrarily short time. Now we traverse the curve, carrying a spear,
|
||
|
|
in a time less than what it takes the lion to move a distance equal to
|
||
|
|
its own length.
|
||
|
|
|
||
|
|
1.7 A topological method
|
||
|
|
|
||
|
|
We observe that the lion possesses the topological gender of a torus.
|
||
|
|
We embed the desert in a four dimensional space. Then it is possible
|
||
|
|
to apply a deformation [2] of such a kind that the lion when returning
|
||
|
|
to the three dimensional space is all tied up in itself. It is then
|
||
|
|
completely helpless.
|
||
|
|
|
||
|
|
1.8 The Cauchy method
|
||
|
|
|
||
|
|
We examine a lion-valued function f(z). Be \zeta the cage. Consider
|
||
|
|
the integral
|
||
|
|
|
||
|
|
1 [ f(z)
|
||
|
|
------- I --------- dz
|
||
|
|
2 \pi i ] z - \zeta
|
||
|
|
|
||
|
|
C
|
||
|
|
|
||
|
|
where C represents the boundary of the desert. Its value is f(zeta),
|
||
|
|
i.e. there is a lion in the cage [3].
|
||
|
|
|
||
|
|
1.9 The Wiener-Tauber method
|
||
|
|
|
||
|
|
We obtain a tame lion, L_0, from the class L(-\infinity,\infinity),
|
||
|
|
whose fourier transform vanishes nowhere. We put this lion somewhere
|
||
|
|
in the desert. L_0 then converges toward our cage. According to the
|
||
|
|
general Wiener-Tauner theorem [4] every other lion L will converge
|
||
|
|
toward the same cage. (Alternatively we can approximate L arbitrarily
|
||
|
|
close by translating L_0 through the desert [5].)
|
||
|
|
|
||
|
|
2 Theoretical Physics Methods
|
||
|
|
|
||
|
|
2.1 The Dirac method
|
||
|
|
|
||
|
|
We assert that wild lions can ipso facto not be observed in the Sahara
|
||
|
|
desert. Therefore, if there are any lions at all in the desert, they
|
||
|
|
are tame. We leave catching a tame lion as an exercise to the reader.
|
||
|
|
|
||
|
|
2.2 The Schroedinger method
|
||
|
|
|
||
|
|
At every instant there is a non-zero probability of the lion being in
|
||
|
|
the cage. Sit and wait.
|
||
|
|
|
||
|
|
2.3 The Quantum Measurement Method
|
||
|
|
|
||
|
|
We assume that the sex of the lion is _ab initio_ indeterminate. The
|
||
|
|
wave function for the lion is hence a superposition of the gender
|
||
|
|
eigenstate for a lion and that for a lioness. We lay these eigenstates
|
||
|
|
out flat on the ground and orthogonal to each other. Since the (male)
|
||
|
|
lion has a distinctive mane, the measurement of sex can safely be made
|
||
|
|
from a distance, using binoculars. The lion then collapses into one of
|
||
|
|
the eigenstates, which is rolled up and placed inside the cage.
|
||
|
|
|
||
|
|
2.4 The nuclear physics method
|
||
|
|
|
||
|
|
Insert a tame lion into the cage and apply a Majorana exchange
|
||
|
|
operator [6] on it and a wild lion.
|
||
|
|
|
||
|
|
As a variant let us assume that we would like to catch (for argument's
|
||
|
|
sake) a male lion. We insert a tame female lion into the cage and
|
||
|
|
apply the Heisenberg exchange operator [7], exchanging spins.
|
||
|
|
|
||
|
|
2.5 A relativistic method
|
||
|
|
|
||
|
|
All over the desert we distribute lion bait containing large amounts
|
||
|
|
of the companion star of Sirius. After enough of the bait has been
|
||
|
|
eaten we send a beam of light through the desert. This will curl
|
||
|
|
around the lion so it gets all confused and can be approached without
|
||
|
|
danger.
|
||
|
|
|
||
|
|
3 Experimental Physics Methods
|
||
|
|
|
||
|
|
3.1 The thermodynamics method
|
||
|
|
|
||
|
|
We construct a semi-permeable membrane which lets everything but lions
|
||
|
|
pass through. This we drag across the desert.
|
||
|
|
|
||
|
|
3.2 The atomic fission method
|
||
|
|
|
||
|
|
We irradiate the desert with slow neutrons. The lion becomes
|
||
|
|
radioactive and starts to disintegrate. Once the disintegration
|
||
|
|
process is progressed far enough the lion will be unable to resist.
|
||
|
|
|
||
|
|
3.3 The magneto-optical method
|
||
|
|
|
||
|
|
We plant a large, lense shaped field with cat mint (nepeta cataria)
|
||
|
|
such that its axis is parallel to the direction of the horizontal
|
||
|
|
component of the earth's magnetic field. We put the cage in one of the
|
||
|
|
field's foci . Throughout the desert we distribute large amounts of
|
||
|
|
magnetized spinach (spinacia oleracea) which has, as everybody knows,
|
||
|
|
a high iron content. The spinach is eaten by vegetarian desert
|
||
|
|
inhabitants which in turn are eaten by the lions. Afterwards the
|
||
|
|
lions are oriented parallel to the earth's magnetic field and the
|
||
|
|
resulting lion beam is focussed on the cage by the cat mint lense.
|
||
|
|
|
||
|
|
[1] After Hilbert, cf. E. W. Hobson, "The Theory of Functions of a Real
|
||
|
|
Variable and the Theory of Fourier's Series" (1927), vol. 1, pp 456-457
|
||
|
|
[2] H. Seifert and W. Threlfall, "Lehrbuch der Topologie" (1934), pp 2-3
|
||
|
|
[3] According to the Picard theorem (W. F. Osgood, Lehrbuch der
|
||
|
|
Funktionentheorie, vol 1 (1928), p 178) it is possible to catch every lion
|
||
|
|
except for at most one.
|
||
|
|
[4] N. Wiener, "The Fourier Integral and Certain of its Applications" (1933),
|
||
|
|
pp 73-74
|
||
|
|
[5] N. Wiener, ibid, p 89
|
||
|
|
[6] cf e.g. H. A. Bethe and R. F. Bacher, "Reviews of Modern Physics", 8
|
||
|
|
(1936), pp 82-229, esp. pp 106-107
|
||
|
|
[7] ibid
|
||
|
|
|
||
|
|
----------
|
||
|
|
|
||
|
|
4 Contributions from Computer Science.
|
||
|
|
|
||
|
|
4.1 The search method
|
||
|
|
|
||
|
|
We assume that the lion is most likely to be found in the direction to
|
||
|
|
the north of the point where we are standing. Therefore the REAL
|
||
|
|
problem we have is that of speed, since we are only using a PC to
|
||
|
|
solve the problem.
|
||
|
|
|
||
|
|
4.2 The parallel search method.
|
||
|
|
|
||
|
|
By using parallelism we will be able to search in the direction to the
|
||
|
|
north much faster than earlier.
|
||
|
|
|
||
|
|
4.3 The Monte-Carlo method.
|
||
|
|
|
||
|
|
We pick a random number indexing the space we search. By excluding
|
||
|
|
neighboring points in the search, we can drastically reduce the number
|
||
|
|
of points we need to consider. The lion will according to probability
|
||
|
|
appear sooner or later.
|
||
|
|
|
||
|
|
4.4 The practical approach.
|
||
|
|
|
||
|
|
We see a rabbit very close to us. Since it is already dead, it is
|
||
|
|
particularly easy to catch. We therefore catch it and call it a lion.
|
||
|
|
|
||
|
|
4.5 The common language approach.
|
||
|
|
|
||
|
|
If only everyone used ADA/Common Lisp/Prolog, this problem would be
|
||
|
|
trivial to solve.
|
||
|
|
|
||
|
|
4.6 The standard approach.
|
||
|
|
|
||
|
|
We know what a Lion is from ISO 4711/X.123. Since CCITT have specified
|
||
|
|
a Lion to be a particular option of a cat we will have to wait for a
|
||
|
|
harmonized standard to appear. $20,000,000 have been funded for
|
||
|
|
initial investigations into this standard development.
|
||
|
|
|
||
|
|
4.7 Linear search.
|
||
|
|
|
||
|
|
Stand in the top left hand corner of the Sahara Desert. Take one step
|
||
|
|
east. Repeat until you have found the lion, or you reach the right
|
||
|
|
hand edge. If you reach the right hand edge, take one step
|
||
|
|
southwards, and proceed towards the left hand edge. When you finally
|
||
|
|
reach the lion, put it the cage. If the lion should happen to eat you
|
||
|
|
before you manage to get it in the cage, press the reset button, and
|
||
|
|
try again.
|
||
|
|
|
||
|
|
4.8 The Dijkstra approach:
|
||
|
|
|
||
|
|
The way the problem reached me was: catch a wild lion in the Sahara
|
||
|
|
Desert. Another way of stating the problem is:
|
||
|
|
|
||
|
|
Axiom 1: Sahara elem deserts
|
||
|
|
Axiom 2: Lion elem Sahara
|
||
|
|
Axiom 3: NOT(Lion elem cage)
|
||
|
|
|
||
|
|
We observe the following invariant:
|
||
|
|
|
||
|
|
P1: C(L) v not(C(L))
|
||
|
|
|
||
|
|
where C(L) means: the value of "L" is in the cage.
|
||
|
|
|
||
|
|
Establishing C initially is trivially accomplished with the statement
|
||
|
|
|
||
|
|
;cage := {}
|
||
|
|
|
||
|
|
Note 0:
|
||
|
|
This is easily implemented by opening the door to the cage and shaking
|
||
|
|
out any lions that happen to be there initially.
|
||
|
|
(End of note 0.)
|
||
|
|
|
||
|
|
The obvious program structure is then:
|
||
|
|
|
||
|
|
;cage:={}
|
||
|
|
;do NOT (C(L)) ->
|
||
|
|
;"approach lion under invariance of P1"
|
||
|
|
;if P(L) ->
|
||
|
|
;"insert lion in cage"
|
||
|
|
[] not P(L) ->
|
||
|
|
;skip
|
||
|
|
;fi
|
||
|
|
;od
|
||
|
|
|
||
|
|
where P(L) means: the value of L is within arm's reach.
|
||
|
|
|
||
|
|
Note 1:
|
||
|
|
Axiom 2 ensures that the loop terminates.
|
||
|
|
(End of note 1.)
|
||
|
|
|
||
|
|
Exercise 0:
|
||
|
|
Refine the step "Approach lion under invariance of P1".
|
||
|
|
(End of exercise 0.)
|
||
|
|
|
||
|
|
Note 2:
|
||
|
|
The program is robust in the sense that it will lead to
|
||
|
|
abortion if the value of L is "lioness".
|
||
|
|
(End of note 2.)
|
||
|
|
|
||
|
|
Remark 0: This may be a new sense of the word "robust" for you.
|
||
|
|
(End of remark 0.)
|
||
|
|
|
||
|
|
Note 3:
|
||
|
|
|
||
|
|
>From observation we can see that the above program leads to the
|
||
|
|
desired goal. It goes without saying that we therefore do not have to
|
||
|
|
run it.
|
||
|
|
(End of note 3.)
|
||
|
|
(End of approach.)
|
||
|
|
|
||
|
|
----------
|
||
|
|
|
||
|
|
For other articles, see also:
|
||
|
|
|
||
|
|
A Random Walk in Science - R.L. Weber and E. Mendoza
|
||
|
|
More Random Walks In Science - R.L. Weber and E. Mendoza
|
||
|
|
In Mathematical Circles (2 volumes) - Howard Eves
|
||
|
|
Mathematical Circles Revisited - Howard Eves
|
||
|
|
Mathematical Circles Squared - Howard Eves
|
||
|
|
Fantasia Mathematica - Clifton Fadiman
|
||
|
|
The Mathematical Magpi - Clifton Fadiman
|
||
|
|
Seven Years of Manifold - Jaworski
|
||
|
|
The Best of the Journal of Irreproducible Results - George H. Scheer
|
||
|
|
Mathematics Made Difficult - Linderholm
|
||
|
|
A Stress-Analysis of a Strapless Evening Gown - Robert Baker
|
||
|
|
The Worm-Runners Digest
|
||
|
|
Knuth's April 1984 CACM article on The Space Complexity of Songs
|
||
|
|
Stolfi and ?? SIGACT article on Pessimal Algorithms and Simplexity Analysis
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
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!!!!!!
|
||
|
|
|
||
|
|
------------------------------------------------------------------------------
|
||
|
|
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.
|
||
|
|
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
Not precisely pure-math, but ...
|
||
|
|
|
||
|
|
Fuller's Law of Cosmic Irreversability:
|
||
|
|
|
||
|
|
1 pot T --> 1 pot P
|
||
|
|
but
|
||
|
|
1 pot P -/-> 1 pot T
|
||
|
|
|
||
|
|
------------------------------------------------------------------------------
|
||
|
|
A tribe of Native Americans generally referred to their woman by the
|
||
|
|
animal hide with which they made their blanket. Thus, one woman might
|
||
|
|
be known as Squaw of Buffalo Hide, while another might be known as
|
||
|
|
Squaw of Deer Hide. This tribe had a particularly large and strong
|
||
|
|
woman, with a very unique (for North America anyway) animal hide for
|
||
|
|
her blanket. This woman was known as Squaw of Hippopotamus hide, and
|
||
|
|
she was as large and powerful as the animal from which her blanket was
|
||
|
|
made.
|
||
|
|
|
||
|
|
Year after year, this woman entered the tribal wrestling tournament,
|
||
|
|
and easily defeated all challengers; male or female. As the men of
|
||
|
|
the tribe admired her strength and power, this made many of the other
|
||
|
|
woman of the tribe extremely jealous. One year, two of the squaws
|
||
|
|
petitioned the Chief to allow them to enter their sons together as a
|
||
|
|
wrestling tandem in order to wrestle Squaw of the Hippopotamus hide as
|
||
|
|
a team. In this way, they hoped to see that she would no longer be
|
||
|
|
champion wrestler of the tribe.
|
||
|
|
|
||
|
|
As the luck of the draw would have it, the two sons who were wrestling
|
||
|
|
as a tandem met the squaw in the final and championship round of the
|
||
|
|
wrestling contest. As the match began, it became clear that the squaw
|
||
|
|
had finally met an opponent that was her equal. The two sons wrestled
|
||
|
|
and struggled vigorously and were clearly on an equal footing with the
|
||
|
|
powerful squaw. Their match lasted for hours without a clear victor.
|
||
|
|
Finally the chief intervened and declared that, in the interests of
|
||
|
|
the health and safety of the wrestlers, the match was to be terminated
|
||
|
|
and that he would declare a winner.
|
||
|
|
|
||
|
|
The chief retired to his teepee and contemplated the great struggle he
|
||
|
|
had witnessed, and found it extremely difficult to decide a winner.
|
||
|
|
While the two young men had clearly outmatched the squaw, he found it
|
||
|
|
difficult to force the squaw to relinquish her tribal championship.
|
||
|
|
After all, it had taken two young men to finally provide her with a
|
||
|
|
decent match. Finally, after much deliberation, the chief came out
|
||
|
|
from his teepee, and announced his decision. He said...
|
||
|
|
|
||
|
|
"The Squaw of the Hippopotamus hide is equal to the sons of the squaws
|
||
|
|
of the other two hides"
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
A topologist is a man who doesn't know the difference between a coffee
|
||
|
|
cup and a doughnut.
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
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 guy decided to go to the brain transplant clinic to refreshen his
|
||
|
|
supply of brains. The secretary informed him that they had three
|
||
|
|
kinds of brains available at that time. Doctors' brains were going
|
||
|
|
for $20 per ounce and lawyers' brains were getting $30 per ounce. And
|
||
|
|
then there were mathematicians' brains which were currently fetching
|
||
|
|
$1000 per ounce.
|
||
|
|
|
||
|
|
"A 1000 dollars an ounce!" he cried. "Why are they so expensive?"
|
||
|
|
|
||
|
|
"It takes more mathematicians to get an ounce of brains," she explained.
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
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."
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
There are three kinds of people in the world;
|
||
|
|
those who can count and those who can't.
|
||
|
|
|
||
|
|
And the related:
|
||
|
|
|
||
|
|
There are two groups of people in the world;
|
||
|
|
those who believe that the world can be
|
||
|
|
divided into two groups of people,
|
||
|
|
and those who don't.
|
||
|
|
|
||
|
|
And then:
|
||
|
|
|
||
|
|
There are two groups of people in the world:
|
||
|
|
Those who can be categorized into one of two
|
||
|
|
groups of people, and those who can't.
|
||
|
|
|
||
|
|
------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
The world is divided into two classes:
|
||
|
|
people who say "The world is divided into two classes",
|
||
|
|
and people who say
|
||
|
|
The world is divided into two classes:
|
||
|
|
people who say: "The world is divided into two classes",
|
||
|
|
and people who say:
|
||
|
|
The world is divided into two classes:
|
||
|
|
people who say ...
|
||
|
|
|
||
|
|
------------------------------------------------------------------------------
|
||
|
|
What follows is a "quiz" a student of mine once showed me (which she'd
|
||
|
|
gotten from a previous teacher, etc...). It's multiple choice, and if
|
||
|
|
you sort the letters (with upper and lower case disjoint) questions
|
||
|
|
and answers will come out next to each other. Enjoy...
|
||
|
|
|
||
|
|
S. What the acorn said when he grew up
|
||
|
|
N. bisects
|
||
|
|
u. A dead parrot
|
||
|
|
g. center
|
||
|
|
F. What you should do when it rains
|
||
|
|
R. hypotenuse
|
||
|
|
m. A geometer who has been to the beach
|
||
|
|
H. coincide
|
||
|
|
h. The set of cards is missing
|
||
|
|
y. polygon
|
||
|
|
A. The boy has a speech defect
|
||
|
|
t. secant
|
||
|
|
K. How they schedule gym class
|
||
|
|
p. tangent
|
||
|
|
b. What he did when his mother-in-law wanted to go home
|
||
|
|
D. ellipse
|
||
|
|
O. The tall kettle boiling on the stove
|
||
|
|
W. geometry
|
||
|
|
r. Why the girl doesn't run a 4-minute mile
|
||
|
|
j. decagon
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
___ 1. That which Noah built.
|
||
|
|
___ 2. An article for serving ice cream.
|
||
|
|
___ 3. What a bloodhound does in chasing a woman.
|
||
|
|
___ 4. An expression to represent the loss of a parrot.
|
||
|
|
___ 5. An appropriate title for a knight named Koal.
|
||
|
|
___ 6. A sunburned man.
|
||
|
|
___ 7. A tall coffee pot perking.
|
||
|
|
___ 8. What one does when it rains.
|
||
|
|
___ 9. A dog sitting in a refrigerator.
|
||
|
|
___ 10. What a boy does on the lake when his motor won't run.
|
||
|
|
___ 11. What you call a person who writes for an inn.
|
||
|
|
___ 12. What the captain said when the boat was bombed.
|
||
|
|
___ 13. What a little acorn says when he grows up.
|
||
|
|
___ 14. What one does to trees that are in the way.
|
||
|
|
___ 15. What you do if you have yarn and needles.
|
||
|
|
___ 16. Can George Washington turn into a country?
|
||
|
|
|
||
|
|
|
||
|
|
A. hypotenuse I. circle
|
||
|
|
B. polygon J. axiom
|
||
|
|
C. inscribe K. cone
|
||
|
|
D. geometry L. coincide
|
||
|
|
E. unit M. cosecant
|
||
|
|
F. center N. tangent
|
||
|
|
G. decagone O. hero
|
||
|
|
H. arc P. perpendicular
|
||
|
|
|
||
|
|
------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
A team of engineers were required to measure the height of a flag
|
||
|
|
pole. They only had a measuring tape, and were getting quite
|
||
|
|
frustrated trying to keep the tape along the pole. It kept falling
|
||
|
|
down, etc.
|
||
|
|
|
||
|
|
A mathematician comes along, finds out their problem, and proceeds to
|
||
|
|
remove the pole from the ground and measure it easily.
|
||
|
|
|
||
|
|
When he leaves, one engineer says to the other: "Just like a
|
||
|
|
mathematician! We need to know the height, and he gives us the
|
||
|
|
length!"
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
A man camped in a national park, and noticed Mr. Snake and Mrs. Snake
|
||
|
|
slithering by. "Where are all the little snakes?" he asked. Mr.
|
||
|
|
Snake replied, "We are adders, so we cannot multiply."
|
||
|
|
|
||
|
|
The following year, the man returned to the same camping spot. This
|
||
|
|
time there were a whole batch of little snakes. "I thought you said
|
||
|
|
you could not multiply," he said to Mr. Snake. "Well, the park ranger
|
||
|
|
came by and built a log table, so now we can multiply by adding!"
|
||
|
|
|
||
|
|
------------------------------------------------------------------------------
|
||
|
|
Einstein dies and goes to heaven only to be informed that his room is
|
||
|
|
not yet ready. "I hope you will not mind waiting in a dormitory. We
|
||
|
|
are very sorry, but it's the best we can do and you will have to share
|
||
|
|
the room with others." he is told by the doorman (say his name is
|
||
|
|
Pete). Einstein says that this is no problem at all and that there is
|
||
|
|
no need to make such a great fuss. So Pete leads him to the dorm.
|
||
|
|
They enter and Albert is introduced to all of the present
|
||
|
|
inhabitants. "See, Here is your first room mate. He has an IQ of
|
||
|
|
180!"
|
||
|
|
"Why that's wonderful!" Says Albert. "We can discuss mathematics!"
|
||
|
|
"And here is your second room mate. His IQ is 150!"
|
||
|
|
"Why that's wonderful!" Says Albert. "We can discuss physics!"
|
||
|
|
"And here is your third room mate. His IQ is 100!"
|
||
|
|
"That Wonderful! We can discuss the latest plays at the theater!"
|
||
|
|
Just then another man moves out to capture Albert's hand and shake it.
|
||
|
|
"I'm your last room mate and I'm sorry, but my IQ is only 80."
|
||
|
|
Albert smiles back at him and says, "So, where to you think interest
|
||
|
|
rates are headed?"
|
||
|
|
|
||
|
|
------------------------------------------------------------------------------
|
||
|
|
97.3% of all statistics are made up.
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
Did you hear the one about the statistician?
|
||
|
|
|
||
|
|
Probably....
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
There was once a very smart horse. Anything that was shown it, it
|
||
|
|
mastered easily, 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 and couldn't. Then a new guy (what the heck, a computer
|
||
|
|
engineer) looked at the problem and said,
|
||
|
|
|
||
|
|
"Of course he can't do it. Why, you're putting Descartes before the
|
||
|
|
horse!"
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
TOP TEN EXCUSES FOR NOT DOING THE MATH HOMEWORK
|
||
|
|
|
||
|
|
1. I accidentally divided by zero and my paper burst into flames.
|
||
|
|
2. 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.
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
The guy gets on a bus and starts threatening everybody: "I'll integrate
|
||
|
|
you! I'll differentiate you!!!" So everybody gets scared and runs
|
||
|
|
away. Only one person stays. The guy comes up to him and says:
|
||
|
|
"Aren't you scared, I'll integrate you, I'll differentiate you!!!" And
|
||
|
|
the other guy says; "No, I am not scared, I am e to the x."
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
A mathematician went insane and believed that he was the
|
||
|
|
differentiation operator. His friends had him placed in a mental
|
||
|
|
hospital until he got better. All day he would go around frightening
|
||
|
|
the other patients by staring at them and saying "I differentiate
|
||
|
|
you!"
|
||
|
|
|
||
|
|
One day he met a new patient; and true to form he stared at him and
|
||
|
|
said "I differentiate you!", but for once, his victim's expression
|
||
|
|
didn't change. Surprised, the mathematician marshalled his energies,
|
||
|
|
stared fiercely at the new patient and said loudly "I differentiate
|
||
|
|
you!", but still the other man had no reaction. Finally, in
|
||
|
|
frustration, the mathematician screamed out "I DIFFERENTIATE YOU!" --
|
||
|
|
at which point the new patient calmly looked up and said, "You can
|
||
|
|
differentiate me all you like: I'm e to the x."
|
||
|
|
|
||
|
|
------------------------------------------------------------------------------
|
||
|
|
/
|
||
|
|
| 1
|
||
|
|
| ----- = log cabin
|
||
|
|
| cabin
|
||
|
|
/
|
||
|
|
|
||
|
|
Oops, you forgot your constant of integration.
|
||
|
|
|
||
|
|
|
||
|
|
/
|
||
|
|
| 1
|
||
|
|
| ----- = log cabin + C
|
||
|
|
| cabin
|
||
|
|
/
|
||
|
|
|
||
|
|
And, as we all know,
|
||
|
|
|
||
|
|
log cabin + C = houseboat
|
||
|
|
|
||
|
|
------------------------------------------------------------------------------
|
||
|
|
8 5
|
||
|
|
If lim - = oo (infinity), then what does lim - = ?
|
||
|
|
x->0 x x->0 x
|
||
|
|
|
||
|
|
answer: (write 5 on it's side)
|
||
|
|
|
||
|
|
------------------------------------------------------------------------------
|
||
|
|
Why did the cat fall off the roof?
|
||
|
|
|
||
|
|
Because he lost his mu. (mew=sound cats make, mu=coeff of friction)
|
||
|
|
|
||
|
|
------------------------------------------------------------------------------
|
||
|
|
Boy's Life, May 1973:
|
||
|
|
|
||
|
|
Ralph: Dad, will you do my math for me tonight?
|
||
|
|
Dad: No, son, it wouldn't be right.
|
||
|
|
Ralph: Well, you could try.
|
||
|
|
|
||
|
|
------------------------------------------------------------------------------
|
||
|
|
Mrs. Johnson the elementary school math teacher was having children do
|
||
|
|
problems on the blackboard that day.
|
||
|
|
|
||
|
|
``Who would like to do the first problem, addition?''
|
||
|
|
|
||
|
|
No one raised their hand. She called on Tommy, and with some help he
|
||
|
|
finally got it right.
|
||
|
|
|
||
|
|
``Who would like to do the second problem, subtraction?''
|
||
|
|
|
||
|
|
Students hid their faces. She called on Mark, who got the problem but
|
||
|
|
there was some suspicion his girlfriend Lisa whispered it to him.
|
||
|
|
|
||
|
|
``Who would like to do the third problem, division?''
|
||
|
|
|
||
|
|
Now a low collective groan could be heard as everyone looked at
|
||
|
|
nothing in particular. The teacher called on Suzy, who got it right
|
||
|
|
(she has been known to hold back sometimes in front of her friends).
|
||
|
|
|
||
|
|
``Who would like to do the last problem, multiplication?''
|
||
|
|
|
||
|
|
Tim's hand shot up, surprising everyone in the room. Mrs. Johnson
|
||
|
|
finally gained her composure in the stunned silence. ``Why the
|
||
|
|
enthusiasm, Tim?''
|
||
|
|
|
||
|
|
``God said to go fourth and multiply!''
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
Definitions of Terms Commonly Used in Higher Math
|
||
|
|
|
||
|
|
The following is a guide to the weary student of mathematics who
|
||
|
|
is often confronted with terms which are commonly used but rarely
|
||
|
|
defined. In the search for proper definitions for these terms we
|
||
|
|
found no authoritative, nor even recognized, source. Thus, we
|
||
|
|
followed the advice of mathematicians handed down from time
|
||
|
|
immortal: "Wing It."
|
||
|
|
|
||
|
|
|
||
|
|
CLEARLY: I don't want to write down all the "in-
|
||
|
|
between" steps.
|
||
|
|
|
||
|
|
TRIVIAL: If I have to show you how to do this, you're
|
||
|
|
in the wrong class.
|
||
|
|
|
||
|
|
OBVIOUSLY: I hope you weren't sleeping when we discussed
|
||
|
|
this earlier, because I refuse to repeat it.
|
||
|
|
|
||
|
|
RECALL: I shouldn't have to tell you this, but for
|
||
|
|
those of you who erase your memory tapes
|
||
|
|
after every test...
|
||
|
|
|
||
|
|
WLOG (Without Loss Of Generality): I'm not about to do all the
|
||
|
|
possible cases, so I'll do one and let you
|
||
|
|
figure out the rest.
|
||
|
|
|
||
|
|
IT CAN EASILY BE SHOWN: Even you, in your finite wisdom, should
|
||
|
|
be able to prove this without me holding your
|
||
|
|
hand.
|
||
|
|
|
||
|
|
CHECK or CHECK FOR YOURSELF: This is the boring part of the
|
||
|
|
proof, so you can do it on your own time.
|
||
|
|
|
||
|
|
SKETCH OF A PROOF: I couldn't verify all the details, so I'll
|
||
|
|
break it down into the parts I couldn't
|
||
|
|
prove.
|
||
|
|
|
||
|
|
HINT: The hardest of several possible ways to do a
|
||
|
|
proof.
|
||
|
|
|
||
|
|
BRUTE FORCE (AND IGNORANCE): Four special cases, three counting
|
||
|
|
arguments, two long inductions, "and a
|
||
|
|
partridge in a pair tree."
|
||
|
|
|
||
|
|
SOFT PROOF: One third less filling (of the page) than
|
||
|
|
your regular proof, but it requires two extra
|
||
|
|
years of course work just to understand the
|
||
|
|
terms.
|
||
|
|
|
||
|
|
ELEGANT PROOF: Requires no previous knowledge of the subject
|
||
|
|
matter and is less than ten lines long.
|
||
|
|
|
||
|
|
SIMILARLY: At least one line of the proof of this case is
|
||
|
|
the same as before.
|
||
|
|
|
||
|
|
CANONICAL FORM: 4 out of 5 mathematicians surveyed
|
||
|
|
recommended this as the final form for their
|
||
|
|
students who choose to finish.
|
||
|
|
|
||
|
|
TFAE (The Following Are Equivalent): If I say this it means that,
|
||
|
|
and if I say that it means the other thing,
|
||
|
|
and if I say the other thing...
|
||
|
|
|
||
|
|
BY A PREVIOUS THEOREM: I don't remember how it goes (come to
|
||
|
|
think of it I'm not really sure we did this
|
||
|
|
at all), but if I stated it right (or at
|
||
|
|
all), then the rest of this follows.
|
||
|
|
|
||
|
|
TWO LINE PROOF: I'll leave out everything but the conclusion,
|
||
|
|
you can't question 'em if you can't see 'em.
|
||
|
|
|
||
|
|
BRIEFLY: I'm running out of time, so I'll just write
|
||
|
|
and talk faster.
|
||
|
|
|
||
|
|
LET'S TALK THROUGH IT: I don't want to write it on the board lest
|
||
|
|
I make a mistake.
|
||
|
|
|
||
|
|
PROCEED FORMALLY: Manipulate symbols by the rules without any
|
||
|
|
hint of their true meaning (popular in pure
|
||
|
|
math courses).
|
||
|
|
|
||
|
|
QUANTIFY: I can't find anything wrong with your proof
|
||
|
|
except that it won't work if x is a moon of
|
||
|
|
Jupiter (Popular in applied math courses).
|
||
|
|
|
||
|
|
PROOF OMITTED: Trust me, It's true.
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
In the bayous of Louisiana, there is a small river called the Dirac.
|
||
|
|
Many wealthy people have their mansions near its mouth. One of the
|
||
|
|
social leaders decided to have a grand ball. Being a cousin of the
|
||
|
|
Governor, she arranged for a detachment of the state militia to serve
|
||
|
|
as guards and traffic directors for the big doings. A captain was
|
||
|
|
sent over with a small company; naturally he asked if there was enough
|
||
|
|
room for him and his unit. The social leader replied, "But of course,
|
||
|
|
Captain! It is well known that the Dirac delta function has unit
|
||
|
|
area."
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
Albert Einstein, who fancied himself as a violinist, was rehearsing a
|
||
|
|
Haydn string quartet. When he failed for the fourth time to get his
|
||
|
|
entry in the second movement, the cellist looked up and said, "The
|
||
|
|
problem with you, Albert, is that you simply can't count."
|
||
|
|
|
||
|
|
------------------------------------------------------------------------------
|
||
|
|
Some famous mathematician was to give a keynote speech at a
|
||
|
|
conference. Asked for an advance summary, he said he would present a
|
||
|
|
proof of Fermat's Last Theorem -- but they should keep it under their
|
||
|
|
hats. When he arrived, though, he spoke on a much more prosaic
|
||
|
|
topic. Afterwards the conference organizers asked why he said he'd
|
||
|
|
talk about the theorem and then didn't. He replied this was his
|
||
|
|
standard practice, just in case he was killed on the way to the
|
||
|
|
conference.
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
When I was a Math/Chem grad student at Princeton in 1973-74, there was
|
||
|
|
a story going around about a grad student. This guy was always late.
|
||
|
|
One day he stumbled into class late, saw seven problems written on the
|
||
|
|
board, and wrote them down. As the week went on he began to panic:
|
||
|
|
the math department at Princeton is fiercely competitive, and here he
|
||
|
|
was unable to do most of a simple homework assignment! When the next
|
||
|
|
class rolled around he only had solved two of the problems, although
|
||
|
|
he had a pretty good idea of how to solve a third but not enough time
|
||
|
|
to complete it.
|
||
|
|
|
||
|
|
When he dejectedly flung his partial assignment on the prof's desk,
|
||
|
|
the prof asked him "What's that?" "The homework." "What homework?"
|
||
|
|
Eventually it came out that what the prof had written on the board
|
||
|
|
were the seven most important unsolved problems in the field.
|
||
|
|
|
||
|
|
This is largely an academic legend, at least according to Jan Harold
|
||
|
|
Brunvand, the author of a series of books on so-called Urban Legends.
|
||
|
|
He talks about it in his latest book _Curses! Broiled Again!_ in the
|
||
|
|
chapter entitled "The Unsolvable Math Problem." It is, however, based
|
||
|
|
in some fact. The Stanford mathematician, George B. Danzig,
|
||
|
|
apparently managed to solve two statistics problems previously
|
||
|
|
unsolved under similar circumstances.
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
The following problem can be solved either the easy way or the hard way.
|
||
|
|
|
||
|
|
Two trains 200 miles apart are moving toward each other; each one is
|
||
|
|
going at a speed of 50 miles per hour. A fly starting on the front of
|
||
|
|
one of them flies back and forth between them at a rate of 75 miles
|
||
|
|
per hour. It does this until the trains collide and crush the fly to
|
||
|
|
death. What is the total distance the fly has flown?
|
||
|
|
|
||
|
|
The fly actually hits each train an infinite number of times before it
|
||
|
|
gets crushed, and one could solve the problem the hard way with pencil
|
||
|
|
and paper by summing an infinite series of distances. The easy way
|
||
|
|
is as follows: Since the trains are 200 miles apart and each train is
|
||
|
|
going 50 miles an hour, it takes 2 hours for the trains to collide.
|
||
|
|
Therefore the fly was flying for two hours. Since the fly was flying
|
||
|
|
at a rate of 75 miles per hour, the fly must have flown 150 miles.
|
||
|
|
That's all there is to it.
|
||
|
|
|
||
|
|
When this problem was posed to John von Neumann, he immediately
|
||
|
|
replied, "150 miles."
|
||
|
|
|
||
|
|
"It is very strange," said the poser, "but nearly everyone tries to
|
||
|
|
sum the infinite series."
|
||
|
|
|
||
|
|
"What do you mean, strange?" asked Von Neumann. "That's how I did it!"
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
Mathematicians are like Frenchmen: whatever you say to them, they
|
||
|
|
translate it into their own language, and forthwith it means something
|
||
|
|
entirely different.
|
||
|
|
-- Johann Wolfgang von Goethe
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
"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."
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
Three mathematicians and a physicist walk into a bar.
|
||
|
|
You'd think the second one would have ducked. (Ha, that quack's me up!)
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
What do you call a young eigensheep?
|
||
|
|
|
||
|
|
A lamb, duh!!!
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
"The world is everywhere dense with idiots."
|
||
|
|
- LFS
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
One day a farmer called up an engineer, a physicist, and a mathematician
|
||
|
|
and asked them to fence of the largest possible area with the least
|
||
|
|
amount of fence. The engineer made the fence in a circle and
|
||
|
|
proclaimed that he had the most efficient design. The physicist made
|
||
|
|
a long, straight line and proclaimed 'We can assume the length is
|
||
|
|
infinite...' and pointed out that fencing off half of the Earth was
|
||
|
|
certainly a more efficient way to do it. The Mathematician just
|
||
|
|
laughed at them. He built a tiny fence around himself and said 'I
|
||
|
|
declare myself to be on the outside.'
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
An engineer, a mathematician, and a computer programmer are driving
|
||
|
|
down the road when the car they are in gets a flat tire. The engineer
|
||
|
|
says that they should buy a new car. The mathematician says they
|
||
|
|
should sell the old tire and buy a new one. The computer programmer
|
||
|
|
says they should drive the car around the block and see if the tire
|
||
|
|
fixes itself.
|
||
|
|
|
||
|
|
------------------------------------------------------------------------------
|
||
|
|
A math/computer science convention was being held. On the train to
|
||
|
|
the convention, a bunch of math majors and a bunch of computer science
|
||
|
|
majors were on the train. Each of the math majors had his/her train
|
||
|
|
ticket. The group of computer science majors had only ONE ticket for
|
||
|
|
all of them. The math majors started laughing and snickering.
|
||
|
|
|
||
|
|
Then, one of the CS majors said "here comes the conductor" and then
|
||
|
|
all of the CS majors went into the bathroom. The math majors were
|
||
|
|
puzzled. The conductor came aboard and said "tickets please" and got
|
||
|
|
tickets from all the math majors. He then went to the bathroom and
|
||
|
|
knocked on the door and said "ticket please" and the CS majors stuck
|
||
|
|
the ticket under the door. The conductor took it and then the CS
|
||
|
|
majors came out of the bathroom a few minutes later. The math majors
|
||
|
|
felt really stupid.
|
||
|
|
|
||
|
|
So, on the way back from the convention, the group of math majors had
|
||
|
|
one ticket for the group. They started snickering at the CS majors,
|
||
|
|
for the whole group had no tickets amongst them. Then, the CS major
|
||
|
|
lookout said "Conductor coming!". All the CS majors went to the
|
||
|
|
bathroom. All the math majors went to another bathroom. Then, before
|
||
|
|
the conductor came on board, one of the CS majors left the bathroom,
|
||
|
|
knocked on the other bathroom, and said "ticket please."
|
||
|
|
|
||
|
|
------------------------------------------------------------------------------
|
||
|
|
The following is supposedly a true story about Russell. It isn't
|
||
|
|
really a math joke since it makes fun of the British hierarchy, but
|
||
|
|
it's funny anyway....
|
||
|
|
|
||
|
|
Around the time when Cold War started, Bertrand Russell was giving a
|
||
|
|
lecture on politics in England. Being a leftist in a conservative
|
||
|
|
women's club, he was not received well at all: the ladies came up to
|
||
|
|
him and started attacking him with whatever they could get their hands
|
||
|
|
on. The guard, being an English gentleman, did not want to be rough
|
||
|
|
to the ladies and yet needed to save Russell from them. He said, "But
|
||
|
|
he is a great mathematician!" The ladies ignored him. The guard said
|
||
|
|
again, "But he is a great philosopher!" The ladies ignore him again.
|
||
|
|
In desperation, finally, he said, "But his brother is an earl!" Bert
|
||
|
|
was saved.
|
||
|
|
|
||
|
|
------------------------------------------------------------------------------
|
||
|
|
Another "true" story, kinda like the aforementioned urban legend:
|
||
|
|
|
||
|
|
Enrico Fermi, while studying in college, was bored by his math
|
||
|
|
classes. He walked up to the professor and said, "My classes are too
|
||
|
|
easy!" The professor looked at him, and said, "Well, I'm sure you'll
|
||
|
|
find this interesting." Then the professor copied 9 problems from a
|
||
|
|
book to a paper and gave the paper to Fermi. A month later, the
|
||
|
|
professor ran into Fermi, "So how are you doing with the problems I
|
||
|
|
gave you?" "Oh, they are very hard. I only managed to solve 6 of
|
||
|
|
them." The professor was visibly shocked, "What!? But those are
|
||
|
|
unsolved problems!"
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
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.
|
||
|
|
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
"A person who can, within a year, solve x^2 - 92y^2 = 1 is a mathematician."
|
||
|
|
-- Brahmagupta
|
||
|
|
|
||
|
|
-------------------------------------------------------------------------------
|
||
|
|
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
|
||
|
|
|
||
|
|
--------------------------------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?"
|