Path: galileo.polito.it!ghost.dsi.unimi.it!univ-lyon1.fr!swidir.switch.ch!scsing.switch.ch!news.dfn.de!darwin.sura.net!howland.reston.ans.net!torn!penage.cs.laurentian.ca!nickel.laurentian.ca!s2700211 From: s2700211@nickel.laurentian.ca Newsgroups: rec.humor Subject: math/science/engineering jokes Part I Date: 10 Mar 94 16:18:08 -0500 Organization: Laurentian University Lines: 696 Message-ID: <1994Mar10.161808.1@nickel.laurentian.ca> NNTP-Posting-Host: nickel.laurentian.ca This is a list of math, and engineering jokes that I have copied from off the net. If you have anymore to add to my collection, or see any errors/repetion in the file, please email them to me. S2700211@nickel.laurentian.ca -- -------------------------------------------------------------------------------- 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!! -------------------------------------------------------------------------------- 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. -------------------------------------------------------------------------------- To tell a difference between a mathematician and an engineer, perform this experiment. Put an empty kettle in the middle of the kitchen floor and tell your subjects to boil some water. The engineer will fill the kettle with water, put it on the stove, and turn the flame on. The mathematician will do the same thing. Next, put the kettle already filled with water on the stove, and ask the subjects to boil the water. The engineer will turn the flame on. The mathematician will empty the kettle and put it in the middle of the kitchen floor... thereby reducing the problem to one that has already been solved! -------------------------------------------------------------------------------- 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 9, 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 9-dimensional space?" M: "Easy, first visualize it in N-dimensional space, then let N go to 9." -------------------------------------------------------------------------------- What is "pi"? Mathematician: Pi is the number expressing the relationship between the circumference of a circle and its diameter. Physicist: Pi is 3.1415927plus or minus 0.000000005 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 a mosquito with a mountain climber. A: You can't do that. A mountain climber is a scalar. Q: What do you get when you cross an elephant with a banana? A: Elephant banana sine theta in a direction mutually perpendicular to the two as determined by the right hand rule. Q: To what question is the answer "9W." A: "Dr. Wiener, do you spell your name with a V?" -------------------------------------------------------------------------------- A somewhat advanced society has figured how to package basic knowledge in pill form. A student, needing some learning, goes to the pharmacy and asks what kind of knowledge pills are available. The pharmacist says "Here's a pill for English literature." The student takes the pill and swallows it and has new knowledge about English literature! "What else do you have?" asks the student. "Well, I have pills for art history, biology, and world history," replies the pharmacist. The student asks for these, and swallows them and has new knowledge about those subjects. Then the student asks, "Do you have a pill for math?" The pharmacist says "Wait just a moment", and goes back into the storeroom and brings back a whopper of a pill and plunks it on the counter. "I have to take that huge pill for math?" inquires the student. The pharmacist replied "Well, you know math always was a little hard to swallow." -------------------------------------------------------------------------------- "A mathematician is a device for turning coffee into theorems" -- P. Erdos -------------------------------------------------------------------------------- Three standard Peter Lax jokes (heard in his lectures) : 1. What's the contour integral around Western Europe? Answer: Zero, because all the Poles are in Eastern Europe! Addendum: Actually, there ARE some Poles in Western Europe, but they are removable! 2. An English mathematician (I forgot who) was asked by his very religious colleague: Do you believe in one God? Answer: Yes, up to isomorphism! 3. What is a compact city? It's a city that can be guarded by finitely many near-sighted policemen! -------------------------------------------------------------------------------- "Algebraic symbols are used when you do not know what you are talking about." -------------------------------------------------------------------------------- Heisenberg might have slept here. Moebius always does it on the same side. Statisticians probably do it Algebraists do it in groups. (Logicians do it) or [not (logicians do it)]. -------------------------------------------------------------------------------- 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. 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 -- This poem was written by Jon Saxton (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... -------------------------------------------------------------------------------- Here's a limerick I picked up off the net a few years back - looks better on paper. \/3 / | 2 3 x 3.14 3_ | z dz x cos( ----------) = ln (\/e ) | 9 / 1 Which, of course, translates to: Integral z-squared dz from 1 to the square root of 3 times the cosine of three pi over 9 equals log of the cube root of 'e'. And it's correct, too. -------------------------------------------------------------------------------- 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." -------------------------------------------------------------------------------- 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 -------------------------------------------------------------------------------- Lemma: All horses are the same color. Proof (by induction): Case n=1: In a set with only one horse, it is obvious that all horses in that set are the same color. Case n=k: Suppose you have a set of k+1 horses. Pull one of these horses out of the set, so that you have k horses. Suppose that all of these horses are the same color. Now put back the horse that you took out, and pull out a different one. Suppose that all of the k horses now in the set are the same color. Then the set of k+1 horses are all the same color. We have k true => k+1 true; therefore all horses are the same color. Theorem: All horses have an infinite number of legs. Proof (by intimidation): Everyone would agree that all horses have an even number of legs. It is also well-known that horses have forelegs in front and two legs in back. 4 + 2 = 6 legs, which is certainly an odd number of legs for a horse to have! Now the only number that is both even and odd is infinity; therefore all horses have an infinite number of legs. However, suppose that there is a horse somewhere that does not have an infinite number of legs. Well, that would be a horse of a different color; and by the Lemma, it doesn't exist. QED -------------------------------------------------------------------------------- Several students were asked the following problem: Prove that all odd integers are prime. Well, the first student to try to do this was a math student. Hey says "Hmmm... Well, 1 is prime, 3 is prime, 5 is prime, and by induction, we have that all the odd integers are prime." Of course, there are some jeers from some of his friends. The physics student then said, "I'm not sure of the validity of your proof, but I think I'll try to prove it by experiment." He continues, "Well, 1 is prime, 3 is prime, 5 is prime, 7 is prime, 9 is ... uh, 9 is an experimental error, 11 is prime, 13 is prime... Well, it seems that you're right." The third student to try it was the engineering student, who responded, "Well, actually, I'm not sure of your answer either. Let's see... 1 is prime, 3 is prime, 5 is prime, 7 is prime, 9 is ..., 9 is ..., well if you approximate, 9 is prime, 11 is prime, 13 is prime... Well, it does seem right." Not to be outdone, the computer science student comes along and says "Well, you two sort've got the right idea, but you'd end up taking too long doing it. I've just whipped up a program to REALLY go and prove it..." He goes over to his terminal and runs his program. Reading the output on the screen he says, "1 is prime, 1 is prime, 1 is prime, 1 is prime...." -------------------------------------------------------------------------------- Mathematician: 3 is a prime, 5 is a prime, 7 is a prime, 9 is not a prime - counter-example - claim is false. Physicist: 3 is a prime, 5 is a prime, 7 is a prime, 9 is an experimental error, 11 is a prime, ... Engineer: 3 is a prime, 5 is a prime, 7 is a prime, 9 is a prime, 11 is a prime, ... Computer scientist: 3's a prime, 5's a prime, 7's a prime, 7's a prime, 7's a prime, ... Computer scientist using Unix: 3's a prime, 5's a prime, 7's a prime, segmentation fault Gosh, they all overlooked that even 2's a prime!! I figure that 2 is the oddest prime of all, because it's the only one that's even! -------------------------------------------------------------------------------- Theorem: a cat has nine tails. Proof: No cat has eight tails. A cat has one tail more than no cat. Therefore, a cat has nine tails. -------------------------------------------------------------------------------- My geometry teacher was sometimes acute, and sometimes obtuse, but always, he was right. -------------------------------------------------------------------------------- And now, for some really bad picture jokes (that I heard at Cal Poly SLO) : Q: What's the title of this picture ? .. .. ____ .. .. \\===/======\\== || | | || || |____| || || ( ) || || \____/ || || || || || || || || || || || || || || || || || || || || (\ || || ) ) || || //||\\ || A: Hypotenuse ------- Q: What quantity is represented by this ? /\ /\ /\ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /______\ /______\ /______\ || || || || || || A: 9, tree + tree + tree Q: A dust storm blows through, now how much do you have ? A: 99, dirty tree + dirty tree + dirty tree Q: Some birds go flying by and leave their droppings, one per tree, how many is that ? A: 100, dirty tree and a turd + dirty tree and a turd + dirty tree and a turd -------------------------------------------------------------------------------- I saw the following scrawled on a math office blackboard in college: 1 + 1 = 3, for large values of 1 -------------------------------------------------------------------------------- lim ---- 8-->9 \/ 8 = 3 -------------------------------------------------------------------------------- Asked how his pet parrot died, the mathematician answered "Polynomial. Polygon." -------------------------------------------------------------------------------- Lumberjacks make good musicians because of their natural logarithms. -------------------------------------------------------------------------------- Pie are not square. Pie are round. Cornbread are square. -------------------------------------------------------------------------------- "The integral of e to the x is equal to f of the quantity u to the n." / x n | e = f(u ) / -------------------------------------------------------------------------------- A physics joke: "Energy equals milk chocolate square" -------------------------------------------------------------------------------- Russell to Whitehead: "My Godel is killing me!" -------------------------------------------------------------------------------- A doctor, a lawyer and a mathematician were discussing the relative merits of having a wife or a mistress. The lawyer says: "For sure a mistress is better. If you have a wife and want a divorce, it causes all sorts of legal problems. The doctor says: "It's better to have a wife because the sense of security lowers your stress and is good for your health. The mathematician says: " You're both wrong. It's best to have both so that when the wife thinks you're with the mistress and the mistress thinks you're with your wife --- you can do some mathematics. -------------------------------------------------------------------------------- Von Neumann and Norbert Weiner were both the subject of many dotty professor stories. Von Neumann supposedly had the habit of simply writing answers to homework assignments on the board (the method of solution being, of course, obvious) when he was asked how to solve problems. One time one of his students tried to get more helpful information by asking if there was another way to solve the problem. Von Neumann looked blank for a moment, thought, and then answered, "Yes". Weiner was in fact very absent minded. The following story is told about him: When they moved from Cambridge to Newton his wife, knowing that he would be absolutely useless on the move, packed him off to MIT while she directed the move. Since she was certain that he would forget that they had moved and where they had moved to, she wrote down the new address on a piece of paper, and gave it to him. Naturally, in the course of the day, an insight occurred to him. He reached in his pocket, found a piece of paper on which he furiously scribbled some notes, thought it over, decided there was a fallacy in his idea, and threw the piece of paper away. At the end of the day he went home (to the old address in Cambridge, of course). When he got there he realized that they had moved, that he had no idea where they had moved to, and that the piece of paper with the address was long gone. Fortunately inspiration struck. There was a young girl on the street and he conceived the idea of asking her where he had moved to, saying, "Excuse me, perhaps you know me. I'm Norbert Weiner and we've just moved. Would you know where we've moved to?" To which the young girl replied, "Yes daddy, mommy thought you would forget." The capper to the story is that I asked his daughter (the girl in the story) about the truth of the story, many years later. She said that it wasn't quite true -- that he never forgot who his children were! The rest of it, however, was pretty close to what actually happened... -------------------------------------------------------------------------------- The USDA once wanted to make cows produce milk faster, to improve the dairy industry. So, they decided to consult the foremost biologists and recombinant DNA technicians to build them a better cow. They assembled this team of great scientists, and gave them unlimited funding. They requested rare chemicals, weird bacteria, tons of quarantine equipment, there was a horrible typhus epidemic they started by accident, and, 2 years later, they came back with the "new, improved cow." It had a milk production improvement of 2% over the original. They then tried with the greatest Nobel Prize winning chemists around. They worked for six months, and, after requisitioning tons of chemical equipment, and poisoning half the small town in Colorado where they were working with a toxic cloud from one of their experiments, they got a 5% improvement in milk output. The physicists tried for a year, and, after ten thousand cows were subjected to radiation therapy, they got a 1% improvement in output. Finally, in desperation, they turned to the mathematicians. The foremost mathematician of his time offered to help them with the problem. Upon hearing the problem, he told the delegation that they could come back in the morning and he would have solved the problem. In the morning, they came back, and he handed them a piece of paper with the computations for the new, 300% improved milk cow. The plans began: "A Proof of the Attainability of Increased Milk Output from Bovines: Consider a spherical cow......" -------------------------------------------------------------------------------- An engineer, a mathematician, and a physicist went to the races one Saturday and laid their money down. Commiserating in the bar after the race, the engineer says, "I don't understand why I lost all my money. I measured all the horses and calculated their strength and mechanical advantage and figured out how fast they could run..." The physicist interrupted him: "...but you didn't take individual variations into account. I did a statistical analysis of their previous performances and bet on the horses with the highest probability of winning..." "...so if you're so hot why are you broke?" asked the engineer. But before the argument can grow, the mathematician takes out his pipe and they get a glimpse of his well-fattened wallet. Obviously here was a man who knows something about horses. They both demanded to know his secret. "Well," he says, between puffs on the pipe, "first I assumed all the horses were identical and spherical..." -------------------------------------------------------------------------------- Theorem : All positive integers are equal. Proof : Sufficient to show that for any two positive integers, A and B, A = B. Further, it is sufficient to show that for all N > 0, if A and B (positive integers) satisfy (MAX(A, B) = N) then A = B. Proceed by induction. If N = 1, then A and B, being positive integers, must both be 1. So A = B. Assume that the theorem is true for some value k. Take A and B with MAX(A, B) = k+1. Then MAX((A-1), (B-1)) = k. And hence (A-1) = (B-1). Consequently, A = B. -------------------------------------------------------------------------------- A bunch of Polish scientists decided to flee their repressive government by hijacking an airliner and forcing the pilot to fly them to a western country. They drove to the airport, forced their way on board a large passenger jet, and found there was no pilot on board. Terrified, they listened as the sirens got louder. Finally, one of the scientists suggested that since he was an experimentalist, he would try to fly the aircraft. He sat down at the controls and tried to figure them out. The sirens got louder and louder. Armed men surrounded the jet. The would be pilot's friends cried out, "Please, please take off now!!! Hurry!!!!!!" The experimentalist calmly replied, "Have patience. I'm just a simple pole in a complex plane." -------------------------------------------------------------------------------- A group of Polish tourists is flying on a small airplane through the Grand Canyon on a sightseeing tour. The tour guide announces: "On the right of the airplane, you can see the famous Bright Angle Falls." The tourists leap out of their seats and crowd to the windows on the right side. This causes a dynamic imbalance, and the plane violently rolls to the side and crashes into the canyon wall. All aboard are lost. The moral to this episode is: always keep your poles off the right side of the plane. Caveat: While this joke mentions Polish people, it is not, in my opinion, in the category of the infamous Polish jokes. I hope no one is offended but only humored. -------------------------------------------------------------------------------- Hiawatha Designs an Experiment Hiawatha, mighty hunter, He could shoot ten arrows upward, Shoot them with such strength and swiftness That the last had left the bow-string Ere the first to earth descended. This was commonly regarded As a feat of skill and cunning. Several sarcastic spirits Pointed out to him, however, That it might be much more useful If he sometimes hit the target. "Why not shoot a little straighter And employ a smaller sample?" Hiawatha, who at college Majored in applied statistics, Consequently felt entitled To instruct his fellow man In any subject whatsoever, Waxed exceedingly indignant, Talked about the law of errors, Talked about truncated normals, Talked of loss of information, Talked about his lack of bias, Pointed out that (in the long run) Independent observations, Even though they missed the target, Had an average point of impact Very near the spot he aimed at, With the possible exception of a set of measure zero. "This," they said, "was rather doubtful; Anyway it didn't matter. What resulted in the long run: Either he must hit the target Much more often than at present, Or himself would have to pay for All the arrows he had wasted." Hiawatha, in a temper, Quoted parts of R. A. Fisher, Quoted Yates and quoted Finney, Quoted reams of Oscar Kempthorne, Quoted Anderson and Bancroft (practically in extenso) Trying to impress upon them That what actually mattered Was to estimate the error. Several of them admitted: "Such a thing might have its uses; Still," they said, "he would do better If he shot a little straighter." Hiawatha, to convince them, Organized a shooting contest. Laid out in the proper manner Of designs experimental Recommended in the textbooks, Mainly used for tasting tea (but sometimes used in other cases) Used factorial arrangements And the theory of Galois, Got a nicely balanced layout And successfully confounded Second order interactions. All the other tribal marksmen, Ignorant benighted creatures Of experimental setups, Used their time of preparation Putting in a lot of practice Merely shooting at the target. Thus it happened in the contest That their scores were most impressive With one solitary exception. This, I hate to have to say it, Was the score of Hiawatha, Who as usual shot his arrows, Shot them with great strength and swiftness, Managing to be unbiased, Not however with a salvo Managing to hit the target. "There!" they said to Hiawatha, "That is what we all expected." Hiawatha, nothing daunted, Called for pen and called for paper. But analysis of variance Finally produced the figures Showing beyond all peradventure, Everybody else was biased. And the variance components Did not differ from each other's, Or from Hiawatha's. (This last point it might be mentioned, Would have been much more convincing If he hadn't been compelled to Estimate his own components From experimental plots on Which the values all were missing.) Still they couldn't understand it, So they couldn't raise objections. (Which is what so often happens with analysis of variance.) All the same his fellow tribesmen, Ignorant benighted heathens, Took away his bow and arrows, Said that though my Hiawatha Was a brilliant statistician, He was useless as a bowman. As for variance components Several of the more outspoken Make primeval observations Hurtful of the finer feelings Even of the statistician. In a corner of the forest Sits alone my Hiawatha Permanently cogitating On the normal law of errors. Wondering in idle moments If perhaps increased precision Might perhaps be sometimes better Even at the cost of bias, If one could thereby now and then Register upon a target. W. E. Mientka, "Professor Leo Moser -- Reflections of a Visit" American Mathematical Monthly, Vol. 79, Number 6 (June-July, 1972) -------------------------------------------------------------------------------- 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. -------------------------------------------------------------------------------- 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'! -------------------------------------------------------------------------------- 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. -------------------------------------------------------------------------------- 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?" -------------------------------------------------------------------------------- 97.37% 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^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 + C = houseboat | cabin / -------------------------------------------------------------------------------- 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 into their own language, and forthwith it is 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." -------------------------------------------------------------------------------- In some foreign country a priest, a lawyer and an engineer are about to be guillotined. The priest puts his head on the block, they pull the rope and nothing happens -- he declares that he's been saved by divine intervention -- so he's let go. The lawyer is put on the block, and again the rope doesn't release the blade, he claims he can't be executed twice for the same crime and he is set free too. They grab the engineer and shove his head into the guillotine, he looks up at the release mechanism and says, "Wait a minute, I see your problem......" ------------------------------------------------------------------------------- What do you get when you cross a tsetse with a mountain climber? Nothing, you can't cross a vector with a scalar. -- - Michael Constant mconst@soda.berkeley.edu ------------------------------------------------------------------------------- In article <2jtloo$oen@xmission.xmission.com>, robertk@xmission.com (robertk) writes: > >There once was a fellow named Blight >Whose speed was much faster than light. >He sat off one day >In a relative way >and returned on the previous night. We've heard of that fellow named Blight, And his trip on that fabulous night, But his increasing mass Would have soon proved so vast He'd have been a most *singular* sight! Relativity Said Einstein, "I have an equation," "Which some might call Rabelaisian:" "Let P be viginity," "Approaching infinity," "And let U be a constant, persuasion." "Now, if P over U be inverted," "And the squareroot of U be inserted," "X times over P," "The result, Q.E.D." "Is a relative." Einstein asserted. ============================================================================== A little neurological put down: You've only got two neurons--and one of them's inhibitory. Last, and certainly least, a little poem... Little Willie was a chemist. Little Willie is no more. For what he thought was H2O, Was H2SO4. ============================================================================== : Two sodium atoms are flying around a cyclotron. Suddenly the first atom : said to the second, `Hey, I think I've just lost an electron.' : `Are you sure?' asked the second atom. : `Yeah,' said the first, `I'm positive.' Of course, the _real_ joke is that neither sodium atom could have been flying around the cyclotron in the first place, unless they were _already_ ionized. ______________________________________________________________________________ An economist, an engineer, and a physicist are marooned on a deserted island. One day they find a can of food washed up on the beach and contrive to open it. The engineer said: "let's hammer the can open between these rocks". The physicist said: "that's pretty crude. We can just use the force of gravity by dropping a rock on the can from that tall tree over there". The economist is somewhat disgusted at these deliberations, and says: "I've got a much more elegant solution. All we have to do is assume a can-opener." ========================================================================= Los Angeles High School Math Exam 1. Johnny has an AK47 with an 80-round clip. If he misses six out of eight shots and shoots 10 times at each drive-by shooting, how many drive-by shootings can be attempted before he has to reload? 2. Paul has 2 ounces of cocaine and he sells 10 grams to Jackson for $820, and 2 grams to Billy for $85 per gram. What is the street value of the balance of the cocaine if he doesn't cut it? 3. Willie gets $200 for stealing a BMW, $50 for a Chevy and $100 for a 4x4. If he has stolen two BMWs and three 4x4s, how many Chevys will he have to steal to make $800? 4. If the contents of an average can of spray paint covers 22 square feet and the average letter is eight square feet, how many letters can a teenager spray with eight cans of paint? 5. Hector got six girls in his gang pregnant. There are 27 girls in the gang. What percentage of girls in the gang has Hector knocked up? 6. Kathy gets $125 for sneaking an illegal alien across the border from Mexico. She sneaked three illegals over the border every night for six days but then one of them ripped her off for $500. How much money does she have left? 7. Byron can trade $150 worth of food stamps for two tickets to a Lakers regular season game. If a play-off game costs 20 percent more, how many play-off tickets can he get for $500 in food stamps? ============================================================================== A challenge for many long ages Had baffled the savants and sages. Yet at last came the light: Seems old Fermat was right-- To the margin add 200 pages. -- Paul Chernoff Q: How many topologists does it take to change a light bulb? A: It really doesn't matter, since they'd rather knot. C programmers do it with long pointers. Three engineering students were gathered together discussing the possible designers of the human body. One said, ``It was a mechanical engineer. Just look at all the joints.'' Another said, ``No, it was an electrical engineer. The nervous system has many thousands of electrical connections.'' The last said, ``Actually it was a civil engineer. Who else would run a toxic waste pipeline through a recreational area?'' ------------------------------------------------------------------------------- Philosophers have long wondered why socks have this habit of getting lost, and why humans always end up with large collections of unmatched odd socks. One school of thought says that socks are very antisocial creatures, and have a deep sense of rivalry. In particular, two socks of the same design have feelings of loathing towards each other and hence it is nearly impossible to pair them (e.g. a blue sock will usually be found nestling up to a black one, rather than its fellow blue sock). On the other hand, quantum theorists explain it all by a generalised exclusion principle --- it is impossible for two socks to be in the same eigen-state, and when it's in danger of happening, one of the socks has to vanish. Indeed the Uncertainty Principle also comes in --- the only time you know where a sock is, is when you're wearing it, and hence unable to be sure exactly how fast it's moving. The moment you stop moving and look at your sock, it then starts falling to pieces, changing colour, or otherwise becoming indeterminate. Either way, socks may possess Colour and Strangeness, but they seem to lack Charm. ------------------------------------------------------------------------------- It may be that human life is "the galaxy's way of evolving a brain." This will come as a surprise to pessimists who, contemplating humankind's destructive tendencies, may be wondering if life isn't the galaxy's way of eliminating certain planets. ------------------------------------------------------------------------------- One attractive young businesswoman to another, over lunch: ``My life is all math. I am trying to add to my income, subtract from my weight, divide my time, and avoid multiplying.'' --------------------------------------------------------------------------- The History of 2 + 2 = 5 by Houston Euler "First and above all he was a logician. At least thirty-five years of the half-century or so of his existence had been devoted exclusively to proving that two and two always equal four, except in unusual cases, where they equal three or five, as the case may be." -- Jacques Futrelle, "The Problem of Cell 13" Most mathematicians are familiar with -- or have at least seen references in the literature to -- the equation 2 + 2 = 4. However, the less well known equation 2 + 2 = 5 also has a rich, complex history behind it. Like any other complex quantitiy, this history has a real part and an imaginary part; we shall deal exclusively with the latter here. Many cultures, in their early mathematical development, discovered the equation 2 + 2 = 5. For example, consider the Bolb tribe, descended from the Incas of South America. The Bolbs counted by tying knots in ropes. They quickly realized that when a 2-knot rope is put together with another 2-knot rope, a 5-knot rope results. Recent findings indicate that the Pythagorean Brotherhood discovered a proof that 2 + 2 = 5, but the proof never got written up. Contrary to what one might expect, the proof's nonappearance was not caused by a cover-up such as the Pythagoreans attempted with the irrationality of the square root of two. Rather, they simply could not pay for the necessary scribe service. They had lost their grant money due to the protests of an oxen-rights activist who objected to the Brotherhood's method of celebrating the discovery of theorems. Thus it was that only the equation 2 + 2 = 4 was used in Euclid's "Elements," and nothing more was heard of 2 + 2 = 5 for several centuries. Around A.D. 1200 Leonardo of Pisa (Fibonacci) discovered that a few weeks after putting 2 male rabbits plus 2 female rabbits in the same cage, he ended up with considerably more than 4 rabbits. Fearing that too strong a challenge to the value 4 given in Euclid would meet with opposition, Leonardo conservatively stated, "2 + 2 is more like 5 than 4." Even this cautious rendition of his data was roundly condemned and earned Leonardo the nickname "Blockhead." By the way, his practice of underestimating the number of rabbits persisted; his celebrated model of rabbit populations had each birth consisting of only two babies, a gross underestimate if ever there was one. Some 400 years later, the thread was picked up once more, this time by the French mathematicians. Descartes announced, "I think 2 + 2 = 5; therefore it does." However, others objected that his argument was somewhat less than totally rigorous. Apparently, Fermat had a more rigorous proof which was to appear as part of a book, but it and other material were cut by the editor so that the book could be printed with wider margins. Between the fact that no definitive proof of 2 + 2 = 5 was available and the excitement of the development of calculus, by 1700 mathematicians had again lost interest in the equation. In fact, the only known 18th-century reference to 2 + 2 = 5 is due to the philosopher Bishop Berkeley who, upon discovering it in an old manuscript, wryly commented, "Well, now I know where all the departed quantities went to -- the right-hand side of this equation." That witticism so impressed California intellectuals that they named a university town after him. But in the early to middle 1800's, 2 + 2 began to take on great significance. Riemann developed an arithmetic in which 2 + 2 = 5, paralleling the Euclidean 2 + 2 = 4 arithmetic. Moreover, during this period Gauss produced an arithmetic in which 2 + 2 = 3. Naturally, there ensued decades of great confusion as to the actual value of 2 + 2. Because of changing opinions on this topic, Kempe's proof in 1880 of the 4-color theorem was deemed 11 years later to yield, instead, the 5-color theorem. Dedekind entered the debate with an article entitled "Was ist und was soll 2 + 2?" Frege thought he had settled the question while preparing a condensed version of his "Begriffsschrift." This condensation, entitled "Die Kleine Begriffsschrift (The Short Schrift)," contained what he considered to be a definitive proof of 2 + 2 = 5. But then Frege received a letter from Bertrand Russell, reminding him that in "Grundbeefen der Mathematik" Frege had proved that 2 + 2 = 4. This contradiction so discouraged Frege that he abandoned mathematics altogether and went into university administration. Faced with this profound and bewildering foundational question of the value of 2 + 2, mathematicians followed the reasonable course of action: they just ignored the whole thing. And so everyone reverted to 2 + 2 = 4 with nothing being done with its rival equation during the 20th century. There had been rumors that Bourbaki was planning to devote a volume to 2 + 2 = 5 (the first forty pages taken up by the symbolic expression for the number five), but those rumor remained unconfirmed. Recently, though, there have been reported computer-assisted proofs that 2 + 2 = 5, typically involving computers belonging to utility companies. Perhaps the 21st century will see yet another revival of this historic equation. ---------------------------------------------------------------------------- From: Mathematics Magazine, December 1990. Subject: Statisticians ( Excerpted from "Quotes, Damned Quotes" by John Bibby ) Mathematicians are like Frenchmen: whatever you say to them they translate into their own language and forthwith it is something entirely different. (Johann Wolfgang von Goethe) If there is a 50-50 chance that something can go wrong, then 9 times out of ten it will. (Paul Harvey News, 1979) ``Give us a copper Guv'' said the beggar to the Treasury statistician, when he waylaid him in Parliament square. ``I haven't eaten for three days.'' ``Ah,'' said the statistician, ``and how does that compare with the same period last year?'' (Russell Lewis) ``I gather, young man, that you wish to be a Member of Parliament. The first lesson that you must learn is, when I call for statistics about the rate of infant mortality, what I want is proof that fewer babies died when I was Prime Minister than when anyone else was Prime Minister. That is a political statistic.'' (Winston Churchill) ``You haven't told me yet,'' said Lady Nuttal, ``what it is your fiance does for a living.'' ``He's a statistician,'' replied Lamia, with an annoying sense of being on the defensive. Lady Nuttal was obviously taken aback. It had not occurred to her that statisticians entered into normal social relationships. The species, she would have surmised, was perpetuated in some collateral manner, like mules. ``But Aunt Sara, it's a very interesting profession,'' said Lamia warmly. ``I don't doubt it,'' said her aunt, who obviously doubted it very much. ``To express anything important in mere figures is so plainly impossible that there must be endless scope for well-paid advice on the how to do it. But don't you think that life with a statistician would be rather, shall we say, humdrum?'' Lamia was silent. She felt reluctant to discuss the surprising depth of emotional possibility which she had discovered below Edward's numerical veneer. ``It's not the figures themselves,'' she said finally. ``It's what you do with them that matters.'' (K.A.C. Manderville, The undoing of Lamia Gurdleneck) ---------------------------------------------------------------------------- _There Once Was a Breathy Baboon_ by Sir Arthur Eddington There once was a breathy baboon Who always breathed down a bassoon, For he said, "It appears That in billions of years I shall certainly hit on a tune." ------------------------------------------------------------------------- We use epsilons and deltas in mathematics because mathematicians tend to make errors. The Stanford Linear Accelerator Center was known as SLAC, until the big earthquake, when it became known as SPLAC. SPLAC? Stanford Piecewise Linear Accelerator. 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 ..." In theory, there is no difference between theory and practice, but in practice there is a great deal of difference. Everyone knows "What's purple and commutes?", but I once heard "What's purple, commutes, and is worshiped by a limited number of people?" A finitely venerated abelian grape. -------------------------------------------------------------------------------- What keeps a square from moving ? why, square roots of course. How many square roots does it have ? why, 2 obviously. An engineer, a physicist, and a mathematician are shown a pasture with a herd of sheep, and told to put them inside the smallest possible amount of fence. The engineer is first. He herds the sheep into a circle and then puts the fence around them, declaring, "A circle will use the least fence for a given area, so this is the best solution." The physicist is next. She creates a circular fence of infinite radius around the sheep, and then draws the fence tight around the herd, declaring, "This will give the smallest circular fence around the herd." The mathematician is last. After giving the problem a little thought, he puts a small fence around himself and then declares, "I define myself to be on the outside!" PROOFS THAT P ============= (attributed to Hartry Field) Davidson's proof that p: Let us make the following bold conjecture: p Wallace's proof that p: Davidson has made the following bold conjecture: p Grunbaum: As I have asserted again and again in previous publications, p. Morgenbesser: If not p, what? q maybe? Putnam: Some philosophers have argued that not-p, on the grounds that q. It would be an interesting exercise to count all the fallacies in this "argument". (It's really awful, isn't it?) Therefore p. Rawls: It would be a nice to have a deductive argument that p from self-evident premises. Unfortunately, I am unable to provide one. So I will have to rest content with the following intuitive considerations in its support: p. Unger: Suppose it were the case that not-p. It would follow from this that someone knows that q. But on my view, no one knows anything whatsoever. Therefore p. (Unger beieves that the louder you say this argument the more persuasive it becomes.) Katz: I have seventeen arguments for the claim that p, and I know of only four for the claim that not-p. Therefore p. Lewis: Most people find the claim that not p completely obvious and when I assert p they give me an incredulous stare. But the fact that they find not-p obvious is no argument that it is true; and I do not know how to refute an incredulous stare. Therefore p. Fodor: My argument for p is based on three premises: (1) q (2) r and (3) p >From these, the claim that p deductively follows. Some people may find the third premise controversial, but it is clear that if we replaced that premise by any other reasonable premise, the argument would go through just as well. Sellars's proof that p: Unfortunately, limitations of space prevent it from being included here, but important parts of the proof can be found in each of the articles in the attached bibliography. Earman: There are solutions to the field equations of general relativity in which space-time has the structure of a four-dimensional klein bottle and in which there is no matter. In each such space-time, the claim that not-p is false. Therefore p. Kripke: OUTLINE OF A "PROOF" THAT P [footnote] Saul Kripke Some philosophers have argued that not-p. But none of them seems to me to have made a convincing argument against the intuitive view that this is not the case. Therefore, p. [footnote]. This outline was prepared hastily--at the editor's insistence---from a taped transcript of a lecture. Since I was not even given the opportunity to revise the first draft before publication, I cannot be held responsible for any lacunae in the (published version of the) argument, or for any fallacious or garbled inferences resulting from faulty preparation of the typescript. Also, the argument now seems to me to have problems which I did not know when I wrote it, but which I can't discuss here, and which are completely unrelated to any criticisms that have appeared in the literature (or that I have seen in manuscript); all such criticisms misconstrue the argument. It will be noted that the present version of the argument seems to presuppose the (intuitionistically unacceptable) law of double negation. But the argument can easily be reformulated in a way that avoids employing such an inference rule. I hope to expand on these matters further in a separate monograph. Routley and Meyer: If (q & not-q) is true, then there is a model for p. Therefore p. ========================================================================== A mathematician named Klein Thought the Mobius Band was divine. Said he, "If you glue The edges of two You get a weird bottle like mine." There once was a fellow named Blight Whose speed was much faster than light. He sat off one day In a relative way and returned on the previous night. There once was a fellow named Fisk Whose fencing was exceedingly brisk. So fast was his action That by the Fitzgerald Contraction His rapier soon was reduced to a disk. ============================================================================ Q: What do you get when you cross an elephant and a grape? A: Elephant-grape-sin(theta) Q: What do you get when you cross an elephant and a mountain climber? A: Nothing. You can't cross scalars. Q: What's purple and commutes? A: An abelian grape. Q: What's yellow and equivalent to the Axiom of Choice? A: Zorn's Lemmon. Finally, a story (possibly apocryphal) relayed to us by a math professor in college: A student was doing miserably on his oral final exam in General Toplogy (yes, this guy _really_ did give oral finals in topology). Exasperated by the student's abysmal performance up to that point, the professor asked the student "So, what _do_ you know about topology?" The student replied, "I know the definition of a topologist." The professor asked him to state the definition, expecting to get the old saw about someone who can't tell the difference between a coffee cup and a doughnut. Instead, the student replied: "A topologist is someone who can't tell the difference between his ass and a hole in the ground, but who can tell the difference between his ass and _two_ holes in the ground." The student passed. ============================================================================== =============================================================================== : This one is old, but I haven't seen it posted in this thread yet. Sorry : if it is often repeated but I just started reading this group. : A mathmatician, a physicist, and an engineer were all given a red rubber : ball and told to find the volume. The mathmatician carefully measured : the diamaeter and evaluated a triple integral. The physicist filled a : beaker with water, put the ball in the water, and measured the total : displacement. The engineer looked up the model and serial numbers in : his red-rubber-ball table. If it was my company: The engineer tried to look up the model and serial numbers, couldn't find them, so told his manager that it's just not going to work. =============================================================================== In article <2jtloo$oen@xmission.xmission.com>, robertk@xmission.com (robertk) writes: > >There once was a fellow named Blight >Whose speed was much faster than light. >He sat off one day >In a relative way >and returned on the previous night. We've heard of that fellow named Blight, And his trip on that fabulous night, But his increasing mass Would have soon proved so vast He'd have been a most *singular* sight! Relativity Said Einstein, "I have an equation," "Which some might call Rabelaisian:" "Let P be viginity," "Approaching infinity," "And let U be a constant, persuasion." "Now, if P over U be inverted," "And the squareroot of U be inserted," "X times over P," "The result, Q.E.D." "Is a relative." Einstein asserted. Mathematical Sex Wherein it is related how that Polygon of Womanly Virtue, your Polly Nomial (our heroine) is accosted by that Notorious Villain Curly Pi, and factored (oh, horror). Once upon a time ( 1/T ), Pretty Polly Nomial was strolling across a field of vectors when she came to the boundary of a singularly large matrix. Now Polly was convergent and her mother had made it an absolute condition that she never enter such an array without her brackets on. Polly, however, who had changed her variables that morning and was feeling particularly badly behaved, ignored this condition on the basis that it was insufficient, and made her way amongst the complex elements. Rows and columns closed in from all sides. Tangents approached her surface. She became tensor and tensor. Quite suddenly, two branches of a hyperbola touched her at a single point. She oscillated violently, lost all sense of directrix, and went completely divergent. As she reached a turning point, she tripped over a square root that was protruding from the erf and plunged headlong down a steep gradient. When she rounded off once more, she found herself inverted, apparently alone, in a non-Euclidian space. She was being watched, however. That smooth operator, Curly Pi, was lurking innerproduct. As his eyes devoured her curvilinear coordinates, a singular expression crossed his face. He wondered, was she still convergent? He decided to integrate improperly at once. Hearing a common fraction behind her, Polly rotated and saw Curly Pi approaching with his power series extrapolated. She could see at once by his degenerate conic and dissipative terms that he was bent on no good. "Arcsinh," she gasped. "Ho, ho," he said. "What a symmetric little asymptote you have. I can see your angles have a lot of secs." "Oh, sir," she protested, "keep away from me. I haven't got my brackets on." "Calm yourself, My Dear," said our Suave Operator. "Your fears are purely imaginary." "I, I," she thought, "perhaps he's not normal but homologous." "What order are you?" the Brute demanded. "Seventeen," replied Polly. Curly leered. "I suppose you've never been operated on." "Of course not," Polly replied quite properly. "I'm absolutely convergent." "Come, come," said Curly, "Let's off to a decimal place I know and I'll take you to the limit." "Never," gasped Polly. "Abscissa," he swore, using the vilest oath he knew. His patience was gone. Coshing her over the coefficient with a log until she was powerless, Curly removed her discontinuities. He stared at her significant places, and began smoothing out her points of inflection. Poor Polly. The algorithmic method was now her only hope. She felt his hand tending to her asymptotic limit. Her convergence would soon be gone forever. There was no mercy, for Curly was a heavyside operator. Curly's radius squared itself; Polly's loci quivered. He integrated by parts. He integrated by partial fractions. After he cofactored, he performed rungecutta on her. The complex beast even went all the way around and did a contour integration. Curly went on operating until he had satisfied her hypothesis, then he exponentiated and became completely orthogonal. When Polly got home that night, her mother noticed that she was no longer piecewise continuous, but had been truncated in several places. But is was too late to differentiate now. As the months went by, Polly's denominator increased monotonically. Finally, she went to the L'Hopital and generated a small but pathological function which left surds all over the place and drove Polly to deviation. The moral of our sad story is this: 'If you want to keep your expressions convergent, never allow them a single degree of freedom...' THE SECOND BOOK OF VECTOR There dwelt in the land of Brit certain high priests who served in the temples of Elektron, which is an invisible god who darteth around in ever-decreasing circles but never into his own nucleus. And the priests of Elektron were devout men, serving no other god but he. And Elektron looked with favour upon them and rewarded them each according to his worth with divers strange gifts. To some he gave power to converse with those from afar off and to others he brought visions of strange happenings in distant lands; yeah, even of the United States cavalry in glorious Technicolor. And to certain other of his high priests Elektron gave powers of levitation, so that they walked with their feet ever- so-slightly off the ground; these dwelt in glass temples called, in the native tongue, Researchlabs or Funnifarms, which were set apart from the common people and to which entrance was denied to all, saving only those having scrips of authority from their chief priest. And these priests were called by the common people Egbonces which meaneth he who knoweth the square root of minus one. And the Egbonces were cunning at fashioning curious devices from boot-latchets and wax so that the populace were astonished and continually cried out, saying, behold, these are great wonders but of what use be they? Yet other high priests of Elektron were followers of the prophet Babbage and these were set in authority over divers machines that brought much benefit to the common people; some computed the numbers of the tribes and the taxes that each man should pay; others controlled the paycheks of these that laboured, so that each man received less than his hire, while others suggested that the inter-city chariots were tardy in arrival. And Elektron taught the high priests to feed the engines with curious symbols engraven upon tablets that they might print out likenesses of the sex-goddess Bardot devoid of her apparel, which gave satisfaction to many. And these priests likewise withdrew the hems of their garments from the common populace and, by conversing in the alien tongues of Fortran and Algol, preserved their mysteries jealously. At this time the skies were filled with heavier-than-air machines of many nations which flew with the noise of emasculated hornets and carried the peoples to and fro, even unto the ends of the earth. These machines were under the auspices of the god Hijak. And certain of the nations had air machines which could drop unpleasantness on the land beneath to discomfort the people; but certain other nations who were poor and backward and, as the saying goeth, not with it, did not possess these amenities. Thus it came to pass that the acquisition of such machines was regarded by all as an outward and visible sign that the possessor nation was emerging from savage practices and an example to others. And certain rich merchants searched diligently and redeemed many heavier-than-air machines; some from the knocker's yard; some which fell from the back of an hangar and yet others which were dislodged privily from the Science Museum. And they purposed to sell these to the heathen for many shekels of gold and at great profit. So it came to pass that the merchants sent envoys to a far country, even to the kingdom of Tsetse-Tsetse. And the envoys said unto the king of Tsetse-Tsetse, O king live for ever but put not thy money upon it. And the king answered saying, What meanest thou? Then did the envoys reply saying, Surely thou knowest that they neighbour the king of Beri- Beri hath cast covetous eyes upon thy lands and they maidens? If only thou hadst an Air Force it would cause thine adversary to wind his neck in. Then did the king beat his breast crying, Wo is me! And the envoys made reply saying Not so, O king, for it so happeneth that we can supply thee with a squadron of Bleriot Mk.Is. And thus it came to pass the king bought from the envoys for much fine gold and slept peacefully with his wives that night. Then did the envoys depart and journeyed to the neighbouring land that is called Beri-Beri. And they said to the king of Beri-Beri, O king live for ever but begin not the reading of any long novels. And the king said What meanest thou? Whereupon the envoys replied saying, Knowest thou not that they neighbour the king of Tsetse-Tsetse hath secretly purchased war-birds and purposeth to ravage thy country? At this the king went as pale as was possible and the end of the matter was that he became Commodore of a squadron of Cabbage White Mk. VIIs. And it came to pass that in Brit the god Elektron gave unto his high priests the power to fashion magick bowls which could divine the presence and movements of heavier-than-air machines even at great distances. Yeah, and not only this, for by gazing into the bowl, vessels having their business in great waters could be made to broach each other with greater certainty. And on land its magick powers enabled the Fuzz to put the finger upon all charioteers who, like their forbear Jehu, drove furiously. And the name of this new wonder was radar, which, being translated, meaneth that which worketh by suction and mirrors. And the rich merchants came unto the high priests of radar and said unto them. Lo, we have heard much of the wonders that they god Elektron hath taught thee and it seemeth that we can do a deal with profit to all. Make for us great numbers of these magick bowls, we pray thee, that we may sell them to the nations for their greater safety. Do this and we will pay thee many shekels of gold; moreover, we will pull down thy temples to the greater glory of Elektron, wherein thou shalt find all the instruments that they heart desirest. And we will clothe thee in white raiment and give thee charge over many. What sayest thou? And the high priest conferred privily and agreed among themselves that they were on to a good thing. So it came to pass that the merchants caused mighty temples to be built wherein the god Elektron might be served, both by day and night; and the high priests, for their part, devised magick bowls with ever greater cunning and these the merchants sold to whoever was in the market place. Thus it came about that both the king of Tsetse-Tsetse and the king of Beri-Beri were persuaded to buy the magick bowls with which to keep vigil each upon the other. Yeah, both primary and secondary radar had they in plenty and certain inhabitants of the two countries were trained to interpret the signs and portents which appeared upon these bowls whenever an heavier- than-air machine was drawing nigh. And behold, it came to pass that upon a certain night there was a watchman in the kingdom of Tsetse-Tsetse who was an exceeding dim lamp; moreover, when interpreting the symbols on the magick bowl, he was, as the saying is, unable to tell Squawk from Clutter. And this watchman, fearful of what he supposed he saw upon the face of the bowl, said unto himself The enemy is upon us, and thereupon smote the Panick Button. Hereupon the Bleriot Mk.Is rose (all excepting one which had broken its elastick band) and brought destruction to the sleeping land of Beri-Beri. But the Cabbage Whites, being forewarned by their magick bowls, were already riding the heavens and bringing affliction upon their neighbours. And, by morning, both countries were bathed in blood. And in the temples of Elektron there was great commotion, for the hot lines were glowing red and the artificial moons which the high priests had raised were overburdened with coloured images of the slaughter, for the delectation of the common people. And when all was accomplished, overseers from the United Nations came and wagged their heads and voted Tsetse-Tsetse and Beri-Beri into their assemblies in recognition of their emergence. V. THE SEX LIFE OF AN ELECTRON One night when his charge was at full capacity, Micro Farad decided to get a cute little coil to discharge him. He picked up Millie Amp and took her for a ride on his megacycle. They rode across the wheat stone bridge, around the sine wave, and into the magnetic field next to the flowing current. Micro Farad, attracted by Millie's characteristic curve, soon had her field fully excited. He laid her on the ground potential, raised her frequency, lowered her resistance, and pulled out his high voltage probe. He inserted it in parallel and began to short circuit her shunt. Fully excited, Millie cried out, "ohm, ohm, give me mho". With his tube at maximum output and her coil vibrating from the current flow, her shunt soon reached maximum heat. The excessive current had shorted her shunt, and Micro's capacity was rapidly discharged, and every electron was drained off. They fluxed all night, tried various connections and hookings until his bar magnet had lost all of its strength, and he could no longer generate enough voltage to sustain his collapsing field. With his battery fully discharged, Micro was unable to excite his tickler, so they ended up reversing polarity and blowing each other's fuses. --------------------------------------------------------------------------- Four men were sitting one day discussing how smart their dog's were. The first man was an Engineer, who said his dog could do math. His dog was named T-Square, and he told him to get some paper and draw a square, a circle, and a triangle, which the dog did with no sweat. The Accountant said that his dog was better. His dog, Slide Rule, was told to fetch a dozen cookies, bring them back, and divide them into piles of 3, which Slide Rule did with no problem. The Chemist said his dog was smarter, his dog named Measure, was told to get a quart of milk, and pour 7 ounces into a 10 ounce glass. The dog did this with no trouble at all, and all three men agreed that their dog's were equally smart. Then they turned to the Union Member and asked, what can your dog do? The Union Member called his dog, who was named Coffee Break, and said, "Show the fellows what you can do". Coffee Break went over and ate the cookies, drank the milk, shit on the paper, fucked the other dogs, and claimed he injured his back while doing so, filed a grievence report for unsafe working conditions, put in for Workmens Compensation, and left for home on sick leave. -------------------------------------------------------------------------- A mathematician and a physicist are given the task of describing a room. They both go in, and spend hours meticulously writing down every detail, each turning in nearly a ream of paper. The next day, the room is changed, and they are again given the task. The physicist spends the better part of the day, but the mathematician, amazingly enough, leaves within a minute. he hands in a single sheet of paper with the following description: Put picture back on wall to return to previously solved state. A mathematician, a physicist, and an engineer are given the task of finding the volume of a red rubber ball. The mathematician carefully measures the diameter and evaluates the volume. The physicist dunks it in a bucket of water and measures the volume of the displacement. The engineer picks up the balls, reads the model and serial number and looks it up in his Red Rubber Ball table. -----------------------------------------------------------------------------