altre barzellette
Moderatore: tutor
ecco alcune barzellette che mi ha dato mio fratello
<BR>
<BR>Al cinema si presenta un uomo con un elefante.
<BR>Ma all\'entrata un addetto lo ferma:
<BR> Guardi signore che gli elefanti non possono entrare!
<BR>Dopo qualche minuto il tizio si ripresenta con l\'elefante
<BR>con indosso un tuta rosa e delle scarpette bianche.
<BR> E questa sarebbe una ballerina? Le ho già
<BR>detto che gli elefanti non possono entrare!
<BR>Dopo altri dieci minuti ritorna il tizio con l\'elefante
<BR>che ha una ruota davanti e una didietro, e dice all\'addetto:
<BR> Scusi, dove la posso lasciare la bicicletta?
<BR> Bicicletta un cavolo! Vada fuori con quell\'elefante!
<BR>Dopo un altro quarto d\'ora però il tale si ripresenta
<BR>con l\'elefante con una fetta di pane sull\'orecchio
<BR>destro ed una sull\'orecchio sinistro.
<BR>Appena lo vede, l\'addetto sta per sbottare ma il tale lo blocca:
<BR> Aoh... io DENTRO AL PANINO ci metto quello che mi pare!!!
<BR>
<BR>
<BR>Un ragazzino, mentre torna da scuola,
<BR>trova una puzzola e se la porta a casa.
<BR>La madre non ne è molto contenta e gli chiede.\"
<BR>Che cosa hai intenzione di fare con quell\' animale?\".
<BR>Il ragazzino risponde:\" La metto sotto il letto\".
<BR>\"E la puzza?\" chiede la madre.
<BR>\" Oh  risponde il ragazzo,  si abituerà!\"
<BR>
<BR>
<BR>Due amici non si sono visti da anni.
<BR>Così ritrovatisi fanno insieme una
<BR>lunga camminata parlando e cercando
<BR>di ricuperare il tempo in cui non si
<BR>sono visti raccontandosi quello
<BR>che hanno fatto durante tutti quegli anni.
<BR>Finalmente il primo invita l\'altro a
<BR>visitarlo nel suo nuovo appartamento.
<BR>\"Ho una moglie e tre figli che sarebbero
<BR>entusiasti di conoscerti\".
<BR>\"Bene, e dove vivi?\". \"Ecco l\'indirizzo.
<BR>C\'è molto spazio dietro alla casa per
<BR>parcheggiare. Parcheggia e vieni davanti
<BR>alla porta principale, aprila colpendola
<BR>col piede, va all\'ascensore e premi
<BR>il bottone con il gomito sinistro e poi entra.
<BR>Quando raggiungi il sesto piano, prosegui
<BR>nel corridoio finché trovi la targhetta
<BR>con il nostro nome. Poi premi il campanello
<BR>con il gomito destro e ti farò entrare\".
<BR>\"Bene, ma dimmi... che cosa sono tutte
<BR>queste storie di aprire con un calcio
<BR>e schiacciare bottoni con il gomito
<BR>destro e col gomito sinistro?\".
<BR>\"Ma scusa, non vorrai mica venire a mani vuote?\".
<BR>
<BR>
<BR>Una bambina assiste per la prima volta a un matrimonio.
<BR>Ad un certo punto chiede alla mamma:
<BR>\"Perché la sposa è vestita di bianco?\".
<BR>Risposta: \"Perché il bianco è il colore della felicità,
<BR>e oggi è il giorno più felice della sua vita!\".
<BR>La bambina riflette un momento, e poi risponde:
<BR>\"Ma allora perché lo sposo è vestito di nero?\".
<BR>
<BR>
<BR>
<BR>Una donna e suo marito vanno da un dentista per un\'emergenza, e gli chiede: \"Presto, dottore, vorrei togliere un dente\", e poi la donna sopraggiunge:
<BR>\"....ma non si preoccupi di fare l\'iniezione anestetica, avrei piuttosto fretta. Lei tolga solo il dente e poi ce ne andremo\". Il dentista ammirato: \"Ma che donna coraggiosa! Di quale dente si tratta?\". La donna: \"Vieni un po\' qui, caro, fagli vedere il dente!\".
<BR>
<BR>
<BR>
<BR>
<BR>
<BR>
<BR>I primi sintomi dell\'abuso di tecnologia.
<BR>
<BR>Devi copiare a penna una pagina, e cerchi il bottone per fare copiaincolla.
<BR>Stai guardando il televideo e cerchi di aprire la pagina 221 in un\'altra finestra
<BR>Quando guardi una partita in televisione, cerchi di interagire con un joystick.
<BR>Usi il verbo \"downloadare\" per chiedere una mano a scaricare la spesa dalla macchina.
<BR>Quando scrivi di pugno cerchi di salvare ogni tanto, ma non trovi il comando.
<BR>Sull\'onda dell\'entusiasmo hai concesso alla colf che ti pulisce la casa di farlo con il telelavoro da casa sua.
<BR>Quando stiri impugni il ferro come un mouse e cerchi di cliccare sulle pieghe come fossero collegamenti ipertestuali.
<BR>In ascensore dopo aver premuto il pulsante del piano, cerchi il tasto \"Invio\".
<BR>Vedi il cestino pieno di carte, accanto al pc, e pensi di svuotarlo cliccando su \"Svuota cestino\". <IMG SRC="images/forum/icons/icon_biggrin.gif"> <IMG SRC="images/forum/icons/icon_biggrin.gif"> <IMG SRC="images/forum/icons/icon_biggrin.gif">
<BR>
<BR>
<BR>
<BR>
<BR>ciao a tutti <IMG SRC="images/forum/icons/icon_smile.gif"> <IMG SRC="images/forum/icons/icon_smile.gif"> <IMG SRC="images/forum/icons/icon_smile.gif"> <IMG SRC="images/forum/icons/icon_smile.gif">
<BR>P.S. sono nuova e cerco persone con cui parlare di tutto; mi suggerireste dei siti, oltre questo, naturalmente, dai quali prendere esercizi per allenarmi per le olimpiadi di matematica? <IMG SRC="images/forum/icons/icon24.gif"> <IMG SRC="images/forum/icons/icon24.gif">
<BR>
<BR>Al cinema si presenta un uomo con un elefante.
<BR>Ma all\'entrata un addetto lo ferma:
<BR> Guardi signore che gli elefanti non possono entrare!
<BR>Dopo qualche minuto il tizio si ripresenta con l\'elefante
<BR>con indosso un tuta rosa e delle scarpette bianche.
<BR> E questa sarebbe una ballerina? Le ho già
<BR>detto che gli elefanti non possono entrare!
<BR>Dopo altri dieci minuti ritorna il tizio con l\'elefante
<BR>che ha una ruota davanti e una didietro, e dice all\'addetto:
<BR> Scusi, dove la posso lasciare la bicicletta?
<BR> Bicicletta un cavolo! Vada fuori con quell\'elefante!
<BR>Dopo un altro quarto d\'ora però il tale si ripresenta
<BR>con l\'elefante con una fetta di pane sull\'orecchio
<BR>destro ed una sull\'orecchio sinistro.
<BR>Appena lo vede, l\'addetto sta per sbottare ma il tale lo blocca:
<BR> Aoh... io DENTRO AL PANINO ci metto quello che mi pare!!!
<BR>
<BR>
<BR>Un ragazzino, mentre torna da scuola,
<BR>trova una puzzola e se la porta a casa.
<BR>La madre non ne è molto contenta e gli chiede.\"
<BR>Che cosa hai intenzione di fare con quell\' animale?\".
<BR>Il ragazzino risponde:\" La metto sotto il letto\".
<BR>\"E la puzza?\" chiede la madre.
<BR>\" Oh  risponde il ragazzo,  si abituerà!\"
<BR>
<BR>
<BR>Due amici non si sono visti da anni.
<BR>Così ritrovatisi fanno insieme una
<BR>lunga camminata parlando e cercando
<BR>di ricuperare il tempo in cui non si
<BR>sono visti raccontandosi quello
<BR>che hanno fatto durante tutti quegli anni.
<BR>Finalmente il primo invita l\'altro a
<BR>visitarlo nel suo nuovo appartamento.
<BR>\"Ho una moglie e tre figli che sarebbero
<BR>entusiasti di conoscerti\".
<BR>\"Bene, e dove vivi?\". \"Ecco l\'indirizzo.
<BR>C\'è molto spazio dietro alla casa per
<BR>parcheggiare. Parcheggia e vieni davanti
<BR>alla porta principale, aprila colpendola
<BR>col piede, va all\'ascensore e premi
<BR>il bottone con il gomito sinistro e poi entra.
<BR>Quando raggiungi il sesto piano, prosegui
<BR>nel corridoio finché trovi la targhetta
<BR>con il nostro nome. Poi premi il campanello
<BR>con il gomito destro e ti farò entrare\".
<BR>\"Bene, ma dimmi... che cosa sono tutte
<BR>queste storie di aprire con un calcio
<BR>e schiacciare bottoni con il gomito
<BR>destro e col gomito sinistro?\".
<BR>\"Ma scusa, non vorrai mica venire a mani vuote?\".
<BR>
<BR>
<BR>Una bambina assiste per la prima volta a un matrimonio.
<BR>Ad un certo punto chiede alla mamma:
<BR>\"Perché la sposa è vestita di bianco?\".
<BR>Risposta: \"Perché il bianco è il colore della felicità,
<BR>e oggi è il giorno più felice della sua vita!\".
<BR>La bambina riflette un momento, e poi risponde:
<BR>\"Ma allora perché lo sposo è vestito di nero?\".
<BR>
<BR>
<BR>
<BR>Una donna e suo marito vanno da un dentista per un\'emergenza, e gli chiede: \"Presto, dottore, vorrei togliere un dente\", e poi la donna sopraggiunge:
<BR>\"....ma non si preoccupi di fare l\'iniezione anestetica, avrei piuttosto fretta. Lei tolga solo il dente e poi ce ne andremo\". Il dentista ammirato: \"Ma che donna coraggiosa! Di quale dente si tratta?\". La donna: \"Vieni un po\' qui, caro, fagli vedere il dente!\".
<BR>
<BR>
<BR>
<BR>
<BR>
<BR>
<BR>I primi sintomi dell\'abuso di tecnologia.
<BR>
<BR>Devi copiare a penna una pagina, e cerchi il bottone per fare copiaincolla.
<BR>Stai guardando il televideo e cerchi di aprire la pagina 221 in un\'altra finestra
<BR>Quando guardi una partita in televisione, cerchi di interagire con un joystick.
<BR>Usi il verbo \"downloadare\" per chiedere una mano a scaricare la spesa dalla macchina.
<BR>Quando scrivi di pugno cerchi di salvare ogni tanto, ma non trovi il comando.
<BR>Sull\'onda dell\'entusiasmo hai concesso alla colf che ti pulisce la casa di farlo con il telelavoro da casa sua.
<BR>Quando stiri impugni il ferro come un mouse e cerchi di cliccare sulle pieghe come fossero collegamenti ipertestuali.
<BR>In ascensore dopo aver premuto il pulsante del piano, cerchi il tasto \"Invio\".
<BR>Vedi il cestino pieno di carte, accanto al pc, e pensi di svuotarlo cliccando su \"Svuota cestino\". <IMG SRC="images/forum/icons/icon_biggrin.gif"> <IMG SRC="images/forum/icons/icon_biggrin.gif"> <IMG SRC="images/forum/icons/icon_biggrin.gif">
<BR>
<BR>
<BR>
<BR>
<BR>ciao a tutti <IMG SRC="images/forum/icons/icon_smile.gif"> <IMG SRC="images/forum/icons/icon_smile.gif"> <IMG SRC="images/forum/icons/icon_smile.gif"> <IMG SRC="images/forum/icons/icon_smile.gif">
<BR>P.S. sono nuova e cerco persone con cui parlare di tutto; mi suggerireste dei siti, oltre questo, naturalmente, dai quali prendere esercizi per allenarmi per le olimpiadi di matematica? <IMG SRC="images/forum/icons/icon24.gif"> <IMG SRC="images/forum/icons/icon24.gif">
Cucci
Prova <A href=\"http://www.chihapauradellamatematica.org\"> www.chihapauradellamatematica.org </A>, è demenziale, ma un po\' divertente...
<BR>
<BR>Se vuoi cerca quello delle olimpiadi di fisica, può essere un allenamento su certi esercizi con la velocità ecc...
<BR>
<BR>Se vuoi cerca quello delle olimpiadi di fisica, può essere un allenamento su certi esercizi con la velocità ecc...
In the break of new dawn
My hope is forlorn
Shadows they will fade
But I'm always in the shade
Without you...
My Selene  Sonata Arctica
My hope is forlorn
Shadows they will fade
But I'm always in the shade
Without you...
My Selene  Sonata Arctica
A mathematician and a physicist were asked the following question:
<BR>
<BR>Suppose you walked by a burning house and saw a hydrant and
<BR>a hose not connected to the hydrant. What would you do?
<BR>
<BR>P: I would attach the hose to the hydrant, turn on the water, and put out
<BR>the fire.
<BR>
<BR>M: I would attach the hose to the hydrant, turn on the water, and put out
<BR>the fire.
<BR>
<BR>Then they were asked this question:
<BR>
<BR>Suppose you walked by a house and saw a hose connected to
<BR>a hydrant. What would you do?
<BR>
<BR>P: I would keep walking, as there is no problem to solve.
<BR>
<BR>M: I would disconnect the hose from the hydrant and set the house on fire,
<BR>reducing the problem to a previously solved form.
<BR>[addsig]
<BR>
<BR>Suppose you walked by a burning house and saw a hydrant and
<BR>a hose not connected to the hydrant. What would you do?
<BR>
<BR>P: I would attach the hose to the hydrant, turn on the water, and put out
<BR>the fire.
<BR>
<BR>M: I would attach the hose to the hydrant, turn on the water, and put out
<BR>the fire.
<BR>
<BR>Then they were asked this question:
<BR>
<BR>Suppose you walked by a house and saw a hose connected to
<BR>a hydrant. What would you do?
<BR>
<BR>P: I would keep walking, as there is no problem to solve.
<BR>
<BR>M: I would disconnect the hose from the hydrant and set the house on fire,
<BR>reducing the problem to a previously solved form.
<BR>[addsig]
[tex]\Im^\heartsuit_\TeX[/tex]
 livingbooks
 Messaggi: 64
 Iscritto il: 01 gen 1970, 01:00
 Contatta:
Eccone alcune:
<BR>
<BR><DIV style=\"fontsize:0.5pt;fontfamily:Arial\">
<BR>
<BR>The USDA once wanted to make cows produce milk faster, to improve the
<BR>dairy industry.
<BR>
<BR>So, they decided to consult the foremost biologists and recombinant
<BR>DNA technicians to build them a better cow. They assembled this team
<BR>of great scientists, and gave them unlimited funding. They requested
<BR>rare chemicals, weird bacteria, tons of quarantine equipment, there
<BR>was a horrible typhus epidemic they started by accident, and, 2 years
<BR>later, they came back with the \"new, improved cow.\" It had a milk
<BR>production improvement of 2% over the original.
<BR>
<BR>They then tried with the greatest Nobel Prize winning chemists around.
<BR>They worked for six months, and, after requisitioning tons of chemical
<BR>equipment, and poisoning half the small town in Colorado where they
<BR>were working with a toxic cloud from one of their experiments, they
<BR>got a 5% improvement in milk output.
<BR>
<BR>The physicists tried for a year, and, after ten thousand cows were
<BR>subjected to radiation therapy, they got a 1% improvement in output.
<BR>
<BR>Finally, in desperation, they turned to the mathematicians. The
<BR>foremost mathematician of his time offered to help them with the
<BR>problem. Upon hearing the problem, he told the delegation that they
<BR>could come back in the morning and he would have solved the problem.
<BR>In the morning, they came back, and he handed them a piece of paper
<BR>with the computations for the new, 300% improved milk cow.
<BR>
<BR>The plans began:
<BR>
<BR>\"A Proof of the Attainability of Increased Milk Output from Bovines:
<BR>
<BR>Consider a spherical cow......\"
<BR>
<BR>
<BR>An engineer, a mathematician, and a physicist went to the races one
<BR>Saturday and laid their money down. Commiserating in the bar after
<BR>the race, the engineer says, \"I don\'t understand why I lost all my
<BR>money. I measured all the horses and calculated their strength and
<BR>mechanical advantage and figured out how fast they could run...\"
<BR>
<BR>The physicist interrupted him: \"...but you didn\'t take individual
<BR>variations into account. I did a statistical analysis of their
<BR>previous performances and bet on the horses with the highest
<BR>probability of winning...\"
<BR>
<BR>\"...so if you\'re so hot why are you broke?\" asked the engineer. But
<BR>before the argument can grow, the mathematician takes out his pipe and
<BR>they get a glimpse of his wellfattened wallet. Obviously here was a
<BR>man who knows something about horses. They both demanded to know his
<BR>secret.
<BR>
<BR>\"Well,\" he says, between puffs on the pipe, \"first I assumed all the
<BR>horses were identical and spherical...\"
<BR>
<BR>
<BR>Theorem : All positive integers are equal.
<BR>
<BR>Proof : Sufficient to show that for any two positive integers, A and B,
<BR>A = B. Further, it is sufficient to show that for all N > 0, if A
<BR>and B (positive integers) satisfy (MAX(A, B) = N) then A = B.
<BR>
<BR>Proceed by induction.
<BR>
<BR>If N = 1, then A and B, being positive integers, must both be 1.
<BR>So A = B.
<BR>
<BR>Assume that the theorem is true for some value k. Take A and B
<BR>with MAX(A, B) = k+1. Then MAX((A1), (B1)) = k. And hence
<BR>(A1) = (B1). Consequently, A = B.
<BR>
<BR>
<BR>A bunch of Polish scientists decided to flee their repressive
<BR>government by hijacking an airliner and forcing the pilot to fly them
<BR>to a western country. They drove to the airport, forced their way on
<BR>board a large passenger jet, and found there was no pilot on board.
<BR>Terrified, they listened as the sirens got louder. Finally, one of
<BR>the scientists suggested that since he was an experimentalist, he
<BR>would try to fly the aircraft.
<BR>
<BR>He sat down at the controls and tried to figure them out. The sirens
<BR>got louder and louder. Armed men surrounded the jet. The would be
<BR>pilot\'s friends cried out, \"Please, please take off now!!!
<BR>Hurry!!!!!!\"
<BR>
<BR>The experimentalist calmly replied, \"Have patience. I\'m just a simple
<BR>pole in a complex plane.\"
<BR>
<BR>
<BR>A group of Polish tourists is flying on a small airplane through the
<BR>Grand Canyon on a sightseeing tour. The tour guide announces: \"On the
<BR>right of the airplane, you can see the famous Bright Angle Falls.\"
<BR>The tourists leap out of their seats and crowd to the windows on the
<BR>right side. This causes a dynamic imbalance, and the plane violently
<BR>rolls to the side and crashes into the canyon wall. All aboard are
<BR>lost. The moral to this episode is: always keep your poles off the
<BR>right side of the plane.
<BR>
<BR>
<BR>Hiawatha Designs an Experiment
<BR>
<BR>Hiawatha, mighty hunter,
<BR>He could shoot ten arrows upward,
<BR>Shoot them with such strength and swiftness
<BR>That the last had left the bowstring
<BR>Ere the first to earth descended.
<BR>
<BR>This was commonly regarded
<BR>As a feat of skill and cunning.
<BR>Several sarcastic spirits
<BR>Pointed out to him, however,
<BR>That it might be much more useful
<BR>If he sometimes hit the target.
<BR>\"Why not shoot a little straighter
<BR>And employ a smaller sample?\"
<BR>Hiawatha, who at college
<BR>Majored in applied statistics,
<BR>Consequently felt entitled
<BR>To instruct his fellow man
<BR>In any subject whatsoever,
<BR>Waxed exceedingly indignant,
<BR>Talked about the law of errors,
<BR>Talked about truncated normals,
<BR>Talked of loss of information,
<BR>Talked about his lack of bias,
<BR>Pointed out that (in the long run)
<BR>Independent observations,
<BR>Even though they missed the target,
<BR>Had an average point of impact
<BR>Very near the spot he aimed at,
<BR>With the possible exception
<BR>of a set of measure zero.
<BR>
<BR>\"This,\" they said, \"was rather doubtful;
<BR>Anyway it didn\'t matter.
<BR>What resulted in the long run:
<BR>Either he must hit the target
<BR>Much more often than at present,
<BR>Or himself would have to pay for
<BR>All the arrows he had wasted.\"
<BR>
<BR>Hiawatha, in a temper,
<BR>Quoted parts of R. A. Fisher,
<BR>Quoted Yates and quoted Finney,
<BR>Quoted reams of Oscar Kempthorne,
<BR>Quoted Anderson and Bancroft
<BR>(practically in extenso)
<BR>Trying to impress upon them
<BR>That what actually mattered
<BR>Was to estimate the error.
<BR>
<BR>Several of them admitted:
<BR>\"Such a thing might have its uses;
<BR>Still,\" they said, \"he would do better
<BR>If he shot a little straighter.\"
<BR>
<BR>Hiawatha, to convince them,
<BR>Organized a shooting contest.
<BR>Laid out in the proper manner
<BR>Of designs experimental
<BR>Recommended in the textbooks,
<BR>Mainly used for tasting tea
<BR>(but sometimes used in other cases)
<BR>Used factorial arrangements
<BR>And the theory of Galois,
<BR>Got a nicely balanced layout
<BR>And successfully confounded
<BR>Second order interactions.
<BR>
<BR>All the other tribal marksmen,
<BR>Ignorant benighted creatures
<BR>Of experimental setups,
<BR>Used their time of preparation
<BR>Putting in a lot of practice
<BR>Merely shooting at the target.
<BR>
<BR>Thus it happened in the contest
<BR>That their scores were most impressive
<BR>With one solitary exception.
<BR>This, I hate to have to say it,
<BR>Was the score of Hiawatha,
<BR>Who as usual shot his arrows,
<BR>Shot them with great strength and swiftness,
<BR>Managing to be unbiased,
<BR>Not however with a salvo
<BR>Managing to hit the target.
<BR>
<BR>\"There!\" they said to Hiawatha,
<BR>\"That is what we all expected.\"
<BR>Hiawatha, nothing daunted,
<BR>Called for pen and called for paper.
<BR>But analysis of variance
<BR>Finally produced the figures
<BR>Showing beyond all peradventure,
<BR>Everybody else was biased.
<BR>And the variance components
<BR>Did not differ from each other\'s,
<BR>Or from Hiawatha\'s.
<BR>(This last point it might be mentioned,
<BR>Would have been much more convincing
<BR>If he hadn\'t been compelled to
<BR>Estimate his own components
<BR>>From experimental plots on
<BR>Which the values all were missing.)
<BR>
<BR>Still they couldn\'t understand it,
<BR>So they couldn\'t raise objections.
<BR>(Which is what so often happens
<BR>with analysis of variance.)
<BR>All the same his fellow tribesmen,
<BR>Ignorant benighted heathens,
<BR>Took away his bow and arrows,
<BR>Said that though my Hiawatha
<BR>Was a brilliant statistician,
<BR>He was useless as a bowman.
<BR>As for variance components
<BR>Several of the more outspoken
<BR>Make primeval observations
<BR>Hurtful of the finer feelings
<BR>Even of the statistician.
<BR>
<BR>In a corner of the forest
<BR>Sits alone my Hiawatha
<BR>Permanently cogitating
<BR>On the normal law of errors.
<BR>Wondering in idle moments
<BR>If perhaps increased precision
<BR>Might perhaps be sometimes better
<BR>Even at the cost of bias,
<BR>If one could thereby now and then
<BR>Register upon a target.
<BR>
<BR>W. E. Mientka, \"Professor Leo Moser  Reflections of a Visit\"
<BR>American Mathematical Monthly, Vol. 79, Number 6 (JuneJuly, 1972)
<BR>
<BR>See also \"Applied Dynamic Programming\" by Bellman and Dreyfuss, prior to 1962.
<BR>
<BR>
<BR>An assemblage of the most gifted minds in the world were all posed the
<BR>following question:
<BR>
<BR>\"What is 2 * 2 ?\"
<BR>
<BR>The engineer whips out his slide rule (so it\'s old) and shuffles it
<BR>back and forth, and finally announces \"3.99\".
<BR>
<BR>The physicist consults his technical references, sets up the problem
<BR>on his computer, and announces \"it lies between 3.98 and 4.02\".
<BR>
<BR>The mathematician cogitates for a while, oblivious to the rest of the
<BR>world, then announces: \"I don\'t what the answer is, but I can tell
<BR>you, an answer exists!\".
<BR>
<BR>Philosopher: \"But what do you _mean_ by 2 * 2 ?\"
<BR>
<BR>Logician: \"Please define 2 * 2 more precisely.\"
<BR>
<BR>Accountant: Closes all the doors and windows, looks around carefully,
<BR>then asks \"What do you _want_ the answer to be?\"
<BR>
<BR>Computer Hacker: Breaks into the NSA supercomputer and gives the answer.
<BR>
<BR>
<BR>Economist: Someone who is good with numbers but lacks the personality
<BR>to be an accountant.
<BR>
<BR>
<BR>Old mathematicians never die; they just lose some of their functions.
<BR>
<BR>
<BR>During a class of calculus my lecturer suddenly checked himself and
<BR>stared intently at the table in front of him for a while. Then he
<BR>looked up at us and explained that he thought he had brought six piles
<BR>of papers with him, but \"no matter how he counted\" there was only five
<BR>on the table. Then he became silent for a while again and then told
<BR>the following story:
<BR>
<BR>\"When I was young in Poland I met the great mathematician Waclaw
<BR>Sierpinski. He was old already then and rather absentminded. Once he
<BR>had to move to a new place for some reason. His wife wife didn\'t trust
<BR>him very much, so when they stood down on the street with all their
<BR>things, she said:
<BR> Now, you stand here and watch our ten trunks, while I go and get a
<BR>taxi.
<BR>
<BR>She left and left him there, eyes somewhat glazed and humming
<BR>absently. Some minutes later she returned, presumably having called
<BR>for a taxi. Says Mr. Sierpinski (possibly with a glint in his eye):
<BR> I thought you said there were ten trunks, but I\'ve only counted to nine.
<BR> No, they\'re TEN!
<BR> No, count them: 0, 1, 2, ...\"
<BR>
<BR>
<BR>What\'s nonorientable and lives in the sea?
<BR>
<BR>Mobius Dick.
<BR>
<BR>
<BR>Philosopher: \"Resolution of the continuum hypothesis will have
<BR>profound implications to all of science.\"
<BR>
<BR>Physicist: \"Not quite. Physics is well on its way without those
<BR>mythical `foundations\'. Just give us serviceable mathematics.\"
<BR>
<BR>Computer Scientist:
<BR>\"Who cares? Everything in this Universe seems to be finite
<BR>anyway. Besides, I\'m too busy debugging my Pascal programs.\"
<BR>
<BR>Mathematician:
<BR>\"Forget all that! Just make your formulae as aesthetically
<BR>pleasing as possible!\"
<BR>
<BR>
<BR>Definition:
<BR>
<BR>Jogging girl scout = Brownian motion.
<BR>
<BR>
<BR>lim sin(x)
<BR>n > oo  = 6
<BR>n
<BR>
<BR>Proof: cancel the n in the numerator and denominator.
<BR>
<BR>
<BR>Two male mathematicians are in a bar.
<BR>
<BR>The first one says to the second that the average person knows very
<BR>little about basic mathematics.
<BR>
<BR>The second one disagrees, and claims that most people can cope with a
<BR>reasonable amount of math.
<BR>
<BR>The first mathematician goes off to the washroom, and in his absence
<BR>the second calls over the waitress.
<BR>
<BR>He tells her that in a few minutes, after his friend has returned, he
<BR>will call her over and ask her a question. All she has to do is
<BR>answer one third x cubed.
<BR>
<BR>She repeats `one thir  dex cue\'? He repeats `one third x cubed\'.
<BR>
<BR>Her: `one thir dex cuebd\'? Yes, that\'s right, he says. So she
<BR>agrees, and goes off mumbling to herself, `one thir dex cuebd...\'.
<BR>
<BR>The first guy returns and the second proposes a bet to prove his
<BR>point, that most people do know something about basic math.
<BR>
<BR>He says he will ask the blonde waitress an integral, and the first
<BR>laughingly agrees.
<BR>
<BR>The second man calls over the waitress and asks `what is the integral
<BR>of x squared?\'.
<BR>
<BR>The waitress says `one third x cubed\' and while walking away, turns
<BR>back and says over her shoulder `plus a constant\'!
<BR>
<BR>
<BR>This was made by Mike Bender and Sarah Herr:
<BR>
<BR>MATHEMATICS PURITY TEST
<BR>
<BR>Count the number of yes\'s, subtract from 60, and divide by 0.6.
<BR>
<BR>
<BR>
<BR>The Basics
<BR>
<BR>1) Have you ever been excited about math?
<BR>2) Had an exciting dream about math?
<BR>3) Made a mathematical calculation?
<BR>4) Manipulated the numerator of an equation?
<BR>5) Manipulated the denominator of an equation?
<BR>6) On your first problem set?
<BR>7) Worked on a problem set past 3:00 a.m.?
<BR><IMG SRC="images/forum/icons/icon_cool.gif"> Worked on a problem set all night?
<BR>9) Had a hard problem?
<BR>10) Worked on a problem continuously for more than 30 minutes?
<BR>11) Worked on a problem continuously for more than four hours?
<BR>12) Done more than one problem set on the same night (i.e. both
<BR>started and finished them)?
<BR>13) Done more than three problem sets on the same night?
<BR>14) Taken a math course for a full year?
<BR>15) Taken two different math courses at the same time?
<BR>16) Done at least one problem set a week for more than four months?
<BR>17) Done at least one problem set a night for more than one month
<BR>(weekends excluded)?
<BR>1<IMG SRC="images/forum/icons/icon_cool.gif"> Done a problem set alone?
<BR>19) Done a problem set in a group of three or more?
<BR>20) Done a problem set in a group of 15 or more?
<BR>21) Was it mixed company?
<BR>22) Have you ever inadvertently walked in upon people doing a problem set?
<BR>23) And joined in afterwards?
<BR>24) Have you ever used food doing a problem set?
<BR>25) Did you eat it all?
<BR>26) Have you ever had a domesticated pet or animal walk over you while you
<BR>were doing a problem set?
<BR>27) Done a problem set in a public place where you might be discovered?
<BR>2<IMG SRC="images/forum/icons/icon_cool.gif"> Been discovered while doing a problem set?
<BR>
<BR>
<BR>Kinky Stuff
<BR>
<BR>29) Have you ever applied your math to a hard science?
<BR>30) Applied your math to a soft science?
<BR>31) Done an integration by parts?
<BR>32) Done two integration by parts in a single problem?
<BR>33) Bounded the domain and range of your function?
<BR>34) Used the domination test for improper integrals?
<BR>35) Done Newton\'s Method?
<BR>36) Done the Method of Frobenius?
<BR>37) Used the Sandwich Theorem?
<BR>3<IMG SRC="images/forum/icons/icon_cool.gif"> Used the Mean Value Theorem?
<BR>39) Used a Gaussian surface?
<BR>40) Used a foreign object on a math problem (eg: calculator)?
<BR>41) Used a program to improve your mathematical technique (eg: MACSYMA)?
<BR>42) Not used brackets when you should have?
<BR>43) Integrated a function over its full period?
<BR>44) Done a calculation in threedimensional space?
<BR>45) Done a calculation in ndimensional space?
<BR>46) Done a change of bases?
<BR>47) Done a change of bases specifically in order to magnify your vector?
<BR>4<IMG SRC="images/forum/icons/icon_cool.gif"> Worked through four complete bases in a single night (eg: using the
<BR>GrahamSchmidt method)?
<BR>49) Inserted a number into an equation?
<BR>50) Calculated the residue of a pole?
<BR>51) Scored perfectly on a math test?
<BR>52) Swallowed everything your professor gave you?
<BR>53) Used explicit notation in your problem set?
<BR>54) Purposefully omitted important steps in your problem set?
<BR>55) Padded your own problem set?
<BR>56) Been blown away on a test?
<BR>57) Blown away your professor on a test?
<BR>5<IMG SRC="images/forum/icons/icon_cool.gif"> Have you ever multiplied 23 by 3?
<BR>59) Have you ever bounded your Bessel function so that the membrane
<BR>did not shoot to infinity?
<BR>69) Have you ever understood the following quote:
<BR>\"The relationship between Z^0 to C_0, B_0, and H_0
<BR>is an example of a general principle which we have
<BR>encountered: the kernel of the adjoint of a linear
<BR>transformation is both the annihilator space of the
<BR>image of the transformation and also the dual space
<BR>of the quotient of the space of which the image is
<BR>a subspace by the image subspace.\"
<BR>(Sternberg & Bamberg\'s _A \"Course\" in Mathematics for
<BR>Students of Physics_, vol. 2)
<BR>
<BR>
<BR>
<BR>
<BR>A somewhat advanced society has figured how to package basic knowledge
<BR>in pill form.
<BR>
<BR>A student, needing some learning, goes to the pharmacy and asks what
<BR>kind of knowledge pills are available. The pharmacist says \"Here\'s a
<BR>pill for English literature.\" The student takes the pill and swallows
<BR>it and has new knowledge about English literature!
<BR>
<BR>\"What else do you have?\" asks the student.
<BR>
<BR>\"Well, I have pills for art history, biology, and world history,\"
<BR>replies the pharmacist.
<BR>
<BR>The student asks for these, and swallows them and has new knowledge
<BR>about those subjects.
<BR>
<BR>Then the student asks, \"Do you have a pill for math?\"
<BR>
<BR>The pharmacist says \"Wait just a moment\", and goes back into the
<BR>storeroom and brings back a whopper of a pill and plunks it on the
<BR>counter.
<BR>
<BR>\"I have to take that huge pill for math?\" inquires the student.
<BR>
<BR>The pharmacist replied \"Well, you know math always was a little hard
<BR>to swallow.\"
<BR>
<BR>
<BR>\"A mathematician is a device for turning coffee into theorems\"
<BR> P. Erdos
<BR>
<BR>
<BR>
<BR>Three standard Peter Lax jokes (heard in his lectures) :
<BR>
<BR>1. What\'s the contour integral around Western Europe?
<BR>Answer: Zero, because all the Poles are in Eastern Europe!
<BR>Addendum: Actually, there ARE some Poles in Western Europe, but
<BR>they are removable!
<BR>
<BR>2. An English mathematician (I forgot who) was asked by his very religious
<BR>colleague:
<BR>Do you believe in one God?
<BR>Answer: Yes, up to isomorphism!
<BR>
<BR>3. What is a compact city?
<BR>It\'s a city that can be guarded by finitely many nearsighted
<BR>policemen!
<BR>
<BR>
<BR>\"Algebraic symbols are used when you do not know what you are talking about.\"
<BR>
<BR>
<BR>Heisenberg might have slept here.
<BR>
<BR>Moebius always does it on the same side.
<BR>
<BR>Statisticians probably do it
<BR>
<BR>Algebraists do it in groups.
<BR>
<BR>(Logicians do it) or [not (logicians do it)].
<BR>
<BR>
<BR>A promising PhD candidate was presenting his thesis at his final
<BR>examination. He proceeded with a derivation and ended up with
<BR>something like:
<BR>
<BR>F = MA
<BR>
<BR>He was embarrassed, his supervising professor was embarrassed, and the
<BR>rest of the committee was embarrassed. The student coughed nervously
<BR>and said \"I seem to have made a slight error back there somewhere.\"
<BR>
<BR>One of the mathematicians on the committee replied dryly, \"Either that
<BR>or an odd number of them!\"
<BR>
<BR>
<BR>There was a mad scientist ( a mad ...social... scientist ) who
<BR>kidnapped three colleagues, an engineer, a physicist, and a
<BR>mathematician, and locked each of them in seperate cells with plenty
<BR>of canned food and water but no can opener.
<BR>
<BR>A month later, returning, the mad scientist went to the engineer\'s
<BR>cell and found it long empty. The engineer had constructed a can
<BR>opener from pocket trash, used aluminum shavings and dried sugar to
<BR>make an explosive, and escaped.
<BR>
<BR>The physicist had worked out the angle necessary to knock the lids off
<BR>the tin cans by throwing them against the wall. She was developing a
<BR>good pitching arm and a new quantum theory.
<BR>
<BR>The mathematician had stacked the unopened cans into a surprising
<BR>solution to the kissing problem; his desiccated corpse was propped
<BR>calmly against a wall, and this was inscribed on the floor in blood:
<BR>
<BR>Theorem: If I can\'t open these cans, I\'ll die.
<BR>
<BR>Proof: assume the opposite...
<BR>
<BR>
<BR>Problem: To Catch a Lion in the Sahara Desert.
<BR>
<BR>(Hunting lions in Africa was originally published as \"A contribution
<BR>to the mathematical theory of big game hunting\" in the American
<BR>Mathematical Monthly in 1938 by \"H. Petard, of Princeton NJ\" [actually
<BR>the late Ralph Boas]. It has been reprinted several times.
<BR>
<BR>1. Mathematical Methods
<BR>
<BR>1.1 The Hilbert (axiomatic) method
<BR>
<BR>We place a locked cage onto a given point in the desert. After that
<BR>we introduce the following logical system:
<BR>Axiom 1: The set of lions in the Sahara is not empty.
<BR>Axiom 2: If there exists a lion in the Sahara, then there exists a
<BR>lion in the cage.
<BR>Procedure: If P is a theorem, and if the following is holds:
<BR>\"P implies Q\", then Q is a theorem.
<BR>Theorem 1: There exists a lion in the cage.
<BR>
<BR>1.2 The geometrical inversion method
<BR>
<BR>We place a spherical cage in the desert, enter it and lock it from
<BR>inside. We then perform an inversion with respect to the cage. Then
<BR>the lion is inside the cage, and we are outside.
<BR>
<BR>1.3 The projective geometry method
<BR>
<BR>Without loss of generality, we can view the desert as a plane surface.
<BR>We project the surface onto a line and afterwards the line onto an
<BR>interior point of the cage. Thereby the lion is mapped onto that same
<BR>point.
<BR>
<BR>1.4 The BolzanoWeierstrass method
<BR>
<BR>Divide the desert by a line running from north to south. The lion is
<BR>then either in the eastern or in the western part. Let\'s assume it is
<BR>in the eastern part. Divide this part by a line running from east to
<BR>west. The lion is either in the northern or in the southern part.
<BR>Let\'s assume it is in the northern part. We can continue this process
<BR>arbitrarily and thereby constructing with each step an increasingly
<BR>narrow fence around the selected area. The diameter of the chosen
<BR>partitions converges to zero so that the lion is caged into a fence of
<BR>arbitrarily small diameter.
<BR>
<BR>1.5 The set theoretical method
<BR>
<BR>We observe that the desert is a separable space. It therefore
<BR>contains an enumerable dense set of points which constitutes a
<BR>sequence with the lion as its limit. We silently approach the lion in
<BR>this sequence, carrying the proper equipment with us.
<BR>
<BR>1.6 The Peano method
<BR>
<BR>In the usual way construct a curve containing every point in the
<BR>desert. It has been proven [1] that such a curve can be traversed in
<BR>arbitrarily short time. Now we traverse the curve, carrying a spear,
<BR>in a time less than what it takes the lion to move a distance equal to
<BR>its own length.
<BR>
<BR>1.7 A topological method
<BR>
<BR>We observe that the lion possesses the topological gender of a torus.
<BR>We embed the desert in a four dimensional space. Then it is possible
<BR>to apply a deformation [2] of such a kind that the lion when returning
<BR>to the three dimensional space is all tied up in itself. It is then
<BR>completely helpless.
<BR>
<BR>1.8 The Cauchy method
<BR>
<BR>We examine a lionvalued function f(z). Be \\zeta the cage. Consider
<BR>the integral
<BR>
<BR>1 [ f(z)
<BR> I  dz
<BR>2 \\pi i ] z  \\zeta
<BR>
<BR>C
<BR>
<BR>where C represents the boundary of the desert. Its value is f(zeta),
<BR>i.e. there is a lion in the cage [3].
<BR>1.9 The WienerTauber method
<BR>
<BR>We obtain a tame lion, L_0, from the class L(\\infinity,\\infinity),
<BR>whose fourier transform vanishes nowhere. We put this lion somewhere
<BR>in the desert. L_0 then converges toward our cage. According to the
<BR>general WienerTauner theorem [4] every other lion L will converge
<BR>toward the same cage. (Alternatively we can approximate L arbitrarily
<BR>close by translating L_0 through the desert [5].)
<BR>
<BR>2 Theoretical Physics Methods
<BR>
<BR>2.1 The Dirac method
<BR>
<BR>We assert that wild lions can ipso facto not be observed in the Sahara
<BR>desert. Therefore, if there are any lions at all in the desert, they
<BR>are tame. We leave catching a tame lion as an exercise to the reader.
<BR>
<BR>2.2 The Schroedinger method
<BR>
<BR>At every instant there is a nonzero probability of the lion being in
<BR>the cage. Sit and wait.
<BR>
<BR>2.3 The Quantum Measurement Method
<BR>
<BR>We assume that the sex of the lion is _ab initio_ indeterminate. The
<BR>wave function for the lion is hence a superposition of the gender
<BR>eigenstate for a lion and that for a lioness. We lay these eigenstates
<BR>out flat on the ground and orthogonal to each other. Since the (male)
<BR>lion has a distinctive mane, the measurement of sex can safely be made
<BR>from a distance, using binoculars. The lion then collapses into one of
<BR>the eigenstates, which is rolled up and placed inside the cage.
<BR>
<BR>2.4 The nuclear physics method
<BR>
<BR>Insert a tame lion into the cage and apply a Majorana exchange
<BR>operator [6] on it and a wild lion.
<BR>
<BR>As a variant let us assume that we would like to catch (for argument\'s
<BR>sake) a male lion. We insert a tame female lion into the cage and
<BR>apply the Heisenberg exchange operator [7], exchanging spins.
<BR>
<BR>2.5 A relativistic method
<BR>
<BR>All over the desert we distribute lion bait containing large amounts
<BR>of the companion star of Sirius. After enough of the bait has been
<BR>eaten we send a beam of light through the desert. This will curl
<BR>around the lion so it gets all confused and can be approached without
<BR>danger.
<BR>
<BR>3 Experimental Physics Methods
<BR>
<BR>3.1 The thermodynamics method
<BR>
<BR>We construct a semipermeable membrane which lets everything but lions
<BR>pass through. This we drag across the desert.
<BR>
<BR>3.2 The atomic fission method
<BR>
<BR>We irradiate the desert with slow neutrons. The lion becomes
<BR>radioactive and starts to disintegrate. Once the disintegration
<BR>process is progressed far enough the lion will be unable to resist.
<BR>
<BR>3.3 The magnetooptical method
<BR>
<BR>We plant a large, lense shaped field with cat mint (nepeta cataria)
<BR>such that its axis is parallel to the direction of the horizontal
<BR>component of the earth\'s magnetic field. We put the cage in one of the
<BR>field\'s foci . Throughout the desert we distribute large amounts of
<BR>magnetized spinach (spinacia oleracea) which has, as everybody knows,
<BR>a high iron content. The spinach is eaten by vegetarian desert
<BR>inhabitants which in turn are eaten by the lions. Afterwards the
<BR>lions are oriented parallel to the earth\'s magnetic field and the
<BR>resulting lion beam is focussed on the cage by the cat mint lense.
<BR>
<BR>[1] After Hilbert, cf. E. W. Hobson, \"The Theory of Functions of a Real
<BR>Variable and the Theory of Fourier\'s Series\" (1927), vol. 1, pp 456457
<BR>[2] H. Seifert and W. Threlfall, \"Lehrbuch der Topologie\" (1934), pp 23
<BR>[3] According to the Picard theorem (W. F. Osgood, Lehrbuch der
<BR>Funktionentheorie, vol 1 (192<IMG SRC="images/forum/icons/icon_cool.gif">, p 17<IMG SRC="images/forum/icons/icon_cool.gif"> it is possible to catch every lion
<BR>except for at most one.
<BR>[4] N. Wiener, \"The Fourier Integral and Certain of its Applications\" (1933),
<BR>pp 7374
<BR>[5] N. Wiener, ibid, p 89
<BR>[6] cf e.g. H. A. Bethe and R. F. Bacher, \"Reviews of Modern Physics\", 8
<BR>(1936), pp 82229, esp. pp 106107
<BR>[7] ibid
<BR>
<BR>
<BR>
<BR>4 Contributions from Computer Science.
<BR>
<BR>4.1 The search method
<BR>
<BR>We assume that the lion is most likely to be found in the direction to
<BR>the north of the point where we are standing. Therefore the REAL
<BR>problem we have is that of speed, since we are only using a PC to
<BR>solve the problem.
<BR>
<BR>4.2 The parallel search method.
<BR>
<BR>By using parallelism we will be able to search in the direction to the
<BR>north much faster than earlier.
<BR>
<BR>4.3 The MonteCarlo method.
<BR>
<BR>We pick a random number indexing the space we search. By excluding
<BR>neighboring points in the search, we can drastically reduce the number
<BR>of points we need to consider. The lion will according to probability
<BR>appear sooner or later.
<BR>
<BR>4.4 The practical approach.
<BR>
<BR>We see a rabbit very close to us. Since it is already dead, it is
<BR>particularly easy to catch. We therefore catch it and call it a lion.
<BR>
<BR>4.5 The common language approach.
<BR>
<BR>If only everyone used ADA/Common Lisp/Prolog, this problem would be
<BR>trivial to solve.
<BR>
<BR>4.6 The standard approach.
<BR>
<BR>We know what a Lion is from ISO 4711/X.123. Since CCITT have specified
<BR>a Lion to be a particular option of a cat we will have to wait for a
<BR>harmonized standard to appear. $20,000,000 have been funded for
<BR>initial investigations into this standard development.
<BR>
<BR>4.7 Linear search.
<BR>
<BR>Stand in the top left hand corner of the Sahara Desert. Take one step
<BR>east. Repeat until you have found the lion, or you reach the right
<BR>hand edge. If you reach the right hand edge, take one step
<BR>southwards, and proceed towards the left hand edge. When you finally
<BR>reach the lion, put it the cage. If the lion should happen to eat you
<BR>before you manage to get it in the cage, press the reset button, and
<BR>try again.
<BR>
<BR>4.8 The Dijkstra approach:
<BR>
<BR>The way the problem reached me was: catch a wild lion in the Sahara
<BR>Desert. Another way of stating the problem is:
<BR>
<BR>Axiom 1: Sahara elem deserts
<BR>Axiom 2: Lion elem Sahara
<BR>Axiom 3: NOT(Lion elem cage)
<BR>
<BR>We observe the following invariant:
<BR>
<BR>P1: C(L) v not(C(L))
<BR>
<BR>where C(L) means: the value of \"L\" is in the cage.
<BR>
<BR>Establishing C initially is trivially accomplished with the statement
<BR>
<BR>;cage := {}
<BR>
<BR>Note 0:
<BR>This is easily implemented by opening the door to the cage and shaking
<BR>out any lions that happen to be there initially.
<BR>(End of note 0.)
<BR>
<BR>The obvious program structure is then:
<BR>
<BR>;cage:={}
<BR>;do NOT (C(L)) >
<BR>;\"approach lion under invariance of P1\"
<BR>;if P(L) >
<BR>;\"insert lion in cage\"
<BR>[] not P(L) >
<BR>;skip
<BR>;fi
<BR>;od
<BR>
<BR>where P(L) means: the value of L is within arm\'s reach.
<BR>
<BR>Note 1:
<BR>Axiom 2 ensures that the loop terminates.
<BR>(End of note 1.)
<BR>
<BR>Exercise 0:
<BR>Refine the step \"Approach lion under invariance of P1\".
<BR>(End of exercise 0.)
<BR>
<BR>Note 2:
<BR>The program is robust in the sense that it will lead to
<BR>abortion if the value of L is \"lioness\".
<BR>(End of note 2.)
<BR>
<BR>Remark 0: This may be a new sense of the word \"robust\" for you.
<BR>(End of remark 0.)
<BR>
<BR>Note 3:
<BR>
<BR>>From observation we can see that the above program leads to the
<BR>desired goal. It goes without saying that we therefore do not have to
<BR>run it.
<BR>(End of note 3.)
<BR>(End of approach.)
<BR>
<BR>
<BR>
<BR>For other articles, see also:
<BR>
<BR>A Random Walk in Science  R.L. Weber and E. Mendoza
<BR>More Random Walks In Science  R.L. Weber and E. Mendoza
<BR>In Mathematical Circles (2 volumes)  Howard Eves
<BR>Mathematical Circles Revisited  Howard Eves
<BR>Mathematical Circles Squared  Howard Eves
<BR>Fantasia Mathematica  Clifton Fadiman
<BR>The Mathematical Magpi  Clifton Fadiman
<BR>Seven Years of Manifold  Jaworski
<BR>The Best of the Journal of Irreproducible Results  George H. Scheer
<BR>Mathematics Made Difficult  Linderholm
<BR>A StressAnalysis of a Strapless Evening Gown  Robert Baker
<BR>The WormRunners Digest
<BR>Knuth\'s April 1984 CACM article on The Space Complexity of Songs
<BR>Stolfi and ?? SIGACT article on Pessimal Algorithms and Simplexity Analysis
<BR>
<BR>
<BR>Not a joke, but a humorous ditty I heard from some guys in an
<BR>engineering fraternity (to the best of my recollection):
<BR>
<BR>I\'ll do it phonetically:
<BR>
<BR>ee to the ex dee ex,
<BR>ee to the why dee why,
<BR>sine x, cosine x,
<BR>natural log of y,
<BR>derivative on the left
<BR>derivative on the right
<BR>integrate, integrate,
<BR>fight! fight! fight!
<BR>
<BR>
<BR>The Programmers\' Cheer 
<BR>
<BR>Shift to the left, shift to the right!
<BR>Pop up, push down, byte, byte, byte!
<BR>
<BR>
<BR>Other cheers:
<BR>
<BR>E to the x dx dy
<BR>radical transcendental pi
<BR>secant cosine tangent sine
<BR>3.14159
<BR>2.71828
<BR>come on folks let\'s integerate!!
<BR>
<BR>
<BR>
<BR>E to the i dx dy
<BR>E to y dy
<BR>cosine secant log of pi
<BR>disintegrate em RPI !!!
<BR>
<BR>
<BR>
<BR>square root, tangent
<BR>hyperbolic sine,
<BR>3.14159
<BR>e to the x, dy, dx,
<BR>sliderule, slipstick, TECH TECH TECH!
<BR>
<BR>
<BR>
<BR>e to the u, du/dx
<BR>e to the x dx
<BR>cosine, secant, tangent, sine,
<BR>3.14159
<BR>integral, radical, u dv,
<BR>slipstick, slide rule, MIT!
<BR>
<BR>
<BR>
<BR>E to the X
<BR>DY, DX
<BR>E to the X
<BR>DX.
<BR>Cosine, Secant, Tangent, Sine
<BR>3.14159
<BR>EI, Radical, Pi
<BR>Fight\'em, Fight\'em, WPI!
<BR>
<BR>Go Worcester Polytechnic Institute!!!!!!
<BR>
<BR>
<BR>Words in {} should be interpreted as greek letters:
<BR>
<BR>Q: I M A {pi}{rho}Maniac. R U 1,2?
<BR>o < read as \"Unot\"
<BR>A: Y ?
<BR>o
<BR>
<BR>(\"I am a pyromaniac. Are you not one, too?\" \"Why not?\")
<BR>
<BR>F U \\{can\\} \\{read\\} Ths U \\{Mst\\} \\{use\\} TeX
<BR>(\"If you can read this, you must use TeX\")
<BR>
<BR>
<BR>Three men are in a hotair balloon. Soon, they find themselves lost
<BR>in a canyon somewhere. One of the three men says, \"I\'ve got an idea.
<BR>We can call for help in this canyon and the echo will carry our voices
<BR>far.\"
<BR>
<BR>So he leans over the basket and yells out, \"Helllloooooo! Where are
<BR>we?\" (They hear the echo several times.)
<BR>
<BR>15 minutes later, they hear this echoing voice: \"Helllloooooo! You\'re
<BR>lost!!\"
<BR>
<BR>One of the men says, \"That must have been a mathematician.\"
<BR>
<BR>Puzzled, one of the other men asks, \"Why do you say that?\"
<BR>
<BR>The reply: \"For three reasons. (1) he took a long time to answer, (2)
<BR>he was absolutely correct, and (3) his answer was absolutely useless.\"
<BR>
<BR>
<BR>Actually, I prefer the IBM version of this joke...
<BR>
<BR>A small, 14seat plane is circling for a landing in Atlanta. It\'s
<BR>totally fogged in, zero visibility, and suddenly there\'s a small
<BR>electrical fire in the cockpit which disables all of the instruments
<BR>and the radio. The pilot continues circling, totally lost, when
<BR>suddenly he finds himself flying next to a tall office building.
<BR>
<BR>He rolls down the window (this particular airplane happens to have
<BR>rolldown windows) and yells to a person inside the building, \"Where
<BR>are we?\"
<BR>
<BR>The person responds \"In an airplane!\"
<BR>
<BR>The pilot then banks sharply to the right, circles twice, and makes a
<BR>perfect landing at Atlanta International.
<BR>
<BR>As the passengers emerge, shaken but unhurt, one of them says to the
<BR>pilot, \"I\'m certainly glad you were able to land safely, but I don\'t
<BR>understand how the response you got was any use.\"
<BR>
<BR>\"Simple,\" responded the pilot. \"I got an answer that was completely
<BR>accurate and totally irrelevant to my problem, so I knew it had to be
<BR>the IBM building.\"
<BR>
<BR>
<BR>(I\'m not sure if the following one is a true story or not)
<BR>The great logician Bertrand Russell (or was it A.N. Whitehead?)
<BR>once claimed that he could prove anything if given that 1+1=1.
<BR>So one day, some smartypants asked him, \"Ok. Prove that
<BR>you\'re the Pope.\"
<BR>He thought for a while and proclaimed, \"I am one. The Pope
<BR>is one. Therefore, the Pope and I are one.\"
<BR>
<BR>[NOTE: The following is from <a href=\"mailto:merritt@Gendev.slc.paramax.com\" target=\"_new\">merritt@Gendev.slc.paramax.com</a> (Merritt).
<BR>The story about 1+1=1 causing ridiculous consequences was, I believe,
<BR>originally the product of a conversation at the Trinity High Table.
<BR>It is recorded in Sir Harold Jeffreys\' Scientific Inference, in a note
<BR>to chapter one. Jeffreys remarks that the fact that everything
<BR>followed from a single contradiction had been noticed by Aristotle (I
<BR>doubt this way of putting it is quite correct, but that is beside the
<BR>point). He goes on to say that McTaggart denied the consequence: \"if
<BR>2+2=5, how can you prove that I am the pope?\" Hardy is supposed to
<BR>have replied: \"if 2+2=5, 4=5; subtract 3; then 1=2; but McTaggart and
<BR>the pope are two; therefore McTaggart and the pope are one.\" When I
<BR>consider this story, I am astonished at how much more brilliant some
<BR>people are than I (quite independent of the fallacies in the
<BR>argument).
<BR>
<BR>Since McTaggart, Hardy, Whitehead, and Russell (the last two of whom
<BR>were credited with a variant of Hardy\'s argument in your post) were
<BR>all fellows of Trinity and Jeffreys (their exact contemporary) was a
<BR>fellow of St. Johns, I suspect that (whatever the truth of Jeffreys\'
<BR>story) it is very unlikely that Whitehead or Russell had anything to do
<BR>with it. The extraordinary point to me about the story is that Hardy
<BR>was able to snap this argument out between mouthfuls, so to speak, and
<BR>he was not even a logician at all. This is probably why it came in
<BR>some people\'s minds to be attributed to one or other of the famous
<BR>Trinity logicians.
<BR>
<BR>
<BR>THE STORY OF BABEL:
<BR>
<BR>In the beginning there was only one kind of Mathematician, created by
<BR>the Great Mathematical Spirit form the Book: the Topologist. And they
<BR>grew to large numbers and prospered.
<BR>
<BR>One day they looked up in the heavens and desired to reach up as far
<BR>as the eye could see. So they set out in building a Mathematical
<BR>edifice that was to reach up as far as \"up\" went. Further and further
<BR>up they went ... until one night the edifice collapsed under the
<BR>weight of paradox.
<BR>
<BR>The following morning saw only rubble where there once was a huge
<BR>structure reaching to the heavens. One by one, the Mathematicians
<BR>climbed out from under the rubble. It was a miracle that nobody was
<BR>killed; but when they began to speak to one another, SUPRISE of all
<BR>surprises! they could not understand each other. They all spoke
<BR>different languages. They all fought amongst themselves and each went
<BR>about their own way. To this day the Topologists remain the original
<BR>Mathematicians.
<BR>
<BR> adapted from an American Indian legend
<BR>of the Mound Of Babel
<BR>
<BR>
<BR>Methods of Mathematical Proof
<BR>
<BR>This is from _A Random Walk in Science_ (by Joel E. Cohen?):
<BR>
<BR>
<BR>To illustrate the various methods of proof we give an example of a
<BR>logical system.
<BR>
<BR>THE PEJORATIVE CALCULUS
<BR>
<BR>Lemma 1. All horses are the same colour.
<BR>(Proof by induction)
<BR>
<BR>Proof. It is obvious that one horse is the same colour. Let us assume
<BR>the proposition P(k) that k horses are the same colour and use this to
<BR>imply that k+1 horses are the same colour. Given the set of k+1 horses,
<BR>we remove one horse; then the remaining k horses are the same colour,
<BR>by hypothesis. We remove another horse and replace the first; the k
<BR>horses, by hypothesis, are again the same colour. We repeat this until
<BR>by exhaustion the k+1 sets of k horses have been shown to be the same
<BR>colour. It follows that since every horse is the same colour as every
<BR>other horse, P(k) entails P(k+1). But since we have shown P(1) to be
<BR>true, P is true for all succeeding values of k, that is, all horses are
<BR>the same colour.
<BR>
<BR>Theorem 1. Every horse has an infinite number of legs.
<BR>(Proof by intimidation.)
<BR>
<BR>Proof. Horses have an even number of legs. Behind they have two legs
<BR>and in front they have fore legs. This makes six legs, which is cer
<BR>tainly an odd number of legs for a horse. But the only number that is
<BR>both odd and even is infinity. Therefore horses have an infinite num
<BR>ber of legs. Now to show that this is general, suppose that somewhere
<BR>there is a horse with a finite number of legs. But that is a horse of
<BR>another colour, and by the lemma that does not exist.
<BR>
<BR>Corollary 1. Everything is the same colour.
<BR>
<BR>Proof. The proof of lemma 1 does not depend at all on the nature of the
<BR>object under consideration. The predicate of the antecedent of the uni
<BR>versallyquantified conditional \'For all x, if x is a horse, then x is
<BR>the same colour,\' namely \'is a horse\' may be generalized to \'is anything\'
<BR>without affecting the validity of the proof; hence, \'for all x, if x is
<BR>anything, x is the same colour.\'
<BR>
<BR>Corollary 2. Everything is white.
<BR>
<BR>Proof. If a sentential formula in x is logically true, then any parti
<BR>cular substitution instance of it is a true sentence. In particular
<BR>then: \'for all x, if x is an elephant, then x is the same colour\' is
<BR>true. Now it is manifestly axiomatic that white elephants exist (for
<BR>proof by blatant assertion consult Mark Twain \'The Stolen White Ele
<BR>phant\'). Therefore all elephants are white. By corollary 1 everything
<BR>is white.
<BR>
<BR>Theorem 2. Alexander the Great did not exist and he had an infinite
<BR>number of limbs.
<BR>
<BR>Proof. We prove this theorem in two parts. First we note the obvious
<BR>fact that historians always tell the truth (for historians always take
<BR>a stand, and therefore they cannot lie). Hence we have the historically
<BR>true sentence, \'If Alexander the Great existed, then he rode a black
<BR>horse Bucephalus.\' But we know by corollary 2 everything is white;
<BR>hence Alexander could not have ridden a black horse. Since the conse
<BR>quent of the conditional is false, in order for the whole statement to
<BR>be true the antecedent must be false. Hence Alexander the Great did not
<BR>exist.
<BR>We have also the historically true statement that Alexander was warned
<BR>by an oracle that he would meet death if he crossed a certain river. He
<BR>had two legs; and \'forewarned is fourarmed.\' This gives him six limbs,
<BR>an even number, which is certainly an odd number of limbs for a man.
<BR>Now the only number which is even and odd is infinity; hence Alexander
<BR>had an infinite number of limbs. We have thus proved that Alexander the
<BR>Great did not exist and that he had an infinite number of limbs.
<BR>
<BR>
<BR>
<BR>
<BR>Not precisely puremath, but ...
<BR>
<BR>Fuller\'s Law of Cosmic Irreversability:
<BR>
<BR>1 pot T > 1 pot P
<BR>but
<BR>1 pot P /> 1 pot T
<BR>
<BR>
<BR>A tribe of Native Americans generally referred to their woman by the
<BR>animal hide with which they made their blanket. Thus, one woman might
<BR>be known as Squaw of Buffalo Hide, while another might be known as
<BR>Squaw of Deer Hide. This tribe had a particularly large and strong
<BR>woman, with a very unique (for North America anyway) animal hide for
<BR>her blanket. This woman was known as Squaw of Hippopotamus hide, and
<BR>she was as large and powerful as the animal from which her blanket was
<BR>made.
<BR>
<BR>Year after year, this woman entered the tribal wrestling tournament,
<BR>and easily defeated all challengers; male or female. As the men of
<BR>the tribe admired her strength and power, this made many of the other
<BR>woman of the tribe extremely jealous. One year, two of the squaws
<BR>petitioned the Chief to allow them to enter their sons together as a
<BR>wrestling tandem in order to wrestle Squaw of the Hippopotamus hide as
<BR>a team. In this way, they hoped to see that she would no longer be
<BR>champion wrestler of the tribe.
<BR>
<BR>As the luck of the draw would have it, the two sons who were wrestling
<BR>as a tandem met the squaw in the final and championship round of the
<BR>wrestling contest. As the match began, it became clear that the squaw
<BR>had finally met an opponent that was her equal. The two sons wrestled
<BR>and struggled vigorously and were clearly on an equal footing with the
<BR>powerful squaw. Their match lasted for hours without a clear victor.
<BR>Finally the chief intervened and declared that, in the interests of
<BR>the health and safety of the wrestlers, the match was to be terminated
<BR>and that he would declare a winner.
<BR>
<BR>The chief retired to his teepee and contemplated the great struggle he
<BR>had witnessed, and found it extremely difficult to decide a winner.
<BR>While the two young men had clearly outmatched the squaw, he found it
<BR>difficult to force the squaw to relinquish her tribal championship.
<BR>After all, it had taken two young men to finally provide her with a
<BR>decent match. Finally, after much deliberation, the chief came out
<BR>from his teepee, and announced his decision. He said...
<BR>
<BR>\"The Squaw of the Hippopotamus hide is equal to the sons of the squaws
<BR>of the other two hides\"
<BR>
<BR>
<BR>A topologist is a man who doesn\'t know the difference between a coffee
<BR>cup and a doughnut.
<BR>
<BR>
<BR>A statistician can have his head in an oven and his feet in ice, and
<BR>he will say that on the average he feels fine.
<BR>
<BR>
<BR>A guy decided to go to the brain transplant clinic to refreshen his
<BR>supply of brains. The secretary informed him that they had three
<BR>kinds of brains available at that time. Doctors\' brains were going
<BR>for $20 per ounce and lawyers\' brains were getting $30 per ounce. And
<BR>then there were mathematicians\' brains which were currently fetching
<BR>$1000 per ounce.
<BR>
<BR>\"A 1000 dollars an ounce!\" he cried. \"Why are they so expensive?\"
<BR>
<BR>\"It takes more mathematicians to get an ounce of brains,\" she explained.
<BR>
<BR>
<BR>A topologist walks into a bar and orders a drink. The bartender,
<BR>being a number theorist, says, \"I\'m sorry, but we don\'t serve
<BR>topologists here.\"
<BR>
<BR>The disgruntled topologist walks outside, but then gets an idea and
<BR>performs Dahn surgery upon herself. She walks into the bar, and the
<BR>bartender, who does not recognize her since she is now a different
<BR>manifold, serves her a drink. However, the bartender thinks she looks
<BR>familiar, or at least locally similar, and asks, \"Aren\'t you that
<BR>topologist that just came in here?\"
<BR>
<BR>To which she responds, \"No, I\'m a frayed knot.\"
<BR>
<BR>
<BR>There are three kinds of people in the world;
<BR>those who can count and those who can\'t.
<BR>
<BR>And the related:
<BR>
<BR>There are two groups of people in the world;
<BR>those who believe that the world can be
<BR>divided into two groups of people,
<BR>and those who don\'t.
<BR>
<BR>And then:
<BR>
<BR>There are two groups of people in the world:
<BR>Those who can be categorized into one of two
<BR>groups of people, and those who can\'t.
<BR>
<BR>
<BR>
<BR>The world is divided into two classes:
<BR>people who say \"The world is divided into two classes\",
<BR>and people who say
<BR>The world is divided into two classes:
<BR>people who say: \"The world is divided into two classes\",
<BR>and people who say:
<BR>The world is divided into two classes:
<BR>people who say ...
<BR>
<BR>
<BR>What follows is a \"quiz\" a student of mine once showed me (which she\'d
<BR>gotten from a previous teacher, etc...). It\'s multiple choice, and if
<BR>you sort the letters (with upper and lower case disjoint) questions
<BR>and answers will come out next to each other. Enjoy...
<BR>
<BR>S. What the acorn said when he grew up
<BR>N. bisects
<BR>u. A dead parrot
<BR>g. center
<BR>F. What you should do when it rains
<BR>R. hypotenuse
<BR>m. A geometer who has been to the beach
<BR>H. coincide
<BR>h. The set of cards is missing
<BR>y. polygon
<BR>A. The boy has a speech defect
<BR>t. secant
<BR>K. How they schedule gym class
<BR>p. tangent
<BR>b. What he did when his motherinlaw wanted to go home
<BR>D. ellipse
<BR>O. The tall kettle boiling on the stove
<BR>W. geometry
<BR>r. Why the girl doesn\'t run a 4minute mile
<BR>j. decagon
<BR>
<BR>
<BR>___ 1. That which Noah built.
<BR>___ 2. An article for serving ice cream.
<BR>___ 3. What a bloodhound does in chasing a woman.
<BR>___ 4. An expression to represent the loss of a parrot.
<BR>___ 5. An appropriate title for a knight named Koal.
<BR>___ 6. A sunburned man.
<BR>___ 7. A tall coffee pot perking.
<BR>___ 8. What one does when it rains.
<BR>___ 9. A dog sitting in a refrigerator.
<BR>___ 10. What a boy does on the lake when his motor won\'t run.
<BR>___ 11. What you call a person who writes for an inn.
<BR>___ 12. What the captain said when the boat was bombed.
<BR>___ 13. What a little acorn says when he grows up.
<BR>___ 14. What one does to trees that are in the way.
<BR>___ 15. What you do if you have yarn and needles.
<BR>___ 16. Can George Washington turn into a country?
<BR>
<BR>
<BR>A. hypotenuse I. circle
<BR>B. polygon J. axiom
<BR>C. inscribe K. cone
<BR>D. geometry L. coincide
<BR>E. unit M. cosecant
<BR>F. center N. tangent
<BR>G. decagone O. hero
<BR>H. arc P. perpendicular
<BR>
<BR>
<BR>
<BR>A team of engineers were required to measure the height of a flag
<BR>pole. They only had a measuring tape, and were getting quite
<BR>frustrated trying to keep the tape along the pole. It kept falling
<BR>down, etc.
<BR>
<BR>A mathematician comes along, finds out their problem, and proceeds to
<BR>remove the pole from the ground and measure it easily.
<BR>
<BR>When he leaves, one engineer says to the other: \"Just like a
<BR>mathematician! We need to know the height, and he gives us the
<BR>length!\"
<BR>
<BR>
<BR>A man camped in a national park, and noticed Mr. Snake and Mrs. Snake
<BR>slithering by. \"Where are all the little snakes?\" he asked. Mr.
<BR>Snake replied, \"We are adders, so we cannot multiply.\"
<BR>
<BR>The following year, the man returned to the same camping spot. This
<BR>time there were a whole batch of little snakes. \"I thought you said
<BR>you could not multiply,\" he said to Mr. Snake. \"Well, the park ranger
<BR>came by and built a log table, so now we can multiply by adding!\"
<BR>
<BR>
<BR>Einstein dies and goes to heaven only to be informed that his room is
<BR>not yet ready. \"I hope you will not mind waiting in a dormitory. We
<BR>are very sorry, but it\'s the best we can do and you will have to share
<BR>the room with others.\" he is told by the doorman (say his name is
<BR>Pete). Einstein says that this is no problem at all and that there is
<BR>no need to make such a great fuss. So Pete leads him to the dorm.
<BR>They enter and Albert is introduced to all of the present
<BR>inhabitants. \"See, Here is your first room mate. He has an IQ of
<BR>180!\"
<BR>\"Why that\'s wonderful!\" Says Albert. \"We can discuss mathematics!\"
<BR>\"And here is your second room mate. His IQ is 150!\"
<BR>\"Why that\'s wonderful!\" Says Albert. \"We can discuss physics!\"
<BR>\"And here is your third room mate. His IQ is 100!\"
<BR>\"That Wonderful! We can discuss the latest plays at the theater!\"
<BR>Just then another man moves out to capture Albert\'s hand and shake it.
<BR>\"I\'m your last room mate and I\'m sorry, but my IQ is only 80.\"
<BR>Albert smiles back at him and says, \"So, where do you think interest
<BR>rates are headed?\"
<BR>
<BR>
<BR>97.3% of all statistics are made up.
<BR>
<BR>
<BR>Did you hear the one about the statistician?
<BR>
<BR>Probably....
<BR>
<BR>
<BR>There was once a very smart horse. Anything that was shown it, it
<BR>mastered easily, until one day, its teachers tried to teach it about
<BR>rectangular coordinates and it couldn\'t understand them. All the
<BR>horse\'s acquaintances and friends tried to figure out what was the
<BR>matter and couldn\'t. Then a new guy (what the heck, a computer
<BR>engineer) looked at the problem and said,
<BR>
<BR>\"Of course he can\'t do it. Why, you\'re putting Descartes before the
<BR>horse!\"
<BR>
<BR>
<BR>TOP TEN EXCUSES FOR NOT DOING THE MATH HOMEWORK
<BR>
<BR>1. I accidentally divided by zero and my paper burst into flames.
<BR>2. Isaac Newton\'s birthday.
<BR>3. I could only get arbitrarily close to my textbook. I couldn\'t
<BR>actually reach it.
<BR>4. I have the proof, but there isn\'t room to write it in this margin.
<BR>5. I was watching the World Series and got tied up trying to prove
<BR>that it converged.
<BR>6. I have a solar powered calculator and it was cloudy.
<BR>7. I locked the paper in my trunk but a fourdimensional dog got in
<BR>and ate it.
<BR>8. I couldn\'t figure out whether i am the square of negative one or
<BR>i is the square root of negative one.
<BR>9. I took time out to snack on a doughnut and a cup of coffee.
<BR>I spent the rest of the night trying to figure which one to dunk.
<BR>10. I could have sworn I put the homework inside a Klein bottle, but
<BR>this morning I couldn\'t find it.
<BR>
<BR>
<BR>The guy gets on a bus and starts threatening everybody: \"I\'ll integrate
<BR>you! I\'ll differentiate you!!!\" So everybody gets scared and runs
<BR>away. Only one person stays. The guy comes up to him and says:
<BR>\"Aren\'t you scared, I\'ll integrate you, I\'ll differentiate you!!!\" And
<BR>the other guy says; \"No, I am not scared, I am e to the x.\"
<BR>
<BR>
<BR>A mathematician went insane and believed that he was the
<BR>differentiation operator. His friends had him placed in a mental
<BR>hospital until he got better. All day he would go around frightening
<BR>the other patients by staring at them and saying \"I differentiate
<BR>you!\"
<BR>
<BR>One day he met a new patient; and true to form he stared at him and
<BR>said \"I differentiate you!\", but for once, his victim\'s expression
<BR>didn\'t change. Surprised, the mathematician marshalled his energies,
<BR>stared fiercely at the new patient and said loudly \"I differentiate
<BR>you!\", but still the other man had no reaction. Finally, in
<BR>frustration, the mathematician screamed out \"I DIFFERENTIATE YOU!\" 
<BR>at which point the new patient calmly looked up and said, \"You can
<BR>differentiate me all you like: I\'m e to the x.\"
<BR>
<BR>
<BR>/
<BR> 1
<BR>  = log cabin
<BR> cabin
<BR>/
<BR>
<BR>Oops, you forgot your constant of integration.
<BR>
<BR>
<BR>/
<BR> 1
<BR>  = log cabin + C
<BR> cabin
<BR>/
<BR>
<BR>And, as we all know,
<BR>
<BR>log cabin + C = houseboat
<BR>
<BR>
<BR>8 5
<BR>If lim  = oo (infinity), then what does lim  = ?
<BR>x>0 x x>0 x
<BR>
<BR>answer: (write 5 on it\'s side)
<BR>
<BR>
<BR>Why did the cat fall off the roof?
<BR>
<BR>Because he lost his mu. (mew=sound cats make, mu=coeff of friction)
<BR>
<BR>
<BR>Boy\'s Life, May 1973:
<BR>
<BR>Ralph: Dad, will you do my math for me tonight?
<BR>Dad: No, son, it wouldn\'t be right.
<BR>Ralph: Well, you could try.
<BR>
<BR>
<BR>Mrs. Johnson the elementary school math teacher was having children do
<BR>problems on the blackboard that day.
<BR>
<BR>``Who would like to do the first problem, addition?\'\'
<BR>
<BR>No one raised their hand. She called on Tommy, and with some help he
<BR>finally got it right.
<BR>
<BR>``Who would like to do the second problem, subtraction?\'\'
<BR>
<BR>Students hid their faces. She called on Mark, who got the problem but
<BR>there was some suspicion his girlfriend Lisa whispered it to him.
<BR>
<BR>``Who would like to do the third problem, division?\'\'
<BR>
<BR>Now a low collective groan could be heard as everyone looked at
<BR>nothing in particular. The teacher called on Suzy, who got it right
<BR>(she has been known to hold back sometimes in front of her friends).
<BR>
<BR>``Who would like to do the last problem, multiplication?\'\'
<BR>
<BR>Tim\'s hand shot up, surprising everyone in the room. Mrs. Johnson
<BR>finally gained her composure in the stunned silence. ``Why the
<BR>enthusiasm, Tim?\'\'
<BR>
<BR>``God said to go fourth and multiply!\'\'
<BR>
<BR>
<BR>Definitions of Terms Commonly Used in Higher Math
<BR>
<BR>The following is a guide to the weary student of mathematics who
<BR>is often confronted with terms which are commonly used but rarely
<BR>defined. In the search for proper definitions for these terms we
<BR>found no authoritative, nor even recognized, source. Thus, we
<BR>followed the advice of mathematicians handed down from time
<BR>immortal: \"Wing It.\"
<BR>
<BR>
<BR>CLEARLY: I don\'t want to write down all the \"in
<BR>between\" steps.
<BR>
<BR>TRIVIAL: If I have to show you how to do this, you\'re
<BR>in the wrong class.
<BR>
<BR>OBVIOUSLY: I hope you weren\'t sleeping when we discussed
<BR>this earlier, because I refuse to repeat it.
<BR>
<BR>RECALL: I shouldn\'t have to tell you this, but for
<BR>those of you who erase your memory tapes
<BR>after every test...
<BR>
<BR>WLOG (Without Loss Of Generality): I\'m not about to do all the
<BR>possible cases, so I\'ll do one and let you
<BR>figure out the rest.
<BR>
<BR>IT CAN EASILY BE SHOWN: Even you, in your finite wisdom, should
<BR>be able to prove this without me holding your
<BR>hand.
<BR>
<BR>CHECK or CHECK FOR YOURSELF: This is the boring part of the
<BR>proof, so you can do it on your own time.
<BR>
<BR>SKETCH OF A PROOF: I couldn\'t verify all the details, so I\'ll
<BR>break it down into the parts I couldn\'t
<BR>prove.
<BR>
<BR>HINT: The hardest of several possible ways to do a
<BR>proof.
<BR>
<BR>BRUTE FORCE (AND IGNORANCE): Four special cases, three counting
<BR>arguments, two long inductions, \"and a
<BR>partridge in a pair tree.\"
<BR>
<BR>SOFT PROOF: One third less filling (of the page) than
<BR>your regular proof, but it requires two extra
<BR>years of course work just to understand the
<BR>terms.
<BR>
<BR>ELEGANT PROOF: Requires no previous knowledge of the subject
<BR>matter and is less than ten lines long.
<BR>
<BR>SIMILARLY: At least one line of the proof of this case is
<BR>the same as before.
<BR>
<BR>CANONICAL FORM: 4 out of 5 mathematicians surveyed
<BR>recommended this as the final form for their
<BR>students who choose to finish.
<BR>
<BR>TFAE (The Following Are Equivalent): If I say this it means that,
<BR>and if I say that it means the other thing,
<BR>and if I say the other thing...
<BR>
<BR>BY A PREVIOUS THEOREM: I don\'t remember how it goes (come to
<BR>think of it I\'m not really sure we did this
<BR>at all), but if I stated it right (or at
<BR>all), then the rest of this follows.
<BR>
<BR>TWO LINE PROOF: I\'ll leave out everything but the conclusion,
<BR>you can\'t question \'em if you can\'t see \'em.
<BR>
<BR>BRIEFLY: I\'m running out of time, so I\'ll just write
<BR>and talk faster.
<BR>
<BR>LET\'S TALK THROUGH IT: I don\'t want to write it on the board lest
<BR>I make a mistake.
<BR>
<BR>PROCEED FORMALLY: Manipulate symbols by the rules without any
<BR>hint of their true meaning (popular in pure
<BR>math courses).
<BR>
<BR>QUANTIFY: I can\'t find anything wrong with your proof
<BR>except that it won\'t work if x is a moon of
<BR>Jupiter (Popular in applied math courses).
<BR>
<BR>PROOF OMITTED: Trust me, It\'s true.
<BR>
<BR>[ Questo Messaggio è stato Modificato da: livingbooks il 04042004 12:07 ]<BR><BR>[ Questo Messaggio è stato Modificato da: livingbooks il 04042004 12:11 ]
<BR>
<BR><DIV style=\"fontsize:0.5pt;fontfamily:Arial\">
<BR>
<BR>The USDA once wanted to make cows produce milk faster, to improve the
<BR>dairy industry.
<BR>
<BR>So, they decided to consult the foremost biologists and recombinant
<BR>DNA technicians to build them a better cow. They assembled this team
<BR>of great scientists, and gave them unlimited funding. They requested
<BR>rare chemicals, weird bacteria, tons of quarantine equipment, there
<BR>was a horrible typhus epidemic they started by accident, and, 2 years
<BR>later, they came back with the \"new, improved cow.\" It had a milk
<BR>production improvement of 2% over the original.
<BR>
<BR>They then tried with the greatest Nobel Prize winning chemists around.
<BR>They worked for six months, and, after requisitioning tons of chemical
<BR>equipment, and poisoning half the small town in Colorado where they
<BR>were working with a toxic cloud from one of their experiments, they
<BR>got a 5% improvement in milk output.
<BR>
<BR>The physicists tried for a year, and, after ten thousand cows were
<BR>subjected to radiation therapy, they got a 1% improvement in output.
<BR>
<BR>Finally, in desperation, they turned to the mathematicians. The
<BR>foremost mathematician of his time offered to help them with the
<BR>problem. Upon hearing the problem, he told the delegation that they
<BR>could come back in the morning and he would have solved the problem.
<BR>In the morning, they came back, and he handed them a piece of paper
<BR>with the computations for the new, 300% improved milk cow.
<BR>
<BR>The plans began:
<BR>
<BR>\"A Proof of the Attainability of Increased Milk Output from Bovines:
<BR>
<BR>Consider a spherical cow......\"
<BR>
<BR>
<BR>An engineer, a mathematician, and a physicist went to the races one
<BR>Saturday and laid their money down. Commiserating in the bar after
<BR>the race, the engineer says, \"I don\'t understand why I lost all my
<BR>money. I measured all the horses and calculated their strength and
<BR>mechanical advantage and figured out how fast they could run...\"
<BR>
<BR>The physicist interrupted him: \"...but you didn\'t take individual
<BR>variations into account. I did a statistical analysis of their
<BR>previous performances and bet on the horses with the highest
<BR>probability of winning...\"
<BR>
<BR>\"...so if you\'re so hot why are you broke?\" asked the engineer. But
<BR>before the argument can grow, the mathematician takes out his pipe and
<BR>they get a glimpse of his wellfattened wallet. Obviously here was a
<BR>man who knows something about horses. They both demanded to know his
<BR>secret.
<BR>
<BR>\"Well,\" he says, between puffs on the pipe, \"first I assumed all the
<BR>horses were identical and spherical...\"
<BR>
<BR>
<BR>Theorem : All positive integers are equal.
<BR>
<BR>Proof : Sufficient to show that for any two positive integers, A and B,
<BR>A = B. Further, it is sufficient to show that for all N > 0, if A
<BR>and B (positive integers) satisfy (MAX(A, B) = N) then A = B.
<BR>
<BR>Proceed by induction.
<BR>
<BR>If N = 1, then A and B, being positive integers, must both be 1.
<BR>So A = B.
<BR>
<BR>Assume that the theorem is true for some value k. Take A and B
<BR>with MAX(A, B) = k+1. Then MAX((A1), (B1)) = k. And hence
<BR>(A1) = (B1). Consequently, A = B.
<BR>
<BR>
<BR>A bunch of Polish scientists decided to flee their repressive
<BR>government by hijacking an airliner and forcing the pilot to fly them
<BR>to a western country. They drove to the airport, forced their way on
<BR>board a large passenger jet, and found there was no pilot on board.
<BR>Terrified, they listened as the sirens got louder. Finally, one of
<BR>the scientists suggested that since he was an experimentalist, he
<BR>would try to fly the aircraft.
<BR>
<BR>He sat down at the controls and tried to figure them out. The sirens
<BR>got louder and louder. Armed men surrounded the jet. The would be
<BR>pilot\'s friends cried out, \"Please, please take off now!!!
<BR>Hurry!!!!!!\"
<BR>
<BR>The experimentalist calmly replied, \"Have patience. I\'m just a simple
<BR>pole in a complex plane.\"
<BR>
<BR>
<BR>A group of Polish tourists is flying on a small airplane through the
<BR>Grand Canyon on a sightseeing tour. The tour guide announces: \"On the
<BR>right of the airplane, you can see the famous Bright Angle Falls.\"
<BR>The tourists leap out of their seats and crowd to the windows on the
<BR>right side. This causes a dynamic imbalance, and the plane violently
<BR>rolls to the side and crashes into the canyon wall. All aboard are
<BR>lost. The moral to this episode is: always keep your poles off the
<BR>right side of the plane.
<BR>
<BR>
<BR>Hiawatha Designs an Experiment
<BR>
<BR>Hiawatha, mighty hunter,
<BR>He could shoot ten arrows upward,
<BR>Shoot them with such strength and swiftness
<BR>That the last had left the bowstring
<BR>Ere the first to earth descended.
<BR>
<BR>This was commonly regarded
<BR>As a feat of skill and cunning.
<BR>Several sarcastic spirits
<BR>Pointed out to him, however,
<BR>That it might be much more useful
<BR>If he sometimes hit the target.
<BR>\"Why not shoot a little straighter
<BR>And employ a smaller sample?\"
<BR>Hiawatha, who at college
<BR>Majored in applied statistics,
<BR>Consequently felt entitled
<BR>To instruct his fellow man
<BR>In any subject whatsoever,
<BR>Waxed exceedingly indignant,
<BR>Talked about the law of errors,
<BR>Talked about truncated normals,
<BR>Talked of loss of information,
<BR>Talked about his lack of bias,
<BR>Pointed out that (in the long run)
<BR>Independent observations,
<BR>Even though they missed the target,
<BR>Had an average point of impact
<BR>Very near the spot he aimed at,
<BR>With the possible exception
<BR>of a set of measure zero.
<BR>
<BR>\"This,\" they said, \"was rather doubtful;
<BR>Anyway it didn\'t matter.
<BR>What resulted in the long run:
<BR>Either he must hit the target
<BR>Much more often than at present,
<BR>Or himself would have to pay for
<BR>All the arrows he had wasted.\"
<BR>
<BR>Hiawatha, in a temper,
<BR>Quoted parts of R. A. Fisher,
<BR>Quoted Yates and quoted Finney,
<BR>Quoted reams of Oscar Kempthorne,
<BR>Quoted Anderson and Bancroft
<BR>(practically in extenso)
<BR>Trying to impress upon them
<BR>That what actually mattered
<BR>Was to estimate the error.
<BR>
<BR>Several of them admitted:
<BR>\"Such a thing might have its uses;
<BR>Still,\" they said, \"he would do better
<BR>If he shot a little straighter.\"
<BR>
<BR>Hiawatha, to convince them,
<BR>Organized a shooting contest.
<BR>Laid out in the proper manner
<BR>Of designs experimental
<BR>Recommended in the textbooks,
<BR>Mainly used for tasting tea
<BR>(but sometimes used in other cases)
<BR>Used factorial arrangements
<BR>And the theory of Galois,
<BR>Got a nicely balanced layout
<BR>And successfully confounded
<BR>Second order interactions.
<BR>
<BR>All the other tribal marksmen,
<BR>Ignorant benighted creatures
<BR>Of experimental setups,
<BR>Used their time of preparation
<BR>Putting in a lot of practice
<BR>Merely shooting at the target.
<BR>
<BR>Thus it happened in the contest
<BR>That their scores were most impressive
<BR>With one solitary exception.
<BR>This, I hate to have to say it,
<BR>Was the score of Hiawatha,
<BR>Who as usual shot his arrows,
<BR>Shot them with great strength and swiftness,
<BR>Managing to be unbiased,
<BR>Not however with a salvo
<BR>Managing to hit the target.
<BR>
<BR>\"There!\" they said to Hiawatha,
<BR>\"That is what we all expected.\"
<BR>Hiawatha, nothing daunted,
<BR>Called for pen and called for paper.
<BR>But analysis of variance
<BR>Finally produced the figures
<BR>Showing beyond all peradventure,
<BR>Everybody else was biased.
<BR>And the variance components
<BR>Did not differ from each other\'s,
<BR>Or from Hiawatha\'s.
<BR>(This last point it might be mentioned,
<BR>Would have been much more convincing
<BR>If he hadn\'t been compelled to
<BR>Estimate his own components
<BR>>From experimental plots on
<BR>Which the values all were missing.)
<BR>
<BR>Still they couldn\'t understand it,
<BR>So they couldn\'t raise objections.
<BR>(Which is what so often happens
<BR>with analysis of variance.)
<BR>All the same his fellow tribesmen,
<BR>Ignorant benighted heathens,
<BR>Took away his bow and arrows,
<BR>Said that though my Hiawatha
<BR>Was a brilliant statistician,
<BR>He was useless as a bowman.
<BR>As for variance components
<BR>Several of the more outspoken
<BR>Make primeval observations
<BR>Hurtful of the finer feelings
<BR>Even of the statistician.
<BR>
<BR>In a corner of the forest
<BR>Sits alone my Hiawatha
<BR>Permanently cogitating
<BR>On the normal law of errors.
<BR>Wondering in idle moments
<BR>If perhaps increased precision
<BR>Might perhaps be sometimes better
<BR>Even at the cost of bias,
<BR>If one could thereby now and then
<BR>Register upon a target.
<BR>
<BR>W. E. Mientka, \"Professor Leo Moser  Reflections of a Visit\"
<BR>American Mathematical Monthly, Vol. 79, Number 6 (JuneJuly, 1972)
<BR>
<BR>See also \"Applied Dynamic Programming\" by Bellman and Dreyfuss, prior to 1962.
<BR>
<BR>
<BR>An assemblage of the most gifted minds in the world were all posed the
<BR>following question:
<BR>
<BR>\"What is 2 * 2 ?\"
<BR>
<BR>The engineer whips out his slide rule (so it\'s old) and shuffles it
<BR>back and forth, and finally announces \"3.99\".
<BR>
<BR>The physicist consults his technical references, sets up the problem
<BR>on his computer, and announces \"it lies between 3.98 and 4.02\".
<BR>
<BR>The mathematician cogitates for a while, oblivious to the rest of the
<BR>world, then announces: \"I don\'t what the answer is, but I can tell
<BR>you, an answer exists!\".
<BR>
<BR>Philosopher: \"But what do you _mean_ by 2 * 2 ?\"
<BR>
<BR>Logician: \"Please define 2 * 2 more precisely.\"
<BR>
<BR>Accountant: Closes all the doors and windows, looks around carefully,
<BR>then asks \"What do you _want_ the answer to be?\"
<BR>
<BR>Computer Hacker: Breaks into the NSA supercomputer and gives the answer.
<BR>
<BR>
<BR>Economist: Someone who is good with numbers but lacks the personality
<BR>to be an accountant.
<BR>
<BR>
<BR>Old mathematicians never die; they just lose some of their functions.
<BR>
<BR>
<BR>During a class of calculus my lecturer suddenly checked himself and
<BR>stared intently at the table in front of him for a while. Then he
<BR>looked up at us and explained that he thought he had brought six piles
<BR>of papers with him, but \"no matter how he counted\" there was only five
<BR>on the table. Then he became silent for a while again and then told
<BR>the following story:
<BR>
<BR>\"When I was young in Poland I met the great mathematician Waclaw
<BR>Sierpinski. He was old already then and rather absentminded. Once he
<BR>had to move to a new place for some reason. His wife wife didn\'t trust
<BR>him very much, so when they stood down on the street with all their
<BR>things, she said:
<BR> Now, you stand here and watch our ten trunks, while I go and get a
<BR>taxi.
<BR>
<BR>She left and left him there, eyes somewhat glazed and humming
<BR>absently. Some minutes later she returned, presumably having called
<BR>for a taxi. Says Mr. Sierpinski (possibly with a glint in his eye):
<BR> I thought you said there were ten trunks, but I\'ve only counted to nine.
<BR> No, they\'re TEN!
<BR> No, count them: 0, 1, 2, ...\"
<BR>
<BR>
<BR>What\'s nonorientable and lives in the sea?
<BR>
<BR>Mobius Dick.
<BR>
<BR>
<BR>Philosopher: \"Resolution of the continuum hypothesis will have
<BR>profound implications to all of science.\"
<BR>
<BR>Physicist: \"Not quite. Physics is well on its way without those
<BR>mythical `foundations\'. Just give us serviceable mathematics.\"
<BR>
<BR>Computer Scientist:
<BR>\"Who cares? Everything in this Universe seems to be finite
<BR>anyway. Besides, I\'m too busy debugging my Pascal programs.\"
<BR>
<BR>Mathematician:
<BR>\"Forget all that! Just make your formulae as aesthetically
<BR>pleasing as possible!\"
<BR>
<BR>
<BR>Definition:
<BR>
<BR>Jogging girl scout = Brownian motion.
<BR>
<BR>
<BR>lim sin(x)
<BR>n > oo  = 6
<BR>n
<BR>
<BR>Proof: cancel the n in the numerator and denominator.
<BR>
<BR>
<BR>Two male mathematicians are in a bar.
<BR>
<BR>The first one says to the second that the average person knows very
<BR>little about basic mathematics.
<BR>
<BR>The second one disagrees, and claims that most people can cope with a
<BR>reasonable amount of math.
<BR>
<BR>The first mathematician goes off to the washroom, and in his absence
<BR>the second calls over the waitress.
<BR>
<BR>He tells her that in a few minutes, after his friend has returned, he
<BR>will call her over and ask her a question. All she has to do is
<BR>answer one third x cubed.
<BR>
<BR>She repeats `one thir  dex cue\'? He repeats `one third x cubed\'.
<BR>
<BR>Her: `one thir dex cuebd\'? Yes, that\'s right, he says. So she
<BR>agrees, and goes off mumbling to herself, `one thir dex cuebd...\'.
<BR>
<BR>The first guy returns and the second proposes a bet to prove his
<BR>point, that most people do know something about basic math.
<BR>
<BR>He says he will ask the blonde waitress an integral, and the first
<BR>laughingly agrees.
<BR>
<BR>The second man calls over the waitress and asks `what is the integral
<BR>of x squared?\'.
<BR>
<BR>The waitress says `one third x cubed\' and while walking away, turns
<BR>back and says over her shoulder `plus a constant\'!
<BR>
<BR>
<BR>This was made by Mike Bender and Sarah Herr:
<BR>
<BR>MATHEMATICS PURITY TEST
<BR>
<BR>Count the number of yes\'s, subtract from 60, and divide by 0.6.
<BR>
<BR>
<BR>
<BR>The Basics
<BR>
<BR>1) Have you ever been excited about math?
<BR>2) Had an exciting dream about math?
<BR>3) Made a mathematical calculation?
<BR>4) Manipulated the numerator of an equation?
<BR>5) Manipulated the denominator of an equation?
<BR>6) On your first problem set?
<BR>7) Worked on a problem set past 3:00 a.m.?
<BR><IMG SRC="images/forum/icons/icon_cool.gif"> Worked on a problem set all night?
<BR>9) Had a hard problem?
<BR>10) Worked on a problem continuously for more than 30 minutes?
<BR>11) Worked on a problem continuously for more than four hours?
<BR>12) Done more than one problem set on the same night (i.e. both
<BR>started and finished them)?
<BR>13) Done more than three problem sets on the same night?
<BR>14) Taken a math course for a full year?
<BR>15) Taken two different math courses at the same time?
<BR>16) Done at least one problem set a week for more than four months?
<BR>17) Done at least one problem set a night for more than one month
<BR>(weekends excluded)?
<BR>1<IMG SRC="images/forum/icons/icon_cool.gif"> Done a problem set alone?
<BR>19) Done a problem set in a group of three or more?
<BR>20) Done a problem set in a group of 15 or more?
<BR>21) Was it mixed company?
<BR>22) Have you ever inadvertently walked in upon people doing a problem set?
<BR>23) And joined in afterwards?
<BR>24) Have you ever used food doing a problem set?
<BR>25) Did you eat it all?
<BR>26) Have you ever had a domesticated pet or animal walk over you while you
<BR>were doing a problem set?
<BR>27) Done a problem set in a public place where you might be discovered?
<BR>2<IMG SRC="images/forum/icons/icon_cool.gif"> Been discovered while doing a problem set?
<BR>
<BR>
<BR>Kinky Stuff
<BR>
<BR>29) Have you ever applied your math to a hard science?
<BR>30) Applied your math to a soft science?
<BR>31) Done an integration by parts?
<BR>32) Done two integration by parts in a single problem?
<BR>33) Bounded the domain and range of your function?
<BR>34) Used the domination test for improper integrals?
<BR>35) Done Newton\'s Method?
<BR>36) Done the Method of Frobenius?
<BR>37) Used the Sandwich Theorem?
<BR>3<IMG SRC="images/forum/icons/icon_cool.gif"> Used the Mean Value Theorem?
<BR>39) Used a Gaussian surface?
<BR>40) Used a foreign object on a math problem (eg: calculator)?
<BR>41) Used a program to improve your mathematical technique (eg: MACSYMA)?
<BR>42) Not used brackets when you should have?
<BR>43) Integrated a function over its full period?
<BR>44) Done a calculation in threedimensional space?
<BR>45) Done a calculation in ndimensional space?
<BR>46) Done a change of bases?
<BR>47) Done a change of bases specifically in order to magnify your vector?
<BR>4<IMG SRC="images/forum/icons/icon_cool.gif"> Worked through four complete bases in a single night (eg: using the
<BR>GrahamSchmidt method)?
<BR>49) Inserted a number into an equation?
<BR>50) Calculated the residue of a pole?
<BR>51) Scored perfectly on a math test?
<BR>52) Swallowed everything your professor gave you?
<BR>53) Used explicit notation in your problem set?
<BR>54) Purposefully omitted important steps in your problem set?
<BR>55) Padded your own problem set?
<BR>56) Been blown away on a test?
<BR>57) Blown away your professor on a test?
<BR>5<IMG SRC="images/forum/icons/icon_cool.gif"> Have you ever multiplied 23 by 3?
<BR>59) Have you ever bounded your Bessel function so that the membrane
<BR>did not shoot to infinity?
<BR>69) Have you ever understood the following quote:
<BR>\"The relationship between Z^0 to C_0, B_0, and H_0
<BR>is an example of a general principle which we have
<BR>encountered: the kernel of the adjoint of a linear
<BR>transformation is both the annihilator space of the
<BR>image of the transformation and also the dual space
<BR>of the quotient of the space of which the image is
<BR>a subspace by the image subspace.\"
<BR>(Sternberg & Bamberg\'s _A \"Course\" in Mathematics for
<BR>Students of Physics_, vol. 2)
<BR>
<BR>
<BR>
<BR>
<BR>A somewhat advanced society has figured how to package basic knowledge
<BR>in pill form.
<BR>
<BR>A student, needing some learning, goes to the pharmacy and asks what
<BR>kind of knowledge pills are available. The pharmacist says \"Here\'s a
<BR>pill for English literature.\" The student takes the pill and swallows
<BR>it and has new knowledge about English literature!
<BR>
<BR>\"What else do you have?\" asks the student.
<BR>
<BR>\"Well, I have pills for art history, biology, and world history,\"
<BR>replies the pharmacist.
<BR>
<BR>The student asks for these, and swallows them and has new knowledge
<BR>about those subjects.
<BR>
<BR>Then the student asks, \"Do you have a pill for math?\"
<BR>
<BR>The pharmacist says \"Wait just a moment\", and goes back into the
<BR>storeroom and brings back a whopper of a pill and plunks it on the
<BR>counter.
<BR>
<BR>\"I have to take that huge pill for math?\" inquires the student.
<BR>
<BR>The pharmacist replied \"Well, you know math always was a little hard
<BR>to swallow.\"
<BR>
<BR>
<BR>\"A mathematician is a device for turning coffee into theorems\"
<BR> P. Erdos
<BR>
<BR>
<BR>
<BR>Three standard Peter Lax jokes (heard in his lectures) :
<BR>
<BR>1. What\'s the contour integral around Western Europe?
<BR>Answer: Zero, because all the Poles are in Eastern Europe!
<BR>Addendum: Actually, there ARE some Poles in Western Europe, but
<BR>they are removable!
<BR>
<BR>2. An English mathematician (I forgot who) was asked by his very religious
<BR>colleague:
<BR>Do you believe in one God?
<BR>Answer: Yes, up to isomorphism!
<BR>
<BR>3. What is a compact city?
<BR>It\'s a city that can be guarded by finitely many nearsighted
<BR>policemen!
<BR>
<BR>
<BR>\"Algebraic symbols are used when you do not know what you are talking about.\"
<BR>
<BR>
<BR>Heisenberg might have slept here.
<BR>
<BR>Moebius always does it on the same side.
<BR>
<BR>Statisticians probably do it
<BR>
<BR>Algebraists do it in groups.
<BR>
<BR>(Logicians do it) or [not (logicians do it)].
<BR>
<BR>
<BR>A promising PhD candidate was presenting his thesis at his final
<BR>examination. He proceeded with a derivation and ended up with
<BR>something like:
<BR>
<BR>F = MA
<BR>
<BR>He was embarrassed, his supervising professor was embarrassed, and the
<BR>rest of the committee was embarrassed. The student coughed nervously
<BR>and said \"I seem to have made a slight error back there somewhere.\"
<BR>
<BR>One of the mathematicians on the committee replied dryly, \"Either that
<BR>or an odd number of them!\"
<BR>
<BR>
<BR>There was a mad scientist ( a mad ...social... scientist ) who
<BR>kidnapped three colleagues, an engineer, a physicist, and a
<BR>mathematician, and locked each of them in seperate cells with plenty
<BR>of canned food and water but no can opener.
<BR>
<BR>A month later, returning, the mad scientist went to the engineer\'s
<BR>cell and found it long empty. The engineer had constructed a can
<BR>opener from pocket trash, used aluminum shavings and dried sugar to
<BR>make an explosive, and escaped.
<BR>
<BR>The physicist had worked out the angle necessary to knock the lids off
<BR>the tin cans by throwing them against the wall. She was developing a
<BR>good pitching arm and a new quantum theory.
<BR>
<BR>The mathematician had stacked the unopened cans into a surprising
<BR>solution to the kissing problem; his desiccated corpse was propped
<BR>calmly against a wall, and this was inscribed on the floor in blood:
<BR>
<BR>Theorem: If I can\'t open these cans, I\'ll die.
<BR>
<BR>Proof: assume the opposite...
<BR>
<BR>
<BR>Problem: To Catch a Lion in the Sahara Desert.
<BR>
<BR>(Hunting lions in Africa was originally published as \"A contribution
<BR>to the mathematical theory of big game hunting\" in the American
<BR>Mathematical Monthly in 1938 by \"H. Petard, of Princeton NJ\" [actually
<BR>the late Ralph Boas]. It has been reprinted several times.
<BR>
<BR>1. Mathematical Methods
<BR>
<BR>1.1 The Hilbert (axiomatic) method
<BR>
<BR>We place a locked cage onto a given point in the desert. After that
<BR>we introduce the following logical system:
<BR>Axiom 1: The set of lions in the Sahara is not empty.
<BR>Axiom 2: If there exists a lion in the Sahara, then there exists a
<BR>lion in the cage.
<BR>Procedure: If P is a theorem, and if the following is holds:
<BR>\"P implies Q\", then Q is a theorem.
<BR>Theorem 1: There exists a lion in the cage.
<BR>
<BR>1.2 The geometrical inversion method
<BR>
<BR>We place a spherical cage in the desert, enter it and lock it from
<BR>inside. We then perform an inversion with respect to the cage. Then
<BR>the lion is inside the cage, and we are outside.
<BR>
<BR>1.3 The projective geometry method
<BR>
<BR>Without loss of generality, we can view the desert as a plane surface.
<BR>We project the surface onto a line and afterwards the line onto an
<BR>interior point of the cage. Thereby the lion is mapped onto that same
<BR>point.
<BR>
<BR>1.4 The BolzanoWeierstrass method
<BR>
<BR>Divide the desert by a line running from north to south. The lion is
<BR>then either in the eastern or in the western part. Let\'s assume it is
<BR>in the eastern part. Divide this part by a line running from east to
<BR>west. The lion is either in the northern or in the southern part.
<BR>Let\'s assume it is in the northern part. We can continue this process
<BR>arbitrarily and thereby constructing with each step an increasingly
<BR>narrow fence around the selected area. The diameter of the chosen
<BR>partitions converges to zero so that the lion is caged into a fence of
<BR>arbitrarily small diameter.
<BR>
<BR>1.5 The set theoretical method
<BR>
<BR>We observe that the desert is a separable space. It therefore
<BR>contains an enumerable dense set of points which constitutes a
<BR>sequence with the lion as its limit. We silently approach the lion in
<BR>this sequence, carrying the proper equipment with us.
<BR>
<BR>1.6 The Peano method
<BR>
<BR>In the usual way construct a curve containing every point in the
<BR>desert. It has been proven [1] that such a curve can be traversed in
<BR>arbitrarily short time. Now we traverse the curve, carrying a spear,
<BR>in a time less than what it takes the lion to move a distance equal to
<BR>its own length.
<BR>
<BR>1.7 A topological method
<BR>
<BR>We observe that the lion possesses the topological gender of a torus.
<BR>We embed the desert in a four dimensional space. Then it is possible
<BR>to apply a deformation [2] of such a kind that the lion when returning
<BR>to the three dimensional space is all tied up in itself. It is then
<BR>completely helpless.
<BR>
<BR>1.8 The Cauchy method
<BR>
<BR>We examine a lionvalued function f(z). Be \\zeta the cage. Consider
<BR>the integral
<BR>
<BR>1 [ f(z)
<BR> I  dz
<BR>2 \\pi i ] z  \\zeta
<BR>
<BR>C
<BR>
<BR>where C represents the boundary of the desert. Its value is f(zeta),
<BR>i.e. there is a lion in the cage [3].
<BR>1.9 The WienerTauber method
<BR>
<BR>We obtain a tame lion, L_0, from the class L(\\infinity,\\infinity),
<BR>whose fourier transform vanishes nowhere. We put this lion somewhere
<BR>in the desert. L_0 then converges toward our cage. According to the
<BR>general WienerTauner theorem [4] every other lion L will converge
<BR>toward the same cage. (Alternatively we can approximate L arbitrarily
<BR>close by translating L_0 through the desert [5].)
<BR>
<BR>2 Theoretical Physics Methods
<BR>
<BR>2.1 The Dirac method
<BR>
<BR>We assert that wild lions can ipso facto not be observed in the Sahara
<BR>desert. Therefore, if there are any lions at all in the desert, they
<BR>are tame. We leave catching a tame lion as an exercise to the reader.
<BR>
<BR>2.2 The Schroedinger method
<BR>
<BR>At every instant there is a nonzero probability of the lion being in
<BR>the cage. Sit and wait.
<BR>
<BR>2.3 The Quantum Measurement Method
<BR>
<BR>We assume that the sex of the lion is _ab initio_ indeterminate. The
<BR>wave function for the lion is hence a superposition of the gender
<BR>eigenstate for a lion and that for a lioness. We lay these eigenstates
<BR>out flat on the ground and orthogonal to each other. Since the (male)
<BR>lion has a distinctive mane, the measurement of sex can safely be made
<BR>from a distance, using binoculars. The lion then collapses into one of
<BR>the eigenstates, which is rolled up and placed inside the cage.
<BR>
<BR>2.4 The nuclear physics method
<BR>
<BR>Insert a tame lion into the cage and apply a Majorana exchange
<BR>operator [6] on it and a wild lion.
<BR>
<BR>As a variant let us assume that we would like to catch (for argument\'s
<BR>sake) a male lion. We insert a tame female lion into the cage and
<BR>apply the Heisenberg exchange operator [7], exchanging spins.
<BR>
<BR>2.5 A relativistic method
<BR>
<BR>All over the desert we distribute lion bait containing large amounts
<BR>of the companion star of Sirius. After enough of the bait has been
<BR>eaten we send a beam of light through the desert. This will curl
<BR>around the lion so it gets all confused and can be approached without
<BR>danger.
<BR>
<BR>3 Experimental Physics Methods
<BR>
<BR>3.1 The thermodynamics method
<BR>
<BR>We construct a semipermeable membrane which lets everything but lions
<BR>pass through. This we drag across the desert.
<BR>
<BR>3.2 The atomic fission method
<BR>
<BR>We irradiate the desert with slow neutrons. The lion becomes
<BR>radioactive and starts to disintegrate. Once the disintegration
<BR>process is progressed far enough the lion will be unable to resist.
<BR>
<BR>3.3 The magnetooptical method
<BR>
<BR>We plant a large, lense shaped field with cat mint (nepeta cataria)
<BR>such that its axis is parallel to the direction of the horizontal
<BR>component of the earth\'s magnetic field. We put the cage in one of the
<BR>field\'s foci . Throughout the desert we distribute large amounts of
<BR>magnetized spinach (spinacia oleracea) which has, as everybody knows,
<BR>a high iron content. The spinach is eaten by vegetarian desert
<BR>inhabitants which in turn are eaten by the lions. Afterwards the
<BR>lions are oriented parallel to the earth\'s magnetic field and the
<BR>resulting lion beam is focussed on the cage by the cat mint lense.
<BR>
<BR>[1] After Hilbert, cf. E. W. Hobson, \"The Theory of Functions of a Real
<BR>Variable and the Theory of Fourier\'s Series\" (1927), vol. 1, pp 456457
<BR>[2] H. Seifert and W. Threlfall, \"Lehrbuch der Topologie\" (1934), pp 23
<BR>[3] According to the Picard theorem (W. F. Osgood, Lehrbuch der
<BR>Funktionentheorie, vol 1 (192<IMG SRC="images/forum/icons/icon_cool.gif">, p 17<IMG SRC="images/forum/icons/icon_cool.gif"> it is possible to catch every lion
<BR>except for at most one.
<BR>[4] N. Wiener, \"The Fourier Integral and Certain of its Applications\" (1933),
<BR>pp 7374
<BR>[5] N. Wiener, ibid, p 89
<BR>[6] cf e.g. H. A. Bethe and R. F. Bacher, \"Reviews of Modern Physics\", 8
<BR>(1936), pp 82229, esp. pp 106107
<BR>[7] ibid
<BR>
<BR>
<BR>
<BR>4 Contributions from Computer Science.
<BR>
<BR>4.1 The search method
<BR>
<BR>We assume that the lion is most likely to be found in the direction to
<BR>the north of the point where we are standing. Therefore the REAL
<BR>problem we have is that of speed, since we are only using a PC to
<BR>solve the problem.
<BR>
<BR>4.2 The parallel search method.
<BR>
<BR>By using parallelism we will be able to search in the direction to the
<BR>north much faster than earlier.
<BR>
<BR>4.3 The MonteCarlo method.
<BR>
<BR>We pick a random number indexing the space we search. By excluding
<BR>neighboring points in the search, we can drastically reduce the number
<BR>of points we need to consider. The lion will according to probability
<BR>appear sooner or later.
<BR>
<BR>4.4 The practical approach.
<BR>
<BR>We see a rabbit very close to us. Since it is already dead, it is
<BR>particularly easy to catch. We therefore catch it and call it a lion.
<BR>
<BR>4.5 The common language approach.
<BR>
<BR>If only everyone used ADA/Common Lisp/Prolog, this problem would be
<BR>trivial to solve.
<BR>
<BR>4.6 The standard approach.
<BR>
<BR>We know what a Lion is from ISO 4711/X.123. Since CCITT have specified
<BR>a Lion to be a particular option of a cat we will have to wait for a
<BR>harmonized standard to appear. $20,000,000 have been funded for
<BR>initial investigations into this standard development.
<BR>
<BR>4.7 Linear search.
<BR>
<BR>Stand in the top left hand corner of the Sahara Desert. Take one step
<BR>east. Repeat until you have found the lion, or you reach the right
<BR>hand edge. If you reach the right hand edge, take one step
<BR>southwards, and proceed towards the left hand edge. When you finally
<BR>reach the lion, put it the cage. If the lion should happen to eat you
<BR>before you manage to get it in the cage, press the reset button, and
<BR>try again.
<BR>
<BR>4.8 The Dijkstra approach:
<BR>
<BR>The way the problem reached me was: catch a wild lion in the Sahara
<BR>Desert. Another way of stating the problem is:
<BR>
<BR>Axiom 1: Sahara elem deserts
<BR>Axiom 2: Lion elem Sahara
<BR>Axiom 3: NOT(Lion elem cage)
<BR>
<BR>We observe the following invariant:
<BR>
<BR>P1: C(L) v not(C(L))
<BR>
<BR>where C(L) means: the value of \"L\" is in the cage.
<BR>
<BR>Establishing C initially is trivially accomplished with the statement
<BR>
<BR>;cage := {}
<BR>
<BR>Note 0:
<BR>This is easily implemented by opening the door to the cage and shaking
<BR>out any lions that happen to be there initially.
<BR>(End of note 0.)
<BR>
<BR>The obvious program structure is then:
<BR>
<BR>;cage:={}
<BR>;do NOT (C(L)) >
<BR>;\"approach lion under invariance of P1\"
<BR>;if P(L) >
<BR>;\"insert lion in cage\"
<BR>[] not P(L) >
<BR>;skip
<BR>;fi
<BR>;od
<BR>
<BR>where P(L) means: the value of L is within arm\'s reach.
<BR>
<BR>Note 1:
<BR>Axiom 2 ensures that the loop terminates.
<BR>(End of note 1.)
<BR>
<BR>Exercise 0:
<BR>Refine the step \"Approach lion under invariance of P1\".
<BR>(End of exercise 0.)
<BR>
<BR>Note 2:
<BR>The program is robust in the sense that it will lead to
<BR>abortion if the value of L is \"lioness\".
<BR>(End of note 2.)
<BR>
<BR>Remark 0: This may be a new sense of the word \"robust\" for you.
<BR>(End of remark 0.)
<BR>
<BR>Note 3:
<BR>
<BR>>From observation we can see that the above program leads to the
<BR>desired goal. It goes without saying that we therefore do not have to
<BR>run it.
<BR>(End of note 3.)
<BR>(End of approach.)
<BR>
<BR>
<BR>
<BR>For other articles, see also:
<BR>
<BR>A Random Walk in Science  R.L. Weber and E. Mendoza
<BR>More Random Walks In Science  R.L. Weber and E. Mendoza
<BR>In Mathematical Circles (2 volumes)  Howard Eves
<BR>Mathematical Circles Revisited  Howard Eves
<BR>Mathematical Circles Squared  Howard Eves
<BR>Fantasia Mathematica  Clifton Fadiman
<BR>The Mathematical Magpi  Clifton Fadiman
<BR>Seven Years of Manifold  Jaworski
<BR>The Best of the Journal of Irreproducible Results  George H. Scheer
<BR>Mathematics Made Difficult  Linderholm
<BR>A StressAnalysis of a Strapless Evening Gown  Robert Baker
<BR>The WormRunners Digest
<BR>Knuth\'s April 1984 CACM article on The Space Complexity of Songs
<BR>Stolfi and ?? SIGACT article on Pessimal Algorithms and Simplexity Analysis
<BR>
<BR>
<BR>Not a joke, but a humorous ditty I heard from some guys in an
<BR>engineering fraternity (to the best of my recollection):
<BR>
<BR>I\'ll do it phonetically:
<BR>
<BR>ee to the ex dee ex,
<BR>ee to the why dee why,
<BR>sine x, cosine x,
<BR>natural log of y,
<BR>derivative on the left
<BR>derivative on the right
<BR>integrate, integrate,
<BR>fight! fight! fight!
<BR>
<BR>
<BR>The Programmers\' Cheer 
<BR>
<BR>Shift to the left, shift to the right!
<BR>Pop up, push down, byte, byte, byte!
<BR>
<BR>
<BR>Other cheers:
<BR>
<BR>E to the x dx dy
<BR>radical transcendental pi
<BR>secant cosine tangent sine
<BR>3.14159
<BR>2.71828
<BR>come on folks let\'s integerate!!
<BR>
<BR>
<BR>
<BR>E to the i dx dy
<BR>E to y dy
<BR>cosine secant log of pi
<BR>disintegrate em RPI !!!
<BR>
<BR>
<BR>
<BR>square root, tangent
<BR>hyperbolic sine,
<BR>3.14159
<BR>e to the x, dy, dx,
<BR>sliderule, slipstick, TECH TECH TECH!
<BR>
<BR>
<BR>
<BR>e to the u, du/dx
<BR>e to the x dx
<BR>cosine, secant, tangent, sine,
<BR>3.14159
<BR>integral, radical, u dv,
<BR>slipstick, slide rule, MIT!
<BR>
<BR>
<BR>
<BR>E to the X
<BR>DY, DX
<BR>E to the X
<BR>DX.
<BR>Cosine, Secant, Tangent, Sine
<BR>3.14159
<BR>EI, Radical, Pi
<BR>Fight\'em, Fight\'em, WPI!
<BR>
<BR>Go Worcester Polytechnic Institute!!!!!!
<BR>
<BR>
<BR>Words in {} should be interpreted as greek letters:
<BR>
<BR>Q: I M A {pi}{rho}Maniac. R U 1,2?
<BR>o < read as \"Unot\"
<BR>A: Y ?
<BR>o
<BR>
<BR>(\"I am a pyromaniac. Are you not one, too?\" \"Why not?\")
<BR>
<BR>F U \\{can\\} \\{read\\} Ths U \\{Mst\\} \\{use\\} TeX
<BR>(\"If you can read this, you must use TeX\")
<BR>
<BR>
<BR>Three men are in a hotair balloon. Soon, they find themselves lost
<BR>in a canyon somewhere. One of the three men says, \"I\'ve got an idea.
<BR>We can call for help in this canyon and the echo will carry our voices
<BR>far.\"
<BR>
<BR>So he leans over the basket and yells out, \"Helllloooooo! Where are
<BR>we?\" (They hear the echo several times.)
<BR>
<BR>15 minutes later, they hear this echoing voice: \"Helllloooooo! You\'re
<BR>lost!!\"
<BR>
<BR>One of the men says, \"That must have been a mathematician.\"
<BR>
<BR>Puzzled, one of the other men asks, \"Why do you say that?\"
<BR>
<BR>The reply: \"For three reasons. (1) he took a long time to answer, (2)
<BR>he was absolutely correct, and (3) his answer was absolutely useless.\"
<BR>
<BR>
<BR>Actually, I prefer the IBM version of this joke...
<BR>
<BR>A small, 14seat plane is circling for a landing in Atlanta. It\'s
<BR>totally fogged in, zero visibility, and suddenly there\'s a small
<BR>electrical fire in the cockpit which disables all of the instruments
<BR>and the radio. The pilot continues circling, totally lost, when
<BR>suddenly he finds himself flying next to a tall office building.
<BR>
<BR>He rolls down the window (this particular airplane happens to have
<BR>rolldown windows) and yells to a person inside the building, \"Where
<BR>are we?\"
<BR>
<BR>The person responds \"In an airplane!\"
<BR>
<BR>The pilot then banks sharply to the right, circles twice, and makes a
<BR>perfect landing at Atlanta International.
<BR>
<BR>As the passengers emerge, shaken but unhurt, one of them says to the
<BR>pilot, \"I\'m certainly glad you were able to land safely, but I don\'t
<BR>understand how the response you got was any use.\"
<BR>
<BR>\"Simple,\" responded the pilot. \"I got an answer that was completely
<BR>accurate and totally irrelevant to my problem, so I knew it had to be
<BR>the IBM building.\"
<BR>
<BR>
<BR>(I\'m not sure if the following one is a true story or not)
<BR>The great logician Bertrand Russell (or was it A.N. Whitehead?)
<BR>once claimed that he could prove anything if given that 1+1=1.
<BR>So one day, some smartypants asked him, \"Ok. Prove that
<BR>you\'re the Pope.\"
<BR>He thought for a while and proclaimed, \"I am one. The Pope
<BR>is one. Therefore, the Pope and I are one.\"
<BR>
<BR>[NOTE: The following is from <a href=\"mailto:merritt@Gendev.slc.paramax.com\" target=\"_new\">merritt@Gendev.slc.paramax.com</a> (Merritt).
<BR>The story about 1+1=1 causing ridiculous consequences was, I believe,
<BR>originally the product of a conversation at the Trinity High Table.
<BR>It is recorded in Sir Harold Jeffreys\' Scientific Inference, in a note
<BR>to chapter one. Jeffreys remarks that the fact that everything
<BR>followed from a single contradiction had been noticed by Aristotle (I
<BR>doubt this way of putting it is quite correct, but that is beside the
<BR>point). He goes on to say that McTaggart denied the consequence: \"if
<BR>2+2=5, how can you prove that I am the pope?\" Hardy is supposed to
<BR>have replied: \"if 2+2=5, 4=5; subtract 3; then 1=2; but McTaggart and
<BR>the pope are two; therefore McTaggart and the pope are one.\" When I
<BR>consider this story, I am astonished at how much more brilliant some
<BR>people are than I (quite independent of the fallacies in the
<BR>argument).
<BR>
<BR>Since McTaggart, Hardy, Whitehead, and Russell (the last two of whom
<BR>were credited with a variant of Hardy\'s argument in your post) were
<BR>all fellows of Trinity and Jeffreys (their exact contemporary) was a
<BR>fellow of St. Johns, I suspect that (whatever the truth of Jeffreys\'
<BR>story) it is very unlikely that Whitehead or Russell had anything to do
<BR>with it. The extraordinary point to me about the story is that Hardy
<BR>was able to snap this argument out between mouthfuls, so to speak, and
<BR>he was not even a logician at all. This is probably why it came in
<BR>some people\'s minds to be attributed to one or other of the famous
<BR>Trinity logicians.
<BR>
<BR>
<BR>THE STORY OF BABEL:
<BR>
<BR>In the beginning there was only one kind of Mathematician, created by
<BR>the Great Mathematical Spirit form the Book: the Topologist. And they
<BR>grew to large numbers and prospered.
<BR>
<BR>One day they looked up in the heavens and desired to reach up as far
<BR>as the eye could see. So they set out in building a Mathematical
<BR>edifice that was to reach up as far as \"up\" went. Further and further
<BR>up they went ... until one night the edifice collapsed under the
<BR>weight of paradox.
<BR>
<BR>The following morning saw only rubble where there once was a huge
<BR>structure reaching to the heavens. One by one, the Mathematicians
<BR>climbed out from under the rubble. It was a miracle that nobody was
<BR>killed; but when they began to speak to one another, SUPRISE of all
<BR>surprises! they could not understand each other. They all spoke
<BR>different languages. They all fought amongst themselves and each went
<BR>about their own way. To this day the Topologists remain the original
<BR>Mathematicians.
<BR>
<BR> adapted from an American Indian legend
<BR>of the Mound Of Babel
<BR>
<BR>
<BR>Methods of Mathematical Proof
<BR>
<BR>This is from _A Random Walk in Science_ (by Joel E. Cohen?):
<BR>
<BR>
<BR>To illustrate the various methods of proof we give an example of a
<BR>logical system.
<BR>
<BR>THE PEJORATIVE CALCULUS
<BR>
<BR>Lemma 1. All horses are the same colour.
<BR>(Proof by induction)
<BR>
<BR>Proof. It is obvious that one horse is the same colour. Let us assume
<BR>the proposition P(k) that k horses are the same colour and use this to
<BR>imply that k+1 horses are the same colour. Given the set of k+1 horses,
<BR>we remove one horse; then the remaining k horses are the same colour,
<BR>by hypothesis. We remove another horse and replace the first; the k
<BR>horses, by hypothesis, are again the same colour. We repeat this until
<BR>by exhaustion the k+1 sets of k horses have been shown to be the same
<BR>colour. It follows that since every horse is the same colour as every
<BR>other horse, P(k) entails P(k+1). But since we have shown P(1) to be
<BR>true, P is true for all succeeding values of k, that is, all horses are
<BR>the same colour.
<BR>
<BR>Theorem 1. Every horse has an infinite number of legs.
<BR>(Proof by intimidation.)
<BR>
<BR>Proof. Horses have an even number of legs. Behind they have two legs
<BR>and in front they have fore legs. This makes six legs, which is cer
<BR>tainly an odd number of legs for a horse. But the only number that is
<BR>both odd and even is infinity. Therefore horses have an infinite num
<BR>ber of legs. Now to show that this is general, suppose that somewhere
<BR>there is a horse with a finite number of legs. But that is a horse of
<BR>another colour, and by the lemma that does not exist.
<BR>
<BR>Corollary 1. Everything is the same colour.
<BR>
<BR>Proof. The proof of lemma 1 does not depend at all on the nature of the
<BR>object under consideration. The predicate of the antecedent of the uni
<BR>versallyquantified conditional \'For all x, if x is a horse, then x is
<BR>the same colour,\' namely \'is a horse\' may be generalized to \'is anything\'
<BR>without affecting the validity of the proof; hence, \'for all x, if x is
<BR>anything, x is the same colour.\'
<BR>
<BR>Corollary 2. Everything is white.
<BR>
<BR>Proof. If a sentential formula in x is logically true, then any parti
<BR>cular substitution instance of it is a true sentence. In particular
<BR>then: \'for all x, if x is an elephant, then x is the same colour\' is
<BR>true. Now it is manifestly axiomatic that white elephants exist (for
<BR>proof by blatant assertion consult Mark Twain \'The Stolen White Ele
<BR>phant\'). Therefore all elephants are white. By corollary 1 everything
<BR>is white.
<BR>
<BR>Theorem 2. Alexander the Great did not exist and he had an infinite
<BR>number of limbs.
<BR>
<BR>Proof. We prove this theorem in two parts. First we note the obvious
<BR>fact that historians always tell the truth (for historians always take
<BR>a stand, and therefore they cannot lie). Hence we have the historically
<BR>true sentence, \'If Alexander the Great existed, then he rode a black
<BR>horse Bucephalus.\' But we know by corollary 2 everything is white;
<BR>hence Alexander could not have ridden a black horse. Since the conse
<BR>quent of the conditional is false, in order for the whole statement to
<BR>be true the antecedent must be false. Hence Alexander the Great did not
<BR>exist.
<BR>We have also the historically true statement that Alexander was warned
<BR>by an oracle that he would meet death if he crossed a certain river. He
<BR>had two legs; and \'forewarned is fourarmed.\' This gives him six limbs,
<BR>an even number, which is certainly an odd number of limbs for a man.
<BR>Now the only number which is even and odd is infinity; hence Alexander
<BR>had an infinite number of limbs. We have thus proved that Alexander the
<BR>Great did not exist and that he had an infinite number of limbs.
<BR>
<BR>
<BR>
<BR>
<BR>Not precisely puremath, but ...
<BR>
<BR>Fuller\'s Law of Cosmic Irreversability:
<BR>
<BR>1 pot T > 1 pot P
<BR>but
<BR>1 pot P /> 1 pot T
<BR>
<BR>
<BR>A tribe of Native Americans generally referred to their woman by the
<BR>animal hide with which they made their blanket. Thus, one woman might
<BR>be known as Squaw of Buffalo Hide, while another might be known as
<BR>Squaw of Deer Hide. This tribe had a particularly large and strong
<BR>woman, with a very unique (for North America anyway) animal hide for
<BR>her blanket. This woman was known as Squaw of Hippopotamus hide, and
<BR>she was as large and powerful as the animal from which her blanket was
<BR>made.
<BR>
<BR>Year after year, this woman entered the tribal wrestling tournament,
<BR>and easily defeated all challengers; male or female. As the men of
<BR>the tribe admired her strength and power, this made many of the other
<BR>woman of the tribe extremely jealous. One year, two of the squaws
<BR>petitioned the Chief to allow them to enter their sons together as a
<BR>wrestling tandem in order to wrestle Squaw of the Hippopotamus hide as
<BR>a team. In this way, they hoped to see that she would no longer be
<BR>champion wrestler of the tribe.
<BR>
<BR>As the luck of the draw would have it, the two sons who were wrestling
<BR>as a tandem met the squaw in the final and championship round of the
<BR>wrestling contest. As the match began, it became clear that the squaw
<BR>had finally met an opponent that was her equal. The two sons wrestled
<BR>and struggled vigorously and were clearly on an equal footing with the
<BR>powerful squaw. Their match lasted for hours without a clear victor.
<BR>Finally the chief intervened and declared that, in the interests of
<BR>the health and safety of the wrestlers, the match was to be terminated
<BR>and that he would declare a winner.
<BR>
<BR>The chief retired to his teepee and contemplated the great struggle he
<BR>had witnessed, and found it extremely difficult to decide a winner.
<BR>While the two young men had clearly outmatched the squaw, he found it
<BR>difficult to force the squaw to relinquish her tribal championship.
<BR>After all, it had taken two young men to finally provide her with a
<BR>decent match. Finally, after much deliberation, the chief came out
<BR>from his teepee, and announced his decision. He said...
<BR>
<BR>\"The Squaw of the Hippopotamus hide is equal to the sons of the squaws
<BR>of the other two hides\"
<BR>
<BR>
<BR>A topologist is a man who doesn\'t know the difference between a coffee
<BR>cup and a doughnut.
<BR>
<BR>
<BR>A statistician can have his head in an oven and his feet in ice, and
<BR>he will say that on the average he feels fine.
<BR>
<BR>
<BR>A guy decided to go to the brain transplant clinic to refreshen his
<BR>supply of brains. The secretary informed him that they had three
<BR>kinds of brains available at that time. Doctors\' brains were going
<BR>for $20 per ounce and lawyers\' brains were getting $30 per ounce. And
<BR>then there were mathematicians\' brains which were currently fetching
<BR>$1000 per ounce.
<BR>
<BR>\"A 1000 dollars an ounce!\" he cried. \"Why are they so expensive?\"
<BR>
<BR>\"It takes more mathematicians to get an ounce of brains,\" she explained.
<BR>
<BR>
<BR>A topologist walks into a bar and orders a drink. The bartender,
<BR>being a number theorist, says, \"I\'m sorry, but we don\'t serve
<BR>topologists here.\"
<BR>
<BR>The disgruntled topologist walks outside, but then gets an idea and
<BR>performs Dahn surgery upon herself. She walks into the bar, and the
<BR>bartender, who does not recognize her since she is now a different
<BR>manifold, serves her a drink. However, the bartender thinks she looks
<BR>familiar, or at least locally similar, and asks, \"Aren\'t you that
<BR>topologist that just came in here?\"
<BR>
<BR>To which she responds, \"No, I\'m a frayed knot.\"
<BR>
<BR>
<BR>There are three kinds of people in the world;
<BR>those who can count and those who can\'t.
<BR>
<BR>And the related:
<BR>
<BR>There are two groups of people in the world;
<BR>those who believe that the world can be
<BR>divided into two groups of people,
<BR>and those who don\'t.
<BR>
<BR>And then:
<BR>
<BR>There are two groups of people in the world:
<BR>Those who can be categorized into one of two
<BR>groups of people, and those who can\'t.
<BR>
<BR>
<BR>
<BR>The world is divided into two classes:
<BR>people who say \"The world is divided into two classes\",
<BR>and people who say
<BR>The world is divided into two classes:
<BR>people who say: \"The world is divided into two classes\",
<BR>and people who say:
<BR>The world is divided into two classes:
<BR>people who say ...
<BR>
<BR>
<BR>What follows is a \"quiz\" a student of mine once showed me (which she\'d
<BR>gotten from a previous teacher, etc...). It\'s multiple choice, and if
<BR>you sort the letters (with upper and lower case disjoint) questions
<BR>and answers will come out next to each other. Enjoy...
<BR>
<BR>S. What the acorn said when he grew up
<BR>N. bisects
<BR>u. A dead parrot
<BR>g. center
<BR>F. What you should do when it rains
<BR>R. hypotenuse
<BR>m. A geometer who has been to the beach
<BR>H. coincide
<BR>h. The set of cards is missing
<BR>y. polygon
<BR>A. The boy has a speech defect
<BR>t. secant
<BR>K. How they schedule gym class
<BR>p. tangent
<BR>b. What he did when his motherinlaw wanted to go home
<BR>D. ellipse
<BR>O. The tall kettle boiling on the stove
<BR>W. geometry
<BR>r. Why the girl doesn\'t run a 4minute mile
<BR>j. decagon
<BR>
<BR>
<BR>___ 1. That which Noah built.
<BR>___ 2. An article for serving ice cream.
<BR>___ 3. What a bloodhound does in chasing a woman.
<BR>___ 4. An expression to represent the loss of a parrot.
<BR>___ 5. An appropriate title for a knight named Koal.
<BR>___ 6. A sunburned man.
<BR>___ 7. A tall coffee pot perking.
<BR>___ 8. What one does when it rains.
<BR>___ 9. A dog sitting in a refrigerator.
<BR>___ 10. What a boy does on the lake when his motor won\'t run.
<BR>___ 11. What you call a person who writes for an inn.
<BR>___ 12. What the captain said when the boat was bombed.
<BR>___ 13. What a little acorn says when he grows up.
<BR>___ 14. What one does to trees that are in the way.
<BR>___ 15. What you do if you have yarn and needles.
<BR>___ 16. Can George Washington turn into a country?
<BR>
<BR>
<BR>A. hypotenuse I. circle
<BR>B. polygon J. axiom
<BR>C. inscribe K. cone
<BR>D. geometry L. coincide
<BR>E. unit M. cosecant
<BR>F. center N. tangent
<BR>G. decagone O. hero
<BR>H. arc P. perpendicular
<BR>
<BR>
<BR>
<BR>A team of engineers were required to measure the height of a flag
<BR>pole. They only had a measuring tape, and were getting quite
<BR>frustrated trying to keep the tape along the pole. It kept falling
<BR>down, etc.
<BR>
<BR>A mathematician comes along, finds out their problem, and proceeds to
<BR>remove the pole from the ground and measure it easily.
<BR>
<BR>When he leaves, one engineer says to the other: \"Just like a
<BR>mathematician! We need to know the height, and he gives us the
<BR>length!\"
<BR>
<BR>
<BR>A man camped in a national park, and noticed Mr. Snake and Mrs. Snake
<BR>slithering by. \"Where are all the little snakes?\" he asked. Mr.
<BR>Snake replied, \"We are adders, so we cannot multiply.\"
<BR>
<BR>The following year, the man returned to the same camping spot. This
<BR>time there were a whole batch of little snakes. \"I thought you said
<BR>you could not multiply,\" he said to Mr. Snake. \"Well, the park ranger
<BR>came by and built a log table, so now we can multiply by adding!\"
<BR>
<BR>
<BR>Einstein dies and goes to heaven only to be informed that his room is
<BR>not yet ready. \"I hope you will not mind waiting in a dormitory. We
<BR>are very sorry, but it\'s the best we can do and you will have to share
<BR>the room with others.\" he is told by the doorman (say his name is
<BR>Pete). Einstein says that this is no problem at all and that there is
<BR>no need to make such a great fuss. So Pete leads him to the dorm.
<BR>They enter and Albert is introduced to all of the present
<BR>inhabitants. \"See, Here is your first room mate. He has an IQ of
<BR>180!\"
<BR>\"Why that\'s wonderful!\" Says Albert. \"We can discuss mathematics!\"
<BR>\"And here is your second room mate. His IQ is 150!\"
<BR>\"Why that\'s wonderful!\" Says Albert. \"We can discuss physics!\"
<BR>\"And here is your third room mate. His IQ is 100!\"
<BR>\"That Wonderful! We can discuss the latest plays at the theater!\"
<BR>Just then another man moves out to capture Albert\'s hand and shake it.
<BR>\"I\'m your last room mate and I\'m sorry, but my IQ is only 80.\"
<BR>Albert smiles back at him and says, \"So, where do you think interest
<BR>rates are headed?\"
<BR>
<BR>
<BR>97.3% of all statistics are made up.
<BR>
<BR>
<BR>Did you hear the one about the statistician?
<BR>
<BR>Probably....
<BR>
<BR>
<BR>There was once a very smart horse. Anything that was shown it, it
<BR>mastered easily, until one day, its teachers tried to teach it about
<BR>rectangular coordinates and it couldn\'t understand them. All the
<BR>horse\'s acquaintances and friends tried to figure out what was the
<BR>matter and couldn\'t. Then a new guy (what the heck, a computer
<BR>engineer) looked at the problem and said,
<BR>
<BR>\"Of course he can\'t do it. Why, you\'re putting Descartes before the
<BR>horse!\"
<BR>
<BR>
<BR>TOP TEN EXCUSES FOR NOT DOING THE MATH HOMEWORK
<BR>
<BR>1. I accidentally divided by zero and my paper burst into flames.
<BR>2. Isaac Newton\'s birthday.
<BR>3. I could only get arbitrarily close to my textbook. I couldn\'t
<BR>actually reach it.
<BR>4. I have the proof, but there isn\'t room to write it in this margin.
<BR>5. I was watching the World Series and got tied up trying to prove
<BR>that it converged.
<BR>6. I have a solar powered calculator and it was cloudy.
<BR>7. I locked the paper in my trunk but a fourdimensional dog got in
<BR>and ate it.
<BR>8. I couldn\'t figure out whether i am the square of negative one or
<BR>i is the square root of negative one.
<BR>9. I took time out to snack on a doughnut and a cup of coffee.
<BR>I spent the rest of the night trying to figure which one to dunk.
<BR>10. I could have sworn I put the homework inside a Klein bottle, but
<BR>this morning I couldn\'t find it.
<BR>
<BR>
<BR>The guy gets on a bus and starts threatening everybody: \"I\'ll integrate
<BR>you! I\'ll differentiate you!!!\" So everybody gets scared and runs
<BR>away. Only one person stays. The guy comes up to him and says:
<BR>\"Aren\'t you scared, I\'ll integrate you, I\'ll differentiate you!!!\" And
<BR>the other guy says; \"No, I am not scared, I am e to the x.\"
<BR>
<BR>
<BR>A mathematician went insane and believed that he was the
<BR>differentiation operator. His friends had him placed in a mental
<BR>hospital until he got better. All day he would go around frightening
<BR>the other patients by staring at them and saying \"I differentiate
<BR>you!\"
<BR>
<BR>One day he met a new patient; and true to form he stared at him and
<BR>said \"I differentiate you!\", but for once, his victim\'s expression
<BR>didn\'t change. Surprised, the mathematician marshalled his energies,
<BR>stared fiercely at the new patient and said loudly \"I differentiate
<BR>you!\", but still the other man had no reaction. Finally, in
<BR>frustration, the mathematician screamed out \"I DIFFERENTIATE YOU!\" 
<BR>at which point the new patient calmly looked up and said, \"You can
<BR>differentiate me all you like: I\'m e to the x.\"
<BR>
<BR>
<BR>/
<BR> 1
<BR>  = log cabin
<BR> cabin
<BR>/
<BR>
<BR>Oops, you forgot your constant of integration.
<BR>
<BR>
<BR>/
<BR> 1
<BR>  = log cabin + C
<BR> cabin
<BR>/
<BR>
<BR>And, as we all know,
<BR>
<BR>log cabin + C = houseboat
<BR>
<BR>
<BR>8 5
<BR>If lim  = oo (infinity), then what does lim  = ?
<BR>x>0 x x>0 x
<BR>
<BR>answer: (write 5 on it\'s side)
<BR>
<BR>
<BR>Why did the cat fall off the roof?
<BR>
<BR>Because he lost his mu. (mew=sound cats make, mu=coeff of friction)
<BR>
<BR>
<BR>Boy\'s Life, May 1973:
<BR>
<BR>Ralph: Dad, will you do my math for me tonight?
<BR>Dad: No, son, it wouldn\'t be right.
<BR>Ralph: Well, you could try.
<BR>
<BR>
<BR>Mrs. Johnson the elementary school math teacher was having children do
<BR>problems on the blackboard that day.
<BR>
<BR>``Who would like to do the first problem, addition?\'\'
<BR>
<BR>No one raised their hand. She called on Tommy, and with some help he
<BR>finally got it right.
<BR>
<BR>``Who would like to do the second problem, subtraction?\'\'
<BR>
<BR>Students hid their faces. She called on Mark, who got the problem but
<BR>there was some suspicion his girlfriend Lisa whispered it to him.
<BR>
<BR>``Who would like to do the third problem, division?\'\'
<BR>
<BR>Now a low collective groan could be heard as everyone looked at
<BR>nothing in particular. The teacher called on Suzy, who got it right
<BR>(she has been known to hold back sometimes in front of her friends).
<BR>
<BR>``Who would like to do the last problem, multiplication?\'\'
<BR>
<BR>Tim\'s hand shot up, surprising everyone in the room. Mrs. Johnson
<BR>finally gained her composure in the stunned silence. ``Why the
<BR>enthusiasm, Tim?\'\'
<BR>
<BR>``God said to go fourth and multiply!\'\'
<BR>
<BR>
<BR>Definitions of Terms Commonly Used in Higher Math
<BR>
<BR>The following is a guide to the weary student of mathematics who
<BR>is often confronted with terms which are commonly used but rarely
<BR>defined. In the search for proper definitions for these terms we
<BR>found no authoritative, nor even recognized, source. Thus, we
<BR>followed the advice of mathematicians handed down from time
<BR>immortal: \"Wing It.\"
<BR>
<BR>
<BR>CLEARLY: I don\'t want to write down all the \"in
<BR>between\" steps.
<BR>
<BR>TRIVIAL: If I have to show you how to do this, you\'re
<BR>in the wrong class.
<BR>
<BR>OBVIOUSLY: I hope you weren\'t sleeping when we discussed
<BR>this earlier, because I refuse to repeat it.
<BR>
<BR>RECALL: I shouldn\'t have to tell you this, but for
<BR>those of you who erase your memory tapes
<BR>after every test...
<BR>
<BR>WLOG (Without Loss Of Generality): I\'m not about to do all the
<BR>possible cases, so I\'ll do one and let you
<BR>figure out the rest.
<BR>
<BR>IT CAN EASILY BE SHOWN: Even you, in your finite wisdom, should
<BR>be able to prove this without me holding your
<BR>hand.
<BR>
<BR>CHECK or CHECK FOR YOURSELF: This is the boring part of the
<BR>proof, so you can do it on your own time.
<BR>
<BR>SKETCH OF A PROOF: I couldn\'t verify all the details, so I\'ll
<BR>break it down into the parts I couldn\'t
<BR>prove.
<BR>
<BR>HINT: The hardest of several possible ways to do a
<BR>proof.
<BR>
<BR>BRUTE FORCE (AND IGNORANCE): Four special cases, three counting
<BR>arguments, two long inductions, \"and a
<BR>partridge in a pair tree.\"
<BR>
<BR>SOFT PROOF: One third less filling (of the page) than
<BR>your regular proof, but it requires two extra
<BR>years of course work just to understand the
<BR>terms.
<BR>
<BR>ELEGANT PROOF: Requires no previous knowledge of the subject
<BR>matter and is less than ten lines long.
<BR>
<BR>SIMILARLY: At least one line of the proof of this case is
<BR>the same as before.
<BR>
<BR>CANONICAL FORM: 4 out of 5 mathematicians surveyed
<BR>recommended this as the final form for their
<BR>students who choose to finish.
<BR>
<BR>TFAE (The Following Are Equivalent): If I say this it means that,
<BR>and if I say that it means the other thing,
<BR>and if I say the other thing...
<BR>
<BR>BY A PREVIOUS THEOREM: I don\'t remember how it goes (come to
<BR>think of it I\'m not really sure we did this
<BR>at all), but if I stated it right (or at
<BR>all), then the rest of this follows.
<BR>
<BR>TWO LINE PROOF: I\'ll leave out everything but the conclusion,
<BR>you can\'t question \'em if you can\'t see \'em.
<BR>
<BR>BRIEFLY: I\'m running out of time, so I\'ll just write
<BR>and talk faster.
<BR>
<BR>LET\'S TALK THROUGH IT: I don\'t want to write it on the board lest
<BR>I make a mistake.
<BR>
<BR>PROCEED FORMALLY: Manipulate symbols by the rules without any
<BR>hint of their true meaning (popular in pure
<BR>math courses).
<BR>
<BR>QUANTIFY: I can\'t find anything wrong with your proof
<BR>except that it won\'t work if x is a moon of
<BR>Jupiter (Popular in applied math courses).
<BR>
<BR>PROOF OMITTED: Trust me, It\'s true.
<BR>
<BR>[ Questo Messaggio è stato Modificato da: livingbooks il 04042004 12:07 ]<BR><BR>[ Questo Messaggio è stato Modificato da: livingbooks il 04042004 12:11 ]
livingbooks
 livingbooks
 Messaggi: 64
 Iscritto il: 01 gen 1970, 01:00
 Contatta:
<DIV style=\"fontsize:1pt;fontfamily:arial\">
<BR>
<BR>In the bayous of Louisiana, there is a small river called the Dirac.
<BR>Many wealthy people have their mansions near its mouth. One of the
<BR>social leaders decided to have a grand ball. Being a cousin of the
<BR>Governor, she arranged for a detachment of the state militia to serve
<BR>as guards and traffic directors for the big doings. A captain was
<BR>sent over with a small company; naturally he asked if there was enough
<BR>room for him and his unit. The social leader replied, \"But of course,
<BR>Captain! It is well known that the Dirac delta function has unit
<BR>area.\"
<BR>
<BR>
<BR>Albert Einstein, who fancied himself as a violinist, was rehearsing a
<BR>Haydn string quartet. When he failed for the fourth time to get his
<BR>entry in the second movement, the cellist looked up and said, \"The
<BR>problem with you, Albert, is that you simply can\'t count.\"
<BR>
<BR>
<BR>Some famous mathematician was to give a keynote speech at a
<BR>conference. Asked for an advance summary, he said he would present a
<BR>proof of Fermat\'s Last Theorem  but they should keep it under their
<BR>hats. When he arrived, though, he spoke on a much more prosaic
<BR>topic. Afterwards the conference organizers asked why he said he\'d
<BR>talk about the theorem and then didn\'t. He replied this was his
<BR>standard practice, just in case he was killed on the way to the
<BR>conference.
<BR>
<BR>
<BR>When I was a Math/Chem grad student at Princeton in 197374, there was
<BR>a story going around about a grad student. This guy was always late.
<BR>One day he stumbled into class late, saw seven problems written on the
<BR>board, and wrote them down. As the week went on he began to panic:
<BR>the math department at Princeton is fiercely competitive, and here he
<BR>was unable to do most of a simple homework assignment! When the next
<BR>class rolled around he only had solved two of the problems, although
<BR>he had a pretty good idea of how to solve a third but not enough time
<BR>to complete it.
<BR>
<BR>When he dejectedly flung his partial assignment on the prof\'s desk,
<BR>the prof asked him \"What\'s that?\" \"The homework.\" \"What homework?\"
<BR>Eventually it came out that what the prof had written on the board
<BR>were the seven most important unsolved problems in the field.
<BR>
<BR>This is largely an academic legend, at least according to Jan Harold
<BR>Brunvand, the author of a series of books on socalled Urban Legends.
<BR>He talks about it in his latest book _Curses! Broiled Again!_ in the
<BR>chapter entitled \"The Unsolvable Math Problem.\" It is, however, based
<BR>in some fact. The Stanford mathematician, George B. Danzig,
<BR>apparently managed to solve two statistics problems previously
<BR>unsolved under similar circumstances.
<BR>
<BR>
<BR>The following problem can be solved either the easy way or the hard way.
<BR>
<BR>Two trains 200 miles apart are moving toward each other; each one is
<BR>going at a speed of 50 miles per hour. A fly starting on the front of
<BR>one of them flies back and forth between them at a rate of 75 miles
<BR>per hour. It does this until the trains collide and crush the fly to
<BR>death. What is the total distance the fly has flown?
<BR>
<BR>The fly actually hits each train an infinite number of times before it
<BR>gets crushed, and one could solve the problem the hard way with pencil
<BR>and paper by summing an infinite series of distances. The easy way
<BR>is as follows: Since the trains are 200 miles apart and each train is
<BR>going 50 miles an hour, it takes 2 hours for the trains to collide.
<BR>Therefore the fly was flying for two hours. Since the fly was flying
<BR>at a rate of 75 miles per hour, the fly must have flown 150 miles.
<BR>That\'s all there is to it.
<BR>
<BR>When this problem was posed to John von Neumann, he immediately
<BR>replied, \"150 miles.\"
<BR>
<BR>\"It is very strange,\" said the poser, \"but nearly everyone tries to
<BR>sum the infinite series.\"
<BR>
<BR>\"What do you mean, strange?\" asked Von Neumann. \"That\'s how I did it!\"
<BR>
<BR>
<BR>Mathematicians are like Frenchmen: whatever you say to them, they
<BR>translate it into their own language, and forthwith it means something
<BR>entirely different.
<BR> Johann Wolfgang von Goethe
<BR>
<BR>
<BR>\"The reason that every major university maintains a department of
<BR>mathematics is that it is cheaper to do this than to institutionalize
<BR>all those people.\"
<BR>
<BR>
<BR>Three mathematicians and a physicist walk into a bar.
<BR>You\'d think the second one would have ducked. (Ha, that quack\'s me up!)
<BR>
<BR>
<BR>What do you call a young eigensheep?
<BR>
<BR>A lamb, duh!!!
<BR>
<BR>
<BR>\"The world is everywhere dense with idiots.\"
<BR> LFS
<BR>
<BR>
<BR>One day a farmer called up an engineer, a physicist, and a mathematician
<BR>and asked them to fence of the largest possible area with the least
<BR>amount of fence. The engineer made the fence in a circle and
<BR>proclaimed that he had the most efficient design. The physicist made
<BR>a long, straight line and proclaimed \'We can assume the length is
<BR>infinite...\' and pointed out that fencing off half of the Earth was
<BR>certainly a more efficient way to do it. The Mathematician just
<BR>laughed at them. He built a tiny fence around himself and said \'I
<BR>declare myself to be on the outside.\'
<BR>
<BR>
<BR>An engineer, a mathematician, and a computer programmer are driving
<BR>down the road when the car they are in gets a flat tire. The engineer
<BR>says that they should buy a new car. The mathematician says they
<BR>should sell the old tire and buy a new one. The computer programmer
<BR>says they should drive the car around the block and see if the tire
<BR>fixes itself.
<BR>
<BR>
<BR>A math/computer science convention was being held. On the train to
<BR>the convention, a bunch of math majors and a bunch of computer science
<BR>majors were on the train. Each of the math majors had his/her train
<BR>ticket. The group of computer science majors had only ONE ticket for
<BR>all of them. The math majors started laughing and snickering.
<BR>
<BR>Then, one of the CS majors said \"here comes the conductor\" and then
<BR>all of the CS majors went into the bathroom. The math majors were
<BR>puzzled. The conductor came aboard and said \"tickets please\" and got
<BR>tickets from all the math majors. He then went to the bathroom and
<BR>knocked on the door and said \"ticket please\" and the CS majors stuck
<BR>the ticket under the door. The conductor took it and then the CS
<BR>majors came out of the bathroom a few minutes later. The math majors
<BR>felt really stupid.
<BR>
<BR>So, on the way back from the convention, the group of math majors had
<BR>one ticket for the group. They started snickering at the CS majors,
<BR>for the whole group had no tickets amongst them. Then, the CS major
<BR>lookout said \"Conductor coming!\". All the CS majors went to the
<BR>bathroom. All the math majors went to another bathroom. Then, before
<BR>the conductor came on board, one of the CS majors left the bathroom,
<BR>knocked on the other bathroom, and said \"ticket please.\"
<BR>
<BR>
<BR>The following is supposedly a true story about Russell. It isn\'t
<BR>really a math joke since it makes fun of the British hierarchy, but
<BR>it\'s funny anyway....
<BR>
<BR>Around the time when Cold War started, Bertrand Russell was giving a
<BR>lecture on politics in England. Being a leftist in a conservative
<BR>women\'s club, he was not received well at all: the ladies came up to
<BR>him and started attacking him with whatever they could get their hands
<BR>on. The guard, being an English gentleman, did not want to be rough
<BR>to the ladies and yet needed to save Russell from them. He said, \"But
<BR>he is a great mathematician!\" The ladies ignored him. The guard said
<BR>again, \"But he is a great philosopher!\" The ladies ignore him again.
<BR>In desperation, finally, he said, \"But his brother is an earl!\" Bert
<BR>was saved.
<BR>
<BR>
<BR>Another \"true\" story, kinda like the aforementioned urban legend:
<BR>
<BR>Enrico Fermi, while studying in college, was bored by his math
<BR>classes. He walked up to the professor and said, \"My classes are too
<BR>easy!\" The professor looked at him, and said, \"Well, I\'m sure you\'ll
<BR>find this interesting.\" Then the professor copied 9 problems from a
<BR>book to a paper and gave the paper to Fermi. A month later, the
<BR>professor ran into Fermi, \"So how are you doing with the problems I
<BR>gave you?\" \"Oh, they are very hard. I only managed to solve 6 of
<BR>them.\" The professor was visibly shocked, \"What!? But those are
<BR>unsolved problems!\"
<BR>
<BR>
<BR>An engineer, a physicist, and a mathematician find themselves in an
<BR>anecdote, indeed an anecdote quite similar to many that you have no
<BR>doubt already heard. After some observations and rough calculations,
<BR>the engineer realizes the situation and starts laughing. A few
<BR>minutes later the physicist understands, too, and chuckles to himself
<BR>happily as he now has enough experimental evidence to publish a paper.
<BR>This leaves the mathematician somewhat perplexed, as he had observed
<BR>right away that he was the subject of an anecdote, and deduced quite
<BR>rapidly the presence of humour from similar anecdotes, but considers
<BR>this anecdote to be too trivial a corollary to be significant, let
<BR>alone funny.
<BR>
<BR>
<BR>
<BR>\"A person who can, within a year, solve x^2  92y^2 = 1 is a mathematician.\"
<BR> Brahmagupta
<BR>
<BR>
<BR>Math and Alcohol don\'t mix, so...
<BR>
<BR>PLEASE DON\'T DRINK AND DERIVE
<BR>
<BR>Then there\'s every parent\'s scream when their child walks into the
<BR>room dazed and staggering:
<BR>
<BR>OH NO...YOU\'VE BEEN TAKING DERIVATIVES!!
<BR>
<BR>
<BR>MADD = Mathematicians
<BR>Against
<BR>Drunk
<BR>Deriving
<BR>
<BR>
<BR>[This limerick was previously posted incorrectly.
<BR>The integral limit has been changed.]
<BR>
<BR>Here\'s a limerick I picked up off the net a few years back  looks better
<BR>on paper.
<BR>
<BR>3_
<BR>\\/3
<BR>/
<BR> 2 3 X pi 3_
<BR> z dz X cos() = ln (\\/e )
<BR> 9
<BR>/
<BR>1
<BR>
<BR>Which, of course, translates to:
<BR>
<BR>Integral zsquared dz
<BR>from 1 to the cube root of 3
<BR>times the cosine
<BR>of three pi over 9
<BR>equals log of the cube root of \'e\'.
<BR>
<BR>And it\'s correct, too.
<BR>
<BR>
<BR>This poem was written by John Saxon (an author of math textbooks).
<BR>
<BR>((12 + 144 + 20 + (3 * 4^(1/2))) / 7) + (5 * 11) = 9^2 + 0
<BR>
<BR>
<BR>Or for those who have trouble with the poem:
<BR>
<BR>A Dozen, a Gross and a Score,
<BR>plus three times the square root of four,
<BR>divided by seven,
<BR>plus five times eleven,
<BR>equals nine squared and not a bit more.
<BR>
<BR>
<BR>\'Tis a favorite project of mine
<BR>A new value of pi to assign.
<BR>I would fix it at 3
<BR>For it\'s simpler, you see,
<BR>Than 3 point 1 4 1 5 9.
<BR>
<BR>(\"The Lure of the Limerick\" by W.S. BaringGould, p.5. Attributed to
<BR>Harvey L. Carter).
<BR>
<BR>
<BR>If inside a circle a line
<BR>Hits the center and goes spine to spine
<BR>And the line\'s length is \"d\"
<BR>the circumference will be
<BR>d times 3.14159
<BR>
<BR>
<BR>
<BR>If (1+x) (real close to 1)
<BR>Is raised to the power of 1
<BR>Over x, you will find
<BR>Here\'s the value defined:
<BR>2.718281...
<BR>
<BR>
<BR>An engineer thinks that his equations are an approximation to reality.
<BR>A physicist thinks reality is an approximation to his equations.
<BR>A mathematician doesn\'t care.
<BR>
<BR>
<BR>Why is the number 10 afraid of seven?
<BR>
<BR> because seven ate nine.
<BR>
<BR>
<BR>We use epsilons and deltas in mathematics because mathematicians tend
<BR>to make errors.
<BR>
<BR>
<BR>
<BR>What\'s big, grey, and proves the uncountability of the reals?
<BR>Cantor\'s Diagonal Elephant!
<BR>
<BR>How can you tell that Harvard was layed out by a mathematician?
<BR>The div school [divinity school] is right next to the grad school...
<BR>
<BR>
<BR>The Stanford Linear Accelerator Center was known as SLAC, until the
<BR>big earthquake, when it became known as SPLAC.
<BR>
<BR>SPLAC? Stanford Piecewise Linear Accelerator.
<BR>
<BR>
<BR>Q: How many topologists does it take to change a light bulb?
<BR>A: It really doesn\'t matter, since they\'d rather knot.
<BR>
<BR>
<BR>
<BR>A mathematician decides he wants to learn more about practical
<BR>problems. He sees a seminar with a nice title: \"The Theory of Gears.\"
<BR>So he goes. The speaker stands up and begins, \"The theory of gears
<BR>with a real number of teeth is well known ...\"
<BR>
<BR>
<BR>A group of scientists were doing an investigation into problemsolving
<BR>techniques, and constructed an experiment involving a physicist, an
<BR>engineer, and a mathematician.
<BR>
<BR>The experimental apparatus consisted of a water spigot and two identical
<BR>pails, one of which was fastened to the ground ten feet from the spigot.
<BR>
<BR>Each of the subjects was given the second pail, empty, and told to fill the
<BR>pail on the ground.
<BR>
<BR>The physicist was the first subject: he carried his pail to the spigot,
<BR>filled it there, carried it full of water to the pail on the ground, and
<BR>poured the water into it. Standing back, he declared, \"There: I have
<BR>solved the problem.\"
<BR>
<BR>The engineer and the mathematician each approached the problem similarly.
<BR>Upon finishing, the engineer noted that the solution was exact, since the
<BR>volumes of the pails were equal. The mathematician merely noted that he
<BR>had proven that a solution exists.
<BR>
<BR>Now, the experimenters altered the parameters of the task a bit: the pail
<BR>on the ground was still empty, but the subjects were presented with a pail
<BR>that was already halffilled with water.
<BR>
<BR>The physicist immediately carried his pail over to the one on the ground,
<BR>emptied the water into it, went back to the spigot, *filled* the pail, and
<BR>finally emptied the entire contents into the pail on the ground,
<BR>overflowing it and spilling some of the water. Upon finishing, he
<BR>commented that the problem should have been better stated.
<BR>
<BR>The engineer, in turn, thought for some time before going into action. He
<BR>then took his halffilled pail to the spigot, filled it to the brim, and
<BR>filled the pail on the ground from it. Again he noted that the problem had
<BR>an exact solution, which of course he had found.
<BR>
<BR>The mathematician thought for a long time before stirring. At last he
<BR>stood up, emptied his pail onto the ground, and declared, \"The problem has
<BR>been reduced to one already solved.\"
<BR>
<BR>
<BR>Professor Dirac, a famous Applied MathematicianPhysicist, had a horse
<BR>shoe over his desk. One day a student asked if he really believed
<BR>that a horse shoe brought luck. Professor Dirac replied, \"I
<BR>understand that it brings you luck if you believe in it or not.\"
<BR>
<BR>
<BR>First of all let me make it clear that I have nothing against
<BR>contravariant functors. Some of my best friends are cohomology
<BR>theories! But now you aren\'t supposed to call them contravariant
<BR>anymore. It\'s Algebraically Correct to call them \'differently
<BR>arrowed\'!!
<BR>
<BR>In the same way that transcendental numbers are polynomially
<BR>challenged?
<BR>
<BR>Manifolds are personifolds (humanifolds).
<BR>
<BR>Neighborhoods are neighbor victims of society.
<BR>
<BR>It\'s the Asian Remainder Theorem.
<BR>
<BR>It isn\'t PC to use \"singularity\"  the function is \"convergently
<BR>challenged\" there.
<BR>
<BR>
<BR>Why did the computer scientist die in the shower?
<BR>Because he read the instructions on the shampoo bottle, \"Lather,
<BR>rinse, repeat.\"
<BR>
<BR>Why did the calculus student have so much trouble making KoolAid?
<BR>Because he couldn\'t figure out how to get a quart of water into the
<BR>little package.
<BR>
<BR>Q: Why do computer scientists confuse Christmas and Halloween?
<BR>A: Because Oct 31 = Dec 25
<BR>
<BR>
<BR>Here are some phrases used to remember SIN, COS, and TAN.
<BR>(SIN = Opposite/Hypotenuse, COS = Adjacent/H, TAN = O/A).
<BR>
<BR>1. SOHCAHTOA (sockatoea)
<BR>
<BR>2. The Cat Sat
<BR>On An Orange
<BR>And Howled Hard
<BR>
<BR>3. Some Old Hulks
<BR>Carry A Huge
<BR>Tub Of Ale
<BR>
<BR>4. Silly Old Hitler
<BR>Caused Awful Headaches
<BR>To Our Airmen
<BR>
<BR>5. Some Old Hag
<BR>Cracked All Her
<BR>Teeth On Asparagus
<BR>
<BR>6. Some Old Hairy
<BR>Camels Are Hairier
<BR>Than Others Are
<BR>
<BR>7. Silly Old Harry
<BR>Caught A Herring
<BR>Trawling Off America
<BR>
<BR>8. SOPHY, CADHY, TOAD
<BR>
<BR>units and dimensions
<BR>
<BR>2 monograms 1 diagram
<BR>8 nickles 2 paradigms
<BR>2 wharves 1 paradox
<BR>
<BR>10E5 bicycles 2 megacycles
<BR>
<BR>1 unit of suspense in an Agatha Christie novel 1 whod unit
<BR>
<BR>
<BR>Three Laws of Thermodynamics (paraphrased):
<BR>
<BR>First Law: You can\'t get anything without working for it.
<BR>
<BR>Second Law: The most you can accomplish by work is to break even.
<BR>
<BR>Third Law: You can\'t break even.
<BR>
<BR>
<BR>Q: What goes \"Pieces of seven! Pieces of seven!\"?
<BR>A: A parroty error!!
<BR>
<BR>Q: What did the circle say to the tangent line?
<BR>A: \"Stop touching me!\"
<BR>
<BR>
<BR>A mathematician is a person who says that, when 3 people are supposed
<BR>to be in a room but 5 came out, 2 have to go in so the room gets
<BR>empty...
<BR>
<BR>
<BR>The upgrade path to the most powerful and satisfying computer:
<BR>
<BR>* Pocket calculator
<BR>
<BR>* Commodore Pet / Apple II / TRS 80 / Commodore 64 / Timex Sinclair
<BR>(Choose any of the above)
<BR>
<BR>* IBM PC
<BR>
<BR>* Apple Macintosh
<BR>
<BR>* Fastest workstation of the time (HP, DEC, IBM, SGI: your choice)
<BR>
<BR>* Minicomputer (HP, DEC, IBM, SGI: your choice)
<BR>
<BR>* Mainframe (IBM, Cray, DEC: your choice)
<BR>
<BR>
<BR>And then you reach the pinnacle of modern computing facilities:
<BR>
<BR>*********************************************************
<BR>******* G R A D U A T E S T U D E N T S ********
<BR>*********************************************************
<BR>
<BR>Yes, you just sit back and do all of your computing through lowly
<BR>graduate students. Imagine the advantages:
<BR>
<BR>* Multiprocessing, with as many processes as you have
<BR>students. You can easily add more power by promising more
<BR>desperate undergrads that they can indeed escape college
<BR>through your guidance. Special student units can even
<BR>handle several tasks *on*their*own*!
<BR>
<BR>* Full voice recognition interface. Never touch a keyboard or
<BR>mouse again. Just mumble commands and they *will* be
<BR>understood (or else!).
<BR>
<BR>* No hardware upgrades and no installation required. Every
<BR>student comes complete with all hardware necessary. Never
<BR>again fry a chip or $10,000 board by improper installation!
<BR>Just sit that sniveling student at a desk, give it writing
<BR>utensils (making sure to point out which is the dangerous
<BR>end) and off it goes.
<BR>
<BR>* Low maintenance. Remember when that hard disk crashed in
<BR>your Beta 9900, causing all of your work to go the great bit
<BR>bucket in the sky? This won\'t happen with grad. students.
<BR>All that is required is that you give them a good *whack!*
<BR>upside the head when they are acting up, and they will run
<BR>good as new.
<BR>
<BR>* Abuse module. Imagine yelling expletives at your computer.
<BR>Doesn\'t work too well, because your machine just sits there
<BR>and ignores you. Through the grad student abuse module you
<BR>can put the fear of god in them, and get results to boot!
<BR>
<BR>* Builtin lifetime. Remember that awful feeling two years
<BR>after you bought your GigaPlutz mainframe when the new
<BR>faculty member on the block sneered at you because his
<BR>FeelyWup workstation could compute rings around your
<BR>dinosaur? This doesn\'t happen with grad. students. When
<BR>they start wearing and losing productivity, simply give them
<BR>the PhD and boot them out onto the street to fend for
<BR>themselves. Out of sight, out of mind!
<BR>
<BR>* Cheap fuel: students run on Coca Cola (or the highoctane
<BR>equivalent  Jolt Cola) and typically consume hot spicy
<BR>chinese dishes, cheap taco substitutes, or completely
<BR>synthetic macaroni replacements. It is entirely unnecessary
<BR>to plug the student into the wall socket (although this does
<BR>get them going a little faster from time to time).
<BR>
<BR>* Expansion options. If your grad. students don\'t seem to be
<BR>performing too well, consider adding a handy system manager
<BR>or software engineer upgrade. These guys are guaranteed to
<BR>require even less than a student, and typically establish
<BR>permanent residence in the computer room. You\'ll never know
<BR>they are around! (Which you certainly can\'t say for an
<BR>AXZ300069 150gigahertz spaceheater sitting on your desk
<BR>with its ten noisy fans....) [Note however that the
<BR>engineering department still hasn\'t worked out some of the
<BR>idiosyncratic bugs in these expansion options, such as
<BR>incessant muttering at nobody in particular, occasionaly
<BR>screaming at your grad. students, and posting ridiculous
<BR>messages on worldwide bulletin boards.]
<BR>
<BR>So forget your Babbage Engines and abacuses (abaci?) and PortaBooks
<BR>and DEK 6663D\'s and all that other silicon garbage. The wave of the
<BR>future is in wetware, so invest in graduate students today! You\'ll never
<BR>go back!
<BR>
<BR>
<BR>If I have seen farther than others, it is because I was
<BR>standing on the shoulder of giants.
<BR> Isaac Newton
<BR>
<BR>If I have not seen as far as others, it is because giants
<BR>were standing on my shoulders.
<BR> Hal Abelson
<BR>
<BR>In computer science, we stand on each other\'s feet.
<BR> Brian K. Reid
<BR>
<BR>
<BR>He thinks he\'s really smooth, but he\'s only C^1.
<BR>He\'s always going off on a tangent.
<BR>
<BR>
<BR>A mathematician and a physicist agree to a psychological experiment.
<BR>The mathematician is put in a chair in a large empty room and a
<BR>beautiful naked woman is placed on a bed at the other end of the room.
<BR>The psychologist explains, \"You are to remain in your chair. Every
<BR>five minutes, I will move your chair to a position halfway between its
<BR>current location and the woman on the bed.\" The mathematician looks
<BR>at the psychologist in disgust. \"What? I\'m not going to go through
<BR>this. You know I\'ll never reach the bed!\" And he gets up and storms
<BR>out. The psychologist makes a note on his clipboard and ushers the
<BR>physicist in. He explains the situation, and the physicist\'s eyes
<BR>light up and he starts drooling. The psychologist is a bit confused.
<BR>\"Don\'t you realize that you\'ll never reach her?\" The physicist smiles
<BR>and replied, \"Of course! But I\'ll get close enough for all practical
<BR>purposes!\"
<BR>
<BR>
<BR>Dean, to the physics department. \"Why do I always have to give you
<BR>guys so much money, for laboratories and expensive equipment and
<BR>stuff. Why couldn\'t you be like the math department  all they need
<BR>is money for pencils, paper and wastepaper baskets. Or even better,
<BR>like the philosophy department. All they need are pencils and paper.\"
<BR>
<BR>
<BR>An engineer, physicist, and mathematician are all challenged with a
<BR>problem: to fry an egg when there is a fire in the house. The
<BR>engineer just grabs a huge bucket of water, runs over to the fire, and
<BR>puts it out. The physicist thinks for a long while, and then measures
<BR>a precise amount of water into a container. He takes it over to the
<BR>fire, pours it on, and with the last drop the fire goes out. The
<BR>mathematician pores over pencil and paper. After a few minutes he
<BR>goes \"Aha! A solution exists!\" and goes back to frying the egg.
<BR>
<BR>Sequel: This time they are asked simply to fry an egg (no fire). The
<BR>engineer just does it, kludging along; the physicist calculates
<BR>carefully and produces a carefully cooked egg; and the mathematician
<BR>lights a fire in the corner, and says \"I have reduced it to the
<BR>previous problem.\"
<BR>
<BR>
<BR>A physicist and a mathematician setting in a faculty lounge.
<BR>Suddenly, the coffee machine catches on fire. The physicist grabs a
<BR>bucket and leaps towards the sink, fills the bucket with water and
<BR>puts out the fire. The second day, the same two sit in the same
<BR>lounge. Again, the coffee machine catches on fire. This time, the
<BR>mathematician stands up, gets a bucket, hands the bucket to the
<BR>physicist, thus reducing the problem to a previously solved one.
<BR>
<BR>
<BR>An engineer, a mathematician, and a physicist are staying in three
<BR>adjoining cabins at a decrepit old motel.
<BR>
<BR>First the engineer\'s coffee maker catches fire on the bathroom vanity.
<BR>He smells the smoke, wakes up, unplugs it, throws it out the window,
<BR>and goes back to sleep.
<BR>
<BR>Later that night the physicist smells smoke too. He wakes up and sees
<BR>that a cigarette butt has set the trash can on fire. He says to
<BR>himself, \"Hmm. How does one put out a fire? One can reduce the
<BR>temperature of the fuel below the flash point, isolate the burning
<BR>material from oxygen, or both. This could be accomplished by applying
<BR>water.\" So he picks up the trash can, puts it in the shower stall,
<BR>turns on the water, and, when the fire is out, goes back to sleep.
<BR>
<BR>The mathematician, of course, has been watching all this out the
<BR>window. So later, when he finds that his pipe ashes have set the
<BR>bedsheet on fire, he is not in the least taken aback. He immediately
<BR>sees that the problem reduces to one that has already been solved and
<BR>goes back to sleep.
<BR>
<BR>
<BR>A mathematician and a physicist were asked the following question:
<BR>
<BR>Suppose you walked by a burning house and saw a hydrant and
<BR>a hose not connected to the hydrant. What would you do?
<BR>
<BR>P: I would attach the hose to the hydrant, turn on the water, and put out
<BR>the fire.
<BR>
<BR>M: I would attach the hose to the hydrant, turn on the water, and put out
<BR>the fire.
<BR>
<BR>Then they were asked this question:
<BR>
<BR>Suppose you walked by a house and saw a hose connected to
<BR>a hydrant. What would you do?
<BR>
<BR>P: I would keep walking, as there is no problem to solve.
<BR>
<BR>M: I would disconnect the hose from the hydrant and set the house on fire,
<BR>reducing the problem to a previously solved form.
<BR>
<BR>
<BR>There were two men trying to decide what to do for a living. They
<BR>went to see a counselor, and he decided that they had good problem
<BR>solving skills.
<BR>
<BR>He tried a test to narrow the area of specialty. He put each man in a
<BR>room with a stove, a table, and a pot of water on the table. He said
<BR>\"Boil the water\". Both men moved the pot from the table to the stove
<BR>and turned on the burner to boil the water. Next, he put them into a
<BR>room with a stove, a table, and a pot of water on the floor. Again,
<BR>he said \"Boil the water\". The first man put the pot on the stove and
<BR>turned on the burner. The counselor told him to be an Engineer,
<BR>because he could solve each problem individually. The second man
<BR>moved the pot from the floor to the table, and then moved the pot from
<BR>the table to the stove and turned on the burner. The counselor told
<BR>him to be a mathematician because he reduced the problem to a
<BR>previously solved problem.
<BR>
<BR>
<BR>So a mathematician, an engineer, and a physicist are out hunting
<BR>together. They spy a deer(*) in the woods.
<BR>
<BR>The physicist calculates the velocity of the deer and the effect of
<BR>gravity on the bullet, aims his rifle and fires. Alas, he misses; the
<BR>bullet passes three feet behind the deer. The deer bolts some yards,
<BR>but comes to a halt, still within sight of the trio.
<BR>
<BR>\"Shame you missed,\" comments the engineer, \"but of course with an
<BR>ordinary gun, one would expect that.\" He then levels his special
<BR>deerhunting gun, which he rigged together from an ordinary rifle, a
<BR>sextant, a compass, a barometer, and a bunch of flashing lights which
<BR>don\'t do anything but impress onlookers, and fires. Alas, his bullet
<BR>passes three feet in front of the deer, who by this time wises up and
<BR>vanishes for good.
<BR>
<BR>\"Well,\" says the physicist, \"your contraption didn\'t get it either.\"
<BR>
<BR>\"What do you mean?\" pipes up the mathematician. \"Between the two of
<BR>you, that was a perfect shot!\"
<BR>
<BR>
<BR>
<BR>(*) How they knew it was a deer:
<BR>
<BR>The physicist observed that it behaved in a deerlike manner, so it
<BR>must be a deer.
<BR>
<BR>The mathematician asked the physicist what it was, thereby reducing it
<BR>to a previously solved problem.
<BR>
<BR>The engineer was in the woods to hunt deer, therefore it was a deer.
<BR>
<BR>
<BR>A computer scientist, mathematician, a physicist, and an engineer were
<BR>travelling through Scotland when they saw a black sheep through the
<BR>window of the train.
<BR>
<BR>\"Aha,\" says the engineer, \"I see that Scottish sheep are black.\"
<BR>
<BR>\"Hmm,\" says the physicist, \"You mean that some Scottish sheep are
<BR>black.\"
<BR>
<BR>\"No,\" says the mathematician, \"All we know is that there is at least
<BR>one sheep in Scotland, and that at least one side of that one sheep is
<BR>black!\"
<BR>
<BR>\"Oh, no!\" shouts the computer scientist, \"A special case!\"
<BR>
<BR>
<BR>A Mathematician (M) and an Engineer (E) attend a lecture by a
<BR>Physicist. The topic concerns KulzaKlein theories involving physical
<BR>processes that occur in spaces with dimensions of 11, 12 and even
<BR>higher. The M is sitting, clearly enjoying the lecture, while the E
<BR>is frowning and looking generally confused and puzzled. By the end
<BR>the E has a terrible headache. At the end, the M comments about the
<BR>wonderful lecture. The E says \"How do you understand this stuff?\"
<BR>M: \"I just visualize the process.\"
<BR>E: \"How can you POSSIBLY visualize something that occurs in
<BR>11dimensional space?\"
<BR>M: \"Easy, first visualize it in Ndimensional space, then let N go to 11.\"
<BR>
<BR>
<BR>What is \"pi\"?
<BR>
<BR>Mathematician: Pi is the number expressing the relationship between the
<BR>circumference of a circle and its diameter.
<BR>
<BR>Physicist: Pi is 3.1415927 plus or minus 0.00000005
<BR>
<BR>Engineer: Pi is about 3.
<BR>
<BR>
<BR>When considering the behaviour of a howitzer:
<BR>
<BR>A mathematician will be able to calculate where the shell will land.
<BR>
<BR>A physicist will be able to explain how the shell gets there.
<BR>
<BR>An engineer will stand there and try to catch it.
<BR>
<BR>
<BR>An engineer, a physicist and a mathematician find themselves in an
<BR>anecdote, indeed an anecdote quite similar to many that you have no
<BR>doubt already heard. After some observations and rough calculations
<BR>the engineer realizes the situation and starts laughing. A few
<BR>minutes later the physicist understands too and chuckles to himself
<BR>happily as he now has enough experimental evidence to publish a paper.
<BR>
<BR>This leaves the mathematician somewhat perplexed, as he had observed
<BR>right away that he was the subject of an anecdote, and deduced quite
<BR>rapidly the presence of humour from similar anecdotes, but considers
<BR>this anecdote to be too trivial a corollary to be significant, let
<BR>alone funny.
<BR>
<BR>
<BR>Q: What\'s purple and commutes?
<BR>A: An abelian grape.
<BR>
<BR>Q: Why did the mathematician name his dog \"Cauchy\"?
<BR>A: Because he left a residue at every pole.
<BR>
<BR>Q: Why is it that the more accuracy you demand from an interpolation
<BR>function, the more expensive it becomes to compute?
<BR>A: That\'s the Law of Spline Demand.
<BR>
<BR>Q: How many mathematicians does it take to screw in a lightbulb?
<BR>A: One, who gives it to six Californians, thereby reducing it to an
<BR>earlier riddle.
<BR> from a button I bought at Nancy Lebowitz\'s table at Boskone
<BR>
<BR>Q: What do a mathematician and a physicist [or engineer, or musician,
<BR>or whatever the profession of the person addressed] have in common?
<BR>A: They are both stupid, with the exception of the mathematician.
<BR>
<BR>Q: What do you call a teapot of boiling water on top of mount everest?
<BR>A: A highpotinuse
<BR>
<BR>Q: What do you call a broken record?
<BR>A: A Deccagone
<BR>
<BR>Q: What do you get when you cross 50 female pigs and 50 male deer?
<BR>A: One hundred sowsandbucks
<BR>
<BR>Q: Why did the chicken cross the Moebius strip?
<BR>A: To get to the other ... er, um ...
<BR>
<BR>Q: What is the world\'s longest song?
<BR>A: \"Alephnought Bottles of Beer on the Wall.\"
<BR>
<BR>Q: What does a mathematician do when he\'s constipated?
<BR>A: He works it out with a pencil.
<BR>
<BR>Q: What\'s yellow and equivalent to the Axiom of Choice.
<BR>A: Zorn\'s Lemon.
<BR>
<BR>Q: What do you get if you cross an elephant with a zebra.
<BR>A: Elephant zebra sin theta.
<BR>
<BR>Q: What do you get if you cross an elephant with a mountain climber.
<BR>A: You can\'t do that. A mountain climber is a scalar.
<BR>
<BR>Q: What do you get when you cross an elephant with a banana?
<BR>A: Elephant banana sine theta in a direction mutually perpendicular to
<BR>the two as determined by the right hand rule.
<BR>
<BR>Q: To what question is the answer \"9W.\"
<BR>A: \"Dr. Wiener, do you spell your name with a V?\"
<BR></DIV>
<BR>viplasent?
<BR>
<BR>
<BR>In the bayous of Louisiana, there is a small river called the Dirac.
<BR>Many wealthy people have their mansions near its mouth. One of the
<BR>social leaders decided to have a grand ball. Being a cousin of the
<BR>Governor, she arranged for a detachment of the state militia to serve
<BR>as guards and traffic directors for the big doings. A captain was
<BR>sent over with a small company; naturally he asked if there was enough
<BR>room for him and his unit. The social leader replied, \"But of course,
<BR>Captain! It is well known that the Dirac delta function has unit
<BR>area.\"
<BR>
<BR>
<BR>Albert Einstein, who fancied himself as a violinist, was rehearsing a
<BR>Haydn string quartet. When he failed for the fourth time to get his
<BR>entry in the second movement, the cellist looked up and said, \"The
<BR>problem with you, Albert, is that you simply can\'t count.\"
<BR>
<BR>
<BR>Some famous mathematician was to give a keynote speech at a
<BR>conference. Asked for an advance summary, he said he would present a
<BR>proof of Fermat\'s Last Theorem  but they should keep it under their
<BR>hats. When he arrived, though, he spoke on a much more prosaic
<BR>topic. Afterwards the conference organizers asked why he said he\'d
<BR>talk about the theorem and then didn\'t. He replied this was his
<BR>standard practice, just in case he was killed on the way to the
<BR>conference.
<BR>
<BR>
<BR>When I was a Math/Chem grad student at Princeton in 197374, there was
<BR>a story going around about a grad student. This guy was always late.
<BR>One day he stumbled into class late, saw seven problems written on the
<BR>board, and wrote them down. As the week went on he began to panic:
<BR>the math department at Princeton is fiercely competitive, and here he
<BR>was unable to do most of a simple homework assignment! When the next
<BR>class rolled around he only had solved two of the problems, although
<BR>he had a pretty good idea of how to solve a third but not enough time
<BR>to complete it.
<BR>
<BR>When he dejectedly flung his partial assignment on the prof\'s desk,
<BR>the prof asked him \"What\'s that?\" \"The homework.\" \"What homework?\"
<BR>Eventually it came out that what the prof had written on the board
<BR>were the seven most important unsolved problems in the field.
<BR>
<BR>This is largely an academic legend, at least according to Jan Harold
<BR>Brunvand, the author of a series of books on socalled Urban Legends.
<BR>He talks about it in his latest book _Curses! Broiled Again!_ in the
<BR>chapter entitled \"The Unsolvable Math Problem.\" It is, however, based
<BR>in some fact. The Stanford mathematician, George B. Danzig,
<BR>apparently managed to solve two statistics problems previously
<BR>unsolved under similar circumstances.
<BR>
<BR>
<BR>The following problem can be solved either the easy way or the hard way.
<BR>
<BR>Two trains 200 miles apart are moving toward each other; each one is
<BR>going at a speed of 50 miles per hour. A fly starting on the front of
<BR>one of them flies back and forth between them at a rate of 75 miles
<BR>per hour. It does this until the trains collide and crush the fly to
<BR>death. What is the total distance the fly has flown?
<BR>
<BR>The fly actually hits each train an infinite number of times before it
<BR>gets crushed, and one could solve the problem the hard way with pencil
<BR>and paper by summing an infinite series of distances. The easy way
<BR>is as follows: Since the trains are 200 miles apart and each train is
<BR>going 50 miles an hour, it takes 2 hours for the trains to collide.
<BR>Therefore the fly was flying for two hours. Since the fly was flying
<BR>at a rate of 75 miles per hour, the fly must have flown 150 miles.
<BR>That\'s all there is to it.
<BR>
<BR>When this problem was posed to John von Neumann, he immediately
<BR>replied, \"150 miles.\"
<BR>
<BR>\"It is very strange,\" said the poser, \"but nearly everyone tries to
<BR>sum the infinite series.\"
<BR>
<BR>\"What do you mean, strange?\" asked Von Neumann. \"That\'s how I did it!\"
<BR>
<BR>
<BR>Mathematicians are like Frenchmen: whatever you say to them, they
<BR>translate it into their own language, and forthwith it means something
<BR>entirely different.
<BR> Johann Wolfgang von Goethe
<BR>
<BR>
<BR>\"The reason that every major university maintains a department of
<BR>mathematics is that it is cheaper to do this than to institutionalize
<BR>all those people.\"
<BR>
<BR>
<BR>Three mathematicians and a physicist walk into a bar.
<BR>You\'d think the second one would have ducked. (Ha, that quack\'s me up!)
<BR>
<BR>
<BR>What do you call a young eigensheep?
<BR>
<BR>A lamb, duh!!!
<BR>
<BR>
<BR>\"The world is everywhere dense with idiots.\"
<BR> LFS
<BR>
<BR>
<BR>One day a farmer called up an engineer, a physicist, and a mathematician
<BR>and asked them to fence of the largest possible area with the least
<BR>amount of fence. The engineer made the fence in a circle and
<BR>proclaimed that he had the most efficient design. The physicist made
<BR>a long, straight line and proclaimed \'We can assume the length is
<BR>infinite...\' and pointed out that fencing off half of the Earth was
<BR>certainly a more efficient way to do it. The Mathematician just
<BR>laughed at them. He built a tiny fence around himself and said \'I
<BR>declare myself to be on the outside.\'
<BR>
<BR>
<BR>An engineer, a mathematician, and a computer programmer are driving
<BR>down the road when the car they are in gets a flat tire. The engineer
<BR>says that they should buy a new car. The mathematician says they
<BR>should sell the old tire and buy a new one. The computer programmer
<BR>says they should drive the car around the block and see if the tire
<BR>fixes itself.
<BR>
<BR>
<BR>A math/computer science convention was being held. On the train to
<BR>the convention, a bunch of math majors and a bunch of computer science
<BR>majors were on the train. Each of the math majors had his/her train
<BR>ticket. The group of computer science majors had only ONE ticket for
<BR>all of them. The math majors started laughing and snickering.
<BR>
<BR>Then, one of the CS majors said \"here comes the conductor\" and then
<BR>all of the CS majors went into the bathroom. The math majors were
<BR>puzzled. The conductor came aboard and said \"tickets please\" and got
<BR>tickets from all the math majors. He then went to the bathroom and
<BR>knocked on the door and said \"ticket please\" and the CS majors stuck
<BR>the ticket under the door. The conductor took it and then the CS
<BR>majors came out of the bathroom a few minutes later. The math majors
<BR>felt really stupid.
<BR>
<BR>So, on the way back from the convention, the group of math majors had
<BR>one ticket for the group. They started snickering at the CS majors,
<BR>for the whole group had no tickets amongst them. Then, the CS major
<BR>lookout said \"Conductor coming!\". All the CS majors went to the
<BR>bathroom. All the math majors went to another bathroom. Then, before
<BR>the conductor came on board, one of the CS majors left the bathroom,
<BR>knocked on the other bathroom, and said \"ticket please.\"
<BR>
<BR>
<BR>The following is supposedly a true story about Russell. It isn\'t
<BR>really a math joke since it makes fun of the British hierarchy, but
<BR>it\'s funny anyway....
<BR>
<BR>Around the time when Cold War started, Bertrand Russell was giving a
<BR>lecture on politics in England. Being a leftist in a conservative
<BR>women\'s club, he was not received well at all: the ladies came up to
<BR>him and started attacking him with whatever they could get their hands
<BR>on. The guard, being an English gentleman, did not want to be rough
<BR>to the ladies and yet needed to save Russell from them. He said, \"But
<BR>he is a great mathematician!\" The ladies ignored him. The guard said
<BR>again, \"But he is a great philosopher!\" The ladies ignore him again.
<BR>In desperation, finally, he said, \"But his brother is an earl!\" Bert
<BR>was saved.
<BR>
<BR>
<BR>Another \"true\" story, kinda like the aforementioned urban legend:
<BR>
<BR>Enrico Fermi, while studying in college, was bored by his math
<BR>classes. He walked up to the professor and said, \"My classes are too
<BR>easy!\" The professor looked at him, and said, \"Well, I\'m sure you\'ll
<BR>find this interesting.\" Then the professor copied 9 problems from a
<BR>book to a paper and gave the paper to Fermi. A month later, the
<BR>professor ran into Fermi, \"So how are you doing with the problems I
<BR>gave you?\" \"Oh, they are very hard. I only managed to solve 6 of
<BR>them.\" The professor was visibly shocked, \"What!? But those are
<BR>unsolved problems!\"
<BR>
<BR>
<BR>An engineer, a physicist, and a mathematician find themselves in an
<BR>anecdote, indeed an anecdote quite similar to many that you have no
<BR>doubt already heard. After some observations and rough calculations,
<BR>the engineer realizes the situation and starts laughing. A few
<BR>minutes later the physicist understands, too, and chuckles to himself
<BR>happily as he now has enough experimental evidence to publish a paper.
<BR>This leaves the mathematician somewhat perplexed, as he had observed
<BR>right away that he was the subject of an anecdote, and deduced quite
<BR>rapidly the presence of humour from similar anecdotes, but considers
<BR>this anecdote to be too trivial a corollary to be significant, let
<BR>alone funny.
<BR>
<BR>
<BR>
<BR>\"A person who can, within a year, solve x^2  92y^2 = 1 is a mathematician.\"
<BR> Brahmagupta
<BR>
<BR>
<BR>Math and Alcohol don\'t mix, so...
<BR>
<BR>PLEASE DON\'T DRINK AND DERIVE
<BR>
<BR>Then there\'s every parent\'s scream when their child walks into the
<BR>room dazed and staggering:
<BR>
<BR>OH NO...YOU\'VE BEEN TAKING DERIVATIVES!!
<BR>
<BR>
<BR>MADD = Mathematicians
<BR>Against
<BR>Drunk
<BR>Deriving
<BR>
<BR>
<BR>[This limerick was previously posted incorrectly.
<BR>The integral limit has been changed.]
<BR>
<BR>Here\'s a limerick I picked up off the net a few years back  looks better
<BR>on paper.
<BR>
<BR>3_
<BR>\\/3
<BR>/
<BR> 2 3 X pi 3_
<BR> z dz X cos() = ln (\\/e )
<BR> 9
<BR>/
<BR>1
<BR>
<BR>Which, of course, translates to:
<BR>
<BR>Integral zsquared dz
<BR>from 1 to the cube root of 3
<BR>times the cosine
<BR>of three pi over 9
<BR>equals log of the cube root of \'e\'.
<BR>
<BR>And it\'s correct, too.
<BR>
<BR>
<BR>This poem was written by John Saxon (an author of math textbooks).
<BR>
<BR>((12 + 144 + 20 + (3 * 4^(1/2))) / 7) + (5 * 11) = 9^2 + 0
<BR>
<BR>
<BR>Or for those who have trouble with the poem:
<BR>
<BR>A Dozen, a Gross and a Score,
<BR>plus three times the square root of four,
<BR>divided by seven,
<BR>plus five times eleven,
<BR>equals nine squared and not a bit more.
<BR>
<BR>
<BR>\'Tis a favorite project of mine
<BR>A new value of pi to assign.
<BR>I would fix it at 3
<BR>For it\'s simpler, you see,
<BR>Than 3 point 1 4 1 5 9.
<BR>
<BR>(\"The Lure of the Limerick\" by W.S. BaringGould, p.5. Attributed to
<BR>Harvey L. Carter).
<BR>
<BR>
<BR>If inside a circle a line
<BR>Hits the center and goes spine to spine
<BR>And the line\'s length is \"d\"
<BR>the circumference will be
<BR>d times 3.14159
<BR>
<BR>
<BR>
<BR>If (1+x) (real close to 1)
<BR>Is raised to the power of 1
<BR>Over x, you will find
<BR>Here\'s the value defined:
<BR>2.718281...
<BR>
<BR>
<BR>An engineer thinks that his equations are an approximation to reality.
<BR>A physicist thinks reality is an approximation to his equations.
<BR>A mathematician doesn\'t care.
<BR>
<BR>
<BR>Why is the number 10 afraid of seven?
<BR>
<BR> because seven ate nine.
<BR>
<BR>
<BR>We use epsilons and deltas in mathematics because mathematicians tend
<BR>to make errors.
<BR>
<BR>
<BR>
<BR>What\'s big, grey, and proves the uncountability of the reals?
<BR>Cantor\'s Diagonal Elephant!
<BR>
<BR>How can you tell that Harvard was layed out by a mathematician?
<BR>The div school [divinity school] is right next to the grad school...
<BR>
<BR>
<BR>The Stanford Linear Accelerator Center was known as SLAC, until the
<BR>big earthquake, when it became known as SPLAC.
<BR>
<BR>SPLAC? Stanford Piecewise Linear Accelerator.
<BR>
<BR>
<BR>Q: How many topologists does it take to change a light bulb?
<BR>A: It really doesn\'t matter, since they\'d rather knot.
<BR>
<BR>
<BR>
<BR>A mathematician decides he wants to learn more about practical
<BR>problems. He sees a seminar with a nice title: \"The Theory of Gears.\"
<BR>So he goes. The speaker stands up and begins, \"The theory of gears
<BR>with a real number of teeth is well known ...\"
<BR>
<BR>
<BR>A group of scientists were doing an investigation into problemsolving
<BR>techniques, and constructed an experiment involving a physicist, an
<BR>engineer, and a mathematician.
<BR>
<BR>The experimental apparatus consisted of a water spigot and two identical
<BR>pails, one of which was fastened to the ground ten feet from the spigot.
<BR>
<BR>Each of the subjects was given the second pail, empty, and told to fill the
<BR>pail on the ground.
<BR>
<BR>The physicist was the first subject: he carried his pail to the spigot,
<BR>filled it there, carried it full of water to the pail on the ground, and
<BR>poured the water into it. Standing back, he declared, \"There: I have
<BR>solved the problem.\"
<BR>
<BR>The engineer and the mathematician each approached the problem similarly.
<BR>Upon finishing, the engineer noted that the solution was exact, since the
<BR>volumes of the pails were equal. The mathematician merely noted that he
<BR>had proven that a solution exists.
<BR>
<BR>Now, the experimenters altered the parameters of the task a bit: the pail
<BR>on the ground was still empty, but the subjects were presented with a pail
<BR>that was already halffilled with water.
<BR>
<BR>The physicist immediately carried his pail over to the one on the ground,
<BR>emptied the water into it, went back to the spigot, *filled* the pail, and
<BR>finally emptied the entire contents into the pail on the ground,
<BR>overflowing it and spilling some of the water. Upon finishing, he
<BR>commented that the problem should have been better stated.
<BR>
<BR>The engineer, in turn, thought for some time before going into action. He
<BR>then took his halffilled pail to the spigot, filled it to the brim, and
<BR>filled the pail on the ground from it. Again he noted that the problem had
<BR>an exact solution, which of course he had found.
<BR>
<BR>The mathematician thought for a long time before stirring. At last he
<BR>stood up, emptied his pail onto the ground, and declared, \"The problem has
<BR>been reduced to one already solved.\"
<BR>
<BR>
<BR>Professor Dirac, a famous Applied MathematicianPhysicist, had a horse
<BR>shoe over his desk. One day a student asked if he really believed
<BR>that a horse shoe brought luck. Professor Dirac replied, \"I
<BR>understand that it brings you luck if you believe in it or not.\"
<BR>
<BR>
<BR>First of all let me make it clear that I have nothing against
<BR>contravariant functors. Some of my best friends are cohomology
<BR>theories! But now you aren\'t supposed to call them contravariant
<BR>anymore. It\'s Algebraically Correct to call them \'differently
<BR>arrowed\'!!
<BR>
<BR>In the same way that transcendental numbers are polynomially
<BR>challenged?
<BR>
<BR>Manifolds are personifolds (humanifolds).
<BR>
<BR>Neighborhoods are neighbor victims of society.
<BR>
<BR>It\'s the Asian Remainder Theorem.
<BR>
<BR>It isn\'t PC to use \"singularity\"  the function is \"convergently
<BR>challenged\" there.
<BR>
<BR>
<BR>Why did the computer scientist die in the shower?
<BR>Because he read the instructions on the shampoo bottle, \"Lather,
<BR>rinse, repeat.\"
<BR>
<BR>Why did the calculus student have so much trouble making KoolAid?
<BR>Because he couldn\'t figure out how to get a quart of water into the
<BR>little package.
<BR>
<BR>Q: Why do computer scientists confuse Christmas and Halloween?
<BR>A: Because Oct 31 = Dec 25
<BR>
<BR>
<BR>Here are some phrases used to remember SIN, COS, and TAN.
<BR>(SIN = Opposite/Hypotenuse, COS = Adjacent/H, TAN = O/A).
<BR>
<BR>1. SOHCAHTOA (sockatoea)
<BR>
<BR>2. The Cat Sat
<BR>On An Orange
<BR>And Howled Hard
<BR>
<BR>3. Some Old Hulks
<BR>Carry A Huge
<BR>Tub Of Ale
<BR>
<BR>4. Silly Old Hitler
<BR>Caused Awful Headaches
<BR>To Our Airmen
<BR>
<BR>5. Some Old Hag
<BR>Cracked All Her
<BR>Teeth On Asparagus
<BR>
<BR>6. Some Old Hairy
<BR>Camels Are Hairier
<BR>Than Others Are
<BR>
<BR>7. Silly Old Harry
<BR>Caught A Herring
<BR>Trawling Off America
<BR>
<BR>8. SOPHY, CADHY, TOAD
<BR>
<BR>units and dimensions
<BR>
<BR>2 monograms 1 diagram
<BR>8 nickles 2 paradigms
<BR>2 wharves 1 paradox
<BR>
<BR>10E5 bicycles 2 megacycles
<BR>
<BR>1 unit of suspense in an Agatha Christie novel 1 whod unit
<BR>
<BR>
<BR>Three Laws of Thermodynamics (paraphrased):
<BR>
<BR>First Law: You can\'t get anything without working for it.
<BR>
<BR>Second Law: The most you can accomplish by work is to break even.
<BR>
<BR>Third Law: You can\'t break even.
<BR>
<BR>
<BR>Q: What goes \"Pieces of seven! Pieces of seven!\"?
<BR>A: A parroty error!!
<BR>
<BR>Q: What did the circle say to the tangent line?
<BR>A: \"Stop touching me!\"
<BR>
<BR>
<BR>A mathematician is a person who says that, when 3 people are supposed
<BR>to be in a room but 5 came out, 2 have to go in so the room gets
<BR>empty...
<BR>
<BR>
<BR>The upgrade path to the most powerful and satisfying computer:
<BR>
<BR>* Pocket calculator
<BR>
<BR>* Commodore Pet / Apple II / TRS 80 / Commodore 64 / Timex Sinclair
<BR>(Choose any of the above)
<BR>
<BR>* IBM PC
<BR>
<BR>* Apple Macintosh
<BR>
<BR>* Fastest workstation of the time (HP, DEC, IBM, SGI: your choice)
<BR>
<BR>* Minicomputer (HP, DEC, IBM, SGI: your choice)
<BR>
<BR>* Mainframe (IBM, Cray, DEC: your choice)
<BR>
<BR>
<BR>And then you reach the pinnacle of modern computing facilities:
<BR>
<BR>*********************************************************
<BR>******* G R A D U A T E S T U D E N T S ********
<BR>*********************************************************
<BR>
<BR>Yes, you just sit back and do all of your computing through lowly
<BR>graduate students. Imagine the advantages:
<BR>
<BR>* Multiprocessing, with as many processes as you have
<BR>students. You can easily add more power by promising more
<BR>desperate undergrads that they can indeed escape college
<BR>through your guidance. Special student units can even
<BR>handle several tasks *on*their*own*!
<BR>
<BR>* Full voice recognition interface. Never touch a keyboard or
<BR>mouse again. Just mumble commands and they *will* be
<BR>understood (or else!).
<BR>
<BR>* No hardware upgrades and no installation required. Every
<BR>student comes complete with all hardware necessary. Never
<BR>again fry a chip or $10,000 board by improper installation!
<BR>Just sit that sniveling student at a desk, give it writing
<BR>utensils (making sure to point out which is the dangerous
<BR>end) and off it goes.
<BR>
<BR>* Low maintenance. Remember when that hard disk crashed in
<BR>your Beta 9900, causing all of your work to go the great bit
<BR>bucket in the sky? This won\'t happen with grad. students.
<BR>All that is required is that you give them a good *whack!*
<BR>upside the head when they are acting up, and they will run
<BR>good as new.
<BR>
<BR>* Abuse module. Imagine yelling expletives at your computer.
<BR>Doesn\'t work too well, because your machine just sits there
<BR>and ignores you. Through the grad student abuse module you
<BR>can put the fear of god in them, and get results to boot!
<BR>
<BR>* Builtin lifetime. Remember that awful feeling two years
<BR>after you bought your GigaPlutz mainframe when the new
<BR>faculty member on the block sneered at you because his
<BR>FeelyWup workstation could compute rings around your
<BR>dinosaur? This doesn\'t happen with grad. students. When
<BR>they start wearing and losing productivity, simply give them
<BR>the PhD and boot them out onto the street to fend for
<BR>themselves. Out of sight, out of mind!
<BR>
<BR>* Cheap fuel: students run on Coca Cola (or the highoctane
<BR>equivalent  Jolt Cola) and typically consume hot spicy
<BR>chinese dishes, cheap taco substitutes, or completely
<BR>synthetic macaroni replacements. It is entirely unnecessary
<BR>to plug the student into the wall socket (although this does
<BR>get them going a little faster from time to time).
<BR>
<BR>* Expansion options. If your grad. students don\'t seem to be
<BR>performing too well, consider adding a handy system manager
<BR>or software engineer upgrade. These guys are guaranteed to
<BR>require even less than a student, and typically establish
<BR>permanent residence in the computer room. You\'ll never know
<BR>they are around! (Which you certainly can\'t say for an
<BR>AXZ300069 150gigahertz spaceheater sitting on your desk
<BR>with its ten noisy fans....) [Note however that the
<BR>engineering department still hasn\'t worked out some of the
<BR>idiosyncratic bugs in these expansion options, such as
<BR>incessant muttering at nobody in particular, occasionaly
<BR>screaming at your grad. students, and posting ridiculous
<BR>messages on worldwide bulletin boards.]
<BR>
<BR>So forget your Babbage Engines and abacuses (abaci?) and PortaBooks
<BR>and DEK 6663D\'s and all that other silicon garbage. The wave of the
<BR>future is in wetware, so invest in graduate students today! You\'ll never
<BR>go back!
<BR>
<BR>
<BR>If I have seen farther than others, it is because I was
<BR>standing on the shoulder of giants.
<BR> Isaac Newton
<BR>
<BR>If I have not seen as far as others, it is because giants
<BR>were standing on my shoulders.
<BR> Hal Abelson
<BR>
<BR>In computer science, we stand on each other\'s feet.
<BR> Brian K. Reid
<BR>
<BR>
<BR>He thinks he\'s really smooth, but he\'s only C^1.
<BR>He\'s always going off on a tangent.
<BR>
<BR>
<BR>A mathematician and a physicist agree to a psychological experiment.
<BR>The mathematician is put in a chair in a large empty room and a
<BR>beautiful naked woman is placed on a bed at the other end of the room.
<BR>The psychologist explains, \"You are to remain in your chair. Every
<BR>five minutes, I will move your chair to a position halfway between its
<BR>current location and the woman on the bed.\" The mathematician looks
<BR>at the psychologist in disgust. \"What? I\'m not going to go through
<BR>this. You know I\'ll never reach the bed!\" And he gets up and storms
<BR>out. The psychologist makes a note on his clipboard and ushers the
<BR>physicist in. He explains the situation, and the physicist\'s eyes
<BR>light up and he starts drooling. The psychologist is a bit confused.
<BR>\"Don\'t you realize that you\'ll never reach her?\" The physicist smiles
<BR>and replied, \"Of course! But I\'ll get close enough for all practical
<BR>purposes!\"
<BR>
<BR>
<BR>Dean, to the physics department. \"Why do I always have to give you
<BR>guys so much money, for laboratories and expensive equipment and
<BR>stuff. Why couldn\'t you be like the math department  all they need
<BR>is money for pencils, paper and wastepaper baskets. Or even better,
<BR>like the philosophy department. All they need are pencils and paper.\"
<BR>
<BR>
<BR>An engineer, physicist, and mathematician are all challenged with a
<BR>problem: to fry an egg when there is a fire in the house. The
<BR>engineer just grabs a huge bucket of water, runs over to the fire, and
<BR>puts it out. The physicist thinks for a long while, and then measures
<BR>a precise amount of water into a container. He takes it over to the
<BR>fire, pours it on, and with the last drop the fire goes out. The
<BR>mathematician pores over pencil and paper. After a few minutes he
<BR>goes \"Aha! A solution exists!\" and goes back to frying the egg.
<BR>
<BR>Sequel: This time they are asked simply to fry an egg (no fire). The
<BR>engineer just does it, kludging along; the physicist calculates
<BR>carefully and produces a carefully cooked egg; and the mathematician
<BR>lights a fire in the corner, and says \"I have reduced it to the
<BR>previous problem.\"
<BR>
<BR>
<BR>A physicist and a mathematician setting in a faculty lounge.
<BR>Suddenly, the coffee machine catches on fire. The physicist grabs a
<BR>bucket and leaps towards the sink, fills the bucket with water and
<BR>puts out the fire. The second day, the same two sit in the same
<BR>lounge. Again, the coffee machine catches on fire. This time, the
<BR>mathematician stands up, gets a bucket, hands the bucket to the
<BR>physicist, thus reducing the problem to a previously solved one.
<BR>
<BR>
<BR>An engineer, a mathematician, and a physicist are staying in three
<BR>adjoining cabins at a decrepit old motel.
<BR>
<BR>First the engineer\'s coffee maker catches fire on the bathroom vanity.
<BR>He smells the smoke, wakes up, unplugs it, throws it out the window,
<BR>and goes back to sleep.
<BR>
<BR>Later that night the physicist smells smoke too. He wakes up and sees
<BR>that a cigarette butt has set the trash can on fire. He says to
<BR>himself, \"Hmm. How does one put out a fire? One can reduce the
<BR>temperature of the fuel below the flash point, isolate the burning
<BR>material from oxygen, or both. This could be accomplished by applying
<BR>water.\" So he picks up the trash can, puts it in the shower stall,
<BR>turns on the water, and, when the fire is out, goes back to sleep.
<BR>
<BR>The mathematician, of course, has been watching all this out the
<BR>window. So later, when he finds that his pipe ashes have set the
<BR>bedsheet on fire, he is not in the least taken aback. He immediately
<BR>sees that the problem reduces to one that has already been solved and
<BR>goes back to sleep.
<BR>
<BR>
<BR>A mathematician and a physicist were asked the following question:
<BR>
<BR>Suppose you walked by a burning house and saw a hydrant and
<BR>a hose not connected to the hydrant. What would you do?
<BR>
<BR>P: I would attach the hose to the hydrant, turn on the water, and put out
<BR>the fire.
<BR>
<BR>M: I would attach the hose to the hydrant, turn on the water, and put out
<BR>the fire.
<BR>
<BR>Then they were asked this question:
<BR>
<BR>Suppose you walked by a house and saw a hose connected to
<BR>a hydrant. What would you do?
<BR>
<BR>P: I would keep walking, as there is no problem to solve.
<BR>
<BR>M: I would disconnect the hose from the hydrant and set the house on fire,
<BR>reducing the problem to a previously solved form.
<BR>
<BR>
<BR>There were two men trying to decide what to do for a living. They
<BR>went to see a counselor, and he decided that they had good problem
<BR>solving skills.
<BR>
<BR>He tried a test to narrow the area of specialty. He put each man in a
<BR>room with a stove, a table, and a pot of water on the table. He said
<BR>\"Boil the water\". Both men moved the pot from the table to the stove
<BR>and turned on the burner to boil the water. Next, he put them into a
<BR>room with a stove, a table, and a pot of water on the floor. Again,
<BR>he said \"Boil the water\". The first man put the pot on the stove and
<BR>turned on the burner. The counselor told him to be an Engineer,
<BR>because he could solve each problem individually. The second man
<BR>moved the pot from the floor to the table, and then moved the pot from
<BR>the table to the stove and turned on the burner. The counselor told
<BR>him to be a mathematician because he reduced the problem to a
<BR>previously solved problem.
<BR>
<BR>
<BR>So a mathematician, an engineer, and a physicist are out hunting
<BR>together. They spy a deer(*) in the woods.
<BR>
<BR>The physicist calculates the velocity of the deer and the effect of
<BR>gravity on the bullet, aims his rifle and fires. Alas, he misses; the
<BR>bullet passes three feet behind the deer. The deer bolts some yards,
<BR>but comes to a halt, still within sight of the trio.
<BR>
<BR>\"Shame you missed,\" comments the engineer, \"but of course with an
<BR>ordinary gun, one would expect that.\" He then levels his special
<BR>deerhunting gun, which he rigged together from an ordinary rifle, a
<BR>sextant, a compass, a barometer, and a bunch of flashing lights which
<BR>don\'t do anything but impress onlookers, and fires. Alas, his bullet
<BR>passes three feet in front of the deer, who by this time wises up and
<BR>vanishes for good.
<BR>
<BR>\"Well,\" says the physicist, \"your contraption didn\'t get it either.\"
<BR>
<BR>\"What do you mean?\" pipes up the mathematician. \"Between the two of
<BR>you, that was a perfect shot!\"
<BR>
<BR>
<BR>
<BR>(*) How they knew it was a deer:
<BR>
<BR>The physicist observed that it behaved in a deerlike manner, so it
<BR>must be a deer.
<BR>
<BR>The mathematician asked the physicist what it was, thereby reducing it
<BR>to a previously solved problem.
<BR>
<BR>The engineer was in the woods to hunt deer, therefore it was a deer.
<BR>
<BR>
<BR>A computer scientist, mathematician, a physicist, and an engineer were
<BR>travelling through Scotland when they saw a black sheep through the
<BR>window of the train.
<BR>
<BR>\"Aha,\" says the engineer, \"I see that Scottish sheep are black.\"
<BR>
<BR>\"Hmm,\" says the physicist, \"You mean that some Scottish sheep are
<BR>black.\"
<BR>
<BR>\"No,\" says the mathematician, \"All we know is that there is at least
<BR>one sheep in Scotland, and that at least one side of that one sheep is
<BR>black!\"
<BR>
<BR>\"Oh, no!\" shouts the computer scientist, \"A special case!\"
<BR>
<BR>
<BR>A Mathematician (M) and an Engineer (E) attend a lecture by a
<BR>Physicist. The topic concerns KulzaKlein theories involving physical
<BR>processes that occur in spaces with dimensions of 11, 12 and even
<BR>higher. The M is sitting, clearly enjoying the lecture, while the E
<BR>is frowning and looking generally confused and puzzled. By the end
<BR>the E has a terrible headache. At the end, the M comments about the
<BR>wonderful lecture. The E says \"How do you understand this stuff?\"
<BR>M: \"I just visualize the process.\"
<BR>E: \"How can you POSSIBLY visualize something that occurs in
<BR>11dimensional space?\"
<BR>M: \"Easy, first visualize it in Ndimensional space, then let N go to 11.\"
<BR>
<BR>
<BR>What is \"pi\"?
<BR>
<BR>Mathematician: Pi is the number expressing the relationship between the
<BR>circumference of a circle and its diameter.
<BR>
<BR>Physicist: Pi is 3.1415927 plus or minus 0.00000005
<BR>
<BR>Engineer: Pi is about 3.
<BR>
<BR>
<BR>When considering the behaviour of a howitzer:
<BR>
<BR>A mathematician will be able to calculate where the shell will land.
<BR>
<BR>A physicist will be able to explain how the shell gets there.
<BR>
<BR>An engineer will stand there and try to catch it.
<BR>
<BR>
<BR>An engineer, a physicist and a mathematician find themselves in an
<BR>anecdote, indeed an anecdote quite similar to many that you have no
<BR>doubt already heard. After some observations and rough calculations
<BR>the engineer realizes the situation and starts laughing. A few
<BR>minutes later the physicist understands too and chuckles to himself
<BR>happily as he now has enough experimental evidence to publish a paper.
<BR>
<BR>This leaves the mathematician somewhat perplexed, as he had observed
<BR>right away that he was the subject of an anecdote, and deduced quite
<BR>rapidly the presence of humour from similar anecdotes, but considers
<BR>this anecdote to be too trivial a corollary to be significant, let
<BR>alone funny.
<BR>
<BR>
<BR>Q: What\'s purple and commutes?
<BR>A: An abelian grape.
<BR>
<BR>Q: Why did the mathematician name his dog \"Cauchy\"?
<BR>A: Because he left a residue at every pole.
<BR>
<BR>Q: Why is it that the more accuracy you demand from an interpolation
<BR>function, the more expensive it becomes to compute?
<BR>A: That\'s the Law of Spline Demand.
<BR>
<BR>Q: How many mathematicians does it take to screw in a lightbulb?
<BR>A: One, who gives it to six Californians, thereby reducing it to an
<BR>earlier riddle.
<BR> from a button I bought at Nancy Lebowitz\'s table at Boskone
<BR>
<BR>Q: What do a mathematician and a physicist [or engineer, or musician,
<BR>or whatever the profession of the person addressed] have in common?
<BR>A: They are both stupid, with the exception of the mathematician.
<BR>
<BR>Q: What do you call a teapot of boiling water on top of mount everest?
<BR>A: A highpotinuse
<BR>
<BR>Q: What do you call a broken record?
<BR>A: A Deccagone
<BR>
<BR>Q: What do you get when you cross 50 female pigs and 50 male deer?
<BR>A: One hundred sowsandbucks
<BR>
<BR>Q: Why did the chicken cross the Moebius strip?
<BR>A: To get to the other ... er, um ...
<BR>
<BR>Q: What is the world\'s longest song?
<BR>A: \"Alephnought Bottles of Beer on the Wall.\"
<BR>
<BR>Q: What does a mathematician do when he\'s constipated?
<BR>A: He works it out with a pencil.
<BR>
<BR>Q: What\'s yellow and equivalent to the Axiom of Choice.
<BR>A: Zorn\'s Lemon.
<BR>
<BR>Q: What do you get if you cross an elephant with a zebra.
<BR>A: Elephant zebra sin theta.
<BR>
<BR>Q: What do you get if you cross an elephant with a mountain climber.
<BR>A: You can\'t do that. A mountain climber is a scalar.
<BR>
<BR>Q: What do you get when you cross an elephant with a banana?
<BR>A: Elephant banana sine theta in a direction mutually perpendicular to
<BR>the two as determined by the right hand rule.
<BR>
<BR>Q: To what question is the answer \"9W.\"
<BR>A: \"Dr. Wiener, do you spell your name with a V?\"
<BR></DIV>
<BR>viplasent?
<BR>
livingbooks

 Messaggi: 153
 Iscritto il: 01 gen 1970, 01:00
 Località: Imola
Cosa realmente accaduta oggi:
<BR>
<BR>Il Rappr. di Classe : Possiamo andare al precetto pascuale:
<BR>
<BR>La prof di Filosofia : Veramente stiamo molto indietro col programma e
<BR> dovrei interrogare ... ma è meglio che andate a messa
<BR> che ne avete bisogno[addsig]
<BR>
<BR>Il Rappr. di Classe : Possiamo andare al precetto pascuale:
<BR>
<BR>La prof di Filosofia : Veramente stiamo molto indietro col programma e
<BR> dovrei interrogare ... ma è meglio che andate a messa
<BR> che ne avete bisogno[addsig]
Voglio sapere come Dio ha creato questo mondo voglio sapere i suoi pensieri tutto il resto è dettaglio (A.Einstein)
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<BR>precetto pascuale
<BR>
<BR></BLOCKQUOTE></FONT></TD></TR><TR><TD><HR></TD></TR></TABLE><! BBCode Quote End >
<BR>
<BR> <IMG SRC="images/forum/icons/icon_eek.gif">
<BR>precetto pascuale
<BR>
<BR></BLOCKQUOTE></FONT></TD></TR><TR><TD><HR></TD></TR></TABLE><! BBCode Quote End >
<BR>
<BR> <IMG SRC="images/forum/icons/icon_eek.gif">
"Signore, (a+b^n)/n=x, dunque Dio esiste!" (L.Euler)
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<BR>On 20040405 16:15, W28 wrote:
<BR>Possiamo andare al precetto pascuale:
<BR></BLOCKQUOTE></FONT></TD></TR><TR><TD><HR></TD></TR></TABLE><! BBCode Quote End >
<BR>
<BR>Cosa sarebbe questo precetto pasquale? (mi scuso per l\'ignoranza)
<BR>On 20040405 16:15, W28 wrote:
<BR>Possiamo andare al precetto pascuale:
<BR></BLOCKQUOTE></FONT></TD></TR><TR><TD><HR></TD></TR></TABLE><! BBCode Quote End >
<BR>
<BR>Cosa sarebbe questo precetto pasquale? (mi scuso per l\'ignoranza)
Dicesi Precetto pascuale quella manifestazione svolta nella settimana santa in un luogo detto casa di Dio (cosa assurda perchè se Onnipotente è in ogni luogo come può avere una casa) richiesta dai professori di una oscura materia , i quali programmi sono sconosciuti e prevedono a scelta degli allievi molte attivitò tra cui : rugby in classe , passeggiata nei corridoi , basket in palestra senonchè ingegneria degli aereoplanini di carta.
<BR>
<BR>Tali professori vengono assunti non dal ministero in cui è al capo la moglie del presidente dell\'inter ma da un individuo strambo vestito di rosso che passa tutta la giornata a dire cose inutili come ad esempio \"Il sesso serve a fare i figli\" con un\'enfasi tale che sembra che l\'abbia appena scoperto e dato che di solito ha circa 6070 anni e non ha figli si vede che con questa frase voglia indurre ai giovani , per non fargli soffrire per la sua stessa ignoranza in materia , a leggere il Kamasutra.
<BR>
<BR>Ma la cosa più straordinaria di questo manicomio e che se ogni anno al precetto partecipano 200 persone (io incluso , ndW2<IMG SRC="images/forum/icons/icon_cool.gif"> loro dicono che invece che hanno partecipato 1500 persone che invece hanno espesso volontà di andarci ma si sono dispersi per le strade cittadine.
<BR>
<BR><! BBCode Quote Start ><TABLE BORDER=0 ALIGN=CENTER WIDTH=85%><TR><TD><font size=1>Quote:</font><HR></TD></TR><TR><TD><FONT SIZE=1><BLOCKQUOTE></BLOCKQUOTE></FONT></TD></TR><TR><TD><HR></TD></TR></TABLE><! BBCode Quote End >
<BR>
<BR>Non è proprio una spiegazione di cos\'è il precetto pascuale o una barzelletta ma è una via di mezzo tra la comicità di Beppe Grillo e ironia di Voltaire[addsig]
<BR>
<BR>Tali professori vengono assunti non dal ministero in cui è al capo la moglie del presidente dell\'inter ma da un individuo strambo vestito di rosso che passa tutta la giornata a dire cose inutili come ad esempio \"Il sesso serve a fare i figli\" con un\'enfasi tale che sembra che l\'abbia appena scoperto e dato che di solito ha circa 6070 anni e non ha figli si vede che con questa frase voglia indurre ai giovani , per non fargli soffrire per la sua stessa ignoranza in materia , a leggere il Kamasutra.
<BR>
<BR>Ma la cosa più straordinaria di questo manicomio e che se ogni anno al precetto partecipano 200 persone (io incluso , ndW2<IMG SRC="images/forum/icons/icon_cool.gif"> loro dicono che invece che hanno partecipato 1500 persone che invece hanno espesso volontà di andarci ma si sono dispersi per le strade cittadine.
<BR>
<BR><! BBCode Quote Start ><TABLE BORDER=0 ALIGN=CENTER WIDTH=85%><TR><TD><font size=1>Quote:</font><HR></TD></TR><TR><TD><FONT SIZE=1><BLOCKQUOTE></BLOCKQUOTE></FONT></TD></TR><TR><TD><HR></TD></TR></TABLE><! BBCode Quote End >
<BR>
<BR>Non è proprio una spiegazione di cos\'è il precetto pascuale o una barzelletta ma è una via di mezzo tra la comicità di Beppe Grillo e ironia di Voltaire[addsig]
Voglio sapere come Dio ha creato questo mondo voglio sapere i suoi pensieri tutto il resto è dettaglio (A.Einstein)
Una curiosità: ma parlate normalmente in inglese?<IMG SRC="images/forum/icons/icon_confused.gif">
<BR>a dire la verità ci ho capito ben poco<IMG SRC="images/forum/icons/icon_razz.gif"> <IMG SRC="images/forum/icons/icon_razz.gif"> . Scusa livingbooks, ma ce le hai in italiano? Complimenti per la tua spiegazione di precetto pasquale, W28. <IMG SRC="images/forum/icons/icon_wink.gif"> <IMG SRC="images/forum/icons/icon_wink.gif">
<BR>a dire la verità ci ho capito ben poco<IMG SRC="images/forum/icons/icon_razz.gif"> <IMG SRC="images/forum/icons/icon_razz.gif"> . Scusa livingbooks, ma ce le hai in italiano? Complimenti per la tua spiegazione di precetto pasquale, W28. <IMG SRC="images/forum/icons/icon_wink.gif"> <IMG SRC="images/forum/icons/icon_wink.gif">
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