A story from the net.

Two mathematicians were having dinner in a restaurant, arguing about the average mathematical knowledge of the American public. One mathematician claimed that this average was woefully inadequate, the other maintained that it was surprisingly high.

"I'll tell you what," said the cynic, "ask that waitress a simple math question. If she gets it right, I'll pick up dinner. If not, you do." He then excused himself to visit the men's room, and the other called the waitress over.

"When my friend comes back," he told her, "I'm going to ask you a question, and I want you to respond 'one third x cubed.' There's twenty bucks in it for you." She agreed.

The cynic returned from the bathroom and called the waitress over. "The food was wonderful, thank you." The other mathematician said, "incidentally, do you know what the integral of x squared is?"

The waitress looked pensive; almost pained. She looked around the room, at her feet, made gurgling noises, and finally said, "Um, one third x cubed?"

So the cynic paid the check.

The waitress wheeled around, walked a few paces away, looked back at the two men, and muttered under her breath, "...plus a constant."

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From time to time, Marilyn Vos Savant presents some amusing and instructive problems. One of these is:

If you buy a hundred pounds of cucumbers which are 99 percent water, and they subsequently dry-out so that they are just 98% water, how much do the cucumbers now weigh?

Here is another:

If you drive on a trip at 25 miles per hour for the first half of the distance, how fast must you travel over the second half to average 50 miles per hour for the whole trip?

And another:

If we know one digit in a four-decimal-digit combination lock, but we do not know the position of that digit, then how many four-digit combinations must we try to be sure of opening the lock? Hint: It is not 4000.

Here are a couple I got from an airline seat-pocket magazine:

Bill played three hands of poker, each time losing three-quarters of his money. He was left with 1.50 dollars. How much money did he lose?

Julie says to her brother Pete, "I have as many sisters as brothers." Pete replies, "I have twice as many sisters as I have brothers." How many sisters and brothers are there altogether?

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More Useful Unit Conversions

(from the Banneker Banner: The Official Journal of the Maryland Council of Teachers of Mathematics)

• 1 million microphones = 1 megaphone
• 1 million bicycles = 2 megacycles
• 365.25 days = 1 unicycle
• 2200 mockingbirds = 2 kilomockingbirds
• 10 cards = 1 decacards
• 1 kilogram of falling figs = 1 fig Newton
• 1000 grams of wet socks = 1 literhosen
• 1 millionth of a fish = 1 microfish
• 1 trillion pins = 1 terrapin
• 1 million billion picolos = 1 gigolo
• 10 rations = 1 decoration
• 100 rations = 1 C-ration
• 10 millipedes = 1 centipede
• 3 1/3 tridents = 1 decadent
• 10 monologs = 5 dialogs
• 5 dialogs = 1 decalog
• 2 monograms = 1 diagram
• 8 nickles = 2 paradigms
• 2 wharves = 1 paradox

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If a basketball team has an overall probability 1/3 of success when they attempt a 3 point shot, and if they have 50% rebound success, Then what is their expected score per possession if they attempt a 3 point shot every time they have the ball? Is this expected score an overestimate or an underestimate due to neglecting occasional tip-ins? What probability of success for 2 point scores would make it wise for this team to sometimes purposely try to score 2 point baskets? Should 3 point goals be tried if 2 point baskets are statistically desirable?

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Given a wheel of radius k and another wheel of radius r, with r<=k, separated so that the distance between their centers is d, what is the length of the belt that is drawn tautly about the two wheels?

Here is an MLAB do-file that computes the answer.

/*MLAB do-file: beltprob.do*/

reset

/*Read-in k,r, and d */

k=kread("enter the larger radius k:")

r=kread("enter the smaller radius r:")

d=kread("enter the distance between the centers d:")

ep=acos((k-r)/d)

len=2*d*sin(ep)+2*ep*r+2*k*(pi-ep)

type len,ep

/*end of beltprob.do */

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Actual Answers

The following excerpts are actual answers given on history tests by children of 5th and 6th grades in Ohio. They were collected over a period of three years by two teachers. Kids should rule the world, as it would be a laugh a minute for us adults and therefore no time to war or argue.

Ancient Egypt was old. It was inhabited by gypsies and mummies who all wrote in hydraulics. They lived in the Sarah Dessert. The climate Of the Sarah is such that all the inhabitants have to live elsewhere.

The Greeks were a highly sculptured people, and without them we wouldn't have history. The Greeks also had myths. A myth is a young female moth.

Socrates was a famous old Greek teacher who went around giving people advice. They killed him. He later died from an overdose of wedlock Which is apparently poisonous. After his death, his career suffered a Dramatic decline.

Julius Caesar extinguished himself on the battlefields of Gaul. The Ides of March murdered him because they thought he was going to be made king. Dying, he gasped out "Same to you, Brutus."

Joan of Arc was burnt to a steak and was canonized by Bernard Shaw for reasons I don't really understand. The English and French still have problems.

It was an age of great inventions and discoveries. Gutenberg invented removable type and the Bible. Another important invention was the circulation of blood.

Sir Walter Raleigh is a historical figure because he invented Cigarettes and started smoking.

The greatest writer of the Renaissance was William Shakespeare. He was born in the year 1564, supposedly on his birthday. He never made much money and is famous only because of his plays. He wrote tragedies, comedies, and hysterectomies, all in Islamic pentameter.

Writing at the same time as Shakespeare was Miguel Cervantes. He Wrote Donkey Hote. The next great author was John Milton. Milton wrote Paradise Lost. Since then no one ever found it.

Delegates from the original 13 states formed the Contented Congress. Thomas Jefferson, a Virgin, and Benjamin Franklin were two singers of the Declaration of Independence. Franklin discovered electricity by Rubbing two cats backward and also declared, "A horse divided against itself cannot stand." He was a naturalist for sure. Franklin died in 1790 and is still dead.

Abraham Lincoln became America's greatest Precedent. Lincoln's Mother died in infancy, and he was born in a log cabin which he built with his ownhands.. Abraham Lincoln freed the slaves by signing the Emasculation Proclamation.

On the night of April 14, 1865, Lincoln went to the theater and got Shot in his seat by one of the actors in a moving picture show. They believe the assinator was John Wilkes Booth, a supposingly insane actor. This ruined Booth's career.

Johann Bach wrote a great many musical compositions and had a large number of children. Bach died from 1750 to the present. Bach was the most famous composer in the world and so was Handel. Handel was half German, half Italian, and half English. He was very large.

Bethoven wrote music even though he was deaf. He was so deaf that he wrote loud music and became the father of rock and roll. He took long walks in the forest even when everyone was calling for him. Beethoven expired in 1827 and later died for this.

The nineteenth century was a time of a great many thoughts and inventions. People stopped reproducing by hand and started reproducing by machine. The invention of the steamboat caused a network of rivers to spring up.

Louis Pasteur discovered a cure for rabbits but I don't know why.

Charles Darwin was a naturalist. He wrote the Organ of the Species. It was very long people got upset about it and had trials to see if it was really true. He sort of said God's days were not just 24 hours but without watches who knew anyhow? I don't get it.

Madman Curie discovered radio. She was the first woman to do what she did. Other women have become scientists since her but they didn't get to find radios because they were already taken.

Karl Marx was one of the Marx Brothers. The other three were in the movies. Karl made speeches and started revolutions. Someone in the family had to have a job, I guess.

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Knowledge and Advice for living?

• Save the whales. Collect the whole set
• A day without sunshine is like, night
• On the other hand, you have different fingers.
• I just got lost in thought. It was unfamiliar territory.
• 42.7 percent of all statistics are made up on the spot.
• 99 percent of lawyers give the rest a bad name.
• I feel like I'm diagonally parked in a parallel universe.
• You have the right to remain silent. Anything you say will be misquoted, then used against you.
• I wonder how much deeper the ocean would be without sponges.
• Honk if you love peace and quiet.
• Remember half the people you know are below average.
• Despite the cost of living, have you noticed how popular it remains?
• Nothing is fool-proof to a talented fool.
• Atheism is a non-prophet organization.
• He who laughs last thinks slowest.
• Depression is merely anger without enthusiasm.
• Eagles may soar, but weasels don't get sucked into jet engines.
• The early bird may get the worm, but the second mouse gets the cheese.
• I drive way too fast to worry about cholesterol.
• I intend to live forever - so far so good.
• Borrow money from a pessimist - they don't expect it back.
• If Barbie is so popular, why do you have to buy her friends?
• My mind like a steel trap - rusty and illegal in 37 states.
• Quantum mechanics: The dreams stuff is made of.
• The only substitute for good manners is fast reflexes.
• Support bacteria - they're the only culture some people have.
• When everything's coming your way, you're in the wrong lane and going the wrong way.
• If at first you don't succeed, destroy all evidence that you tried.
• A conclusion is the place where you got tired of thinking.
• Experience is something you don't get until just after you need it.
• For every action there is an equal and opposite criticism.
• Bills travel through the mail at twice the speed of checks
• Never do card tricks for the group you play poker with.
• No one is listening until you make a mistake.
• Success always occurs in private and failure in full view.
• The colder the x-ray table the more of your body is required on it.
• The hardness of butter is directly proportional to the softness of the bread.
• The severity of the itch is inversely proportional to the ability to reach it.
• To steal ideas from one person is plagiarism; to steal from many is research.
• To succeed in politics, it is often necessary to rise above your principles.
• Monday is an awful way to spend 1/7th of your life.
• You never really learn to swear until you learn to drive.
• Two wrongs are only the beginning.
• The problem with the gene pool is that there is no lifeguard.
• The sooner you fall behind the more time you'll have to catch up.
• A clear conscience is usually the sign of a bad memory.
• Change is inevitable except from vending machines.
• Get a new car for your spouse - it'll be a great trade!
• Plan to be spontaneous - tomorrow.
• Always try to be modest and be proud of it!
• If you think nobody cares, try missing a couple of payments.
• How many of you believe in telekinesis? Raise my hand...
• Love may be blind but marriage is a real eye-opener.
• If at first you don't succeed, then skydiving isn't for you.

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An Aptitude Test for Lawyers

• 1.) Some months have 30 days, some months have 31 days. How many months have 28 days?
  
  
• 2.) If a doctor gives you 3 pills and tells you to take one pill every half hour, how long would it be before all the pills had been taken?
  
  
• 3.) I went to bed at eight o'clock in the evening and wound up my clock and set the alarm to sound at nine o'clock in the morning. How many hours sleep would I get before being awaken by the alarm?
  
  
• 4.) Divide 30 by half and add ten. What do you get?
  
  
• 5.) A farmer had 17 sheep. All but 9 died. How many live sheep were left?
  
  
• 6.) If you had only one match and entered a COLD and DARK room, where there was an oil heater, an oil lamp and a candle, which would you light first?
  
  
• 7.) A man builds a house with four sides of rectangular construction, each side having a southern exposure. A big bear comes along. What color is the bear?
  
  
• 8.) Take 2 apples from 3 apples. What do you have?
  
  
• 9.) How many animals of each species did Moses take with him in the Ark?
  
  
• 10.) If you drove a bus with 43 people on board from Chicago and stopped at Cleveland to pick up 7 more people and drop off 5 passengers and at Pittsburg to drop off 8 passengers and pick up 4 more and eventually arrive at Philadelphia 20 hours later, what's the name of the driver?
  
  
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• ANSWERS: (So - you're looking anyway!)
• 1.) All of them. Every month has at least 28 days.
• 2.) 1 hour. If you take a pill at 1 o'clock, then another at 1:30 and the last at 2 o'clock = 3 pills in 1 hour.
• 3.) 1 hour. It is a wind up alarm clock -- It cannot discriminate a.m. from p.m.
• 4.) 70. Dividing by half is the same as multiplying by 2.
• 5.) 9 live sheep.
• 6.) The match -- Try the match!
• 7.) White. If all walls face south, the house must be on the North Pole.
• 8.) 2 apples.
• 9.) None. It was Noah, not Moses.
• 10.) YOU are the driver.

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Consuming Statistics: A Gourmet Guide.

Imagine you have two different treatments A and B for a disease - maybe this is just going to hospital A or hospital B.

Now suppose treatment A is given to 200 hard-to-cure cases, and succeeds in 40 of these (cure percentage=20%).

Treatment B is given to some other 200 hard-to-cure cases, and succeeds in 30 of these (cure percentage=15%)

Treatment A is given to 100 easy-to-cure cases, and succeeds in 85 of these (cure percentage=85%)

Treatment B is given to 400 easy-to-cure cases, and succeeds in 300 of these (cure-percentage=75%)

But the overall cure-percentage of treatment A is 42%, and the overall cure-percentage of treatment B is 55% !!

1. Show that these overall percentages are correct.

2. Explain what is happening (is this a paradox?)

3. Which treatment would you choose?

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Seems Like a Good Idea.

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EUROPEAN UNION LANGUAGE HARMONISATION

The European Union commissioners have announced that agreement has been reached to adopt English as the preferred language for European communications, rather than German, which was the other possibility.

As part of the negotiations, the British Government conceded that English had some room for improvement and has accepted a five year phased plan for what will be known as Euroenglish (Euro, for short).

In the first year, 's' will be used instead of the soft 'c'. Sertainly, sivil servants will resieve this news with joy. Also, the hard 'c' will be replaced with 'k'. Not only will this klear up konfusion but typewriters kan have one less letter.

There will be growing publik enthusiasm in the sekond year, when the troublesome 'ph' will be replaced by 'f'. This will make words like 'fotograph' 20 persent shorter.

In the third year, publik akseptanse of the new spelling kan be expekted to reach the stage where more komplikated changes are possible. Governments will enkourage the removal of double letters, which have always ben a deterent to akurate speling. Also, al wil agre that the horible mes of silent 'e's in the languag is disgracful, and they would go.

By the fourth year, peopl wil be reseptiv to steps such as replasing 'th' by 'z' and 'w' by 'v'.

During ze fifze year, ze unesesary 'o' kan be dropd from vords kontaning 'ou' and similar changs vud, of kors, be aplid to ozer kombinations of leters.

Aftr zis fifz yer, ve vil hav a reli sensibl writen styl. Zer vil be no mor trubls or difikultis and evrivun vil find it ezi tu understand ech ozer. Ze drem vil vinali kum tru!

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I think George Bernard Shaw would approve, and perhaps this undertaking was reported by the Readers Digest some time ago.

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Hated Neologisms By Andrew West, CFA, globalinsights@iaac.com

Sometimes when I read research on Internet companies, I just want to scream. Oh, it's not the valuations, I'm gradually building up a tolerance on that front, emerging from my dark "value" cave into the luminous sunlight of the "triple-digit-everything" cyber-millennium. No, what really irks me is the horrible writing and the twisting of the English language.

One of the most popular techniques for communicators within the technology sector is to invent new terms that sound much more exciting than standard words. Failure to use the new terminology risks the loss of billions in market capitalization and, ultimately, obsolescence.

Consider these examples:"B2B," a.k.a. "business to business" - was once termed "wholesaling", "business services", or "selling industrial products" . But writing "B2B" really communicates how little time there is when one has so many "dynamic", "synergistic", and limitless "cyber-opportunities" to attend to.

"B2C", a.k.a. "business to consumer"- was once called "retailing", or more recently, "e-tailing". "B2C" is becoming passe and is "soooo 1999," yet it still has its fans because after all, "B2C" contains two-thirds of "B2B"'s characters.

"Space" is another example, as in "Amazon is first mover in the e-tailing space." "Industry" had customarily been used to denote a field of business, but that term has been ditched because of its sinister connotations of steel, coal, and actual profits from operations. "Space" as in "losing money in cyber-space" is considered much more futuristic and suggestive of a potential "ten-bagger."

"Scale" and "Scalable" are also leaping off the lips of savvy CEO's and analysts. Once primarily found on fish, or used to weigh things, "scale" is making huge leaps from the bottom of the linguistic charts. Years ago, super-obscure engineers used the term "scalability" to indicate that something could be uniformly multiplied or divided while maintaining its original structure. Now it seems that everybody is saying "our online business is infinitely scalable to the needs of our customers". Here's a tip: use the old but reliable term "expandable", because "expand" always indicates an increase, while scalable can also mean a decrease (unless of course you want to emphasize that you can easily shrink your Internet system after customer demand dries up).

I recently found the following passage penned by an analyst at a major brokerage: "Given that the financial markets have already largely anticipated the growth of the web, and that many growth drivers have yet to be fully exploited, timing is primordial; the value usually goes to the first mover, unless its rivals respond immediately."

Let me explain why I consider this the apex of bad writing. For clarification, "growth drivers" are what were once called "opportunities." "Primordial" means "existing from the beginning of time" which makes no sense in the sentence, but "timing is primordial" undoubtedly looks much more impressive and worthy of a $250k/year salary than "timing is primary."

He certainly didn't miss the chance to employ one of Wall Street's hottest catch-phrases, "first mover". The explosive spread of "first mover" shows me that Wall Street (and Silicon Valley) is either more full of philosophers than I'd realized, or full of buzzword-spewing hacks. On Wall Street, "first mover" is a package-deal which suggests that whoever gets into a "space" first, becomes a billionaire (unless you're underwriting their competitor's IPO).

In most circumstances, "first mover" can be replaced by the simpler "first", but then we would miss the historical and metaphysical significance of the phrase. Since my favorite philosopher is Ayn Rand, who encouraged the study of my second favorite, Aristotle, I immediately noticed the use of "first mover" a term which until recently I had only encountered in Aristotelian studies. In Book 12 of his "Metaphysics", Aristotle arrived at his conception of God, as being the first, or unmoved, mover. Being the fountainhead of all motion, Aristotle considered the First Mover the ultimate cause of everything that happened in the world.

So do these analysts really think that Amazon.Com is God? No wonder the stock is so high.

Note: The above represents the personal outrage of Andrew West and may not represent the comprehensive outrage of all.

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From Jeanne Hernandez: Subject: FW: Physics Exam

The following concerns a question in a physics degree exam at the University of Copenhagen:

"Describe how to determine the height of a skyscraper with a barometer."

One student replied:

"You tie a long piece of string to the neck of the barometer, then lower the barometer from the roof of the skyscraper to the ground. The length of the string plus the length of the barometer will equal the height of the building."

This highly original answer so incensed the examiner that the student was failed immediately. The student appealed on the grounds that his answer was indisputably correct, and the university appointed an independent arbiter to decide the case. The arbiter judged that the answer was indeed correct, but did not display any noticeable knowledge of physics. To resolve the problem it was decided to call the student in and allow him six minutes in which to provide a verbal answer which showed at least a minimal familiarity with the basic principles of physics.

For five minutes the student sat in silence, forehead creased in thought. The arbiter reminded him that time was running out, to which the student replied that he had several extremely relevant answers, but couldn't make up his mind which to use. On being advised to hurry up the student replied as follows:

"Firstly, you could take the barometer up to the roof of the skyscraper, drop it over the edge, and measure the time it takes to reach the ground. The height of the building can then be worked out from the formula H = 0.5g x t squared. But bad luck on the barometer."

"Or if the sun is shining you could measure the height of the barometer, then set it on end and measure the length of its shadow. Then you measure the length of the skyscraper's shadow, and thereafter it is a simple matter of proportional arithmetic to work out the height of the skyscraper."

"But if you wanted to be highly scientific about it, you could tie a short piece of string to the barometer and swing it like a pendulum, first at ground level and then on the roof of the skyscraper. The height is worked out by the difference in the gravitational restoring force T = 2 pi sqrroot (l / g)."

"Or if the skyscraper has an outside emergency staircase, it would be easier to walk up it and mark off the height of the skyscraper in barometer lengths, then add them up."

"If you merely wanted to be boring and orthodox about it, of course, you could use the barometer to measure the air pressure on the roof of the skyscraper and on the ground, and convert the difference in millibars into feet to give the height of the building."

"But since we are constantly being exhorted to exercise independence of mind and apply scientific methods, undoubtedly the best way would be to knock on the janitor's door and say to him 'If you would like a nice new barometer, I will give you this one if you tell me the height of this skyscraper'."

[The student was Niels Bohr, the only Dane to win the Nobel prize for Physics].

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