Contradictory Proverbs

Look before you leap.
He who hesitates is lost.

Absence makes the heart grow fonder.
Out of sight, out of mind.

You’re never too old to learn.
You can’t teach an old dog new tricks.

A word to the wise is sufficient.
Talk is cheap.

Fools rush in where angels fear to tread.
Nothing ventured, nothing gained.

Actions speak louder than words.
The pen is mightier than the sword.

Many hands make light work.
Too many cooks spoil the broth.

Seek and ye shall find.
Curiosity killed the cat.

Don’t look a gift horse in the mouth.
Beware of Greeks bearing gifts.

The best things in life are free.
There’s no such thing as a free lunch.

G.K. Chesterton said, “I owe my success to having listened respectfully to the very best advice, and then going away and doing the exact opposite.”

| Literature

Down and Out

http://commons.wikimedia.org/wiki/File:Die_Gartenlaube_(1871)_b_416.jpg

Three robbers, Babylas, Hilary, and Sosthenes, are stealing a treasure chest from the top of an old tower. Unfortunately, they’ve had to destroy their ladder to avoid pursuit, so they’ll have to descend using a crude tackle — a single pulley and a long rope with a basket at each end.

Babylas weighs 170 pounds, Hilary 100 pounds, Sosthenes 80 pounds, and the treasure 60 pounds. If the difference in weight between the two baskets is greater than 20 pounds then the heavier basket will descend too quickly and injure its occupant (though the treasure chest can withstand this). How can the three of them safely escape the tower with the treasure?

Click for Answer
| Puzzles

Toes Up

http://commons.wikimedia.org/wiki/File:Winslow_Homer_002.jpg

In logic, the contrapositive of “If A, then B” is “If not B, then not A”: “If Socrates is a man, then Socrates is human” carries the same message as “If Socrates is not human, then Socrates is not a man.”

To make this vivid for his geometry students, W.P. Cooke of West Texas State University enlisted Tex Ritter’s song “Rye Whiskey”:

If the ocean was whiskey and I was a duck,
I’d swim to the bottom and never come up.
But the ocean ain’t whiskey and I ain’t no duck,
So I’ll play Jack-O-Diamonds and trust to my luck.
For it’s whiskey, rye whiskey, rye whiskey, I cry,
If I don’t get rye whiskey, I surely will die.

In contrapositive form, Cooke said, Ritter would sing:

If I never reach bottom or sometimes come up,
Then the ocean ain’t whiskey or I ain’t a duck.
But my luck can’t be trusted or the cards I’ll not buck,
So the ocean is whiskey or I am a duck.
For it’s whiskey, rye whiskey, rye whiskey, I cry,
If my death is uncertain then I get whiskey (rye).

(American Mathematical Monthly, November 1969)

01/31/2012 Related:

Andrew Marvell’s “To His Coy Mistress” is constructed as a three-paragraph logical argument:

“Had we but world enough, and time,
This coyness, lady, were no crime…”
(If A, then B)

“But at my back I always hear
Time’s winged chariot hurrying near…”
(Not A)

“Now therefore, while the youthful hue
Sits on thy skin like morning dew…
Now let us sport us while we may…”
(Therefore Not B)

Unfortunately, he’s trying to argue his way from “If A, then B” to “Not A, therefore not B,” which is invalid. One wonders how his coy mistress responded.

(Thanks, Cleve.)

| Science & Math

Unquote

“I must ask anyone entering the house never to contradict me or differ from me in any way, as it interferes with the functioning of the gastric juices and prevents my sleeping at night.” — Sir George Sitwell

| Quotations

Cold Shoulder

http://commons.wikimedia.org/wiki/File:Penguin_2_(PSF).png

In 1944 a children’s book club sent a volume about penguins to a 10-year-old girl, enclosing a card seeking her opinion.

She wrote, “This book gives me more information about penguins than I care to have.”

American diplomat Hugh Gibson called it the finest piece of literary criticism he had ever read.

| Literature

Road Games

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The world’s shortest street is Ebenezer Place, in Wick, Caithness, Scotland. It’s 6 feet 9 inches long, just enough to accommodate a single door at the end of Mackays Hotel.

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The longest street, arguably, is the Pan-American Highway, which extends some 29,800 miles from Prudhoe Bay, Alaska, to Ushuaia, Argentina. It’s 23,310,222 times as long as Ebenezer Place.

http://commons.wikimedia.org/wiki/File:Engste_Stra%C3%9Fe_der_Welt.jpg

The world’s narrowest street is the Spreuerhofstraße in Reutlingen, Baden-Württemberg, Germany, which varies between 19.7 inches and 12.2 inches in width.

http://commons.wikimedia.org/wiki/File:Buenos_Aires_-_Monserrat_-_Avenida_9_de_Julio.jpg

Avenida 9 de Julio, in Buenos Aires, by contrast, is a full city block wide, with up to seven traffic lanes in each direction.

http://commons.wikimedia.org/wiki/File:LombardStreet.jpg

San Francisco’s Lombard Street may be the world’s most crooked, with eight hairpin turns in a single block.

There must be many contenders for the world’s straightest street; the straightest railway line cuts like an arrow across 297 miles of Australia’s Nullarbor Plain. Jerome Meyer calls this “undoubtedly the world’s most boring trip.”

(Images: Wikimedia Commons)

| Oddities

Handcraft

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He killed the noble Mudjokivis.
Of the skin he made him mittens,
Made them with the fur side inside,
Made them with the skin side outside.
He, to get the warm side inside,
Put the inside skin side outside;
He, to get the cold side outside,
Put the warm side fur side inside.
That’s why he put the fur side inside,
Why he put the skin side outside,
Why he turned them inside outside.

— George A. Strong, “The Modern Hiawatha,” in The Home Book of Verse, 1918

Ofttimes when I put on my gloves,
I wonder if I’m sane,
For when I put the right one on,
The right seems to remain
To be put on–that is, ‘t is left;
Yet if the left I don,
The other one is left, and then
I have the right one on.
But still I have the left on right;
The right one, though, is left
To go right on the left right hand
All right, if I am deft.

— Ray Clarke Rose, “Simple English,” in Wallace Rice, A Book of American Humorous Verse, 1903

“What can be more similar in every respect and in every part more alike to my hand and to my ear, than their images in a mirror?” wrote Kant in 1783. “And yet I cannot put such a hand as is seen in the glass in the place of its archetype; for if this is a right hand, that in the glass is a left one, and the image or reflection of the right ear is a left one which never can serve as a substitute for the other. There are in this case no internal differences which our understanding could determine by thinking alone. Yet the differences are internal as the senses teach, for, notwithstanding their complete equality and similarity, the left hand cannot be enclosed in the same bounds as the right one (they are not congruent); the glove of one hand cannot be used for the other.”

| Language · Science & Math