Fish Scales

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

While a student at Cambridge, Paul Dirac attended a mathematical congress that posed the following problem:

After a big day’s catch, three fisherman go to sleep next to their pile of fish. During the night, one fisherman decides to go home. He divides the fish in three and finds that this leaves one extra fish. He throws this into the water, takes one third of the remaining fish, and departs.

The second fisherman awakes. Not knowing that the first has left, he too divides the fish into three piles, finds one fish left over, discards it, and takes a third of the remainder. The third fisherman does the same. What is the least number of fish that the fishermen could have started with?

Dirac proposed that they had begun with -2 fish. The first fisherman threw one into the water, leaving -3, and took a third of this, leaving -2. The second and third fisherman followed suit.

This story was recalled by “a well-meaning experimenter” in the Russian miscellany Physicists Continue to Laugh (1968). “I could tell many other stories about theoreticians and their work,” he wrote, “but they have told me that one theoretician is writing a story under the title ‘How Experimental Physicists Work.’ That, of course, will be presented upside down.”

| Science & Math

Odd and Even

A puzzle by Noboyuki Yoshigahara:

“An odd number plus an odd number makes an even number. An even number plus an odd number makes an odd number. An even number plus an even number is an even number. Right?”

“Yes.”

“An odd number times an odd number is an odd number. An even number times an odd number is an even number. Right?”

“Sure.”

“An even number times an even number is an odd number. Right?”

“Huh?”

“You don’t think so? An even number times an even number is an odd number.”

“Why?”

Click for Answer
| Puzzles

The Elizabeth Whitman Mystery

http://books.google.com/books?id=eUwzAQAAMAAJ&source=gbs_navlinks_s

In May 1788, an expectant mother arrived in Danvers, Mass., and took a room at the Bell Tavern. Friendless and a stranger to the area, she said that her husband would join her shortly, but she would not give her family name. Evidently from a genteel family, she kept to her room, reading, writing, and sitting anxiously at her window. A woman who saw her during evening walks described her as handsome, with a sad face.

June passed into July, no husband appeared, and she became the subject of local gossip. At length she gave birth to a stillborn child, and she herself died two weeks later, of puerperal fever. Among her effects was found a letter:

Must I die alone? Shall I never see you more? I know that you will come, but you will come too late. This is, I fear, my last ability. Tears fall so, I know not how to write. Why did you leave me in so much distress? But I will not reproach you. All that was dear I left for you; but I do not regret it. May God forgive in both what was amiss. When I go from hence, I will leave you some way to find me; if I die, will you come and drop a tear over my grave?

With it was a poem:

With fond impatience all the tedious day
I sigh’d, and wish’d the lingering hours away;
For when bright Hesper led the starry train,
My shepherd swore to meet me on the plain;
With eager haste to that dear spot I flew,
And linger’d long, and then with tears withdrew:
Alone, abandon’d to love’s tenderest woes,
Down my pale cheeks the tide of sorrow flows;
Dead to all joys that fortune can bestow,
In vain for me her useless bounties flow;
Take back each envied gift, ye pow’rs divine,
And only let me call FIDELIO mine.

A newspaper appeal eventually confirmed that she was Elizabeth Whitman, a minister’s daughter from Hartford, but the identity of her lover has never been discovered. Her epitaph reads:

“This humble stone, in memory of Elizabeth Whitman, is inscribed by her weeping friends, to whom she endeared herself by uncommon tenderness and affection. Endowed with superior genius and acquirements, she was still more endeared by humility and benevolence. Let candor throw a veil over her frailties, for great was her charity to others. She sustained the last painful scene far from every friend, and exhibited an example of calm resignation. Her departure was on the 25th of July, A.D. 1788,in the 37th year of her age, and the tears of strangers watered her grave.”

| Society

In a Word

procerity
n. tallness

leptodactylous
adj. having slender toes or fingers

leptorrhine
adj. having a long, narrow nose

leptosome
n. a thin, frail, or slender person

windlestraw
n. a tall, thin person

| Language

Limericks

There was an old lady of Ryde
Who ate some green apples and died.
The apples, fermented
Inside the lamented,
Made cider inside ‘er inside.

— Anonymous

A gallant young man of Duquesne
Went home with a girl in the ruesne;
She said, with a sigh,
“I wonder when Igh
Shall see such a rain-beau aguesne.”

— Stanton Vaughn, ed., Limerick Lyrics, 1904

There was an old man said, “I fear
That life, my dear friends, is a bubble,
Still, with all due respect to a Philistine ear,
A limerick’s best when it’s double.”
When they said, “But the waste
Of time, temper, taste!”
He gulped down his ink with cantankerous haste,
And chopped off his head with a shubble.

— Walter de la Mare

| Poems

All Greek

In 1948, George Washington University doctoral student Ralph Alpher was working on a cosmology thesis under physicist George Gamow. As the paper took shape, “Gamow, with the usual twinkle in his eye, suggested that we add the name of Hans Bethe to an Alpher-Gamow letter to the editor of the Physical Review,” listing the authors as Alpher-Bethe-Gamow.

Bethe agreed to join, and the result, now known as the αβγ paper, was published on April 1, 1948 (“believe it or not, a date not of our asking”). “The response was fascinating,” Alpher later recalled, “ranging from feature articles, Sunday supplement stories, newspaper cartoons and voluminous mail from religious fundamentalists, to a packed audience of over 200, including members of the press, at the traditionally public (though usually not in this sense) ‘defence’ of the thesis.”

Gamow added, “There was, however, a rumor that later, when the alpha, beta, gamma theory went temporarily on the rocks, Dr. Bethe seriously considered changing his name to Zacharias.”

| Science & Math

Strong, Silent

http://www.google.com/patents/US5035072

Rayma Rich’s “collapsible riding companion,” patented in 1991, offers female travelers an inventive way to deter criminals: Set up the false head and torso in your passenger seat, dress it in a suitable shirt, and you have a devoted male escort who will accompany you anywhere and never ask for overtime.

When you get back to the airport, disconnect the head, stow it in the torso, and “the riding companion becomes a lightweight, easy-to-carry rectanglar case for traveling.”

| Technology

Intro Zoology

http://books.google.com/books?id=grpBAAAAIAAJ&source=gbs_navlinks_s

How to tell a parrot from a carrot, from American physicist Robert W. Wood’s extracurricular How to Tell the Birds From the Flowers: A Manual of Flornithology for Beginners (1907):

The Parrot and the Carrot we may easily confound,
They’re very much alike in looks and similar in sound.
We recognize the Parrot by his clear articulation,
For Carrots are unable to engage in conversation.

Below: A further distinction.

http://books.google.com/books?id=grpBAAAAIAAJ&source=gbs_navlinks_s

| Humor · Science & Math

Circles and Squares

circles and squares 1

Here are three circles and two squares, inscribed successively as shown.

If the diameter of the largest circle is 10, what is the diameter of the smallest circle?

Click for Answer
| Puzzles

Rules of Engagement

http://commons.wikimedia.org/w/index.php?title=File:Gen._%22Stonewall%22_Jackson,_C.S.A_-_NARA_-_529728.tif&page=1

Stonewall Jackson’s precepts for good conversation, from a book of maxims he collected in the 1850s:

  1. Ascertain in your conversation as well as you can wherein the skill & excellence of the individual lies & put him upon his favorite subject. Every person will of his own accord fall to talking on his favorite subject or topic if you will follow and not attempt to lead him.
  2. If you seek to improve in the greatest degree from the conversation of another, allow him to take his own course. If called upon, converse in turn upon your favorite topic.
  3. Never interrupt another but hear him out. There are certain individuals from whom little information is to be desired such as use wanton, obscene or profane language.
  4. If you speak in company, speak late.
  5. Let your words be as few as will express the sense you wish to convey & above all let what you say be true.
  6. Do not suffer your feelings to betray you into too much vehemence or earnestness or to being overbearing.
  7. Avoid triumphing over an antagonist.
  8. Never engross the whole conversation to yourself.
  9. Sit or stand still while another is speaking to you. [Do]not dig in the earth with your foot nor take your knife from your pocket & pare your nales nor other such action.
  10. Never anticipate for another to help him out. It is time enough for you to make corrections after he has concluded, if any are necessary. It is impolite to interrupt another in his remarks.
  11. Say as little of yourself & friends as possible.
  12. Make it a rule never to accuse without due consideration any body or association of men.
  13. Never try to appear more wise or learned than the rest of the company. Not that you should affect ignorance, but endeavor to remain within your own proper sphere.
  14. Let ease & gracefulness be the standard by which you form your estimation (taken from etiquett).

“Good breeding, or true politeness, is the art of showing men by external signs the internal regard we have for them,” he wrote. “It arises from good sense, improved by good company. It must be acquired by practice and not by books.”

| History · Society