In a Word

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interturb
v. to disturb by interrupting

In late 1908 Douglas Mawson, Alastair Mackay, and Edgeworth David left Ernest Shackleton’s party in hopes of discovering the location of the South Magnetic Pole. On Dec. 11, while Mackay left the camp to reconnoiter, David prepared to sketch the mountains and Mawson retired into the tent to work on his camera equipment:

I was busy changing photographic plates in the only place where it could be done — inside the sleeping bag. … Soon after I had done up the bag, having got safely inside, I heard a voice from outside — a gentle voice — calling:

‘Mawson, Mawson.’

‘Hullo!’ said I.

‘Oh, you’re in the bag changing plates, are you?’

‘Yes, Professor.’

There was a silence for some time. Then I heard the Professor calling in a louder tone:

‘Mawson!’

I answered again. Well the Professor heard by the sound I was still in the bag, so he said:

‘Oh, still changing plates, are you?’

‘Yes.’

More silence for some time. After a minute, in a rather loud and anxious tone:

‘Mawson!’

I thought there was something up, but could not tell what he was after. I was getting rather tired of it and called out:

‘Hullo. What is it? What can I do?’

‘Well, Mawson, I am in a rather dangerous position. I am really hanging on by my fingers to the edge of a crevasse, and I don’t think I can hold on much longer. I shall have to trouble you to come out and assist me.’

I came out rather quicker than I can say. There was the Professor, just his head showing and hanging on to the edge of a dangerous crevasse.

David later explained, “I had scarcely gone more than six yards from the tent, when the lid of a crevasse suddenly collapsed under me. I only saved myself from going right down by throwing my arms out and staying myself on the snow lid on either side.”

Mawson helped him out, and David began his sketching. The party reached the pole in January.

In a Word

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antelucan
adj. before dawn

finitor
n. the horizon

flavescent
adj. turning pale yellow

day-peep
n. the first appearance of daylight; the earliest dawn

Eoan
adj. of or pertaining to the dawn; eastern

Young Riders

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Sons of Jack “Catch-‘Em-Alive” Abernathy, the youngest U.S. Marshal in history, Louis and Temple Abernathy inherited their father’s self-reliance: In 1910, when they were 10 and 6 years old, they rode on horseback from their Oklahoma ranch to Manhattan to greet Theodore Roosevelt as he returned from Africa. After riding behind Roosevelt’s car in a ticker-tape parade, they drove home in a new car.

The following year, apparently bored, they accepted a $10,000 challenge to ride on horseback from New York to San Francisco in 60 days or less, never eating or sleeping indoors. They missed the deadline by two days but still established a speed record. And in 1913 they rode by motorcycle from Oklahoma to New York City.

The two went on to successful careers in law and oil. “Teach a boy self-reliance from the moment he tumbles out of the cradle, make him keep his traces taut and work well forward in his collar, and 99 times out of a hundred his independence will assert itself before he is 2 years old,” their father told a newspaper after their first trip. “That’s my rule, and if you don’t think I’ve taken the right tack talk to my boys for five minutes and they’ll convince you that they are men in principles even if they are babies in years. God bless ‘em.”

Book Codes

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Benedict Arnold encrypted his messages to the British Army using Blackstone’s Commentaries on the Laws of England. Arnold would replace each word in his message with a triplet of numbers representing the page number, line number, and word position where the word might be found in Blackstone. For example:

The 166.8.11 of the 191.9.16 are 129.19.21 266.9.14 of the .286.8.20, and 291.8.27 to be on 163.9.4 115.8.16 114.8.25ing — 263.9.14 are 207.8.17ed 125.8.15 103.8.60 from this 294.8.50 104.9.26 — If 84.8.9ed — 294.9.12 129.8.7 only to 193.8.3 and the 64.9.5 290.9.20 245.8.3 be at an 99.8.14.

British Army Major John André could then look up the words in his own copy of Blackstone to discover Arnold’s meaning:

The mass of the People are heartily tired of the War, and wish to be on their former footing — They are promised great events from this year’s exertion — If disappointed — you have only to persevere and the contest will soon be at an end.

The danger in using a book code is that the enemy can decode the messages if he can identify the book — and sometimes even if he can’t. In the comic strip Steve Roper, a reporter once excitedly telephoned the coded message 188-1-22 71-2-13 70-2-11 68-1-25 19-1-6 112-2-10 99-1-35. Reader Sean Reddick suspected that this message had been encoded using a dictionary, with each triplet of numbers denoting page, column, and word number. He never did discover the book that had been used, but by considering the ratios involved and consulting half a dozen dictionaries he managed to break the code anyway — he sent his solution to a nationally known columnist, who verified his feat when the comic strip bore out his solution. What was the message? (Hint: In the comic, the reporter mentions significantly that the plaintext message was given to him by “the delivery boy.”)

Click for Answer

The Pythagoras Paradox

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Draw a right triangle whose legs a and b each measure 1. Draw d and e to complete a unit square. Clearly d + e = 2.

Now if we cut a “step” into the square as shown, then f + h = 1 and g + i = 1, so the total length of the “staircase” is still 2. Cut still finer steps and j + k + l + m + n + o + p + q is likewise 2.

And so on: The more finely we cut the steps, the more closely their shape approximates that of the original triangle’s diagonal. Yet the total length of the stairstep shape remains 2, the sum of its horizontal and vertical elements. At the limit, then, it would seem that c must measure 2 … but we know that the length of a unit square’s diagonal is the square root of 2. Where is the error?

(Thanks, Alex.)

One Two Three

Each point on a straight line is either red or blue. Show that it’s always possible to find three points of the same color in which one is the midpoint of the other two.

Click for Answer

Gender in Swearing

In An Encyclopedia of Swearing (2006), University of the Witwatersrand linguist Geoffrey Hughes notes that terms of vehement personal abuse seem to attach disproportionately to the male sex:

gender in swearing table

In his analysis, even terms derived from female anatomy are applied to men rather than women (at least in British usage). Terms such as bugger, motherfucker, and sod[omite] understandably derive from sexual role, but why are devil, fucker, moron, and cretin applied generally to men and not women?

“All the indeterminate terms, such as bastard, idiot, and shit, which should logically be ‘bisexual’ in application, are invariably applied only to males,” Hughes writes. (Also, strangely, there seems to be no vehement term of abuse that’s used freely of both sexes.) “However, the historical perspective shows one significant trend, namely that several of the terms, like bitch and sow, were first used of males (or of both sexes) and only later applied exclusively to women.”

Mixed Greens

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Professor Starr Jordan, President of Leland Stanford University, told of a case where nature had juggled with real estate during the San Francisco earthquake. An earthquake crack had passed directly in front of three cottages, and moved the rose-garden from the middle cottage to the furthest one, and the raspberry patch from the near cottage exactly opposite the middle one. History does not relate how the law decided who owned the roses and the raspberries after their rearrangement.

— M.E. David, Professor David: The Life of Sir Edgeworth David, 1937

The Winner’s Curse

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In 1983, Max Bazerman and William Samuelson asked M.B.A. students in 12 Boston University microeconomics classes to estimate the value of each of four commodities: jars containing 800 pennies, 160 nickels, 200 large paper clips each worth 4 cents, and 400 small paper clips each worth 2 cents. Thus each jar had a value of $8.00, though the students didn’t know this. They asked the students to bid on the value of each commodity. The student whose bid came closest to the true value in each auction would win a $2 prize.

The average estimated value of all the commodities was $5.13, $2.87 less than the true value. But the average winning bid was $10.01, resulting in an average loss to the winner of $2.01. The average winning bid produced a loss in more than half of all the auctions.

This is the “winner’s curse”: The winner of an auction tends to be one of those who form the highest estimate of an item’s value — and hence one of those most at risk of overpaying.

“If an individual assumes that his or her bid will win the auction, this piece of data should indicate that the bidder has probably overestimated the value of the commodity in comparison to other competitors,” write Bazerman and Samuelson. “When the correct inference is drawn, the bidder should revise the estimate of the true value of the item downward and lower the bid accordingly. By failing to take this inference into account, the winning bidder risks paying too much for the ‘prize.'”

(Max Bazerman and William Samuelson, “I Won the Auction But Don’t Want the Prize,” Journal of Conflict Resolution 27:4 [December 1983], 618-634.)

Round Numbers

A curiosity attributed to a Professor E. Ducci in the 1930s:

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Arrange four nonnegative integers in a circle, as above. Now construct further “cyclic quadruples” of integers by subtracting consecutive pairs, always subtracting the smaller number from the larger. So the quadruple above would produce 22, 8, 38, 8, then 14, 30, 30, 14, and so on.

Ducci found that eventually four equal numbers will occur.

A proof appears in Ross Honsberger’s Ingenuity in Mathematics (1970).

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