Stump Trouble

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

The voting paradox shows that conflicting majorities can prevent a clear winner even in a fair election.

Sadly, this can be true even if the candidates specify platforms. Suppose there are two issues, x and y, each of which admits two possible positions, x and x’ and y and y’. Then a candidate can have four possible platforms: xy, xy’, x’y, and x’y’. Now suppose there are three voters, each of whom ranks her preferences in a different order:

Voter 1: xy, xy’, x’y, x’y’
Voter 2: xy’, x’y’, xy, x’y
Voter 3: x’y, x’y’, xy, xy’

If the voters could vote on the individual issues instead of having to choose a platform, Voters 1 and 2 would prefer x to x’, and Voters 1 and 3 would prefer y to y’. These are clear majorities. But in practice platform x’y’ will defeat platform xy, since it’s preferred by a majority (Voters 2 and 3).

“Thus, a platform whose alternatives, when considered separately, are both favored by a majority may be defeated by a platform containing alternatives that only minorities favor,” writes Steven J. Brams in Paradoxes in Politics. Public policy scholar Anthony Downs argues that the fact that a majority platform can be constructed from minority positions may make it rational for politicians to appeal to coalitions of minorities.

Safety First

http://www.google.com/patents/about?id=NUQpAAAAEBAJ

Patented by Deloris Gray Wood in 1998, the “kissing shield” makes pretty good sense:

It is customary when we kiss to come in contact with another’s lips, and in certain cultures, to follow with a kiss on the skin of each cheek; thus germs can be passed from one person to another. In keeping with one aspect of the invention, if casual contact is necessary and a kiss is appropriate, one can protect oneself from the germs present in saliva or other secretions which might be transmitted from kissing by using a kissing shield.

What sets Wood’s application apart is its comprehensiveness: The shield “can be used especially by a politician who kisses babies” — and one variant has “a pocket sized and shaped to receive the tongue of one of the two persons” to permit French kissing.

“I kissed my first girl and smoked my first cigarette on the same day,” wrote Toscanini. “I haven’t had time for tobacco since.”

Round Trip

http://books.google.com/books?id=7CTOAAAAMAAJ&printsec=frontcover#v=onepage&q&f=false

John A. “Colonial Jack” Krohn pushed a wheelbarrow out of Portland, Maine, on June 1, 1908, and he pushed it back 357 days later. In the interval he pushed it around the perimeter of the contiguous United States, a journey of 9,024 miles on which he wore out 119 pairs of socks and lost 17 pounds.

On his return Krohn’s barrow was covered with cards; he had delivered a letter to the postmaster of Portland’s namesake in Oregon and returned with the reply. He’d completed the trip in 43 days fewer than expected, he said, though he hadn’t walked on Sundays and had lost 19 days to sickness.

“With some there had been doubts regarding his being able to accomplish such an unusual undertaking, considering his frail appearance when he first started out,” ran one contemporary account. “The great benefits of an out of door life could be readily noted on his return, through his improved look and action in every respect, showing the benefits derived from many weeks and months passed in the open air.”

He didn’t rest long — after writing a book about the adventure, he hit the road again to promote it.

An Early iPod

J.G. Christopher, of Minneapolis, Minn., is the possessor of a canary bird, the voice of which has been developed in a peculiarly painstaken manner, so that now this ‘educated’ songster can successfully render the well-known air, ‘A Life on the Ocean Wave.’ The bird will commence to warble like any other of these pets, and after uttering a few notes will immediately strike into the tune, and when its voice has attained full height the above tune will be sung entire, and in a manner that sounds singularly melodious and attractive, literally setting to note its natural vocal powers. This was only achieved after the most diligent and patient attention. As soon as the bird was old enough to pick up a living it was put in a room apart from all others, and a music-box also placed in the apartment and kept perpetually going, so that this singular pupil had nothing to learn from but that. After four months of such apprentice-ship, the owner was rewarded by hearing his little favorite render ‘A Life on the Ocean Wave’ as naturally and perfectly as if that was the song of its ancestors.

— James Baird McClure, ed., Entertaining Anecdotes From Every Available Source, 1879

Sitting In

http://commons.wikimedia.org/wiki/File:Ford-Oval_Office-Pipe.jpg

Gerald Ford served as both vice president and president but was elected to neither office.

He was appointed to the vice presidency when Spiro Agnew resigned, and he succeeded Richard Nixon as president.

Riddle

If there was a time when nothing existed, then there must have been a time before that — when even nothing did not exist. Suddenly, when nothing came into existence, could one really say whether it belonged to the category of existence or of non-existence?

— Chuang-Tzu

Kindled Ambition

http://books.google.com/books?id=bbURAAAAYAAJ&printsec=frontcover#v=onepage&q&f=false

From Strand, January 1898: When match manufacturers S.I. Moreland and Sons challenged their customers to create “the greatest novelty of any sort that can be made with not less than 1,000 of our match-boxes,” G.W. Roberts of Birmingham submitted a full-size piano composed of 3,776 matchboxes and 5 pounds of glue.

http://books.google.com/books?id=bbURAAAAYAAJ&printsec=frontcover#v=onepage&q&f=false

Among other entries, F. Marshall’s 10-foot-6-inch model of the Forth Bridge is a marvel of engineering — other than 3,000 matchboxes, “no material whatever is used in the construction of the bridge — not even in the stays. When completed it stood the test of 42 lb. weight in the centre of either arch. I never saw the original bridge, but got an idea of it from a lithograph in a railway guide.”

http://books.google.com/books?id=bbURAAAAYAAJ&printsec=frontcover#v=onepage&q&f=false

And above is a model of Nelson’s ship Victory passing a large lighthouse, by Mr. Grubb of Atherstone, who worked three hours a night for five months. The ship is 3 feet 6 inches long and the lighthouse 5 feet 2 inches high.

The Strand also reports that a Lewis Sheldon constructed a double-masted turret ship-of-war 8 feet 3 inches long that carried 15 guns and six lifeboats, all made out of matchboxes. Sadly, they don’t include a photo.

“The Cavalry Skirmish”

the cavalry skirmish

This puzzle, by Les Marvin and Sherry Nolan, appeared in the Journal of Recreational Mathematics in 1977. “White to play in the adjoining diagram. If both players play optimally, will White win, lose, or draw?”

I don’t believe JRM ever published the solution. My stab: Either king is vulnerable to a check from the bishop file, and White will win a straight race. So I think Black must play defense. But if White attacks c7 with both knights and Black defends it doubly, then White can simply trade off all four knights (1. Nc7+ Nxc7 2. Nxc7+ Nxc7 bxc7) and the pawn will queen. So I think White wins.

This isn’t a very “mathematical” solution, but I can’t find a reliable alternative involving the parity of the knights’ moves, which seems to be what’s expected. Any ideas?

06/06/2014 UPDATE: A reader ran this position through a couple of strong chess engines and finds that it’s likely a draw — here’s one example:

[Event “?”]
[Site “?”]
[Date “????.??.??”]
[Round “?”]
[White “?”]
[Black “?”]
[Result “*”]
[FEN “k6n/Pp4n1/1P6/8/8/6p1/1N4Pp/N6K w – – 0 1”]

1.Nd1 Nf7 2.Nc2 Ne5 3.Nce3 Nd7 4.Nd5 Nxb6 5.Nxb6+ Kxa7 6.Nc8+ Ka6 7.Ne3 b5 8.Nd6 b4 9.Ne4 Nh5 10.Nc2 Kb5 11.Nxb4 Kxb4 12.Nxg3 Nxg3+ 13.Kxh2 Nf1+ 14.Kh3 Ne3 15.g4 Kb3 16.g5 Nd5 17.g6 Nf4+ 18.Kg3 Nxg6

There doesn’t seem to be a sure way for either side to reach a win. I suspect that Marvin and Nolan thought otherwise, but they were writing in 1977, without the benefit of computer analysis. Without a published solution, we can’t be sure.

(Thanks, Emilio.)

A Lasting Gift

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

Letter from Richard Byrd to his son shortly after establishing Marie Byrd Land, Feb. 22, 1929:

Dear Dickie–

I have named a big new land after mommie because mommie is the sweetest finest and nicest and best person in the world. Take good care of her and be awfully sweet to her while I’m away.

I love you my dear boy.

Daddy
Little America
Antarctica