Math Notes

20864448472975628947226005981267194447042584001 = (2 + 0 + 8 + 6 + 4 + 4 + 4 + 8 + 4 + 7 + 2 + 9 + 7 + 5 + 6 + 2 + 8 + 9 + 4 + 7 + 2 + 2 + 6 + 0 + 0 + 5 + 9 + 8 + 1 + 2 + 6 + 7 + 1 + 9 + 4 + 4 + 4 + 7 + 0 + 4 + 2 + 5 + 8 + 4 + 0 + 0 + 1)20

Moving Without Motion?

Achilles-weed is prostrate and grows along the ground at the amazing rate of 10 cm per hour. An exceeding slow tortoise munches one end of the Achilles-weed at the same rate as it grows at the other end. So the tortoise appears to chase the Achilles-weed round the garden. But, strictly speaking, the Achilles-weed does not move at all, it grows and is eaten. Yet its location changes, and it is made up of parts whose location changes (the left and right-hand halves of the Achilles-weed). Hence being made up of parts whose location changes is not sufficient for motion.

— Peter Forrest, “Is Motion Change of Location?”, Analysis, 1984

Dueling Doppelgängers

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

When World War I broke out in August 1914, Germany enlisted a large ocean liner, the Cap Trafalgar, to attack British merchant ships around Cape Horn. While at a supply base on Trinidade, it was surprised by the HMS Carmania, a British liner that had been similarly pressed into service by the British navy.

The two enormous ships squared off and fought a murderous sea battle. In the end the Cap Trafalgar sank, and the Carmania limped away to a Brazilian port.

An observer might still have wondered which side won — by an ironic coincidence, the Cap Trafalgar had been disguised as the Carmania and the Carmania as the Cap Trafalgar.

Smoldering Chic

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

This should have caught on — Watson P. Aull’s “cigarette ring,” patented in 1938, clamps a cigarette in a ring worn on the left forefinger, so that the smoker has full use of her hands.

Here’s a related stunt from R.M. Abraham’s Diversions & Pastimes (1933):

“A cigarette may be lit quite easily by holding it 4 or 5 inches above the flame of the match.”

I haven’t tried it.

Book Perils

“I suppose every old scholar has had the experience of reading something in a book which was significant to him, but which he could never find again. Sure he is that he read it there, but no one else ever read it, nor can he find it again, though he buy the book, and ransack every page.” — Emerson

“When we read, we are, we must be, repeating the words to ourselves unconsciously; for how else should we discover, as we have all discovered in our time, that we have been mispronouncing a word which, in fact, we have never spoken? I refer to such words as ‘misled,’ which I, and millions of others when young, supposed to be ‘mizzled.'” — A.A. Milne

“It is one of the oddest things in the world that you can read a page or more and think of something utterly different.” — Christian Morgenstern

A Pretty Problem

In Longfellow’s novel Kavanagh, Mr. Churchill reads a word problem to his wife:

“In a lake the bud of a water-lily was observed, one span above the water, and when moved by the gentle breeze, it sunk in the water at two cubits’ distance. Required the depth of the water.”

“That is charming, but must be very difficult,” she says. “I could not answer it.”

Is it? If a span is 9 inches and a cubit is 18 inches, how deep is the water?

Click for Answer

Missing Person

At 5 p.m. on Dec. 2, 1919, Canadian theater magnate Ambrose Small met with a lawyer in his Toronto office. The lawyer departed at 5:30 p.m. Between 5:30 and 6:00, Small vanished.

No one saw him leave the office, and no body was ever found. The disappearance seemed senseless. Small was a self-made millionaire; no money was missing, there was no evidence of kidnapping, and no ransom note was ever received.

Curiously, writer Ambrose Bierce had disappeared in Mexico six years earlier. Charles Fort wondered, “Was somebody collecting Ambroses?”

Found Out

http://commons.wikimedia.org/wiki/File:Aldous_Huxley.JPG

In spite of twenty-five years in Southern California, [Aldous Huxley] remains an English gentleman. The scientist’s habit of examining everything from every side and of turning everything upside down and inside out is also characteristic of Aldous. I remember him leafing through a copy of Transition, reading a poem in it, looking again at the title of the magazine, reflecting for a moment, then saying, ‘Backwards it spells NO IT ISN(T) ART.’

— Igor Stravinsky, Dialogues, 1982