Only six numbers have this curious property:
1 = 1; 13 = 1
8 = 5 + 1 + 2; 83 = 512
17 = 4 + 9 + 1 + 3; 173 = 4913
18 = 5 + 8 + 3 + 2; 183 = 5832
26 = 1 + 7 + 5 + 7 + 6; 263 = 17576
27 = 1 + 9 + 6 + 8 + 3; 273 = 19683
They’re called Dudeney numbers, after the English author and mathematician who discovered them. (Regular readers know I’m something of a fan.)
This is the largest gathering of human beings in the history of the world — in January 2001, 70 million Hindu pilgrims met in Prayaga, India, for a religious festival called the Kumbh Mela.
Three years later, 30 million met in Ujjain.
At sunrise on April 14, 1561, the citizens of Nuremberg, Germany, witnessed a strange aerial spectacle. According to a contemporary broadsheet, large numbers of red, blue and black “globes” or “plates” appeared near the sun, “some three in a row, now and then four in a square, also some standing alone. And amongst these globes some blood-colored crosses were seen.” Two great tubes also appeared, “in which three, four and more globes were to be seen. They then all began to fight one another.”
After an hour, “they all fell … from the sun and sky down to the earth, as if everything were on fire, then it slowly faded away on the earth, producing a lot of steam.”
Strangely, the same thing happened five years later in Basel, Switzerland. On Aug. 7, 1566, also at sunrise, “many large black globes were seen in the air, moving before the sun with great speed, and turning against each other as if fighting. Some of them became red and fiery and afterwards faded and went out.”
Well, here’s a cheery scene. Laughing children, a bright fire, and … wait a minute, is that a dog on a treadmill?
Once common, turnspit dogs were specially bred to run on wheels and turn meat. Typically they were kept in pairs so they could take turns at the hot and unpleasant work, which largely went unappreciated. In Of English Dogs (1576) they’re described as “long-bodied, crooked-legged and ugly dogs, with a suspicious, unhappy look about them.”
Perhaps fortunately, the breed is extinct now, made obsolete by the mechanized kitchen.
Add counterfeiting to Kim Jong-il’s other crimes. Since the late 1980s, North Korea has been quietly making “superdollars,” nearly perfect forgeries of U.S. banknotes, painstakingly re-creating all the necessary inks, threads, fibers, and watermarks. They’re doing a good job — experts have to study the notes closely to detect the forgery. In fact, when a defector brought one to South Korean intelligence officials, they refused to believe it was fake.
Reportedly the Koreans print the currency in Pyongsong and spread it via diplomats and the British criminal underworld. Apparently they’re doing it for income and to undermine the U.S. economy. The North Koreans call these accusations “sheer lies” and claim that the U.S. itself is manufacturing the bills as a pretext for war. A crackdown has been underway since 2004, so this may come to a head soon.
“Only one man in a thousand is a leader of men. The other 999 follow women.” — Groucho Marx
Isaac Asimov proposed a simple way to distinguish chemists from non-chemists: Ask them to read aloud the word unionized.
Non-chemists will pronounce it “union-ized”, he said — and chemists will pronounce it “un-ionized.”
Sixteenth-century prophet Nostradamus predicted three Antichrists. The first two are thought to have been Napoleon and Hitler, but the third, known only as “Mabus,” hasn’t shown up yet. Here are the relevant quatrains:
Mabus will soon die, then will come
A horrible undoing of man and beast,
We will see vengeance at once,
One hundred powers, thirst, famine, when passes the comet.
His hand finally through the bloody ALUS,
He will be unable to protect himself by sea,
Between two rivers he will fear the military hand,
The black and angry one will make him repent of it.
What does this mean? Who knows? Presumably it’ll make sense at the time.
San Francisco after the 1906 earthquake. (See also George Lawrence’s kite photo.)
More than 80 percent of the city was destroyed in the quake and subsequent fire. One journalist wrote that it was not a fire in San Francisco, but a fire of San Francisco.
Every October, glowing balls rise from the depths of the Mekong River in Thailand and Laos. Each night hundreds of reddish orbs, each the size of an egg, rise to about 200 meters above the river and disappear.
No one’s sure what’s causing them. Possibly the river’s sediment is fermenting and combusting. Villagers attribute the fireballs to the phaya naga, which they say lives in the Mekong. Whatever the cause, they make for a good festival.