The Kruskal Count

http://www.sxc.hu/photo/434247

Here’s a card trick devised by Rutgers physicist Martin Kruskal. Give a friend a deck of cards and ask her to follow these instructions:

  1. Think of a “secret number” from 1 to 10. (Example: 6)
  2. Shuffle the deck and deal the cards face up one at a time, counting silently as you go.
  3. When you reach the secret number, note the value of that card and adopt it as your new secret number. Aces count as 1; face cards count as 5. (Example: If the 6th card is a 4, then 4 becomes your new secret number.)
  4. Continue dealing, counting silently anew from 1 each time you adopt a new number. Remember the last secret card you reach.

That’s it. You just stand there and watch her deal. When she’s finished, you can identify her final secret card in any way you please, preferably through a grotesquely extortionate wager.

You can do this because you’ve simply played along. When she’s dealing, note the value of an early card and then silently follow the same steps that she is. Five times out of six, your “paths” through the deck will intersect and your final secret card will match hers. That’s far from obvious, though; the trick can be baffling if you refuse to explain it.

| Science & Math

The Wheel of Orffyreus

http://en.wikipedia.org/wiki/Image:OrffyreusWheel.png

On Nov. 12, 1717, German inventor Johann Bessler invited a committee of witnesses to a special room in the ducal castle at Weissenstein. In the room was a large wheel, 12 feet in diameter and 14 inches thick. At a push from Bessler it accelerated to about 26 rpm and maintained that speed. Under the committee’s supervision, the windows were secured and the Landgrave’s own seal was put on the door. The room was reopened twice in 54 days, and on both occasions the wheel was still spinning.

Bessler demanded 20,000 pounds for his secret. (He said the weights inside the wheel “could never obtain equilibrium.”) But while the Royal Society was debating whether to pay him, Bessler discovered one witness examining the axle, accused him of duplicity, and angrily smashed the wheel. He vanished into obscurity after that, dying in 1745.

The demonstration has never been explained. If Bessler had a secret, he took it with him.

| Oddities

Free Won’t

Zeno once caught a slave stealing and began to beat him.

Knowing the philosopher’s penchant for paradoxes, the slave cried, “But it was fated that I should steal!”

Zeno said, “And that I should beat you.”

| History

Kaprekar’s Constant

Choose four distinct digits and arrange them into the largest and smallest numbers possible (e.g., 9751 and 1579). Subtract the smaller from the larger to produce a new number (9751 – 1579 = 8172) and repeat the operation.

Within seven iterations you’ll always arrive at 6174.

With three-digit numbers you’ll aways arrive at 495.

| Science & Math

Unquote

“We do not err because truth is difficult to see. It is visible at a glance. We err because this is more comfortable.” — Aleksandr Solzhenitsyn

| Quotations

Naturally

Someone once asked Jean Cocteau, “Suppose your house were on fire and you could remove only one thing. What would you take?”

Cocteau considered, then said, “I would take the fire.”

| Art

Gifted

‘Did you hear the story of the extraordinary precocity of Mrs. Perkins’s baby that died last week?’ asked Mrs. Allgood. ‘It was only three months old, and lying at the point of death, when the grief-stricken mother asked the doctor if nothing could save it. “Absolutely nothing!” said the doctor. Then the infant looked up pitifully into its mother’s face and said—absolutely nothing!’

‘Impossible!’ insisted Mildred. ‘And only three months old!’

— Henry Ernest Dudeney, Amusements in Mathematics, 1917

| Humor