Conway’s Prime-Producing Machine

Here’s something amazing — a machine made of fractions:

conway's prime-producing machine

Start with the number 2 as your seed. Multiply it by each of the fractions above, in order, until you find one that produces an integer. (It’s 15/2.) Now adopt that integer (15) as the new seed, and multiply that by each of the fractions until you produce another integer. Keep this up, making a note whenever you produce a power of 2.

The first such power (4, or 22) appears after 19 steps. Fifty steps later, 23 turns up. Then 25 appears about 200 steps further on. A pattern emerges: the exponents are 2, 3, 5 …

It turns out that “these fourteen fractions alone have it in them to produce an infinity of primes, even those that no one yet knows about,” writes Dominic Olivastro. “There is something enormously magical about it.” John Horton Conway devised the technique; it’s an instance of his Fractran computing algorithm.

| Science & Math

The Breaks

I once had a friend who objected to assigning chores by lot on the grounds that random selection was biased in favour of lucky people. He claimed to be serious and went on to compare unlucky people with … groups he took to be victims of discrimination. Sincere or not, wherein lies the absurdity of my friend’s objection?

— Roy A. Sorensen, Blindspots, 1988

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Adventures in Tuition

In 1987, University of Illinois freshman Mike Hayes wrote to Chicago Tribune columnist Bob Greene with a modest proposal: that each of Greene’s readers contribute a penny to finance his education.

“Just one penny,” he told Greene. “A penny doesn’t mean anything to anyone. If everyone who is reading your column looks around the room right now, there will be a penny under the couch cushion, or on the corner of the desk, or on the floor. That’s all I’m asking. A penny from each of your readers.”

Greene published the appeal in 200 newspapers via his syndicated column — and Hayes received 77,000 letters and enough pennies to break his bank’s coin-counting machine three times. He easily reached his goal of $28,000, enough for four years of tuition, room and board, and books.

He graduated with a degree in food science. Asked why the scheme worked, he said, “I didn’t ask for a lot of money. I just asked for money from a lot of people.”

| Oddities · Society

Deep Freeze

http://commons.wikimedia.org/wiki/File:Behouden_Huys_in_1881.jpg

In 1871, a Norwegian seal hunter discovered a wooden hut on Novaya Zemlya in the Arctic Ocean. In it he found clothing, cooking pots, a tool chest, a clock, a flute, a cooking tripod, and several pictures.

It was the lodge of Willem Barentsz, who had passed the winter there in 1597 while seeking a northern route to China. Barentsz had died on the return journey, and the hut had stood for 270 years, awaiting rediscovery.

According to an 1877 report, later investigations recovered Barentsz’s quill pen, a translation of a work on seamanship printed in 1580, “some candles nearly 280 years old, but still capable of giving light” — and “the Amsterdam flag, the first European colour that passed a winter in the Arctic region.”

| Oddities

On the House

The thirsty but impecunious soul approaches the bar-tender with a request for brandy, or what not. He takes a sip, pronounces it detestable, and offers to change it for a glass of whiskey. The obliging bar-tender substitutes the whiskey. The customer drinks, smacks his lips, and prepares to depart. ‘Here,’ says the bar-tender, ‘you haven’t paid for your whiskey.’ ‘No,’ is the innocent response; ‘I gave you the brandy in exchange for it.’ ‘But you didn’t pay for the brandy.’ ‘But I didn’t drink it.’ And while the publican intellect is vainly struggling with the mathematical puzzle involved, the puzzler makes good his escape.

— William Shepard Walsh, Handy-Book of Literary Curiosities, 1892

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Fun With Bones

http://books.google.com/books?id=u1GZEdfvaZwC&printsec=frontcover&source=gbs_atb#v=onepage&q&f=false

In 1840, Albert Koch made a sensation in London with the “Missouri Leviathan,” an enormous monster whose remains he purported to have discovered in Benton County, Mo. It turned out to be “a mastodon preposterously mounted.” From Scribner’s Magazine:

Koch had added an extra dozen or more joints to the back-bone and ribs to the chest, turned the tusks outward into a semicircle, and converted the animal into an aquatic monster which anchored itself to trees by means of its sickle-shaped tusks and then peacefully slumbered on the bosom of the waves.

The British Museum bought this up and, sniffing, reassembled it into a mastodon. Koch only warmed to his work — in Alabama he turned up the remains of two basilosauri and, writes Rupert Gould, arranged them to form “a serpentine creature 114 feet long, for which he manufactured, from any spare bones that were handy, a corresponding skull, ribs and paddles” (below). He had time to exhibit “Hydrarchos sillimani” in New York and Boston before outraged naturalists finally shut him down; the restored basilosaurs found a home in Berlin.

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

| Oddities

Enjoy Your Flight

Items prohibited from carry-on baggage by the Transportation Security Administration, as of June 2010:

  • Meat cleavers
  • Spear guns
  • Sabers
  • Hatchets
  • Cattle prods
  • Swords
  • Brass knuckles
  • Nunchakus
  • Throwing stars
  • Blasting caps
  • Dynamite
  • Hand grenades

And “snow globes … even with documentation.”

| Society

Noble Wisdom

Maxims of Rochefoucauld:

  • “Few men are able to know all the ill they do.”
  • “We are never made so ridiculous by the qualities we have, as by those we affect to have.”
  • “In every profession, every individual affects to appear what he would willingly be esteemed; so that we may say, the world is composed of nothing but appearances.”
  • “We like better to see those on whom we confer benefits, than those from whom we receive them.”
  • “Everybody takes pleasure in returning small obligations; many go so far as to acknowledge moderate ones; but there is hardly any one who does not repay great obligations with ingratitude.”
  • “In misfortunes we often mistake dejection for constancy; we bear them without daring to look on them, as cowards suffer themselves to be killed without resistance.”
  • “None but the contemptible are apprehensive of contempt.”
  • “We want strength to act up to our reason.”
  • “We easily forget crimes that are known only to ourselves.”
  • “It is as easy to deceive ourselves without our perceiving it, as it is difficult to deceive others without their perceiving it.”
  • “We are sometimes less unhappy in being deceived than in being undeceived by those we love.”

And “Those who apply themselves too much to little things commonly become incapable of great ones.”

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