Null and Loyd?

The stupendously brilliant Sam Loyd’s Cyclopedia of 5000 Puzzles, Tricks and Conundrums, with Answers, originally published in 1914, is now available online.

The riddles are pathetic (“What vine does beef grow on? The bo-vine”), but the rest is mostly terrific. One problem: Loyd withheld the solutions to some puzzles, offering a cash prize. He never followed up with the solutions, so they’ve become stumpers. Here’s one, called “The Trader’s Profit”:

A dealer sold a bicycle for $50, and then bought it back for $40, thereby clearly making $10, as he had the same bicycle back and $10 besides. Now having bought it for $40, he resold it for $45, and made $5 more, or $15 in all.

“But,” says a bookkeeper, “the man starts off with a wheel worth $50, and at the end of the second sale has just $55! How then could he make more than $5? You see the selling of the wheel at $50 is a mere exchange, which shows neither profit nor loss, but when he buys at $50 and sells at $45, he makes $5, and that is all there is to it.”

“I claim,” says an accountant, “that when he sells at $50 and buys back at $40, he has clearly and positively made $10, because he has the same wheel and $10, but when he now sells at $45 he makes that mere exchange referred to, which shows neither profit nor loss, and does not affect his first profit, and has made exactly $10.”

“It is a simple transaction, which any scholar in the primary class should be able to figure out mentally, and yet we are confronted by three different answers,” Loyd says. “The first shows a profit of $15, such as any bicycle dealer would; while the bookkeeper is clearly able to demonstrate that more than $5 could not be made, and yet the President of the New York Stock Exchange was bold enough to maintain over his own signature that the correct profit should be $10.”

I’m thinking the accountant’s right, but then I was a journalism major.

| Puzzles

So Long, Khufu

http://commons.wikimedia.org/wiki/File:Pyramids_of_Egypt1.jpgWe need some new wonders. The old ones wore out some time ago, as you may have noticed. Of the seven wonders of the ancient world — the Pyramids of Giza, the Hanging Gardens of Babylon, the Statue of Zeus, the Temple of Artemis, the Mausoleum of Halicarnassus, the Colossus of Rhodes, and the Lighthouse of Alexandria — only the pyramids are left. The hanging gardens may never have existed.

Well, there are lots of wonderful things in the world. Can’t we just choose a better list? That depends on who does the choosing. In 1994 the American Society of Civil Engineers took a shot at it and proposed these modern replacements:

  1. Empire State Building, New York
  2. Itaipu Dam, Brazil and Paraguay
  3. CN Tower, Toronto, Canada
  4. Panama Canal, Panama
  5. Channel Tunnel, United Kingdom and France
  6. Delta Works, North Sea protection works, Netherlands
  7. Golden Gate Bridge, San Francisco

Not so great. I mean, you can’t compare the Chunnel with Zeus.

Fortunately, now we can all vote on it. In 2001, the Swiss filmmaker, adventurer and explorer Bernard Weber founded the NewOpenWorld Foundation to reach a global consensus on seven new wonders. It hasn’t made a big splash in this country, but it’s been huge in China and in India, which is lobbying hard for the Taj Mahal.

With 17 million votes in, here are the current leaders:

  1. Wall of China (11.01 percent)
  2. Potala Palace, Lhasa, Tibet (8.52 percent)
  3. Taj Mahal, India (7.70 percent)
  4. Colosseum, Rome (7.00 percent)
  5. Pyramids of Chichen Itza, Yucatan, Mexico (6.33 percent)
  6. Statues of Easter Island, Chile (6.03 percent)
  7. Tower of Pisa, Italy (5.98 percent)

So that’s looking pretty good. They’ll announce the final list next January. I figure if we can get 2 million Americans to vote, we can push Wal-Mart to the top of the list.

| History · Science & Math · Society

Sign Here

http://en.wikipedia.org/wiki/Image:John_Hancock_Signature_DOI.jpgLast month, Donald Rumsfeld got into a flap when it was revealed that his condolence letters to troops’ families were signed by a machine.

Some critics, like retired Army colonel David Hackworth, compared using a machine to “having it signed by a monkey.” But in the digital age, signing your name on paper is a pretty quaint custom. Was Rumsfeld’s decision really inappropriate?

Legally, your signature shows you’ve deliberated about something and given your informed consent. So if you asked Donald Trump to “autograph” your mortgage, you couldn’t claim he’d agreed to pay it.

But if it’s really the act of consent that’s significant, then how you express it shouldn’t matter, right? When I sign a credit-card receipt, most retail clerks don’t even glance at my signature.

Congress even ratified this view when it passed a new law in 2000, legally recognizing an “electronic sound, symbol, or process” as a signature. That means you can now “sign” an Internet transaction with an e-mail message or even a Touch-Tone beep.

So is Rumsfeld still wrong? Unfortunately, yes. In this case his signature is neither an autograph nor an endorsement, but a sign of his personal attention.

As Hackworth told Stars and Stripes, “Using those machines is pretty common, but it shouldn’t be in cases of those who have died in action. How can [officials] feel the emotional impact of that loss if they’re not even looking at the letters?”

That may be one thing a technocrat can’t understand.

| Society · Technology

Can We Start Over?

Big Numbers gives real-world examples of various orders of magnitude, from the number of Earths that would fit into the sun (106) to the number of fish in the world (1012).

The only trouble is, once you get past 1042, it’s hard to find things to count. There are 1057 atoms in the sun, and 1066 atoms in our galaxy. An octovigintillion (1087) is a lonely number — outside of pure math, it has almost nothing to do.

| Science & Math