Dead Issues

https://commons.wikimedia.org/wiki/File:Dracula_1931.jpg

In his early handwritten notes for Dracula, Bram Stoker considered giving the vampire these attributes:

  • can banish good thoughts, create evil thoughts and destroy will
  • is affected only by relics that are older than he is
  • cannot be painted, any portrait looks like someone else
  • cannot be photographed, photographs come out black or like a skeleton corpse
  • insensitive to music
  • cannot cross thresholds without assistance, stumbles on threshold
  • can determine and prove if people are sane
  • leeches are attracted to him, then repulsed
  • can pick out murderers
  • despises death and the dead
  • can tell if bodies are dead or alive

Jonathan Harker’s stay at Castle Dracula was originally to include “an encounter with a ‘wehr wolf’,” and at the London zoological gardens “Dracula enrages eagles and lions but intimidates wolves and hyenas.”

The notes also shed some light on a puzzle I’d mentioned earlier: Why does Dracula choose England in the first place? Stoker’s notes include the phrase “English law directory sortes Virgilianae central place marked with point of knife.” Sortes Virgilianae is Latin for Virgilian lots, a form of divination in which advice or predictions are sought by interpreting passages from Virgil. In Bram Stoker’s Notes for Dracula, Robert Eighteen-Bisang writes, “Did Dracula choose his law firm by a stabbing a knife into a law directory, or decide on the location of his new home by thrusting a knife into a map? The vampire’s use of divination is in keeping with the supposition that he is a sorcerer.” None of this made it into the final novel, but it might still be the explanation that Stoker had in mind.

The Fifth Card

http://www.publicdomainpictures.net/view-image.php?image=65774&picture=playing-card

I hand you an ordinary deck of 52 cards. You inspect and shuffle it, then choose five cards from the deck and hand them to my assistant. She looks at them and passes four of them to me. I name the fifth card.

At first this appears impossible. The hidden card is one of 48 possibilities, and by passing me four cards in some order my assistant can have sent me only 1 of 4! = 24 messages. How am I able to name the card?

Part of the secret is that my assistant gets to choose which card to withhold. The group of five cards that you’ve chosen must contain two cards of the same suit. My assistant chooses one of these to be the hidden card and passes me the other one. Now I know the suit of the hidden card, and there are 12 possibilities as to its rank. But my assistant can pass me only three more cards, with 3! = 6 possible messages, so the task still appears impossible.

The rest of the secret lies in my assistant’s choice as to which of the two same-suit cards to give me. Think of the 13 card ranks arranged in a circle (with A=1, J=11, Q=12, and K=13). Given two ranks, it’s always possible to get from one to the other in at most 6 steps by traveling “the short way” around the circle. So we agree on a convention beforehand: We’ll imagine that the ranks increase in value A-K, and the suits as in bridge (or alphabetical) order, clubs-diamonds-hearts-spades. This puts the whole deck into a specified order, and my assistant can pass me the three remaining cards in one of six ways:

{low, middle, high} = 1
{low, high, middle} = 2
{middle, low, high} = 3
{middle, high, low} = 4
{high, low, middle} = 5
{high, middle, low} = 6

So if my assistant knows that I’ll always travel clockwise around the imaginary circle, she can choose the first card to establish the suit of the hidden card and to specify one point on the circle, and then order the remaining three cards to tell me how many clockwise steps to take from that point to reach the hidden rank.

“If you haven’t seen this trick before, the effect really is remarkable; reading it in print does not do it justice,” writes mathematician Michael Kleber. “I am forever indebted to a graduate student in one audience who blurted out ‘No way!’ just before I named the hidden card.”

It first appeared in print in Wallace Lee’s 1950 book Math Miracles. Lee attributes it to William Fitch Cheney, a San Francisco magician and the holder of the first math Ph.D. ever awarded by MIT.

(Michael Kleber, “The Best Card Trick,” Mathematical Intelligencer 24:1 [December 2002], 9-11.)

Self-Effacing

In introducing the puzzle-loving logician Raymond Smullyan, the chairman of a meeting praised him as unique.

“I’m sorry to interrupt you, sir,” said Smullyan, “but I happen to be the only one in the entire universe who is not unique.”

Podcast Episode 107: Arthur Nash and the Golden Rule

https://en.wikipedia.org/wiki/File:Arthur_Nash,_formal_sitting,_circa_1927.jpg

In 1919, Ohio businessman Arthur Nash decided to run his clothing factory according to the Golden Rule and treat his workers the way he’d want to be treated himself. In this week’s episode of the Futility Closet podcast we’ll visit Nash’s “Golden Rule Factory” and learn the results of his innovative social experiment.

We’ll also marvel at metabolism and puzzle over the secrets of Chicago pickpockets.

Sources for our feature on Arthur Nash:

Arthur Nash, The Golden Rule in Business, 1923.

(Undercover journalist Ruth White Colton’s September 1922 article for Success Magazine is quoted in full in this book.)

Jeffrey Wattles, The Golden Rule, 1996.

Arthur Nash, “A Bible Text That Worked a Business Miracle,” American Magazine 92:4 (October 1921), 37.

“Golden Rule Plan at Clothing Mill Makes Profits for Owners,” Deseret News, Dec. 16, 1920.

“Golden Rule Nash Offers 7-Hour Day,” Schenectady Gazette, July 4, 1923.

“Arthur Nash, Who Shared With Employees, Is Dead,” Associated Press, Oct. 31, 1927.

The poem “Miss T.” appears in Walter de la Mare’s 1913 collection Peacock Pie:

It’s a very odd thing —
As odd as can be —
That whatever Miss T. eats
Turns into Miss T.;
Porridge and apples,
Mince, muffins and mutton,
Jam, junket, jumbles —
Not a rap, not a button
It matters; the moment
They’re out of her plate,
Though shared by Miss Butcher
And sour Mr. Bate;
Tiny and cheerful,
And neat as can be,
Whatever Miss T. eats
Turns into Miss T.

This week’s lateral thinking puzzle is taken from Henry O. Wills’ memorably titled 1890 autobiography Twice Born: Or, The Two Lives of Henry O. Wills, Evangelist (Being a Narrative of Mr. Wills’s Remarkable Experiences as a Wharf-Rat, a Sneak-Thief, a Convict, a Soldier, a Bounty-Jumper, a Fakir, a Fireman, a Ward-Heeler, and a Plug-Ugly. Also, a History of His Most Wondrous Conversion to God, and of His Famous Achievements as an Evangelist).

You can listen using the player above, download this episode directly, or subscribe on iTunes or Google Play Music or via the RSS feed at http://feedpress.me/futilitycloset.

Please consider becoming a patron of Futility Closet — on our Patreon page you can pledge any amount per episode, and all contributions are greatly appreciated. You can change or cancel your pledge at any time, and we’ve set up some rewards to help thank you for your support. You can also make a one-time donation on the support page of the Futility Closet website.

Many thanks to Doug Ross for the music in this episode.

If you have any questions or comments you can reach us at podcast@futilitycloset.com. Thanks for listening!

Risky Business

https://commons.wikimedia.org/wiki/File:Antipasto_all%27italiana.jpg
Image: Wikimedia Commons

In 1982, MIT physicist A.P. French received this letter from a writer in New Rochelle, N.Y.:

Being a safety minded individual I thought I would write you before experimenting on my own. Is it safe to mix Antipasto and Pasta together and could this be a future energy supply?

He responded:

I believe that your thoughtful and interesting suggestion about the mixing of pasta and antipasto deserves some acknowledgment. This process might well be a significant energy source — but only, I think, intragastrically. I estimate that the digestion of 1 lb of the mixture would release energy equivalent to about 0.001 megawatt hours or 0.000001 kilotons of TNT. I would not foresee any unusual hazards.

(From Robert L. Weber, ed., Science With a Smile, 1992.)

A Loss for Words

In a 2013 study of tongue twisters, MIT psychologist Stefanie Shattuck-Hufnagel found that some volunteers who tried to say this phrase stopped talking altogether:

pad kid poured curd pulled cod

“If anyone can say this ten times quickly, they get a prize,” she said.

Another, from my notes:

She (to workman finishing bottom of flying boat hull) — Are you copper-bottoming ’em, my man?

He — No; I’m aluminuming ’em, mum.

Aerial Age Weekly, Oct. 4, 1915

Short Takes

Artist Jason Shulman has an interesting exhibit this month at London’s Cob Gallery: Photographs of Films condenses the entirety of a given film into a single exposure.

“There are roughly 130,000 frames in a 90-minute film, and every frame of each film is recorded in these photographs,” Shulman says. “You could take all these frames and shuffle them like a deck of cards, and no matter the shuffle, you would end up with the same image I have arrived at. Each of these photographs is the genetic code of a film — its visual DNA.”

Some examples:

Le Voyage dans la Lune (1902):

http://www.jasonshulmanstudio.com/

The Wizard of Oz (1939):

http://www.jasonshulmanstudio.com/

Citizen Kane (1941):

http://www.jasonshulmanstudio.com/

Rear Window (1954):

http://www.jasonshulmanstudio.com/

2001: A Space Odyssey (1968):

http://www.jasonshulmanstudio.com/

The Shining (1980):

http://www.jasonshulmanstudio.com/

More at Shulman’s site. Japanese artist Hiroshi Sugimoto was conducting similar experiments about 20 years ago, and Kevin L. Ferguson has assembled an impressive collection of his own.

Fellow Travelers

https://commons.wikimedia.org/wiki/File:Soybean_cyst_nematode_and_egg_SEM.jpg

In short, if all the matter in the universe except the nematodes were swept away, our world would still be dimly recognizable, and if, as disembodied spirits, we could then investigate it, we should find its mountains, hills, vales, rivers, lakes, and oceans represented by a film of nematodes. The location of towns would be decipherable, since for every massing of human beings there would be a corresponding massing of certain nematodes. Trees would still stand in ghostly rows representing our streets and highways. The location of the various plants and animals would still be decipherable, and, had we sufficient knowledge, in many cases even their species could be determined by an examination of their erstwhile nematode parasites.

— Nathan Cobb, “Nematodes and Their Relationships,” Yearbook United States Department of Agriculture, 1914

(Thanks, Mick.)

The Four Travelers Problem

four travelers problem

Four straight roads cross a plain. No two are parallel, and no three meet in a point. On each road is a traveler who moves at some constant speed. If Blue and Red meet each other at their crossroad, and each of them meets Yellow and Green at their respective crossroads, will Yellow and Green necessarily meet at their own crossroad?

Suprisingly, the answer is yes. Rob Fatland offers a beautiful solution at the CTK Exchange:

Imagine the whole scenario unfolding from Blue’s rest frame; that is, regard Blue as unmoving and consider the movements of the other travelers relative to him. What does he see? Objectively we know that each traveler moves along a straight line at a constant speed, eventually encounters Blue, and moves on, so from Blue’s perspective each of them moves directly toward him on a straight line, passes through his position, and continues.

Very well, let Red do that. But we know that Red also encounters Yellow and Green without deviating from his own path. And we know that (from Blue’s perspective) Yellow and Green are also traveling straight lines that intersect Blue’s position. This can only mean that Red, Yellow, and Green are all traveling along the same straight line from Blue’s point of view. And this means that Yellow and Green must meet one another.

(It might be objected that two points traveling the same line needn’t meet if they’re going in the same direction at the same speed. But here this would mean that two of the roads are parallel, and that possibility is excluded by the conditions of the problem.)

05/27/2016 UPDATE: Reader Derek Christie recalls a three-dimensional solution: “Make a time axis perpendicular to the plane. Then each traveller moves in a straight line trajectory through this 3D space. Blue and Red meet at a particular place and time, so their two trajectories must meet at a point, and these two trajectories define a plane. Both Yellow and Green trajectories meet the Blue and Red trajectories and so also lie in this same plane. So Yellow and Green must also meet somewhere in that plane.”

Okay Then

Edwin S. Porter’s 1903 feature The Great Train Robbery was distributed with a special segment that the projectionist could insert at the beginning or end of the film. In it, actor George Barnes fires his pistol directly at the audience.

The shot was labeled “REALISM.”