e-mergence

1!, 22!, 23!, and 24! contain 1, 22, 23, and 24 digits, respectively.

266!, 267!, and 268! contain 2 × 266, 2 × 267, and 2 × 268 digits, respectively.

2,712! and 2,713! contain 3 × 2,712 and 3 × 2,713 digits, respectively.

27,175! and 27,176! contain 4 × 27,175 and 4 × 27,176 digits, respectively.

271,819!, 271,820!, and 271,821! contain 5 × 271,819, 5 × 271,820, and 5 × 271,821 digits, respectively.

2,718,272! and 2,718,273! contain 6 × 2,718,272, and 6 × 2,718,273 digits, respectively.

27,182,807! and 27,182,808! contain 7 × 27,182,807, and 7 × 27,182,808 digits, respectively.

271,828,170! 271,828,171!, and 271,828,172! contain 8 × 271,828,170, 8 × 271,828,171, and 8 × 271,828,172 digits, respectively.

2,718,281,815! and 2,718,281,816! contain 9 × 2,718,281,815, and 9 × 2,718,281,816 digits, respectively.

27,182,818,270! and 27,182,818,271! contain 10 × 27,182,818,270 and 10 × 27,182,818,271 digits, respectively.

271,828,182,830! and 271,828,182,831! contain 11 × 271,828,182,830, and 11 × 271,828,182,831 digits, respectively.

The pattern continues at least this far:

271,828,182,845,904,523,536,028,747,135,266,249,775,724,655!, 271,828,182,845,904,523,536,028,747,135,266,249,775,724,656!, and 271,828,182,845,904,523,536,028,747,135,266,249,775,724,657! contain 59 × 271,828,182,845,904,523,536,028,747,135,266,249,775,724,655, 59 × 271,828,182,845,904,523,536,028,747,135,266,249,775,724,656, and 59 × 271,828,182,845,904,523,536,028,747,135,266,249,775,724,657 digits, respectively.

(By Robert G. Wilson. More at the Online Encyclopedia of Integer Sequences. Thanks, David.)

| Science & Math

Misc

  • Seattle is closer to Finland than to England.
  • Is a candle flame alive?
  • ABANDON is an anagram of A AND NO B.
  • tan-1(1) + tan-1(2) + tan-1(3) = π
  • “A thing is a hole in a thing it is not.” — Carl Andre

Detractors of Massachusetts governor Endicott Peabody said that three of the state’s towns had been named for him: Peabody, Marblehead, and Athol.

| Language · Science & Math · Trivia

Take Two

http://en.wikipedia.org/wiki/File:TheTwilightZoneLogo.png

Rod Serling’s original opening narration for The Twilight Zone read, “There is a sixth dimension, beyond that which is known to man. It is a dimension as vast as space and as timeless as infinity. It is the middle ground between light and shadow, and it lies between the pit of man’s fear and the sunlight of his knowledge. This is the dimension of imagination. It is an area that might be called The Twilight Zone.”

Producer Bill Self questioned the line There is a sixth dimension … “I said, ‘Rod, what is the fifth one?’ And he said, ‘I don’t know. Aren’t there five?’ I said, ‘I can only think of four.’ So we rewrote it and rerecorded it and said, ‘There is a fifth dimension, beyond that which is known to man …'”

Asked how he came up with the title The Twilight Zone, Serling said, “I thought I’d made it up, but I’ve heard since that there is an Air Force term relating to a moment when a plane is coming down on approach and it cannot see the horizon. It’s called the twilight zone, but it’s an obscure term which I had not heard before.”

(From Marc Scott Zicree, The Twilight Zone Companion, 1982.)

| Entertainment

“No, No, Mr. Nash”

http://en.wikipedia.org/wiki/File:Ogden_Nash.jpg

Let us begin by saying we have nothing but the deepest aversion
Against casting an aspersion
On the beautiful works of Ogden Nash.
In fact we might say we go for his stuff like a vegetarian goes for his succotash.
But the thing that swerves us
From downright admiration is the length of his lines which sometimes look more like paragraphs than lines — frankly it unnerves us.
In fact we have it from unreliable sources
That several people have narrowly missed death by asphyxiation while attempting to read aloud one of these book-length sentences in one breath, all of which forces
Us to request that Mr. Nash please stick to a line that can be written entirely on one page, for when we see one of these endless lines looming up over the edge of the next stanza, we have been known to turn the page and start something else; while on the other hand, when Mr. Nash sticks to a briefer line with definite rhythm,
We’re whythym.

— An unnamed college humor magazine, quoted in Richard Koppe et al., A Treasury of College Humor, 1950

| Humor · Poems

Fearless

Founded in the 1880s by Manhattan rationalists, the 13 Club held a regular dinner on the 13th of each month, seating 13 members at each table deliberately to laugh at superstition.

“I have given some attention to popular superstitions, and let me tell you that argument is powerless against them,” founding member Daniel Wolff told journalist Philip Hubert in 1890. “They have a grip upon the imagination that nothing but ridicule will lessen.” As an example he cited the tradition that the mirrors must be removed from a room in which a corpse is lying. “Make the experiment yourself, and the next time you are called upon to sit up with a corpse, notice how uncomfortable a mirror will make you feel,” he said. “Of course it is a matter of the imagination, but you can’t reason against it. All the ingrained terrors of six thousand years are in your bones. You walk across the floor and catch a glimpse of yourself in the glass. You start; was there not a spectral something behind you? So you cover it up.”

As honorary members the club recruited 16 U.S. senators, 12 governors, and six Army generals. Robert Green Ingersoll ended one 1886 toast by declaring, “We have had enough mediocrity, enough policy, enough superstition, enough prejudice, enough provincialism, and the time has come for the American citizen to say: ‘Hereafter I will be represented by men who are worthy, not only of the great Republic, but of the Nineteenth Century.'”

But Oscar Wilde, for one, turned them down. “I love superstitions,” he wrote. “They are the colour element of thought and imagination. They are the opponents of common sense. Common sense is the enemy of romance. The aim of your society seems to be dreadful. Leave us some unreality. Don’t make us too offensively sane.”

(Thanks, David.)

| Science & Math · Society

In a Word

http://commons.wikimedia.org/wiki/File:%C5%9Alewi%C5%84ski_W%C5%82adys%C5%82aw,_Czesz%C4%85ca_si%C4%99,_1897.jpg

auricomous
adj. golden-haired

flavicomous
adj. having yellow hair

melanocomous
adj. black-haired

lissotrichous
adj. having smooth hair

cymotrichous
adj. having wavy hair

crinicultural
adj. caring for the condition or appearance of the hair

floricomous
adj. having the head adorned with flowers

| Language

Podcast Episode 43: Ben Franklin’s Guide to Living

http://commons.wikimedia.org/wiki/File:Franklin-Benjamin-LOC.jpg

As a young man, Benjamin Franklin drew up a “plan for attaining moral perfection” based on a list of 13 virtues. Half a century later he credited the plan for much of his success in life. In this episode of the Futility Closet podcast we’ll explore Franklin’s self-improvement plan and find out which vices gave him the most trouble.

We’ll also learn how activist Natan Sharansky used chess to stay sane in Soviet prisons and puzzle over why the Pentagon has so many bathrooms.

See full show notes …

| History · Literature · Podcast

The Paradox of the Muddy Children

http://commons.wikimedia.org/wiki/File:First_Rain_(228226305).jpg
Image: Wikimedia Commons

Three children return home after playing outside, and their father tells them that at least one of them has a muddy face. He repeats the phrase “Step forward if you have a muddy face” until all and only the children with muddy faces have stepped forward.

If there’s only one child with a muddy face, then she’ll step forward immediately — she can see that no other children have muddy faces, so her father must be talking about her. Each of the other children will see her muddy face and stand fast, since they have no way of knowing whether their own faces are muddy.

If there are two children with muddy faces, then no one will step forward after the first request, since each might think the father is addressing the other one. But when no one steps forward after the first request, each will realize that there must be two children with muddy faces, and that she herself must be one of them. So both will step forward after the second request, and the rest will stand fast.

A pattern emerges: If there are n children with muddy faces, then n will step forward after the nth request.

But now imagine a scenario in which more than one of the children has a muddy face, but the father does not tell them that at least one of them has a muddy face. Now no one steps forward after the first request, for the same reason as before. But no one steps forward at the second request either, because the fact that no one stepped forward after the first request no longer means that there is more than one child with a muddy face.

This is perplexing. In the second scenario all the children can see that at least one of them has a muddy face, so it seems needless for the father to tell them so. But without his statement the argument never gets going; despite his repeated requests, no child will ever step forward. What’s missing?

(From Michael Clark, Paradoxes From A to Z, 2007.)

| Oddities

Punctual

Ernest Hemingway published this “blank verse” in his high school literary magazine in 1916:

hemingway blank verse

Get it? David Morice followed up with this “punctuation poem” in Word Ways in February 2012:

% , & —
+ . ? /
” :
% ;
+ $ [ \

It’s a limerick:

Percent comma ampersand dash
Plus period question mark slash
Quotation mark colon
Percent semicolon
Plus dollar sign bracket backslash

(Thanks, Volodymyr.)

| Humor · Language · Poems