Illumination

night gallery

In the 1969 Night Gallery episode “Eyes,” Joan Crawford plays Claudia Menlo, a ruthless dowager who blackmails a doctor into performing a nerve transplant that will grant her vision for 11 hours. Afterward, alone in her apartment, she impatiently removes the bandages prematurely. She catches a glimpse of a crystal chandelier and then everything goes black. She rampages through her suite and collapses in tears, unaware that the city has suffered a power outage. At dawn, through dimming vision, she sees the rising sun, rushes to grasp it, and crashes through a window to her death.

Now: “How many things did Claudia Menlo see?” asks Dartmouth philosopher Roy Sorensen. “Most people say she saw only the chandelier and the sun (and possibly the pavement on the way down). But I say Claudia saw something in between seeing the crystal chandelier and the rising sun: the darkness of her blacked-out apartment. Claudia had never seen darkness before and mistook this visual experience for an absence of visual experience.”

Can we see darkness? Sorensen pictures a cave explorer in a completely dark cave. If the explorer is asleep and dreaming that he is in a completely dark cave, he does not see the darkness — but when he wakes up, he does. If the explorer then stands too quickly and the blood rushes from his head, he sees stars against an accurately perceived black background — the surrounding darkness. In contrast, his blind companion can’t tell whether the cave is dark; “only the sighted man can tell whether the cave is dark just by looking.”

This raises a puzzle: Suppose you’re in a light-tight container that’s suspended within a larger light-tight container. If the interior of the larger container is illuminated, then of course the darkness you see is the darkness of the smaller container. But what happens if the illumination of the larger space is turned off? You certainly can’t see beyond the walls of the small container in any circumstances. And only the larger container is blocking light. Does it follow that you’re seeing the darkness of the large container within the small container?

(Roy Sorensen, “We See in the Dark,” Noûs 38:3 [2004], 456-480.)

| Oddities

Podcast Episode 82: Stealing Abe Lincoln

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

In 1876, a gang of inept Chicago counterfeiters launched an absurd plot to steal the body of Abraham Lincoln and hold it for ransom. In today’s episode of the Futility Closet podcast, we’ll follow their comical attempts to carry out the bizarre scheme, and uncover the secret society that was formed afterward to protect Lincoln’s corpse.

We’ll also puzzle over an overlooked way to reduce the odds of dying of a heart attack.

See full show notes …

| Crime · Death · History · Podcast

Home Free

https://commons.wikimedia.org/wiki/File:Baseball_pun_9.jpg

A baseball poser from Clark Kinnaird’s 1946 Encyclopedia of Puzzles and Pastimes:

“In a spring training game with the Dodgers at bat, the first man up hit a triple, the second man hit a double, the third man hit a double, the fourth man hit a single, the fifth man hit a single, the sixth man hit a single. Yet the Dodgers did not score a run in that inning. How could this have happened? These were the only men who went to bat in the inning.”

Click for Answer
| Puzzles

The Thought That Counts

A Mississippi soldier’s incoherent letter to his fiancée, quoted in Bell Irvin Wiley’s The Life of Johnny Reb, 1943:

I can bare the Storms of the wintery Blast for thy sake oh Miss S.J.H be thou ever Bless as Butiful as thou art and idol to my throbbing hart oh had I the mind of the poet So that I could penetrate the verry depts of my hart but I can but express my Simple thoughts I am hear but my heart is Theire, we are in four miles of the yankees … could we not enjoy ourselves better if was at home with the girles … vainley I alas thou woulds soothe the pangs I feel, fond love betrayed what hopes I can poses Death alone my greaf may heal then farewell for ever more welth I have none they Farthers care thearefore I love one on Earth that I adore my only wealth is the love I bare then farewel perhaps for ever more never forsake me I Still will faithfull be Still on thy hand every bliss I will imploy Hence duty calls me they first my only love farewell perhaps for ever more but my hopes if far different I think will again meet if nothing happens more then I expect one thought from you would cheer my dropping mind I have more in my hart then ten thousand toungs can express if I had wings of and Eagle to the I would fly me thinks I can hear in my midnight drams thy Soft and gentle voice but alas when I awake I am in a Soldier tent

He adds, “I have nothing of importance to write you at this time but I will write soon and let you know all that happens.”

| History

Expression

https://commons.wikimedia.org/wiki/File:Remscheid_Lennep_-_Deutsches_R%C3%B6ntgenmuseum_04_ies.jpg
Image: Wikimedia Commons

Eight ways to pronounce the letter X, from wordplay maven Dmitri Borgmann:

eks: x-ray
gz: exist
gzh: luxurious
kris: Xmas
ks: sex
ksh: anxious
z: xylophone
__: faux pas

He adds three more: According to Webster’s Second Edition, xeres is an alternate name for sherry wine in which the X can be pronounced either as H or as SH. And arguably the X in except is pronounced like the letter K, as “the sibilant portion of the usual X sound has fused with the sound of the C immediately following.” If we accept these, then the total rises to 11.

(Dmitri A. Borgmann, “The Ultimate Homonym Group,” Word Ways 17:4 [November 1984], 224-228.)

| Language

Surface Matters

https://commons.wikimedia.org/wiki/File:GabrielHorn.png

In the 17th century, Italian mathematician Evangelista Torricelli experimented with a figure known as Gabriel’s Horn. Rotate the function y = 1/x about the x-axis for x ≥ 1. The resulting figure has finite volume but infinite surface area — it’s sometimes said that, while the horn could be filled up with π cubic units of paint, an infinite number of square units of paint would be needed to cover its surface.

English cosmologist John D. Barrow describes an infinite wedding cake in which each tier is a solid cylinder 1 unit high; the bottom tier has radius 1, the second radius 1/2, the third radius 1/3, and so on. Now the total volume of the cake is π3/6, but the area of its surface is infinite. Barrow writes, “Our infinite cake recipe requires a finite volume of cake to make but it can never be iced because it has an infinite surface area!”

Mike Steuben, a correspondent of Martin Gardner, imagined a set of boxes, each with area 1 × 1. If the height of the first box is 1, the second 1/2, the third 1/4, and so on, then the total volume of the group is 2 cubic units, but the length and the total area of the tops are infinite.

(Barrow’s example is from 100 Essential Things You Didn’t Know You Didn’t Know About Math and the Arts, 2014.)

| Science & Math

Logic and Belief

A syllogism is a logical argument in which a conclusion is inferred from a set of premises:

All men are mortal.
Socrates is a man.
Therefore, Socrates is mortal.

The conclusion can be valid without actually stating a true fact; to be valid it just needs to follow logically from the premises. Which of these syllogisms are valid?

No cigarettes are inexpensive.
Some addictive things are inexpensive.
Therefore, some addictive things are not cigarettes.

No addictive things are inexpensive.
Some cigarettes are inexpensive.
Therefore, some cigarettes are not addictive.

In fact both of them are valid. But, interestingly, here the first conclusion seems plausible, while the second does not. That shouldn’t matter, but it does: When Plymouth Polytechnic psychologist J. St. B.T. Evans presented a set of these arguments to subjects in 1983, he found a substantial “belief bias” — the subjects tended to judge the believable conclusions to be valid more than the unbelievable ones. If the conclusion was believable, 92% of the subjects accepted it, regardless of its validity. If the conclusion was unbelievable, 46% accepted it if it was valid, 8% if it was invalid.

Evans wrote, “These findings not only provide a challenge for existing models of syllogistic reasoning but also raise broader questions about people’s rational competence to generate and assess logical arguments in real life, whenever they have clear a priori beliefs about the subject under discussion.”

(J. St. B.T. Evans et al., “On the Conflict Between Logic and Belief in Syllogistic Reasoning,” Memory & Cognition, 11(3), 295-306.)

| Science & Math · Society