Condolence

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A letter from Abraham Lincoln to Fanny McCullough of Bloomington, Ill., whose father had died leading a charge in Mississippi, Dec. 23, 1862:

Dear Fanny: It is with deep regret that I learn of the death of your brave and kind father, and especially that it is affecting your young heart beyond what is common in such cases. In this sad world of ours sorrow comes to all, and to the young it comes with bitterer agony because it takes them unawares. The older have learned ever to expect it. I am anxious to afford some alleviation of your present distress. Perfect relief is not possible, except with time. You cannot now realize that you will ever feel better. Is not this so? And yet it is a mistake. You are sure to be happy again. To know this, which is certainly true, will make you some less miserable now. I have had experience enough to know what I say, and you need only to believe it to feel better at once. The memory of your dear father, instead of an agony, will yet be a sad, sweet feeling in your heart of a purer and holier sort than you have known before.

Please present my kind regards to your afflicted mother.

Your sincere friend,

A. Lincoln

The Barbershop Paradox

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In 1894 Lewis Carroll published a conundrum that, he wrote, presents “a very real difficulty in the Theory of Hypotheticals.” Suppose that Allen, Brown, and Carr run a shop. At least one of them must always be present to mind the shop, and whenever Allen leaves he always takes Brown with him. Now, suppose that Carr is out. In that case then if Allen is out then Brown must be in, in order to tend the shop. But we know that this isn’t true — we’ve been told that whenever Allen is out then Brown is out.

Since the supposition that Carr is out leads to a falsehood, then it must itself be false. Confusingly, the laws of logic seem to require that Carr never leave the shop.

“I greatly hope that some of the readers of Mind who take an interest in logic will assist in clearing up these curious difficulties,” Carroll wrote. Modern logicians would say that this is a simple error in reasoning, rather than a logical disaster. But what is the error?

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Unquote

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“What I cannot create, I do not understand.” — On Richard Feynman’s Caltech blackboard at the time of his death in 1988

The Falling Chain

Here are two identical rope ladders with slanting rungs. One falls to the floor, the other onto a table. The ladders are released at the same time and fall freely, but the one on the left falls faster, as if the table is “sucking” it downward. Why does this happen?

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Dream Cuisine

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Image: Wikimedia Commons

In 1973 and 1974, the U.S. armed forces gave a food preference survey to about 4,000 members of the Army, Air Force, Navy, and Marine Corps.

The examiners included three fake dishes “to provide an estimate of how much someone will respond to a word which sounds like a food name or will answer without reading.”

The three fake dishes were “funistrada,” “buttered ermal,” and “braised trake.” The Washington Post reported, “Out of the 378 foods listed, braised trake came in 362, buttered ermal was 356 and funistrada finished several foods above the bottom 40, coming in between brussels sprouts and fried okra.”

For the record, here are the nine lowest-ranked foods, from the bottom up — all nine are so bad that service members ranked them beneath foods that don’t exist at all:

Buttermilk, skimmed milk, fried parsnips, low-calorie soda, mashed rutabagas, french fried carrots, prune juice, stewed prunes, french fried cauliflower.

(“The Ranking of the Favorites,” Washington Post, July 1, 1987. The Army survey is here: PDF.)

Watkin’s Folly

http://publicdomainreview.org/collections/catalogue-of-the-68-competitive-designs-for-the-great-tower-for-london-1890/

In 1890, inspired by France’s new Eiffel Tower, railway entrepreneur Sir Edward Watkin proposed building an even larger tower at Wembley as the centerpiece of a new amusement park there. He sponsored an architectural design competition that attracted 68 designs inspired by everything from the Tower of Pisa to the Great Pyramid of Giza. The winning design, number 37 (center), was to measure 366 meters tall, 45.8 meters taller than Eiffel’s tower. Foundations were laid in 1892, but funding troubles forced a redesign and in the end only the first stage was finished (below). The site was closed in 1902 and the aborted tower was dynamited five years later, but the surrounding park remained popular — it’s now the site of Wembley Stadium.

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

(Thanks, Meaghan.)

Mallows Bay

mallows bay

About 30 miles south of Washington D.C., on the Maryland side of the Potomac River, lies a curious collection of lozenge-shaped islands, the remains of a mighty fleet of wooden steamships built hurriedly during World War I and made obsolete by the end of the war. The unused ships became the center of a political scandal, “the grandest white elephant” ever built, and for decades the government and various salvage companies dithered over what to do with them. Eventually nature herself decided the question: The sunken hulls had consolidated and enriched the sediment in which they lay, creating a valuable new ecosystem. So the armada remains where it is, the largest collection of wrecked ships in the Western Hemisphere.

(Thanks, Craig.)

Perspective

perspective puzzle

AB and CD are consecutive ties across a pair of railroad tracks that appear to meet at O on the horizon, H. If the ties are parallel to the horizon and are equally spaced along the tracks, how can we draw the next tie in this perspective figure?

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