Tilt

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As early as the 1st century B.C., the Chinese text Zhou Bi Suan Jing reflected the reasoning of the Pythagorean theorem, showing how to find the hypotenuse of the 3-4-5 triangle. Arrange four 3×4 rectangles around a unit square, as shown, producing a 7×7 square. The diagonals of the four rectangles produce a tilted square. Now, the area of the 7×7 square is 49, and the area of one right triangle with legs 3 and 4 is 6. So the area of the tilted square is 49 – (4 × 6), or 25. This shows that the hypotenuse of each of the right triangles is 5.

In Mathematics and the Aesthetic (2007), Nathalie Sinclair writes, “The Chinese diagram … is the same as one given by the twelfth-century Indian scholar Bhaskara, whose one-word injunction Behold! recorded his sense of awe.”

Part Two

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Image: Wikimedia Commons

In 1907, two years after Jules Verne’s death, sculptor Albert Roze added a striking monument to Verne’s grave in the cemetery of La Madeleine in Amiens: a sculpture of the author smashing his tombstone, shedding his shroud, and hoisting himself toward the sky.

The work is called Toward Immortality and Eternal Youth, and the face is Verne’s own — Roze used the author’s death mask.

Precocious

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John Quincy Adams wrote this letter to his father at age 10, June 2, 1777:

DEAR SIR,–I love to receive letters very well; much better than I love to write them. I make but a poor figure at composition, my head is too fickle, my thoughts are running after birds eggs play and trifles, till I get vexed with myself. Mamma has a troublesome task to keep me steady, and I own I am ashamed of myself. I have but just entered the third volume of Smollett, tho’ I had designed to have got it half through by this time. I have determined this week to be more diligent, as Mr. Thaxter will be absent at Court, and I cannot pursue my other studies. I have Set myself a Stent and determine to read the 3rd volume Half out. If I can but keep my resolution, I will write again at the end of the week and give a better account of myself. I wish, Sir, you would give me some instructions, with regard to my time, and advise me how to proportion my Studies and my Play, in writing, and I will keep them by me, and endeavor to follow them. I am, dear Sir, with a present determination of growing better, yours.

P.S.–Sir, if you will be so good as to favor me with a Blank Book, I will transcribe the most remarkable occurances I meet with in my reading, which will serve to fix them upon my mind.

Five years later, at age 14, he was serving as private secretary to the American minister to Russia.

The Giant of Castelnau

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Anthropologist Georges Vacher de Lapouge turned up a surprise in 1890: While excavating a Bronze Age cemetery at Castelnau, near Montpellier, France, he discovered three apparently human bones of gigantic size. On the left is the “giant’s” femur, or thigh bone; on the right is a tibia, or shin bone. Between them is a normal humerus, or upper arm bone, from the same cemetery. At the bottom is a fragment that may belong to either a femur or a humerus; if it’s the latter then it must have belonged to the same giant. If this is right, then the individual would have stood between 10 and 11 feet tall.

Lapouge published his discovery in La Nature that year. “I think it unnecessary to note that these bones are undeniably human, despite their enormous size,” he wrote. “The volumes of the bones were more than double the normal pieces to which they correspond.”

The specimens were examined by zoologists and paleontologists at the University of Montpellier and passed eventually to pathological anatomist Paul Kiener of the Montpellier School of Medicine; the London Globe noted that “Kieger, who, while admitting that the bones are those of a very tall race, nevertheless finds them abnormal in dimensions and apparently of morbid growth.”

“There has been an old tradition among the peasants of the vicinity that a cavern in the valley was, in olden times, occupied by a giant,” noted Popular Science News. “It would be curious if the discovery of M. Lapouge should show it to be founded on fact.”

Interestingly, the bones of further French giants were reported to have turned up near the same location a few years later. From the Princeton Union, Oct. 11, 1894: “In a prehistoric cemetery recently uncovered at Montpellier, France, while workmen were excavating a waterworks reservoir, human skulls were found measuring 28, 31 and 32 inches in circumference. The bones which were found with the skulls were also of gigantic proportions. These relics were sent to the Paris academy, and a learned ‘savant’ who lectured on the find says that they belonged to a race of men between ten and fifteen feet in height.”

But that seems to be the end of it. Was the whole thing a hoax?

Forgotten Pearls

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Lesser-known maxims from Poor Richard’s Almanac:

  • You may be too cunning for One, but not for All.
  • Who is rich? He that rejoices in his Portion.
  • By diligence and patience, the Mouse bit in two the Cable.
  • To be intimate with a foolish Friend, is like going to Bed to a Razor.
  • A false Friend and a Shadow attend only while the Sun shines.
  • He that goes far to marry, will either deceive or be deceived.
  • ‘Tis easy to see, hard to foresee.
  • Many Foxes grow grey, but few grow good.
  • Paintings and Fightings are best seen at a distance.
  • Fly pleasures, and they’ll follow you.
  • Gifts burst rocks.
  • Historians relate, not so much what is done, as what they would have believed.
  • Let thy vices die before thee.
  • Men differ daily, about things which are subject to sense, is it likely then they should agree about things invisible?
  • What signifies your Patience, if you can’t find it when you want it?

And “Let all Men know thee, but no man know thee thoroughly: Men freely ford that see the shallows.”

Enduring Advice

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Image: Flickr

During the Great Depression, Babson College founder Roger Babson commissioned unemployed stonecutters to carve inspiring inscriptions on 25 boulders in Dogtown, an abandoned settlement in Gloucester, Massachusetts:

  • COURAGE
  • IDEAS
  • HELP MOTHER
  • KINDNESS
  • LOYALTY
  • IF WORK STOPS, VALUES DECAY
  • BE ON TIME
  • GET A JOB
  • INDUSTRY
  • INITIATIVE
  • INTEGRITY
  • KEEP OUT OF DEBT
  • SAVE
  • SPIRITUAL POWER
  • STUDY
  • TRUTH
  • WORK
  • BE CLEAN
  • BE TRUE
  • PROSPERITY FOLLOWS SERVICE
  • USE YOUR HEAD
  • IDEALS
  • INTELLIGENCE
  • NEVER TRY/NEVER WIN

Babson did some of the work himself. “Another thing I have been doing, which I hope will be carried on after my death, is the carving of mottoes on the boulders at Dogtown, Gloucester, Massachusetts,” he wrote in 1935. “My family says that I am defacing the boulders and disgracing the family with these inscriptions, but the work gives me a lot of satisfaction, fresh air, exercise and sunshine. I am really trying to write a simple book with words carved in stone instead of printed paper. Besides, when on Dogtown common, I revert to a boyhood which I once enjoyed when driving cows there many years ago.”

The boulders are extant today and can be visited on a hiking trail.

Second Thoughts

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Literary scholar Robert Hauptman calls this “marginal emendation run amok” — it’s a page from Henry James’ 1877 novel The American as James revised it anxiously in 1907 for a “definitive” edition in New York. He had decided the plot was unconvincing and required so many changes that two copies of the book had to be inlaid page by page on larger sheets to give him room to mark all the revisions.

On the last page, above, “James has partially or fully crossed out 16 of the 19 lines and rewritten the text for the definitive New York edition in the margins and at the foot of the page,” notes Hauptman. “His scrawling alterations cover virtually all of the generous white space and must be inserted in at least three different locations in the original text. Words are blotted out or struck in the new version, and as he approaches the bottom of the page, the lettering diminishes in size, because he realizes that he will run out of room.”

“The work on the earlier novels has involved much labour — to the best effect for the vile things, I’m convinced,” James had written to Grace Norton that March. Modern critics generally disagree — most editions today use the original version.

(From Robert Hauptman, Documentation, 2008, and Harvard’s Marks in Books, 1985.)

A Feathered Nest

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Image: Flickr

Characterizations of Scrooge McDuck’s wealth in the drawn stories of creator Carl Barks:

  • 250 umptillion fabulatillion dollars
  • 500,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000.16 dollars
  • Fantasticatrillionaire
  • Five billion quadruplatillion umtuplatillion multuplatillion fantasticatillion centrifugalillion dollars and sixteen cents
  • Five billion quintuplatillion umptuplatillion multuplatillion impossibidillion and so forth dollars and extra odd cents
  • Five hundred triplicatillion multipludillion quadruplicatillion centrifugalillion dollars and sixteen cents
  • Hyperfantasticatillionaire
  • Nine fantasticatillion, four billionjillion, centrifugalillion dollars and sixteen cents
  • Nine hundred fantasticatillion, seven hundred doubledecadecillion, eight hundred kumquatmafrillion …
  • One quadrillion amplifatillion dollars
  • One umptillion uncountabalillions of dollars
  • Seven hundred and eighty-eight billion, four hundred and twenty-three million seventeen dollars and sixteen cents
  • Ten skyrillion dollars
  • Three cubic acres
  • Three skyrillion dollars

In Forbes‘ estimation, McDuck’s wealth rose from $28.8 billion in 2007 to $44.1 billion in 2011 due to a rise in gold prices, but his total worth is notoriously hard to estimate. The famous money bin, he once told his nephews, is “just petty cash.”

Mama Bird

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The Soviet Union redefined heavy bombers in 1930 with the introduction of the Tupolev TB-3, a four-engine behemoth so large that it could serve as a mothership to five little fighters, which could be released in flight and even hooked back onto the aircraft in order to refuel.

A TB-3 once did manage to take off with four fighters attached, then joined up with a fifth while circling the airfield, with a combined nine engines going. Then all five fighters were released at once. “The thing about events like that is, you always wonder how they entered the flight in their log books afterwards,” writes James Gilbert in The World’s Worst Aircraft. “I mean, if you were the pilot of one of the fighters, you could hardly log the take-off because you hadn’t made it, except as a passenger. But how can you log a landing with no prior take-off?”

The whole contraption, known as Vakhmistrov’s Circus, saw some early wartime service, but it was too complex and vulnerable to be adopted widely. Today it’s a historical curiosity.