Cameo

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The last canto of Dante’s Purgatorio contains this perplexing sentence:

And if perchance
My saying, dark as Themis or as Sphinx,
Fail to persuade thee, (since like them it foils
The intellect with blindness) yet ere long
Events shall be the Naiads, that will solve
This knotty riddle, and no damage light
On flock or field.

When did water nymphs solve the riddle of the Sphinx? It turns out that Dante was relying on a flawed medieval edition of Ovid’s Metamorphoses that rendered Laïades (meaning Oedipus, the son of Laius) as Naïades, or naiads. He believed that water nymphs had ridden their sea monsters across the desert to solve the Sphinx’s riddle.

The version of the story that we know, in which Oedipus solves the riddle, comes from Sophocles’ Oedipus, which, being written in Greek, was unavailable to Dante. And he cast his own version in such exquisite language that it’s now immortal — one classic work misquoting another.

(Thanks, Jim.)

Pi Without Circles

The sum of the squares of the reciprocals of the positive integers is π2/6.

The sum of their fourth powers is π4/90.

The sum of their sixth powers is π6/945.

The area of the region under the Gaussian curve y = e-x2 is the square root of π.

The probability that two integers chosen at random will have no prime factor in common is 6/π2.

The integer 8 can be written as the sum of two squares of integers, m2 + n2, in four ways, when (m, n) is (2, 2), (2, -2), (-2, 2), or (-2, -2). The integer 7 can’t be written at all as the sum of such squares. Over a very large collection of integers from 1 to n, the average number of ways an integer can be written as the sum of two squares approaches π. Why?

Unquote

http://www.archives.gov

“Mr. Hoover, if you see ten troubles coming down the road, you can be sure that nine will run into the ditch before they reach you and you have to battle with only one of them.” — Calvin Coolidge, to Herbert Hoover

Podcast: Episode 2

As skywatchers prepared for the return of Halley’s comet in 1910, they heard some alarming scientific predictions: Poisonous gases in the comet’s tail might “snuff out all life on the planet,” “leaving the burnt and drenched Earth no other atmosphere than the nitrogen now present in the air.” How should a responsible citizen evaluate a dire prediction by a minority of experts? In this week’s episode of the Futility Closet podcast, we explore the Halley’s hysteria, remember the alarming predictions made for Y2K, and recall a forgotten novella in which Arthur Conan Doyle imagined a dead Earth fumigated by cosmic ether.

We also consider the odd legacy of an Australian prime minister who disappeared in 1967, investigate the role of balloon-borne sheepdogs during the Siege of Paris, learn why Mark Twain’s brother telegraphed the entire Nevada constitution to Washington D.C. in 1864, and offer a chance to win a book in the next Futility Closet Challenge.

You can listen using the player above, or subscribe on iTunes or via the RSS feed at http://feedpress.me/futilitycloset. The show notes are on the blog, where you can also enter your submissions in this week’s Challenge. Many thanks to Doug Ross for the music in this episode.

Next week we plan to discuss the sad, enigmatic tale of Lillian Alling, an immigrant who grew disenchanted with New York and decided to walk home to Siberia; explore the curious significance of October 4 to Samuel Taylor Coleridge; and offer a new Futility Closet Challenge. If you have any questions or comments you can reach us at podcast@futilitycloset.com. Thanks for listening!

In a Word

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bibliotaph
n. a hoarder of books

In the rare book collection of the archives at Caltech is a copy of Adrien-Marie Legendre’s 1808 text on number theory. It comes from the collection of Eric Temple Bell, who taught mathematics at Caltech from 1926 to 1953. Inside the book is an inscription in Bell’s handwriting:

This book survived the San Francisco Earthquake and Fire of 18 April, 1906. It was buried with about 600 others, in a vacant lot, before the fire reached the spot. The house next door to the lot fell upon the cache; the tar from the roof baked the 4 feet of dirt, covering the books, to brick, and incinerated all but 4 books, of which this is one. Signed: E. T. Bell. Book buried just below Grace Church, at California and Stockton Streets. House number 729 California Street.

During the Great Fire of London in 1666, Samuel Pepys came upon Sir William Batten burying his wine in a pit in his garden. Pepys “took the opportunity of laying all the papers of my office that I could not otherwise dispose of” and later buried “my Parmazan cheese, as well as my wine and some other things.” I don’t know whether he ever recovered them.

Moments of Inspiration

James Watt perfects the steam engine, 1765:

I had gone to take a walk on a fine Sunday afternoon. I had entered the Green and had passed the old washing house. I was thinking up on the engine at the time and had got as far as the herd’s house, when the idea came into my mind that as steam was an elastic body it would rush into a vacuum, and that if a communication were made between the cylinder and an exhausted vessel it would rush into it and might there be condensed without cooling the cylinder. I had not walked farther than the golf house when the whole thing was arranged clearly in my mind.

Charles Darwin realizes why species diverge, 1840s:

I can remember the very spot in the road, whilst in my carriage, when to my joy the solution occurred to me; and this was long after I had come to Down. The solution, as I believe, is that the modified offspring of all dominant and increasing forms tend to become adapted to many and highly diversified places in the economy of nature.

Walter Cannon recognizes the fight-or-flight response, 1911:

As a matter of routine I have long trusted unconscious processes to serve me. … [One] example I may cite was the interpretation of the significance of bodily changes which occur in great emotional excitement, such as fear and rage. These changes — the more rapid pulse, the deeper breathing, the increase in sugar in the blood, the secretion from the adrenal glands — were very diverse and seemed unrelated. Then, one wakeful night, after a considerable collection of these changes had been disclosed, the idea flashed through my mind that they could be nicely integrated if conceived as bodily preparations for supreme effort in flight or in fighting.

William Rowan Hamilton conceives the fundamental formula for quaternions, 1843:

But on the 16th day of the same month — which happened to be a Monday, and a Council day of the Royal Irish Academy — I was walking in to attend and preside, and your mother was walking with me, along the Royal Canal, to which she had perhaps driven; and although she talked with me now and then, yet an under-current of thought was going on in my mind, which gave at last a result, whereof it is not too much to say that I felt at once the importance. An electric circuit seemed to close; and a spark flashed forth, the herald (as I foresaw, immediately) of many long years to come of definitely directed thought and work, by myself if spared, and at all events on the part of others, if I should even be allowed to live long enough distinctly to communicate the discovery.

Hamilton adds: “Nor could I resist the impulse — unphilosophical as it may have been — to cut with a knife on a stone of Brougham Bridge, as we passed it, the fundamental formula with the symbols, i, j, k; namely,

i2 = j2 = k2 = ijk = -1

which contains the Solution of the Problem, but of course, as an inscription, has long since mouldered away.” The bridge now bears a permanent plaque marking Hamilton’s achievement (below), and mathematicians undertake an annual walk from Dunsink Observatory to commemorate it.

“A Magic-Ridden People”

Excerpts from “Body Ritual Among the Nacirema,” a paper published by Horace Miner in the June 1956 edition of American Anthropologist:

  • “They are a North American group living in the territory between the Canadian Cree, the Yaqui and Tarahumare of Mexico, and the Carib and Arawak of the Antilles. Little is known of their origin, although tradition states that they came from the east.”
  • “The fundamental belief underlying the whole system appears to be that the human body is ugly and that its natural tendency is to debility and disease. Incarcerated in such a body, man’s only hope is to avert these characteristics through the use of ritual and ceremony. Every household has one or more shrines devoted to this purpose.”
  • “In addition to the private mouth-rite, the people seek out a holy-mouth-man once or twice a year. These practitioners have an impressive set of paraphernalia, consisting of a variety of augers, awls, probes, and prods. The use of these items in the exorcism of the evils of the mouth involves almost unbelievable ritual torture of the client.”
  • “There are ritual fasts to make fat people thin and ceremonial feasts to make thin people fat. Still other rites are used to make women’s breasts larger if they are small, and smaller if they are large. A few women afflicted with almost inhuman hyper-mammary development are so idolized that they make a handsome living by simply going from village to village and permitting the natives to stare at them for a fee.”

It’s a satire. What’s Nacirema spelled backward?

Special Delivery

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Mark Twain’s 3-year-old daughter Susie found this letter waiting for her on Christmas morning 1875:

Palace of St. Nicholas,
In the Moon,
Christmas Morning.

My Dear Susie Clemens:

I have received & read all the letters which you & your little sister have written me by the hand of your mother & your nurses; & I have also read those which you little people have written me with your own hands — for although you did not use any characters that are in grown people’s alphabets, you used the character which all children, in all lands on earth & in the twinkling stars use; & as all my subjects in the moon are children & use no character but that, you will easily understand that I can read your & your baby sister’s jagged & fantastic marks without any trouble at all. But I had trouble with those letters which you dictated through your mother & the nurses, for I am a foreigner & cannot read English writing well. You will find that I made no mistakes about the things which you & the baby ordered in your own letters — I went down your chimney at midnight & when you were asleep, & delivered them all, myself — & kissed both of you, too, because you are good children, well trained, nice-mannered, & about the most obedient little people I ever saw. But in the letters which you dictated, there were some words which I could not make out, for certain, & one or two small orders which I couldn’t fill because we ran out of stock. Our last lot of kitchen furniture for dolls had just gone to a very poor little child in the North Star, away up in the cold country above the Big Dipper. Your mama can show you that star, & you will say, ‘Little Snow Flake (for that is the child’s name,) I’m glad you got that furniture, for you need it more than I.’ That is, you must write that, with your own hand, & Snow Flake will write you an answer. If you only spoke it, she wouldn’t hear you. Make your letter light & thin, for the distance is great & the postage very heavy.

There was a word or two in your mama’s letter which I couldn’t be certain of. I took it to be ‘trunk full of doll’s clothes?’ Is that it? I will call at your kitchen door about nine o’clock this morning to inquire. But I must not see anybody, & I must not speak to anybody but you. When the kitchen door-bell rings, George must be blindfolded & sent to open the door, & then he must go back to the dining room or the china closet & take the cook with him. You must tell George he must walk on tip-toe and not speak — otherwise he will die some day. Then you must go up to the nursery & stand on a chair or the nurse’s bed, & put your ear to the speaking tube that leads down to the kitchen, & when I whistle through it, you must speak in the tube & say, ‘Welcome, Santa Claus!’ Then I will ask whether it was a trunk you ordered or not? If you say it was, I shall ask you what color you want the trunk to be. Your mama will help you to name a nice color, & then you must tell me every single thing, in detail, which you want the trunk to contain. Then when I say ‘Good bye & a Merry Christmas to my little Susie Clemens!’ You must say, ‘Good bye, good old Santa Claus, & thank you very much — & please tell that little Snow Flake I will look at her star to-night & she must look down here — I will be right in the west bay-window; & every fine night I will look at her star & say, I know somebody up there, & like her, too.’ Then you must go down in the library, & make George close all the doors that open into the main hall, & everybody must keep still for a little while. I will go to the moon & get those things, & in a few minutes I will come down the chimney which belongs to the fire-place that is in the hall — if it is a trunk you want, because I couldn’t get such a thing as a trunk down the nursery-chimney, you know.

People may talk, if they want to, till they hear my footsteps in the hall — then you tell them to keep quiet a little while till I go back up the chimney. Maybe you will not hear my foot steps at all — so you may go now & then & peep through the dining room doors, & by & by you will see that thing which you want, right under the piano in the drawing room — for I shall put it there. If I should leave any snow in the hall, you must tell George to sweep it into the fireplace, for I haven’t time to do such things. George must not use a broom, but a rag — else he will die some day. You must watch George, & not let him run into danger. If my boot should leave a stain on the marble, George must not holy-stone it away. Leave it there always in memory of my visit; & whenever you look at it or show it to anybody you must let it remind you to be a good little girl. Whenever you are naughty, & somebody points to that mark which your good old Santa Claus’s boot made on the marble, what will you say, little Sweetheart?

Good-bye, for a few minutes, till I come down to the world & ring the kitchen door-bell.

Your loving

Santa Claus,

Whom people sometimes call ‘The Man in the Moon.’

Slippery

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Image: Flickr

Andy Warhol made a significant statement with Brillo Boxes, first exhibited at New York’s Stable Gallery in 1964. The banal collection of soap boxes seemed indistinguishable from those found at any supermarket. Warhol seemed to be saying that it’s not the visual appeal of an object that determines its status as art; rather, it’s the artist’s intention, his decision to regard an object as art, that confers that status. But this creates some puzzles:

For one, ironically, the original Brillo packaging had itself been designed by an abstract expressionist, James Harvey, who had been driven into commercial art to make a living. Arthur Danto writes, “The question was why Warhol’s boxes should have been worth $200 when that man’s products were not worth a dime.” Does Warhol’s stance mean that concepts entirely trump beauty, that one should properly judge an artwork by what it means rather than how it looks?

If so, is this art?

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Image: Flickr

It’s not Warhol, but “Not Warhol,” by artist Mike Bidlo, displayed in the northeast corner of the lobby at New York’s Lever House in 2010. If Warhol can co-opt Harvey, can Bidlo co-opt Warhol? Why not? “At the time that they were shown, the Brillo Boxes were underappreciated,” Bidlo told the New York Times. “This is a different context and a different audience, but it’s a great opportunity for so many people to see them.”

Where does this end? Museum director Pontus Hultén claimed he’d created more than 100 wooden Brillo boxes in 1968 “according to Andy Warhol’s instructions,” but in 2010 the Andy Warhol Art Authentication Board determined that “there is no known documentation that Warhol authorised their production.” What then is the status of these boxes? If art is in the mind of the creator, how do we resolve a dispute as to the contents of the creator’s mind? By committee?

Consequences

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In May 1875, Frederick Law Olmsted received a letter from his 4-year-old son Henry, asking him to send the family dog to Massachusetts, where he and his mother were visiting family friends. Olmsted replied:

Dear Henry:

The cats keep coming into the yard, six of them every day, and Quiz drives them out. If I should send Quiz to you to drive the cows away from your rhubarb he would not be here to drive the cats out of the yard. If six cats should keeping coming into the yard every day and not go out, in a week there would be 42 of them and in a month 180 and before you came back next November 1260. Then if there should be 1260 cats in the yard before next November half of them at least would have kittens and if half of them should have 6 kittens apiece, there would be more than 5000 cats and kittens in the yard. There would not be any place for Rosanna to spread the clothes unless she drove them all off the grass plot, and if she did they would have to crowd at the end of the yard nearest the house, and if they did that they would make a great pile as high as the top of my windows. A pile of 5000 cats and kittens, some of them black ones, in front of my window would make my office so dark I should not be able to write in it. Besides that those underneath, particularly the kittens, would be hurt by those standing on top of them and I expect they would make such a great squalling all the time that I should not be able to sleep, and if I was not able to sleep, I should not be able to work, and if I did not work I should not have any money, and if I had not any money, I could not send any to Plymouth to pay your fare back on the Fall River boat, and I could not pay my fare to go to Plymouth and so you and I would not ever see each other any more. No, Sir. I can’t spare Quiz and you will have to watch for the cows and drive them off yourself or you will raise no rhubarb.

Your affectionate father.

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