You know the singularity has arrived when the robots start playing marimbas. Shimon, engineer Guy Hoffman’s robot musician, doesn’t play programmed music — it improvises in ensembles with human players, communicating with a “socially expressive head” and favoring musical ideas that are unlikely to be chosen by humans, so as to lead the performance in genuinely novel directions.
“The project, therefore, aims to combine human creativity, emotion, and aesthetic judgment with algorithmic computational capability of computers, allowing human and artificial players to cooperate and build off each other’s ideas,” notes the Georgia Tech Center for Music Technology, Shimon’s patron. “Unlike computer- and speaker-based interactive music systems, an embodied anthropomorphic robot can create familiar, acoustically rich, and visual interactions with humans.”
“Two great duties, I think, we owe to posterity: one is progress, the other history. Only the former can we share in. The fruits of progress often apply to the generation which bears them. But the records of that progress come closer to being pure charity than any form of charity I know.” — Richard E. Byrd
A harmonic progression is a progression formed by taking the reciprocals of an arithmetic progression (so an example is 1/1, 1/2, 1/3, 1/4 …). When tutoring mathematics at Oxford, Charles Dodgson had a favorite example to illustrate this:
According to him, it is (or was) the rule at Christ Church that, if an undergraduate is absent for a night during term-time without leave, he is for the first offence sent down for a term; if he commits the offence a second time, he is sent down for two terms; if a third time, Christ Church knows him no more. This last calamity Dodgson designated as ‘infinite.’ Here, then, the three degrees of punishment may be reckoned as 1, 2, infinity. These three figures represent three terms in an ascending series of Harmonic Progression, being the counterparts of 1, 1/2, 0, which are three terms in a descending Arithmetical Progression.
— Lionel A. Tollemache, “Reminiscences of ‘Lewis Carroll,'” Literature, Feb. 5, 1898
Heather Ackroyd and Dan Harvey make photographs using grass. When grass is grown from seed on a vertical surface, it can record complex images much as photographic film does: Each germinating blade produces chlorophyll in proportion to the light that reaches it. Stronger light produces greener grass, and blades deprived of light grow but produce no chlorophyll, leaving them yellow. “In a sense we have adapted the photographic art of producing pictures on a sensitive film to the light sensitivity of emergent blades of young grass; the equivalent tonal range of black-and-white photographic paper is created within the grass in shades of yellow and green.”
“A grass photograph has the power to elicit strong emotional responses in the viewer, and it is undeniable that the beauty of the freshly grown grass canvas suggests all that is fertile and life-enhancing. Our desire to alleviate the process of decay has encouraged us to journey into the world of science and genetics, and has opened our work to a greater number of people throughout the world.”
Dentist William T.G. Morton was the first to use sulfuric ether as an anaesthetic, but he’d learned about this property at the chemistry lectures of Charles T. Jackson.
Which of them deserved a monument? Oliver Wendell Holmes suggested setting up statues of both men on the same pedestal, with the inscription:
England went mad for water lilies after an Amazon lily was named after Queen Victoria in 1837. The plants balked at English weather, but when gardener Joseph Paxton put one in an experimental conservatory it flowered in three months.
Ultimately the lilies inspired their own greenhouse: Impressed that their radiating ribs could support his daughter Annie, Paxton borrowed this “natural feat of engineering” to design a new conservatory with a ridge-and-furrow roof. In time this led to his masterpiece: the Crystal Palace of the Great Exhibition of 1851.
(From the Illustrated London News, Nov. 17, 1849.)
In a case regarding the value of a dead horse, Judge Squire Sprigg of Butler County, Ohio, charged the jury as follows:
Gentlemen of the Jury: This is a hoss case. We make quick work of hoss cases in this court. These people killed Doc’s old hoss; if Doc’s hoss was worth anything, then he is entitled to recover; if he wasn’t worth anything, then he ain’t. Some hosses are worth something and a good many more are worth nothing. So, it is for you to say, whether this hoss was worth anything or not. You are to be governed by the preponderance of testimony. Preponderance is a big word, which I must explain to you. It means this: If one side has fifty witnesses and you think they are all liars, and the other side has one witness, and you don’t think he is a liar, or at least as big a liar as the other fifty, then the testimony of the one will preponderate over that of the others, and will knock the socks off of the other fifty. Now, if by a preponderance of the testimony, as I have explained it to you, you think the Doc’s old hoss was worth anything, find what that is and give it to him; if you think he was worth nothing, why say so. Doc will think this is pretty hard on the medical profession, but he will have to take the medicine which the law prescribes. The law provides for just such cases; it calls this damnum absque injuria, which means, as I interpret it, that a man is usually hurt a damned sight less than he thinks he is.
Now, gentlemen, I believe I have covered the whole case. You have heard the evidence and the law as I have given it to you. Remember that you are under oath in this business and that the court expects quick verdicts, especially in hoss cases.
They found for the defendant, the SPCA, and declared that Doc must pay the costs. “I stood true to the honor of our noble profession, and put a chattel mortgage on my household goods, and paid it off in weekly installments like a man,” he wrote. “But I have never had a law suit since.”
When critics dismissed his paintings, Dutch artist Han van Meegeren decided to seek his revenge on the art world: He devoted himself to forgery and spent six years fabricating a Vermeer masterpiece. In this week’s episode of the Futility Closet podcast, we’ll recount the career of a master forger and the surprising mistake that eventually brought him down.
We’ll also drop in on D.B. Cooper and puzzle over an eyeless fruit burglar.
asteism
n. genteel irony, polite and ingenious mockery
The prolixity of counsel has provoked much good-and-bad-humored interruption from the Bench; and first for the good:– In Mr. Justice Darling’s court a few years ago, counsel, in cross-examining a witness, was very diffuse, and wasted much time. He had begun by asking the witness how many children she had, and concluded by asking the same question. Before the witness could reply, Justice Darling interposed with the suave remark — ‘When you began, she had three.’
In 1965, as they were writing the first draft of 2001: A Space Odyssey, Stanley Kubrick showed Arthur C. Clarke a set of 12 plastic tiles. Each tile consisted of five squares joined along their edges. These are known as pentominoes, and a set of 12 includes every possible such configuration, if rotations and reflections aren’t considered distinct. The challenge, Kubrick explained, is to fit the 12 tiles together into a tidy rectangle. Because 12 five-square tiles cover 60 squares altogether, there are four possible rectangular solutions: 6 × 10, 5 × 12, 4 × 15, and 3 × 20. (A 2 × 30 rectangle would be too narrow to accommodate all the shapes.)
Clarke, who rarely played intellectual games, found that this challenge “can rather rapidly escalate — if you have that sort of mind — into a way of life.” He stole a set of tiles from his niece, spent hundreds of hours playing with it, and even worked the shapes into the design of a rug for his office. “That a jigsaw puzzle consisting of only 12 pieces cannot be quickly solved seems incredible, and no one will believe it until he has tried,” he wrote in the Sunday Telegraph Magazine. It took him a full month to arrange the 12 shapes into a 6 × 10 rectangle — a task that he was later abashed to learn can be done in 2339 different ways. There are 1010 solutions to the 5 × 12 rectangle and 368 solutions to the 4 × 15.
But “The most interesting case, however, is that of the long, thin rectangle only 3 units wide and 20 long.” Clarke became fascinated with this challenge when Martin Gardner revealed that only two solutions exist. He offered 10 rupees to anyone who could find the solutions, and was delighted when a friend produced them, as he’d calculated that solving the problem by blind permutation would take more than 20 billion years.
Clarke even worked the 3 × 20 problem into his 1975 novel Imperial Earth. Challenged by his grandmother, the character Duncan struggles with the task and declares it impossible. “I’m glad you made the effort,” she says. “Generalizing — exploring every possibility — is what mathematics is all about. But you’re wrong. It can be done. There are just two solutions; and if you find one, you’ll also have the other.”
